HABITS OF KNOWLEDGE:

ARTISANS, SAVANTS AND MECHANICAL DEVICES IN SEVENTEENTH-CENTURY FRENCH NATURAL PHILOSOPHY

A dissertation presented by

Jean-François Gauvin

to

The Department of the History of Science

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in the subject of

History of Science

Harvard University Cambridge, Massachusetts

November 2008

© 2008 — Jean-François Gauvin All rights reserved.

Advisor: Mario Biagioli Jean-François Gauvin

HABITS OF KNOWLEDGE: ARTISANS, SAVANTS AND MECHANICAL DEVICES IN SEVENTEENTH-

CENTURY FRENCH NATURAL PHILOSOPHY

ABSTRACT

This dissertation examines the relationships between savants, artisans and machines in

seventeenth-century France (1630-1690). I argue that French natural philosophy was not

exclusively a matter of reason and rational thinking (Cartesianism), commonly

distinguished from the experimentally-inclined England of Francis Bacon and Robert

Boyle or the Italy of Galileo Galilei. Generating scientific knowledge in early modern

France involved rather a combination of intellectual and hands-on practical skills, usually

aimed at the production of instruments and complex machines. I suggest throughout the

dissertation that artisans and savants intersected in technological spaces, where they

formulated epistemic dialogues anchored in the tools and machines created within those

spaces. Looking in turn at Marin Mersenne, René Descartes, and Blaise Pascal I show

how their respective description and interpretation of the pneumatic organ, lens-grinding

machine, and arithmetical machine depended not only upon their knowledge of music,

optics and mathematics but most importantly upon their familiarity with the work of

organ makers, opticians and clockmakers—with whom they were in regular contact.

Within these machines was embedded a plurality of practices (theoretical, experimental

and artisanal) that Mersenne, Descartes, and Pascal themselves understood and

expounded in their writing. Such habits of knowledge, as I call them, though distinctive

were not as unconnected and compartmentalized as they are usually represented in the

literature. The association of theory and practice, in relation to the material culture of

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Advisor: Mario Biagioli Jean-François Gauvin

science, became a common trope in the seventeenth century, including in France. The

chapter on Christiaan Huygens and the Académie des sciences shows best how

academicians, savants, honnêtes hommes and artisans formed in the latter seventeenth

century an extended network inside and outside the royal institution, where intellectual

ideas, practical knowledge, and instrumental inventions were shared and fought over by

everyone for privilege and authority. Lastly, by fully integrating instruments and

machines into the intellectual and hands-on practices of knowledge-production in early

modern France, I describe how the concepts of habitus (of the mind and the body) and

organum (instrument) were understood and how historically fitting they are in order to

understand the coordination and tuning of the mind and the body for the production of

science (scientia).

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TABLE OF CONTENTS

ABSTRACT ................................................................................................................................................ III LIST OF ILLUSTRATIONS ...................................................................................................................VII ACKNOWLEDGEMENTS....................................................................................................................... IX INTRODUCTION.........................................................................................................................................1

CHAPTER 1 ORGAN MAKING: MERSENNE’S MUSICAL INSTRUMENTS AND THE PRACTICE OF NATURAL PHILOSOPHY..................................................................................28

GIVING A “VOICE” AND MEANING TO MUSICAL INSTRUMENTS IN THE RENAISSANCE..............................35 MERSENNE’S SEVEN BOOKS ON INSTRUMENTS IN THE HARMONIE UNIVERSELLE .......................................48 THE ORGAN AS A POWERFUL SYMBOL OF CHRISTIANITY .........................................................................62 MERSENNE’S ORGAN: THEORY, EXPERIMENT AND ARTISANAL KNOWLEDGE REVEALED .............................77

I. Pipe experiments and the production of sounds ...............................................................................79 II. Organology, or the art of musical instrument making.....................................................................93 III. The theory of organ claviers ........................................................................................................106

MUSICAL INSTRUMENTS AND THE “PARFAIT MUSICIEN” .........................................................................114

CHAPTER 2 LENS MAKING: ARTISANS, MACHINES, AND DESCARTES’S ORGANON ................................................................................................................................................120

HABITUS AND DESCARTES’S LOGIC OF PRACTICE....................................................................................124 ORDER AND THE MATHÉMATICITÉ OF MATHESIS ........................................................................................131 ÂMES RÉGLÉES AND THE IDEA OF ARTISAN..............................................................................................135 THE DIOPTRIQUE AND THE RATIONALIZATION OF THE MECHANICAL ARTS............................................146 BODY, MACHINES, AND THE DISCIPLINE OF KNOWLEDGE.......................................................................156

CHAPTER 3 CLOCKMAKING: PASCAL’S MACHINES, ARITHMETIC, AND THE EPISTEMOLOGY OF COUTUME.........................................................................................................167

‘ARITHMETIQVE MADE EASIE’: CALCULATION TECHNIQUES AND THE PRINT CULTURE ........................173 I. Napier’s rabdology, or reckoning rods ...........................................................................................178 II. Napier’s logarithms.......................................................................................................................185

SITUATING PASCAL’S ARITHMETICAL MACHINE.....................................................................................200 ETIENNE PASCAL’S TAX BURDEN AND THE ORIGINS OF THE PASCALINE ................................................204 A MATHEMATICAL INSTRUMENT? THE RHETORICAL ARGUMENT BEHIND THE MACHINE.................................211

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CLOCKMAKING AND PASCAL’S PRIVILEGE..............................................................................................221 THE PASCALINE AND THE MARRIAGE BETWEEN THEORY AND PRACTICE...............................................237 MEMORY, COUTUME, AND THE EMBODIMENT OF KNOWLEDGE IN MACHINES.........................................241

CHAPTER 4 MANUFACTURING MACHINES: CHRISTIAAN HUYGENS AND THE ACADÉMIE ROYALE DES SCIENCES ...............................................................................................256

AN URBAN COMMODITY: HUYGENS AND CARRIAGES ............................................................................260 I. The chaise roulante and the business of patents.............................................................................261 II. The theory, practice, and uncertainty of machine design ..............................................................267

APPROVED BY THE ACADÉMIE DES SCIENCES .........................................................................................280 HUYGENS AND THE BUSINESS OF AUTHORSHIP.......................................................................................295

I. Huygens’s barometer, Hubin’s thermometer and the trajectory of an instrument..........................................302 MACHINES, THE ACADEMY’S IMPRIMATUR, AND THE JOURNAL DES SÇAVANS.......................................311

CHAPTER 5 THE ORGANUM SCIENTIAE AND THE PRODUCTION OF NATURAL PHILOSOPHICAL KNOWLEDGE .......................................................................................................325

THE ORGANUM AS AN EARLY MODERN EPISTEMIC INSTRUMENT OF KNOWLEDGE .................................328 THE HABITUS ORGANICUS OR THE LOGIC OF PRACTICE IN NATURAL PHILOSOPHY...................................341

REFERENCES..........................................................................................................................................368 Primary literature ...............................................................................................................................368 Secondary literature ...........................................................................................................................378

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LIST OF ILLUSTRATIONS

FIGURE 1.1: GERMAN INTABULATION SYSTEM...............................................................................................39

FIGURE 1.2: MERSENNE’S FOREIGN AND ANCIENT MUSICAL INSTRUMENTS REPRESENTATION ......................53

FIGURE 1.3: MERSENNE’S HURDY-GURDY .....................................................................................................59

FIGURE 1.4: TWO IMAGES OF ST. CECILIA......................................................................................................69

FIGURE 1.5: MERSENNE’S PORTATIVE ORGAN AND ROUEN’S ST. MACLOU CHURCH ORGAN .........................78

FIGURE 1.6: MERSENNE’S TABLE OF ORGAN PIPE DIAPASONS ........................................................................91

FIGURE 1.7: MERSENNE’S ILLUSTRATIONS OF AN ORGAN WIND-CHEST AND CLAVIER MECHANISMS .............95

FIGURE 1.8: MERSENNE’S ORGAN CLAVIERS................................................................................................109

FIGURE 2.1: RATIONAL AND GEOMETRIC WEAVING PATTERNS.....................................................................143

FIGURE 2.2: DESCARTES’S LENS-GRINDING MACHINE..................................................................................150

FIGURE 2.3: ARTIFICIAL “ORGANS”..............................................................................................................159

FIGURE 3.1: PRATT’S ARITHMETICALL JEWEL AND THE PLUME & JETONS ARITHMETIC ..................................176

FIGURE 3.2: EXAMPLE OF NAPIER’S BONES..................................................................................................179

FIGURE 3.3 KIRCHER’S ORGANUM MATHEMATICUM ......................................................................................182

FIGURE 3.4: PETIT’S CYLINDRE ARITHMETIQUE .............................................................................................185

FIGURE 3.5: GUNTER’S CANON TRIANGVLORVM AND WINGATE’S LINE OF PROPORTION................................191

FIGURE 3.6: HENRION’S REGLE PROPORTIONNELLE AND DELAMAIN’S MATHEMATICALL RING .......................196

FIGURE 3.7: THE PASCALINE ........................................................................................................................214

FIGURE 3.8: THE PASCALINE’S MECHANISM ILLUSTRATED...........................................................................224

FIGURE 4.1: THE CHAISE ROULANTE OR MACHINE ROANESQUE.....................................................................263

FIGURE 4.2: VARIATIONS OF THE CHAISE ROULANTE.....................................................................................268

FIGURE 4.3: HUYGENS’S MECHANICAL EXPLANATION OF THE MODIFIED CHAISE ROULANTE ........................269

FIGURE 4.4: A NEW TYPE OF FOUR-WHEEL CALÈCHE IN PARIS......................................................................270

FIGURE 4.5: HUYGENS’S IDEAS ABOUT CARRIAGE SUSPENSIONS..................................................................272

FIGURE 4.6: HUYGENS’S OWN CALÈCHE .......................................................................................................275

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FIGURE 4.7: SUPPORT SYSTEMS FOR LARGE TELESCOPE ...............................................................................289

FIGURE 4.8: VARIOUS TYPES OF LEVELS ......................................................................................................291

FIGURE 4.9: COMIERS’S HERO FOUNTAIN ....................................................................................................294

FIGURE 4.10: DE HAUTEFEUILLE’S AND HUYGENS’S BALANCE-SPRING WATCHES ......................................300

FIGURE 4.11: HUYGENS’S BAROMETERS ......................................................................................................303

FIGURE 4.12: VARIOUS MATHEMATICAL INSTRUMENTS...............................................................................317

FIGURE 5.1: THE HAND AS AN “INSTRUMENT” .............................................................................................338

FIGURE 5.2: GOCLENIUS’S DEFINITION OF HABITUS ......................................................................................345

FIGURE 5.3: GOCLENIUS’S DEFINITION OF HABITUS INTELLECTUS .................................................................346

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ACKNOWLEDGEMENTS

I have anticipated this moment with pleasure and dread for a couple of years now, torn

between the joy of thanking those who helped me make it through graduate studies at

Harvard and, simultaneously, the fear of forgetting someone or not finding the

appropriate words of acknowledgement. That said, one thing is clear: my deepest

gratitude goes to my advisor—my Doktorvater—Mario Biagioli. During my all-to

unorthodox graduate school journey, Mario has been there for moral support (sometimes

badly needed), opening doors and providing academic opportunities of all sorts. Most

importantly, he helped me understand what it really meant to study history of science. His

intellectual acumen, persistent questioning and incisive remarks have forced me to go

beyond what I thought I could accomplish. Involved but not always looking over my

shoulder, Mario encouraged me to explore and tackle issues about the early modern

material culture of natural philosophy that, at first, I believed I would never contemplate

nor write about. (Ending, for him, in having to read too many half-baked historical and

theoretical assumptions.) He had faith in the project from the onset, which gave me in

return the necessary confidence to pull this through. Mille grazie Mario.

My co-advisors, Ann Blair and Peter Galison, were likewise of seminal

importance. Ann Blair has given me the training in early modern France that was lacking

to embark on this project. Thanks to her teaching, I have acquired a goût prononcé and

the basis of an expertise in early modern French thought and culture. She has been very

patient as regards my slow progress and peculiar parcours, and to my great benefit has

kindly read this tome chapter by chapter, as they were coming out pêle-mêle. Though I

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tried my best, I am afraid I have not always been able to find le mot juste, as she pointed

out to me so many times. I feel fortunate to have been guided by such an accomplished

and generous scholar. Peter Galison, no less an accomplished scholar and filmmaker, is

the reason why I came to Harvard in the first place. In fact, he was the one I contacted

when I decided to apply to Harvard—after I finished reading his monumental Image &

Logic. Since my arrival, Peter’s scholarship has been a constant source of inspiration,

somewhat reflected in my own views of early modern material culture. His assistance,

availability and encouragements then and now, as the Director of the Collection of

Historical Scientific Instruments (more on this below), have provided me with more than

I ever expected or hoped for in launching the first phase of my career.

Finally, over the past two years, Matthew L. Jones has been a source of

inspiration and a wonderful reader. He provided thoughtful insights on various technical

fine points of the dissertation and warnings when I went too far astray in intellectual

analyses of early modern material culture (I’m sure he still does not agree with a few

assertions I make regarding Pascal and the arithmetical machine). I was most fortunate

for having the opportunity to work with such a rising star in the field. Matt has still a lot

to teach me, and I am one of his most eager students.

Several other people (now begins my fear) have helped tremendously by reading,

criticizing and discussing with me various drafts of the following chapters. I benefited

over the years from the expertise and intellectual generosity of Jean-Baptiste Fressoz,

Simon Schaffer, Daniel Garber, Lorraine Daston, Elly Truitt, Will Thomas, Justin

Grosslight, Rob Iliffe, Alison Simmons, and Myles Jackson. Though not directly

involved with the dissertation, I was privileged enough to receive training in history of

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science from scholars who greatly influenced how I look at the discipline. For that, I am

enormously grateful to Steven Shapin, Naomi Oreskes, Olivier Darrigol, Steve Harris,

John Murdoch, David Kaiser, Bob Brain, and Katy Park.

On the institutional side, besides Harvard’s full scholarship, I was awarded a

Merit Fellowship from Harvard in the Fall of 2006 and a Dibner Institute Graduate

Fellowship (then at MIT) for the year 2005-2006. These two awards, combining for a

continuous year and half of full-time work on my dissertation, allowed me to draft no less

than three chapters. Without this coordinated—and precious—time of research and

writing, I would not pen these acknowledgements right now. Another institution in

Germany, the Max Planck Institute for the History of Science, provided me with a unique

opportunity to travel around Europe for two months in the summer of 2006, in order to

visit and study museum collections and practices. This project, dubbed the Wandering

Seminar, opened my eyes to a lot of issues regarding the relationships between museum

work, academic traditions and the significane of the material culture of science in

studying history of science. Thanks to Lorraine Daston, head of this pioneering project, I

was able to connect with fourteen other “wanderers” and exchange about the theory and

practices of historical objects—dating from the Renaissance to the present day. The

intellectual rewards and lessons learned during this experience will stay with me far

beyond graduate school. (For a summary of this modern intellectual Grand Tour and a

brief biography of my fellow wanderers, from which I learned plenty, please visit this fun

and valuable website, based on our experience: http://scientificobjects.mpiwg-

berlin.mpg.de/scientificobjects/home/Wandering-Seminar/Website.html. Pisa was such an

incredible experience!)

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For the past year and a half, I am also working on a fantastic project right in my

alley: the cataloguing, photographying and online publishing of the Collection of

Historical Scientific Instruments at Harvard. This project (examine its ongoing progress

on Waywiser — http://dssmhi1.fas.harvard.edu/emuseumdev/code/emuseum.asp — our online

database) occupies me full-time, and though it is unrelated to my dissertation, it forces

me more than ever to ponder and question the role of instruments and the material culture

of science in the context of academia and academic scholarship. Most importantly, it puts

me in contact with colleagues and other graduate students that I greatly appreciate for

their professionalism, expertise, passion, dedication and good humor: Sara Schechner,

Marty Richardson, Samantha van Gerbig, Phil Loring, Dave Unger, Michael Kelley, Dick

Broadbent, Justin Grosslight, Juan Andrès León, Christina Ramos and Latif Nasser. I

want to especially thank Judith Lajoie and Peter Galison, respectively Director of

Administration and Director of the CHSI, for the confidence they put in me since the

beginning of the project in early 2007, a confidence that has led to the present—and

unexpected—curatorship position.

My mom and dad were pillars of support, psychologically and materially. Maman,

especially, has driven down several times from Chambly to help us take care of the one,

then two little ones, providing me with precious time of dissertation work. Lastly, how

can I ever thank enough my wife Nathalie and my two adorable children, Camille and

Simon, for their love, patience, attention, support, tolerance, and fortitude (did I mention

patience?) in putting up for so many years with my absences, mood swings, anxieties,

and writing dry spells (did I mention absences?) so I could finish my gros livre, as

Camille says. More than anything I could have done had had been alone, they provided

xii

me with a concrete goal, a terminus ad quem I could never have set for myself otherwise.

This goal, and the efforts required to reach it, made me realize more than ever that je vous

aime de tout mon coeur.

MEDFORD, JULY 2008

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INTRODUCTION

In 1671, the Capucin father Chérubin d’Orléans published what should be understood as

a sign of the fast eroding epistemic boundary between theory, experiments and artisanal

knowledge in early modern France. D’Orléans’s study of the telescope, entitled La

Dioptrique oculaire, has a remarkable and telling subtitle: ou la théorique, la positive, et

la méchanique, de l’oculaire dioptrique en toutes ses especes.1 What is argued in this

dissertation about theory, experimental and artisanal practices, and mechanical devices in

seventeenth-century France is here explicitly enunciated in just a few eloquent words.

The overall structure of d’Orléans’s La Dioptrique oculaire is analogous to René

Descartes’s Dioptrique—which was very influential in France in the 1670s.2 First comes

the theory of light (how reflection and refraction work); second, the theory of the

telescope (what d’Orléans called the oculaire dioptrique); and third, the positive and

mechanique of the telescope, respectively how to make and use the telescope and how to

cut, grind and polish the most perfect spherical (not Descartes’s hyperbolic) lenses using

specially designed machines.3 Unlike his famous predecessor, however, d’Orléans

1 Cherubin d’Orléans, La Dioptrique oculaire, ou la théorique, la positive, et la méchanique, de l’oculaire dioptrique en toutes ses especes (Paris, 1671).

2 The author of the review of Isaac Barrow’s Lectiones opticæ et geometricæ for the Journal des sçavans (Monday, 18 November 1675) mentioned upfront that “L’Optique est une des matieres sur lesquelles on a fait en ce siecle de plus belles & plus curieuses découvertes. On admire encore tous les jours la subtilité avec laquelle Mr. Descartes a découvert sur la Dioptrique plusieurs choses qui avoient été inconnuës aux Anciens… Le principe de M. Descartes sur la Dioptrique est quasi universellement receu.” (pp. 241-242)

3 A summary of the book, enumerating every section, is found in English in the Philosophical Transactions 6 (1671), 3045-3050. It provides no analysis of its content.

Introduction

emphasized a new way of thinking about machines, artisananal practices and theory.

Where Descartes endeavored to reform—rationalize—artisanal skills and mechanical

practices by getting rid of the artisan altogether from the actual manufacture of lenses

(see Chapter two), La Dioptrique oculaire was about the creation of a new kind of

Artiste, someone that would exist in the intersection of theory, practices and mechanical

devices. As D. Graham Burnett suggests, “The essential character of the [lens-grinding]

machine could be discovered and demonstrated by mathematics, but the accidental

character of the machine had to be shaped by experience and attention to the natural and

real characteristics of materials, and the abilities of the human body.”4 Only those artistes

who embraced at once the theory of light, the positive of telescope making and use, and

the necessary skills of the mechanical arts would gain complete knowledge of the science

of optics. D’Orléans introduced one of the most remarkable and comprehensive epistemic

schemes of the period.

The author’s statement in the foreword is categorical: “I have given no use of the

telescope [Oculaire] that I did not positively reduced to practice, with all the diligence

and exactness required to convince me it was thus.”5 The theory of optics—the first part

of the work—was in a sense easy, or rather straightforward. It was fairly well understood

at the time and, most of all, certain, based on mathematical principles and ideal mirrors

and lenses. In real life, d’Orléans contended, it obviously was not the case. An almost

4 D. Graham Burnett has no doubt offered the best analysis of d’Orléans’s work in the general context of early modern lens making machines. See his Descartes and the hyperbolic quest: Lens making machines and their significance in the seventeenth century (Philadelphia: American Philosophical Society, 2005), 107-121, quote on p. 112.

5 D’Orléans, La Dioptrique oculaire, iijr (Ordre et dessein de l’auteur): “Je n’ay donné aucun usage de l’Oculaire, que je n’aye reduit positivement à la pratique, avec toute la diligense, & l’exactitude, qu’il requeroit pour m’en faire certain.”

2

Introduction

perfect understanding of the making and use of the telescope could however be achieved

if someone’s long experience in the matter was positively reduced to practice.

Experiments, arbitrarily produced and reproduced, had eventually to be ordered in a

specific way to generate new knowledge about nature. Yet not all experiments and

expérience were useful. According to d’Orléans, one had to ascertain those giving the

most certain of results—the positive part of the process. The term “positif” in early

modern French meant something that was certain and real, something regular and

assured.6 D’Orléans, in other words, insisted that the making and use of telescopes could

be reduced to principles, just like the theory of optics was.7 The positive of telescope

making was thus a specialized practice—based on experiments and sometimes on a life-

long experience—that had become as certain as the “practice” of theory.

Yet again, the positive of telescope making was based on ideal lenses—how to

arrange multiple (perfect) lenses to obtain the best results. The final ambition was in

achieving these perfect spherical lenses enabling the assured practice of telescope

making. This was the domain of the mechanique, which was quite distinct from the

positive.8 Here, d’Orléans distinguished between the simple artisan—the oculariste

vulgaire—and the Artiste curieux, an enlightened craftsman that combined reason to

mechanical skills.9 These skills, however, had to be used in conjunction with a lens-

6 Antoine Furetière, Dictionnaire universel (1690), s.v. positif: “Qui est certain & effectif, qu’on met en fait comme une chose constante & assûrée. Cela n’est point imaginaire, mais est positif. Ce fait est positif, & il en offre la preuve. Ce ne sont pas des offres labiales, mais reelles & positives.”

7 D’Orléans, La Dioptrique oculaire, 172, where he summarizes the chief principles for making a telescope, six in all. See, on p. 189, the table constructed from experience (positive) to build four-lenses telescope of different sizes.

8 D’Orléans, La Dioptrique oculaire, 337, “réellement, tres-differentes & distinctes.” 9 D’Orléans, La Dioptrique oculaire, 393, for example, where he states: “La maniere, que tiennent

les Ocularistes vulgaires, a concaver les verres, n’estant qu’une routine grossiere, & sans esprit: je ne l’ay

3

Introduction

grinding machine. Not the compound sort, such as Descartes’s, which joined two or more

spinning motions and where the Artiste was completely left out of the grinding process.

The machines designed by d’Orléans were simpler, so that one motion was mechanical

and one regulated by the hands of the Artiste curieux, hands that were guided by his

reason. The lens-grinding machine and the Artiste thus formed a new type of entity in

d’Orléans mechanical rhetoric, the Artiste being seen as the soul of the machine.10 As

Graham Burnett puts it: “The artisan was the maker, but he had to make through the

machine, which had to be an extension of himself, just as he had to become a

‘component’ within it. The successful system for making had to bind the artisan, the

mechanism, and the analytical ‘essence’ into a tight unit, a unit necessitating the

mechanization of the artisan himself.”11 The Artiste curieux, to whom was intended

d’Orléans’s book, thus brought into play the theory of optics, experience and experiments

in the form of positive, and manual skills in order to manufacture an instrument such as

the telescope, which was then employed to generate new knowledge about nature.

D’Orléans’s epistemic novelty is evident and striking. He was certainly more

explicit in writing than most of his contemporaries in juxtaposing these three

characteristics—theory, practices and instruments—of early modern natural philosophy,

too often categorized and compartmentalized into separate activities. The chief argument

pas jugée meriter, ny l’estime, ny la main, de nostre Artiste curieux, ny consequemment, la peine d’estre rectifiée, & corrigée des defauts tres-considerables, qu’elle admet dans la pratique.”

10 D’Orléans, La Dioptrique oculaire, 380-381: “Car estant animée, & guidée de sa raison, elle est d’autant moins sujète l’erreur, qu’estant encore doüée de sentiment, elle fait connoistre en sa maniere, si elle applique exactement, estant libre en cette action, & non necessitée, ou contrainte d’ailleurs, comme seroit une machine inanimée. C’est donc icy une verité connuë, que nostre Artiste doit tenir pour maxime: de ne jamais pretendre, pouvoir construire une machine, par le moyen de laquelle il puisse aussi exactement effectuer en cet art, par un mouvement compliqué, ce que celle d’un simple mouvement, peut faire aidée de sa main, qui luy en supplée un second.”

11 Graham Burnett, Descartes and the hyperbolic quest, 120.

4

Introduction

of this dissertation, however, is to show that what d’Orléans asserted haut et fort in 1671

was an epistemology of knowledge-making already familiar to savants and natural

philosophers, going back to the first decades of the century.

Contemporary to d’Orléans a physician from Toulouse, François Bayle, published

in 1675 a Discours emphasizing the importance of joining reason to experiments. Though

most savants, according to Bayle, were claiming these two activities had to be joined, few

actually did so. Natural philosophy, or physique, had indeed become “a chaos of

metaphysical speculations.” Medicine, Bayle’s own specialty, was in no better shape.

Descartes, for instance, was completely mistaken in his analysis of the heart’s movement,

as he was regarding the function of the pineal gland. Jean Pecquet, who discovered the

thoracic canal by reason and by performing experiments, was condemned by Jean Riolan,

who preferred to remain faithful to the Galenic doctrine. Experiments only, on the other

hand, carried out by empirics without the help of reason, were not the solution either. In

medicine, to formulate a diagnostic without the help of reason was endangering the

patient’s life. Similarly with prescribing medication, since a remedy that worked for some

persons (determined by experiments) may not do so for others. Only reason could

ascertain why it was so. Experiment was blind without the light of reason, whereas reason

was too vague and too uncertain when not grounded on experiments. By the time Bayle

and d’Orléans published their respective work on optics and medicine in the first half of

the 1670s, this rhetoric had become a locus communis in France.12

12 François Bayle, Discours sur l’experience et la raison, dans lequel on montre la necessité de les joindre dans la physique, dans la medecine, & dans la chirurgie (Paris, 1675). The book was reviewed in the Journal des sçavans, 17 June 1675, 161-162. On Descartes’s medicine, see Vincent Aucante, La Philosophie médicale de Descartes (Paris: Presses Universitaires de France, 2006), esp. 163-185 and 239-247. Regarding experiments on the heart’s movement, Aucante says: “L’utilisation que fait Descartes des

5

Introduction

What was lacking in Bayle’s analysis was the material culture of natural

philosophy and medicine: the tools, instruments and machines involved in producing the

right kind of experiments joined to reason. The abbé Pierre Michon Bourdelot, well-

known for his Parisian academy of savants, and to whom Bayle dedicated his Discours,

addressed this issue in his commentary at the end of Bayle’s book. In complete

agreement with the author’s assessment, Bourdelot mentioned how experiments alone

had given prestige (éclat) to people with little knowledge. Machines of all sorts were also

a great seductress of audiences. (Perhaps he was thinking here of Rohault, famous for his

experimental practices and his vast array of instruments.) Fortunately, savants (habilles

gens) knew how to discourse about them and how to create new knowledge using them.13

By themselves, machines were no better than reason nor experiments—perhaps even

worst, considering who made and displayed them.

Machines, nonetheless, were in the second half of the seventeenth century an

important ingredient of philosophizing. During Christiaan Huygens’s Parisian visit in the

early 1660s, he did not omit to mention in his Journal what he saw in Henri Louis Habert

de Montmor’s cabinet. He also visited on many occasions the clockmaker Martinot, the

expériences pour ce qui concerne le mouvement du coeur est finalement assez décevante. Sa thèse semble empruntée à ‘Hippocrate’, mais il en change les causes, introduisant les résultats de sa physique des trois éléments, qu’il pourrait bien avoir reprise aussi au traité Des chairs de la Collection hippocratique.” (p. 184) Jacques Rohault said similar things to Bayle and d’Orléans in the preface of his Traité de physique (Paris, 1671).

13 Bourdelot in Bayle, Discours sur l’experience et la raison, 86-87 where he mentions: “Il est étrange de voir combien ces Experiences toutes seules ont donné d’éclat à des gens munis de tres petit sçavoir: Ceux qui en font parade y acquerent de l’estime à bon marché, ils ont la foule pour eux, car tout le monde ayme le spectacle; on court après des choses extraordinaires, & quand on en fait le récit, n’admirez-vous point avec quelle avidité on les écarte?” A few sentences later he adds: “Le manege des machines est for seduisant & tient toûjours l’Auditoire remply, mais il ne s’en faut pas tenir là: Les habilles Gens sçavent discourir dessus, les véritables Philosophes assemblent des Experiences diverses, & en tirent des inductions qui s’écartent du sujet le moins qu’il est possible, ils les verifient par d’autres Experiences, virent toûjours à ce qui peut estre utile.”

6

Introduction

optician Ménard and the instrument maker Blondeau.14 Samuel Sorbière, member and

secretary of the Montmor academy, did not himself miss an opportunity to visit

workshops and to report on instruments and machines he came across during his travels

throughout Europe. In his personal letters and talks at the Montmor academy, he often

mentioned the role of experiments in knowledge-production.15 Balthasar de Monconys

did the same, especially during his stay in London, where he visited the workshops of

Ralph Greatorex, Anthony Thompson and especially Richard Reeve. According to

Sorbière, who visited London at the same time as Monconys, “I found [Monconys] in his

element, immersed in the conversation of natural philosophers and breathing nothing but

machines and new experiments.” Huygens, who was also visiting London at that time,

gave Monconys a drawing of his air pump, which Monconys reproduced in his Journal

and showed to a few people after he left London. There is even a special and useful table

on machines and artifices divers at the end of Monconys’s work.16

14 Henri-L. Brugmans, Le séjour de Christian Huygens à Paris et ses relations avec les milieux scientifiques français, suivi de son Journal de voyage à Paris et à Londres (Paris: Impressions Pierre André, 1935), 143: “Vu son cabinet. Tableaux, instruments de mathema[tique]. Venus d’Aleaume. Pierres d’aimant. Figures d’Albert Dürer. Jouet des petites planches liées avec des rubans. Esguille suspendue tournant a tous sens. Petites bouteilles dans l’eau qui montent et descendent, sans qu’on s’en aperçoive.” Ménard is also mentioned several times in Huygens’s Correspondance.

15 Samuel Sorbiere, Relations, lettres et discours de Mr de Sorbiere sur diverses matieres curieuses (Paris, 1660) and Sorbiere, Lettres et discours de Mr de Sorbiere sur diverses matieres curieuses (Paris, 1660), where he mentions during a talk at the Montmor academy that “Nous nous sommes dauantage preualus des experiences & de la pratique de nos Cuisiniers, de nos Architectes, & de tous nos autres Artisans; que de toutes les speculations des Physiciens qui ont pris l’essor, & que nous auons perdu de veuë incontinent... Euitons le plus que nous pourrons ce langage, & fuyons les inutiles subtilités. Tendons au plustost à la pratique dans nos raisonnemens sur les causes naturelles que nous recherchons.” (p. 200)

16 Balthasar de Monconys, Journal des voyages de Monsieur Monconys, Conseiller du Roy en ses Conseils d’Estat & Privé, & Lieutenant Criminel au Siege Presidial de Lyon. Où les Sçavants trouveront un nombre infini de nouveautez, en Machines de Mathematique, Experiences Physiques, Raisonnemens de la belle Philosophie, curiositez de Chymie, & conversations des Illustres de ce Siecle... 3 vols. (Lyon, 1665-6). For Huygens’s air pump, see vol. 2, p. 73. For Sorbière’s quote, see James A. Bennett, “Shopping for instruments in Paris and London,” in Merchants & marvels: Commerce, science and art in early modern Europe, ed. by Pamela H. Smith and Paula Findlen (New York: Routledge, 2002), 370-395, on p.

7

Introduction

At the Paris Académie des sciences, instruments and machines were omnipresent,

as the well-known engravings from Sébastien Le Clerc illustrates—especially the one

showing the king’s 1671 fictitious visit to the Academy. (Louis XVI did actually pay a

visit to his Academy a decade later.) When William III, king of England, graced the

Academy with his presence in 1690, he was shown all sorts of astronomical instruments

made for the Observatory, and even the salle des machines, where the English monarch

admired Ole Rømer’s two planetaria (built by Thuret) and discoursed on various

mechanical machines. Experiments were performed, machines were seen and operated,

and theoretical claims discussed in the presence of the king of England, all under one

roof.17 By fully reintegrating the notion of material culture into the domain of French

seventeenth-century knowledge-production, I demonstrate in this dissertation that artisans

and savants—natural philosophers—did not work in a vacuum, oblivious to what each

other was doing. As I suggest, artisans and savants intersected in technological spaces,

where in order to communicate they formulated epistemic dialogues founded on the tools

and machines enclosed within their space.18

372. Huygens had an unfavorable bias against this work, mentioning in one of his correspondence that “Ie n’ay pas leu encore les voiages de Monsieur de Monconis, ma curiositè ayant estè diminuee par le raport de quelques uns qui m’ont dit que c’est un ouurage fort mal digerè, et ou il y a quantitè de choses de peu d’importance, l’autheur ayant eu de curiositez vaines en plusieurs choses comme en l’astrologie, alchimie &c. Mais puis que vous dites y avoir pris de la satisfaction j’ay envie de veoir ce que c’est.” Huygens to Philips Doublet, 6 August 1666, in Oeuvres complètes, 22 vols. (The Hague: M. Nijhoff, 1888-), vol. 6, no. 1555, p. 73. [Hereafter cited as OC(6), no. 1555, p. 73.]

17 E. C. Watson, “The early days of the Académie des sciences as portrayed in the engravings of Sébastien Le Clerc,” Osiris 7 (1939), 556-587. On William III’s visit, see Bernard Le Bovier de Fontenelle’s Histoire de l’Académie royale des sciences, 2 vols (Paris, 1733), ii:94-104, esp. 102-104.

18 Richard Westfall has shown, based on a prosopography of early modern natural philosophers, that more than one fifth were involved in one manner or another with instrumentation, and about three quarters participated in some technological enterprise. Westfall, “Science and technology during the Scientific Revolution: An empirical approach,” in Renaissance and revolution: Humanists, scholars, craftsmen and natural philosophers in early modern Europe, ed. by J. V. Field and Frank A. J. L. James (Cambridge: Cambridge University Press, 1993), 63-72.

8

Introduction

I have chosen to limit my analysis to France because the history of science

historiography has always overemphasized and contrasted the rationalism—

Cartesianism—of the continental philosophical powerhouse with the experimentally-

driven Baconianism (later Boyleanism) of England and the Galileanism of Italy. What is

shown in the following chapters is the repeated and significant contact with artisans and

instruments “rationalists,” theory-minded individuals such as Marin Mersenne, René

Descartes, Blaise Pascal and Christiaan Huygens had over the course of their careers. In

France, I argue, it was “natural” for a savant to work (and later network in the case of the

Académie des sciences) with artisans, who provided various types of machines and

mechanical skills.19 I am not trying to argue that Descartes, for instance, was strictly an

empiricist rather than a rationalist.20 Or that by focusing my attention on instruments and

artisans the latter—not the natural philosophers—ushered in the so-called Scientific

Revolution.21 Though in the last two decades historians of science have worked toward a

19 It could even be argued that this happened earlier in the sixteenth century. Decades ago, Paolo Rossi, Edgard Zilsel, and Franz Borkenau (to name but a few) directed their writings towards unlikely scholarly figures such as Petrus Ramus and Juan Luis Vives, the latter urging humanists “not be ashamed to enter into the workshops and into the factories, asking questions of the artisans and trying to become cognizant of the details of their work.” To place an emphasis on the foundation of a more practical approach to natural philosophy—searching in other words for the rise of an experimental method—gave these scholars munitions against the tendency to grant natural philosophy an authority solely derived from theoretical presuppositions due to high culture elites. Paolo Rossi, Philosophy, technology, and the arts in the early modern era, transl. by Savaltor Attanasio (New York: Harper & Row, 1970), quote on p. 6. Edgar Zilsel, “The origins of William Gilbert’s scientific method,” in The social origins of modern science, ed. by Diederick Raven, Wolfgang Krohn, and Robert S. Cohen (Dordrecht: Kluwer Academic Publishers, 2000), 71-95. Franz Borkenau, “The sociology of the mechanistic world-picture,” Science in Context 1 (1988): 109-27.

20 Desmond M. Clarke, Descartes’s philosophy of science (Manchester: Manchester University Press, c1982).

21 Several of these approaches emphasizing technology and artisanal epistemologies over “pure” science would have been labeled “postmoderns” by Paul Forman had he dealt with the early modern era. Forman, “The primacy of science in modernity, of technology in postmodernity, and of ideology in the history of technology,” History and Technology 23 (2007), 1-152. The Smithsonian Institution curator claims that since circa 1980 the historical, sociological and philosophical discourse about science and technology has been completely overturned, shifting gears from a primacy of science over technology

9

Introduction

rapprochement between craftsmen and learned individuals in early modern Europe, very

few have studied France.22 Or, for that matter, tried to understand what a book like

d’Orléans’s La Dioptrique oculaire really represented in linking theory, practice and

machines into a single knowledge-production unit.

This dissertation, in other words, attempts to strike a balance between purely

theoretical and experimental (or artisanal) interpretations of early modern science. It

moves away from these old compartmentalizations of knowledge by integrating

theoretical conceptions, experimental practices and instrumentation into an epistemic

(modern times) to a primacy of technology over science (postmodern times). For instance, Pamela Smith argues that “it was the actions of these people [craftsmen] that brought about the institutionalization of the new philosophy and, more importantly, made the new method of pursuing knowledge part of the habits of mind and action of European scholarly culture.” Pamela H. Smith, The body of the artisan: Art and experience in the Scientific Revolution (Chicago: The University of Chicago Press, 2004), 18. See also the essay review by Bruce T. Moran, “Knowing how and knowing that: Artisans, bodies, and natural knowledge in the Scientific Revolution,” Studies in the History and Philosophy of Science 36 (2005), 577-585. According to Deborah Harkness, the Elizabethan craftsmen’s “significance lies not in the elucidation of new formulas or the construction of new consmological systems, but in the ways that they organized their communities and settled disputes; the value they placed on the acquisition of various literacies…; and the practices they developed that led to an increasingly sophisticated hands-on exploration of the natural world. These contributions … laid the social foundations for the Scientific Revolution in England and did the groundwork that was required so that a man like Boyle knew whom to ask, and what to ask for, when he sought out a man to assist him in his air pump experiments.” Deborah E. Harkness, The jewel house: Elizabethan London and the Scientific Revolution (New Haven: Yale University Press, 2007), 10. Clifford D. Conner is much less nuanced and far more “postmodern” (used here pejoratively) than the previous two very good scholars, when he says that “The historical priority of technology over theoretical science is most generally exemplified by the central theme of this book, which is that artisans contributed not only the mass of empirical knowledge that furnished the raw material of the Scientific Revolution, but the empirical method itself… It is my contention that the foundations of scientific knowledge owe far more to experiment and ‘hands-on’ trial-and-error procedures than to abstract thought.” Conner, A people’s history of science: Miners, midwives, and “low mechanicks” (New York: Nation Books, 2005), 17 and 10 (emphasis original).

22 Pamela Long, “Power, patronage, and the authorship of ars: From mechanical know-how to mechanical knowledge in the last scribal age,” Isis 88 (1997), 1-41. Long, Openness, secrecy, authorship: Technical arts and the culture of knowledge from Antiquity to the Renaissance (Baltimore: The Johns Hopkins University Press, 2001), esp. chaps. 6-7. Paula Findlen, Possessing nature: Museums, collecting, and scientific culture in early modern Italy (Berkeley: University of California Press, 1994). Lorraine Daston and Katharine Park, Wonders and the order of nature (New York: Zone Books, 1998). Steven Shapin A social history of truth: Civility and science in seventeenth-century England, (Chicago: The University of Chicago Press, 1994), chap. 8. Steven Shapin and Simon Schaffer, Leviathan and the air-pump: Hobbes, Boyle, and the experimental life (Princeton: Princeton University Press, 1985). For France, the best analysis comes from Anthony Turner, “Mathematical instrument-making in early modern Paris,” in Luxury trades and consumerism in ancien régime Paris: Studies in the history of the skilled workforce, ed. by Robert Fox and Anthony Turner (Aldershot, UK: Ashgate, 1998), 63-96.

10

Introduction

whole. My work is somewhat related to John V. Pickstone’s recent concept of “working

knowledges,” which claims that “most, perhaps all, practices of knowledge production

and technics can be analyzed in terms of elemental ways of working and knowing or, to

abbreviate, in terms of working knowledges.” This dissertation is about the plurality of

practices (theoretical, experimental, artisanal), the shared knowledges that were co-

ordinated in order to generate new discoveries about nature. It is about, to borrow from

another recent book in line with my own work, “the mindful hands and handy minds that

collaboratively engaged in inquiry and invention” in France during the seventeenth

century.23

The following five chapters deal with this plurality of practices, the shared

knowledge that I describe as habits of knowledge (habitus scientiæ). As explained in

more detail in the concluding chapter, the concept of habitus goes back to Greek

Antiquity, in Aristotle especially, and was somewhat systematized in the Middle Ages

through the writings of Aquinas in his Summa theologica. In the early modern period,

Descartes wanted to rid natural philosophy of this scholastic concept, which essentially

promoted habitus to an intellectual faculty linking the mind and the body: habitus in

23 John V. Pickstone, “Working knowledges before and after circa 1800: Practices and disciplines in the history of science, technology, and medicine,” Isis 98 (2007), 489-516, quote on p. 494. See also idem, Ways of knowing: A new history of science, technology and medicine (Chicago: The University of Chicago Press, 2000). Lissa Roberts, Simon Schaffer, and Peter Dear, eds., The mindful hand: Inquiry and invention from the late Renaissance to early industrialisation (Amsterdam: Koninklijke Nederlandse Akademie van Wetenschappen, 2007), xv. On a similar topic see Horst Bredekamp, Galilei der Künstler: der Mond, die Sonne, die Hand (Berlin: Akademie Verlag, 2007). Matteo Valleriani also looked at Galileo in a more nuanced way, dubbing him an “engineer-scientist” rather than a theoretical genius or simply a very able practitioner. Valleriani, Galileo engineer (Ph.D. dissertation, Max Planck Institute for the History of Science, 2007). On Galileo, see also Jochen Büttner et al., Galileo and the shared knowledge of his time (Max Planck Institute for the History of Science, Preprint 228, 2002). Christiaan Huygens has been studied as well from the practitioner’s side in Maria Helena Marconell, Christiaan Huygens: A foreign inventor in the Court of Louis XIV. His role as a forerunner of mechanical engineering (Ph.D. dissertation, Open University, 1999). Another recent example focusing on shared practices between various communities of practitioners is Pamela H. Smith and Benjamin Schmidt, eds., Making knowledge in early modern Europe: Practices, objects, and texts, 1400-1800 (Chicago: The University of Chicago Press, 2007).

11

Introduction

anima and habitus in corpore. By confining habitus to the realm of the artisan (the body)

and putting forward the notion of intuitus (the mind’s eye) for the discovery of true

knowledge, Descartes aimed at a complete mind-body disconnection. But as I show in

Chapter two, Descartes’s early understanding of the practice of knowledge was strongly

inspired by the fact that the artisan’s habitus increased with training, as the intellectual

Cartesian notion of perspicacitas and sagacitas actually did—reminiscent of Aquinas’s

increase of science (scientiæ) by habitus.24 I likewise demonstrate in Chapter three,

regarding Pascal’s arithmetical machine, that the concept of habitude (and coutume) was

pregnant with intellectual and moral possibilities, not only limited to artisanal labor.25

Every chapter in this dissertation deals with theoretical, practical and instrumental

approaches to natural philosophy, and how they interacted together. These habits of

knowledge, though separate and often completely different from one another, were not as

unconnected and compartmentalized as they are usually represented in the literature.

Chapter four, dealing with the Académie royale des sciences, shows best how

academicians, savants, honnêtes hommes and artisans formed an extended network

around and inside the Academy where intellectual ideas, practical knowledge and

instrumental inventions were shared and fought over by all for privilege and authority. In

24 Aquinas writes: “science can increase in itself by addition; thus when anyone learns several conclusions of geometry, the same specific habit of science increases in that man. Yet a man’s science increases, as to the subject’s participation thereof, in intensity, in so far as one man is quicker and readier than another in considering the same conclusions.” Thomas Aquinas, The Summa theologica of St. Thomas Aquinas, 2nd ed. (1920), internet resource <http://www.newadvent.org/summa/> (accessed on 1 August 2007), prima secundæ partis, question 52, art. 2. Félix Ravaisson writes similarly that “L’habitude a d’autant plus de force, que la modification qui l’a produite se prolonge ou se répète davantage. L’habitude est donc une disposition, à l’égard d’un changement, engendrée dans un être par la continuité ou la répétition de ce même changement.” Ravaisson, De l’habitude [and] Métaphysique et morale (Paris: Presses universitaires de France, 1999 [1838]), 106.

25 The best discussion of habitude in relation to Pascal is Gérard Ferreyrolles, Les Reines du monde. L’Imagination et la coutume chez Pascal (Paris: Honoré Champion Editeur, 1995), esp. 66-80.

12

Introduction

sociology and philosophy, Emile Durkheim, Max Weber, Pierre Maine de Biran, Félix

Ravaisson and Pierre Bourdieu have all studied and interpreted the social and intellectual

epistemic attributes of habitus or habits of knowledge.26 By fully integrating instrument

and machines—the material culture of natural philosophy—into the practice of early

modern knowledge production, I describe and illustrate in five chapters how habitus and

organum were co-ordinated and tuned to the production of science (scientia).

CHAPTER ONE, on organ making, deals with Marin Mersenne and his most

important treatise, the Harmonie universelle, contenant la théorie et la pratique de la

musique (1636-37)—the first publication of the young science of mechanics according to

Robert Lenoble.27 Mersenne’s music theory was indeed a powerful approach in the

establishment of a mechanical philosophy aimed at surpassing conventional knowledge—

the somewhat prevalent Greciae fides. Peter Dear, for instance, says that for Mersenne a

“deep and reciprocal relationship” existed between the sciences of mechanics and music,

insofar as universal harmony “functioned not merely as a metaphysical ornament to

technical work in the mathematical sciences but as a vital heuristic and tacit

demonstrative premise in specific pieces of mathematical natural philosophy.”28 Not only

in natural philosophy, according to the minim Father, but also in politics, moral, religious

contemplation, and the art of war. What has been much less investigated, however, is the

26 On Durkheim and Weber, see the analysis by Charles Camic, “The matter of habit,” The American Journal of Sociology 91 (1986), 1039-1087. Pierre Maine de Biran, Influence de l’habitude sur la faculté de penser, in Oeuvres complètes, ed. by Pierre Tisserand, 14 vols. (Geneva: Slatkine, 1982 [1920-1949]), vol. 2. Ravaisson, De l’habitude. Pierre Bourdieu, Le Sens pratique (Paris: Les Editions de Minuit, 1980).

27 Robert Lenoble, Mersenne, ou la naissance du mécanisme (Paris: J. Vrin, 1943). 28 Peter Dear, Mersenne and the learning of the schools (Ithaca: Cornell University Press,

1988), 116.

13

Introduction

place musical instruments take in this notion of harmonie universelle. What role did they

play in Mersenne’s thinking vis-à-vis the mathematical science of music? Did they share

some cognitive claims in Mersenne’s understanding of the classical science of music?

What was his relationship with musical instrument makers? Was Mersenne only trying to

teach the facteurs d’instruments rational methods in crafting the instruments (as he

mentions in the préface), or did he actually learn from them? How did these instruments

help Mersenne think about music theory?

These questions lie at the heart of this first chapter—and, somewhat similarly,

throughout the dissertation. Scholars, to my knowledge, have neglected to study the

specific role of Mersenne’s detailed descriptions bestowed to a variety of musical

instruments, especially the organ. Book three of the Harmonie universelle is thick and

probably remains the best historical reference to early modern musical instruments owing

to its long descriptions and numerous engravings. Mersenne made clear in the preface of

this book that he was applying théorie to pratique. But for what purpose exactly? Was he

simply trying to guide the hand of artisans? To give such detailed descriptions on how to

work with wood and metals, Mersenne had first to penetrate into the workshops and see

for himself how it was done before considering to return the favor. But why spend so

much energy (and expensive paper) in describing musical instruments? Focusing on the

organ, I will show that Mersenne wanted to convey one of the chief principles of

seventeenth-century natural philosophy: i.e. instruments were a fundamental part of

knowledge-production. Through the organ, I argue, Mersenne displayed how much

artisan, experiment and theory were tightly joined into the nascent mechanical

philosophy. The organ, owing to its complexity—it was undoubtedly the most intricate

14

Introduction

machine of the period—and socio-cultural and religious status during the early modern

period, became for Mersenne the paradigmatic material emblem of the new science of

sound—a special instance of the more general natural philosophy. Not only did the organ

epitomize the nature of sound, it proved his harmonie universelle was not purely

conjectural and metaphysical, confirming he had concretely surpassed ancient

knowledge. The organ, and most musical instruments, once they had received the lights

of theory, would embody the mathematical knowledge at the center of his harmonie

universelle. Yet these same instruments, used as natural philosophical tools, generated

experimental data from which a theory of sound could be “soundly” established. And to

ensure these musical instruments were adequately manufactured, a thorough knowledge

of artisanal craftsmanship was necessary. I will show, in short, that the organ in

Mersenne’s view became the instrument or organum of universal harmony, the material

extension of music theory and mechanical philosophy.

In CHAPTER TWO, on lens making, I continue to show how interrelated

artisans, machines and theory were in French natural philosophy. In this chapter, I first

demonstrate that René Descartes’s notion of natural philosophy was to some extent

rooted in the concept of artisan and craftsmanship. When one takes a closer look at some

of Descartes’s pivotal philosophical writings, the artisan emerges under a more nuanced

and fundamental light. Remarkably enough, even the most unassuming of artisans were

converted into archetypal models of rational discipline and ordered thought. This

assertion is not as bold as it appears, however, because it is in truth the concept of artisan

that the Cartesian method exhibited. The artisan qua genuine homo faber was

metamorphosed into an idealization in Descartes’s writings, a disembodied heuristic

15

Introduction

metaphor of knowledge production. The Cartesian artisan was not as much “invisible” as

he was “virtual,” an imaginary or simulated concept put forth as a heuristic strategy

developed precisely in order to communicate a novel understanding of the practice of

natural philosophy, one struggling to break with the tradition of scholasticism. By way of

the “idealized artisan,” Descartes attempted to introduce an unconventional method

firmly established on theory, practice, and material culture.

Secondly, I show that the Cartesian machines are better understood when one

explores the concept of organon as the mechanical principle behind Descartes’s early

natural philosophy. My focus will be set on two famous Cartesian machines: the lens-

grinding machine of the Dioptrique and the mathematical compass of the Géométrie. In

the first example, although Descartes required skilled artisans to build his lens-grinding

machine, he did not trust them in shaping perfect hyperbolic lenses; only the machine

could.29 Described at the end of the Dioptrique, this machine was the natural culmination

of Descartes’s optics: only through the perfection of the machine could he prove his

theory right. Said otherwise, the lens-grinding machine helped embody Descartes’s

optical theory since its sole purpose was to reduce the whole of his optics into a simple

hyperbolic lens. In a similar fashion, the Cartesian compass embodied Descartes’s

geometrical curves because it could generate high-degree curves otherwise impossible to

draw. Both the lens-grinding machine and compass, left alone, were machines. In the

hands of somebody, however, the machine became an instrument, an organon, a genuine

extension of the body. Such an understanding of the role of machines is, I believe, in

29 Burnett, Descartes and the hyperbolic quest.

16

Introduction

close relation to Descartes’s interest in anatomy, the study of human organs.30

CHAPTER THREE, on clockmaking, carries on the dissertation’s main argument

by focusing next on Blaise Pascal’s arithmetical machine, or pascaline, as another perfect

example of the interaction between the mind (Pascal), the body (artisans), and finally a

machine (pascaline) understood as a spiritual organ, a material extension of the mind. To

Pascal, the machine would work flawlessly if and only if some skilled artisan could

reproduce in minute details the design he had imagined. In his Lettre dédicatoire à

Monseigneur le Chancelier regarding the pascaline, Pascal recognized that without an

habile artisan he would not have been able by himself to build the machine. Conversely,

an artisan without an understanding of theory could never make one on its own—as it

happened when one Rouen clockmaker tried to copy the arithmetical machine without

Pascal’s assistance. Therefore, Pascal talked about “la légitime et nécessaire alliance de la

théorie avec l’art.” Theory and practice had to be incorporated together in order to

produce new knowledge and technological products. Mind and body were essential; they

were reinforcing themselves, not fighting against one another. That was, according to

Pascal, the major fault of both savants and artisans. As Mersenne and Descartes

emphasized before him, Pascal was convinced that theory and practice had to work

simultaneously to generate new knowledge about nature. A dichotomy between the mind

and the hand was no longer suitable to the new natural philosophy.

This arithmetical machine, ultimately, was more than a mechanical tour de force,

as was usually acknowledged. The pascaline became a genuine “thinking machine,” one

30 On Descartes’s interest in anatomical studies, intricately linked to his stay in The Netherlands and the latter’s empire based on materialism and commercial activities, see Harold J. Cook, Matters of exchange: Commerce, medicine, and science in the Dutch Golden Age (New Haven: Yale University Press, 2007), chapter 6.

17

Introduction

that rendered arithmetic as mechanical as, say, an orgue de barbarie; one could now do

mathematics as s/he could play music, without ever knowing anything theoretical about

either science. Pascal’s sister Gilberte later observed this fundamental meaning of the

pascaline when she wrote that his brother’s invention “was considered a novelty since it

reduced to a machine a science that resided completely in the mind.” I also want to stress

in this chapter how Pascal, in creating this machine, shifted the habit of doing arithmetics

from the mind to the body. Before Pascal, arithmetics was performed with pen, paper and

tokens. The mind was constantly solicited in making addition, substraction,

multiplication and division. A habit of the mind had to be acquired to carry out these

arithmetical operations. With Pascal’s machine, I argue, the habit shifted from the mind

to the body. What one had to learn was how to use a stylus, what wheel to turn when,

what manual operations, in sequence, were required in order to perform an addition or a

division. Knowing arithmetics was no longer necessary, according to Pascal. One only

had to be trained to do a bodily algorithm, the machine was now doing the thinking. The

machine, though powered by the hand, was thus a mechanical extension of the mind.

Bodily habits, through the medium of a machine, acted like the mind. This, I believe, was

one of Pascal’s most provocative claim about his invention.

CHAPTER FOUR, on manufacturing machines, takes a closer look at one final

individual, Christiaan Huygens, in relation to an institution, the French Académie royale

des sciences. Regarding instruments and machines, Huygens is well known for his air

pump, clocks, and telescope lenses. Though they are still of interest, I emphasize instead

other aspects of his instrument-making contributions to the French scientific life.

Specifically, how favorably connected Huygens was with both the Parisian intellectual

18

Introduction

and artisanal milieux. By looking first at his long involvement in carriage designs, I

ground the chapter on two themes: 1) technical design and manufacture of machines and

2) authorship. I show throughout the chapter that these two themes were simply the faces

of the same scientific coin for Huygens. Not only did he invent and manufacture (or had

manufactured) instruments such as the double barometer, the surveying level and the

ones mentioned above, which all had their own authorship issues, as a member of the

Academy Huygens also had the responsibility of assessing inventions from other savants,

gentlemen and artisans—hence of granting legitimate authorship himself. In other words,

I argue, Huygens was continually working with machines and their inventors (of all

social status, including artisans), dealing with technical design and authorship matters.

All of these facets were fully integrated to his natural philosophy. The epistemic space in

which Huygens worked was thus defined as much by his skills in mathematics as it was

by his regular contact with machines and their makers.31 Around the same time, other

French savants close to the Academy began to see the role of machines and artisans as an

integral part of their natural philosophy. What I show is that by the late 1660s natural

philosophy in France was no longer a matter of great intellectual geniuses, but rather a

profound symbiosis of minds, hands, and machines.

31 Scholarship on Huygens’s pendulum clocks, for instance, tend to demonstrate that he first tackled the mathematical properties of the cycloid and only then applied the curve to the construction of an isochronous clock. Although the mathematical treatment of the cycloid is to Huygens of the utmost importance to fully understand this new invention, mathematics was not the only force at work here. As Fokko Jan Dijksterhuis has shown, Huygens’s study of optics was closely related to his hands-on grinding of telescope lenses. Towards his goal, he combined a theoretical and practical understanding of spherical lenses to produce in the end a better instrument. In fact, contrary to Descartes and his fundamental treatment of hyperbolic lenses, Huygens did not try to improve a highly skilled manual savoir-faire by perfecting a theoretical design. By carefully studying common spherical lenses rather then theoretically proving that hyperbolic lenses would rid telescopes of their aberrations, “Huygens started out with what was practically feasible instead of what was theoretically desirable.” Fokko Jan Dijksterhuis, Lenses & waves: Christiaan Huygens and the mathematical science of optics in the seventeenth century (Dordrecht: Kluwer Academic Publishers, 2004), 67.

19

Introduction

The center of this extended network of minds, hands and machines was the

Académie royale des sciences, founded in 1666. It not only endorsed but institutionalized

the new epistemic method displayed by a growing number of natural philosophers. For

this to happen, the Academy had to create its own epistemic space and networking

between savants, artisans, and machines. To understand and examine this networking,

however, one needs to unpack the early rhetorical narrative of the Academy as described

by Christian Licoppe: the authoritarian and collective “on” found in the official records

of the institution.32 This official “on” spoke initially for the entire institution, concealing

in words the individual academicians and their everyday interactions with other members

and non-members alike. The Academy’s rhetoric, imposed on its members, projected the

image of a stable, unique, legitimate, and all-knowing corpus scientiæ, where the messy

stuff of expériences lay hidden within the discourse of the Republic of Letters. What I

show is that behind this collective “on” there was an important networking of savants,

gentlemen and artisans, sometimes in fierce competition against one another over the

authorship and production of machines.

To unpack this rhetorical discourse one can start with an anonymous mémoire

received by Huygens around 1663. First, this project of a learned scientific institution put

emphasis on machines and artisanal knowledge, in tune with what French natural

philosophers had been doing for over half a century. As Huygens could read,

We will make an effort to learn all the practices of the Arts, as much as those who use them in France and in other Countries and to obtain the design of all the Machines, and of all the instruments that prove useful, and to know all that the Workers remark in the materials that they employ, all of the difficulties they

32 Christian Licoppe, La Formation de la pratique scientifique: le discours de l'expérience en France et en Angleterre, 1630-1820 (Paris: La Découverte, 1996), chap. 2.

20

Introduction

encounter in their Works, all they research or even that they wish for in perfecting their arts, and of all the things from which one makes a List or a Table, so that the learned can think on it, and they can try by Mechanics or Chemistry or by the discussion of diverse arts to apply to certain ones, by Analogy, that which applies to others. [my emphasis]

This somewhat Baconian approach to knowledge hinted at an institutionalized

rapprochement between simple workers and the learned world of the future Academy. In

fact, I show that the aura of secrecy coming from the Academy has perhaps been

overstated in the traditional historiography of the institution.

Second, there is an explicit account later in the text about who should eventually

become an académicien:

The Company will be composed of the most learned people in all the true Sciences that one can find, as in Geometry, Mechanics, Optics, Astronomy, Geography &c. in Physics, Medicine, Chemistry, Anatomy, &c. or in the practice of the Arts, as in Architecture, fortifications, Sculpture, painting, design, Conduits [Conduite] and the elevation of the Waters, Metallurgy, Agriculture, navigation, &c. Or of those who will make known to the Company some secret, or some considerable Invention that they have found, in order to inspire everyone to invent something of whatever nature it might be, since there is nothing new from which, with time, one does not find some considerable usefulness.33

Though no “mechanics” were ever granted membership to the Academy, dozens were

closely linked to the later royal institution and its influential members in order to achieve

the goals described above. The Academy was an elitist institution, yet was an open

epistemic space where artisans, savants and gentlemen met and interacted regularly on

the business of machines. An epistemic space and extensive networking where machine

authorship became an important aspect of the day. Ending the chapter with a short study

of machine authorship as displayed within the Journal des sçavans, the Academy’s

33 Huygens, OC(4), ? to Huygens, [1663?], no. 1105, pp. 325-329. The English translations were taken from Robert A. Hatch’s The Scientific Revolution Homepage website, accessed on 29 January 2008.

21

Introduction

unofficial journal, I expound the significance of printing for machine authorship.

Moreover, I show that most individuals publishing in the Journal des sçavans, whether

artisan, gentleman or savant, often sought beforehand the imprimatur of the Academy,

seeking even more legitimacy for their invention than print itself. Machine authorship in

late-seventeenth-century France was created within the Academy’s epistemic space, by

means of its networking involving artisans, honnêtes hommes, and savants.

The Academy thus epitomized and institutionalized a scientific method based on

the technical and theoretical savoir-faire of artisans and savants. Instruments and

machines had not only become the foundation of the experimental era, but also one of the

chief media through which artisans and savants communicated. By focusing on

Huygens’s and his fellow academicians’ respective and simultaneous theoretical,

instrumental, and experimental approaches to natural philosophy, I demonstrate how

“modern” was their knowledge-producing method. The sheer importance of the Academy

then ensured the adoption of this method by the end of the seventeenth century.

In CHAPTER FIVE, on the organum scientiæ, I end the dissertation with a

historical study on the concept of instrument—or organum. In the previous four chapters,

several types of instruments and machines are encountered, ranging from musical,

mathematical, and optical instruments, to barometers, surveyor levels and clocks. I

demonstrate that these were not only an essential part of the practice of natural

philosophy between 1630 and 1680, but were involved as well in outlining the strong

relationship between French artisans and savants. But what exactly was an instrument in

early modern Europe. How was the concept of instrument understood? Using the

inclusive concept of organum, I show that early modern “instruments” were a key

22

Introduction

ingredient to our understanding of a logic of practice in natural philosophy. Whether it

was material (object) or intangible (mind), early modern instruments played a

fundamental role in determining the interaction between theory and practice, and between

savants and artisans.

By studying primarily Mersenne’s musical instruments, Descartes’s lens-grinding

machine, Pascal’s arithmetical machine, and Huygens’s carriages and other instruments

of knowledge-production, I looked at concrete and tangible objects—complex devices—

that embodied within their mechanisms notions of natural philosophy. This dissertation is

not about applied metaphysics. I did not try to move orthogonally from the plane of the

debate about what should count as a “natural” (real) in opposition to a “constructed”

(historical) object of scientific inquiry. The applied metaphysics of scientific objects, as

described and understood by Lorraine Daston et al., refers to objects, whether in

substance or not, that display “the dynamic world of what emerges and disappears from

the horizon of working scientists.” The material things forming the core of my study are

certainly more “quotidian” than monsters, dreams, cytoplasmic particles or even culture

itself. Yet I believe that, similarly to these scientific objects, “they grow more richly real

as they become entangled in webs of cultural significance, material practices, and

theoretical derivations.” Applied metaphysics is as valuable an epistemic concept as there

is, one in fact that helps focus attention to a number of “things” that otherwise would

never be perceived as scientific. Yet applied metaphysics bears the risk of losing contact

with what it really means to live in a material world.34

34 Lorraine Daston, ed., Biographies of scientific objects (Chicago: the University of Chicago Press, 2000), 1 and 13 for the respective quotes. Ian Hacking has come up with a somewhat similar notion in coining the expression “historical ontology.” To him, “Historical ontology is about the ways in which the

23

Introduction

That said, material things are no longer perceived as inert and passive objects of

study solely defined by thinking subjects. Historians, sociologists and especially

anthropologists recognized several decades before historians of science that things had a

life of their own: they shape the subject and its social context as much as they are shaped

by the latter. Without loosing any of the things’ distinctive materiality, gaining rather a

better understanding of it, scholars have worked out “thing theories” that have become

essential in explaining and confronting their interaction with the human world.35

Historians and philosophers of science have barely begun sketching such materialists

theory of scientific knowledge, where instruments are considered more than “inscription

devices,” exclusively providing visual displays in scientific texts. Instruments and

machines have matured in some cases into “thing knowledge,” not only raised up to the

level of theory and experiment but literally on a par with the spoken words.36 They do not

need, that is, to be associated with a written text to signify something. As a thing

possibilities for choice, and for being, arise in history.” It is not “about the coming into being of objects of study” but rather about “the coming into being of objects, period.” The essence of these objects is historical, and found somewhere in the grid formed by the three axes of knowledge, power and ethics. Hacking, Historical ontology (Cambridge, MA.: Harvard University Press, 2002), 23 and 11 respectively for the quotes. Latour’s “actor-network theory” and Pickering’s “mangle of practice” are other manifestations of applied metaphysics.

35 Bill Brown, “Thing theory,” Critical Inquiry 28 (2001), 1-22. The whole issue is dedicated to this topic. The literature is rich and vast here. For an historical perspective, see Daniel Roche, Histoires des choses banales. Naissances de la consommation, XVIIe-XIXe siècle (Paris: Fayard, 1997) and Curtis Perry, ed., Material culture and cultural materialisms in the Middle Ages and Renaissance (Turnhout, Belgium: Brepols, 2001). A good summary on the theoretical concepts of things is found in Christopher Tilley, ed., Reading material culture: Structuralism, hermeneutics, and post-structuralism (Cambridge, MA.: B. Blackwell, 1990).

36 Davis Baird, Thing knowledge: A philosophy of scientific instruments (Berkeley: University of California Press, 2004). See also Robert J. Ackermann, Data, instruments, and theory: A dialectical approach to understanding (Princeton: Princeton University Press, 1985) and Don Ihde, Instrumental realism: The interface between philosophy of science and philosophy of technology (Bloomington: Indiana University Press, 1991). On inscription devices, Latour, Science in action: How to follow scientists and engineers through society (Cambridge, MA: Harvard University Press, 1987), 64-70, where he writes: “What is behind a scientific text? Inscriptions. How are these inscriptions obtained? By setting up instruments.” (p. 69)

24

Introduction

knowledge, an instrument bears insights about the craft, skill, experimental practice and

theory involved in its coming into being: it can (and does) speaks volume about the

practice of science if one avoids letting it drown in words.37 Instruments, in other words,

have acquired layers upon layers of meanings in recent decades. They cannot be reduced

anymore to simple matrices of functional performances. They now have to be considered

“thick things,” objects representing multiple (and divergent) points of view.38

Instruments are “thick” because they are never created without purpose, and on no

account exist isolated from a specific socio-cultural, experimental and rational context.

The goal of this last chapter is thus to give a historical and intellectual account,

not a philosophical analysis, of the use of instruments in the early modern period.39 Here,

the concept of organum is precious because it encompasses both the material objects as

well as the instrument of the mind, as I explained in the case of Descartes’s méthode in

Chapter two. Organon in Greek, or instrumentum in Latin, is a notion that goes back to

Antiquity, to the idea of nature as a craftsman. Nature, the analogy goes, is as dependent

of its instruments as the artisan is to generate forms. Like the artisan, nature uses tools,

37 Lorraine Daston, ed., Things that talk: Object lessons from art and science (New York: Zone Books, 2004). In the introduction, Daston pointedly remarks that “If things are ‘speechless,’ perhaps it is because they are drowned out by all the talk about them.” (p. 9)

38 Ken Alder, ed., “Focus: Thick things,” Isis 98 (2007), 80-142. See also Alder, “Making things the same: Representation, tolerance, and the end of the Old Regime in France,” Social Studies of Science 28 (1998), 499-545.

39 The philosophical approach has generated a great amount of significant scholarship on the concept of instrument in the practice of modern science. See, for instance, Hans-Jörg Rheinberger, Toward a history of epistemic things: Synthesizing proteins in the test tube (Stanford: Stanford University Press, 1997); Peter Keating and Albert Cambrosio, Biomedical platforms: Realigning the normal and the pathological in late-twentieth-century medicine (Cambridge, MA.: MIT Press, 2003); Peter Galison, Image and logic: A material culture of microphysics (Chicago: The University of Chicago Press, 1997) and Galison, Einstein’s clocks, Poincaré’s maps: Empires of time (New York: W.W. Norton & Company, 2003); Andrew Pickering, The mangle of practice: Time, agency & science (Chicago: The University of Chicago Press, 1995); Hans Radder, ed. The philosophy of scientific experimentation (Pittsburgh: University of Pittsburgh Press, 2003).

25

Introduction

instrumenta, to produce forms; they participate, in other words, in the causa

instrumentalis, the instrumental cause that makes things happen. Instruments, however,

do not act by themselves; they are inherently linked to a causa principalis, a principal

cause that guides their every action in shaping matter. In the craftsman’s analogy, the

behavior of the hammer cannot be understood unless you study in detail the artisan who

holds it. Although Aristotle never emphasized the materiality of nature’s instruments,

focusing instead on their purposefulness, one influential consequence of the notion of

organon remains his idea that body parts are instruments, or “organs.” Aristotle did not

see the human body as a machine—as Descartes did in his Traité de l’homme. Yet

organs, analogous to the artisan’s tools, displayed routinized and regularized bodily

functions with specific goal-oriented and result-oriented purposes—the purpose of the

heart, which it does machine-like, is to heat the blood. For natural philosophers like

Descartes and William Harvey, the notion of organon epitomized the regularities of

nature; for the artisans, instruments exemplified their way of life. This is where I see an

epistemic terrain d’entente between artisans and savants, framed through the concept of

organon, instrumentum, or tools of knowledge. These mechanical “organs” were nothing

less than vital to the health of natural philosophy. To isolate musical instruments or

mathematical compasses from Mersenne’s musical theory or Descartes’s geometry

respectively, I argue, is no worse than dismembering their natural philosophy.

Yet behind each instrument of science—organum scientiæ—laid a special

training, a particular practice—in short a habitus—that involved either the mind or the

body. (In the case of Pascal’s arithmetical machine, as already mentioned, the habitus of

doing arithmetic shifted from the mind to the body.) Though instruments were essential

26

Introduction

to the practice of early modern science, these were useless if the required habitus was not

properly carried out. Looking at the habitus in anima and the habitus in corpore, I stress

in this last chapter how the body and the mind were both dynamically engaged (not

necessarily at the same time) toward the production of knowledge in the early modern

period. The habits of knowledge, as the title of this dissertation proposes, expose this

juxtaposition of mind and body in early modern natural philosophy. In what follows,

taking as a point of departure instruments and well-known natural philosophers (or an

institution in the case of the Paris Académie royale des sciences), I demonstrate that

French seventeenth-century natural philosophy was in fact the result of a conjunction

between machines, the individuals who made them, and the savants who used them to

investigate—or reflect upon—nature. The notions of organum and habitus are, I believe,

the most fitting (and historically appropriate) concepts one can think of and elaborate

upon when dealing with the role played by instruments and machines vis-à-vis their

inventors and manufacturers along with the investigators of natural philosophy.

27

CHAPTER ONE

ORGAN MAKING: MERSENNE’S MUSICAL INSTRUMENTS

AND THE PRACTICE OF NATURAL PHILOSOPHY

HE BAROQUE ERA SAW MANY TRANSFORMATIONS AND NOVELTIES IN MUSIC: the

Italian opera, the rebirth of monody, the spread of chamber cantata, and new

genres of instrumental ensemble music, to name but a few. Regarding instrumental

music, its renovation during the Renaissance found a natural setting within natural

philosophy. Due in large part to the influence of instrumental music, the late sixteenth-

and early seventeenth-century musica scientia was amended from being a purely

speculative mathematical science to becoming a more pragmatic analysis of sound—the

nascent acoustics.40

T

Within this changing epistemic context, Marin Mersenne’s books on musical

instruments, featured in his well-known Harmonie universelle (1636-37), were

undoubtedly the best early modern illustration of the developing experimental and

mechanistic approach to the study of sound. Although most early modernists—whether

historians, historians of music or historians of science—know about Mersenne’s books of

40 John Walter Hill, Baroque music: Music in Western Europe, 1580-1750 (New York: W.W. Norton & Company, 2005). Tim Carter and John Butt, eds., The Cambridge history of seventeenth-century music (Cambridge: Cambridge University Press, 2005), esp. Penelope Gouk’s chapter “Music and the sciences,” 132-157. Ann E. Moyer, Musica scientia: Musical scholarship in the Italian Renaissance (Ithaca: Cornell University Press, 1992) is a very good overview of the science of music before the “experimental turn.” See also Cristle Collins Judd, Reading Renaissance music theory: Hearing with the eyes (Cambridge: Cambridge University Press, 2000). On the role of musical instruments in the transformation of instrumental music, Jonathan Wainwright and Peter Holman, eds., From Renaissance to Baroque: Change in instruments and instrumental music in the seventeenth century (Aldershot, UK: Ashgate, 2005).

Organ Making: Mersenne’s Musical Instruments

instruments no one (to my knowledge) has attempted to establish the exact meaning and

epistemic function of their publication.41 H. Floris Cohen, for example, describes well the

overall goal and achievements of Mersenne’s commitment to the material culture of

music:

In Mersenne’s hands a process was completed that had started with father and son Galilei: the musical instrument was turned into a scientific instrument, capable of revealing nature’s hidden properties. Not the least important reason why the Traité des instrumens in Harmonie universelle contains such important information is the fact that Mersenne used the instrument makers themselves as a direct source of knowledge. It was one thing to speculate freely on what happens in an organ pipe; it was something different, and, for the theorist, new, to inquire of the organ builders after the secrets of their trade. Of course the latter could only provide the raw material for theoretical reflection, but the point is that without it no sensible theory formation was at all possible.42

Though accurate, this assessment strictly remains a theoretical statement. Cohen does not

investigate the strong epistemic communion musical instruments, musical instrument

makers, and music theory came to form in Mersenne’s conception of music and universal

harmony.43 Such an investigation is precisely the objective of the present chapter.

41 For example, Monique Escudier, Introduction à une étude musicale de la correspondance du Père Marin Mersenne de 1617 au 20 mars 1634, 2 vols (Paris: Conservatoire national supérieur de musique, thèse présentée pour le Prix de Musicologie, 1972) is a very useful survey of Mersenne’s music in his correspondence, but offers no in-depth analysis of musical instruments. Robert Lenoble, Mersenne, ou la naissance du mécanisme (Paris: Librairie philosophique J. Vrin, 1943) is the classic study on Mersenne, in which the emergence of the concept of mechanism is explained in detail, but without any consideration to the material culture of music (or mechanics for that matter). Peter Dear, Mersenne and the learning of the schools (Ithaca: Cornell University Press, 1988) is essential in understanding where Mersenne’s concept of universal harmony came from. It offers, however, no indication whatsoever as to the significance of instruments in Mersenne’s study of music and mechanics, although Dear argues that Mersenne’s appeal to empiricism was total. From historians of music, most references to Mersenne’s instruments are in relation to the history of a particular musical instrument, nothing else.

42 H. Floris Cohen, Quantifying music: The science of music at the first stage of the Scientific Revolution, 1580-1650 (Dordrecht: D. Reidel Publishing Company, 1984), 102.

43 A few scholars have dealt with some of these issues within the English context. Penelope Gouk, Music, science and natural magic in seventeenth-century England (New Haven: Yale University Press, 1999), shows a “gallery of instruments” that, unfortunately, does not provide much detailed analysis on the epistemic role of musical instruments. She simply mentions the familiar interpretation of musical instruments as experimental tools. In a recent book review on early modern music, Myles Jackson argues for an opening of the disciplinary fields of music and science. One venue is to look at the material culture

29

Organ Making: Mersenne’s Musical Instruments

The first question that came to my mind was this one: why would a seventeenth-

century savant such as Mersenne give a thorough and comprehensive examination of the

material culture of music? A Father Minim educated by Jesuits in the traditional ratio

studiorum, who never played on an instrument, who never wrote music (except perhaps

for one minor composition44), and who never attempted to build even one lute? Why does

the elaborate description of musical instruments fill up seven out of seventeen books of

the Harmonie universelle, or more than a third of Mersenne’s magnum opus? We know

that printed collections of objects (natural and artificial) were an important part of the

culture of collecting and knowledge dissemination to early modern natural history.

Within the architectural and engineering fields, manuscripts drawings and large folio

theaters of machines came to symbolize the powerful network established between the

knowledge makers and the learned elite. No such compendia, however, existed for the

mathematical sciences (music being one of the quadrivium’s four mathematical

disciplines). Books on surveying, astronomy, dialing and usu et fabrica treatises alike

dealt with one or a cluster of instruments, but never gave a comprehensive and

encyclopedic material-culture overview of a discipline. No book from the mathematical

of music and at the instrument maker’s shop. Myles W. Jackson, “Music and science during the Scientific Revolution,” Perspectives on Science 9 (2001), 106-115. A concrete example is Jackson’s own Harmonious triads: Physicists, musicians, and instrument makers in nineteenth-century Germany (Cambridge, MA: MIT Press, 2006). Jamie C. Kassler, Inner music: Hobbes, Hooke and North on internal character (London: Athlone, 1995) emphasizes the role of musical instruments, or “resonating systems,” as controlling metaphors toward the improvement of internal character, linking music to the physiology of the human body. More recently, see Benjamin Wardhaugh, Mathematical and mechanical studies of music in late seventeenth-century England (D. Phil., University of Oxford, 2006). I thank Stephen Johnston for pointing out this reference.

44 Titelouze to Mersenne, 26 March 1628, in Correspondance du P. Marin Mersenne: religieux minime, ed. and annotated by Cornélis de Waard (with the collaboration of René Pintard), 17 vols. (Paris: G. Beauchesne, 1933-1988), vol. 2, 43-46 (hereafter cited as CM II, 43-46). The title of the piece was Vexilla. It was composed by Mersenne in the form of mathematical numbers, which were then entabulated by Titelouze. According to the editors of Mersenne’s correspondance, Vexilla is found in Mersenne’s Harmonicorum libri XII, but not in his Harmonie universelle.

30

Organ Making: Mersenne’s Musical Instruments

or natural philosophical traditions can actually be likened to Mersenne’s intricately

detailed, wide-ranging and encompassing books on musical instruments—described in

the second section below. Why did Mersenne do it? Because musical instruments, I claim

in this chapter, were not only data-gathering tools, but also powerful symbols of the

emergent mechanical philosophy. Since music was Mersenne’s paradigmatic scientia of

the harmonie universelle, musical instruments became ipso facto the paradigmatic

instruments of the mechanical sciences, and consequently of Mersenne’s universal

harmony and of the “modern” natural philosopher.45

As much as other material objects of the period, musical instruments played an

important role in the daily life of early modern Europeans. They were heard everywhere,

all the time, for all circumstances and by all walks of life. They were purchased as well in

larger quantity than never before by the end of the sixteenth century—especially the lute,

given that it was still fairly inexpensive.46 Yet the fact remains that epistemologically

45 In the Minim’s mind musical instruments were actually linked to our understanding of the mechanical laws of art and nature. Peter Dear demonstrates that the concept of universal harmony emerged from Mersenne’s study of mechanics, which itself was a science wholy dependent on material objects. “By integrating music with a mechanical account of sound,” Dear argues, Mersenne “succeeded in creating a way of treating mechanics itself as an exemplification of the harmonious relationships for which music provided the prototype.” Musical harmony was thus explained by the science of mechanics; yet, Mersenne strongly believed that the concept of harmony itself laid at a deeper level than mechanics. Harmony, according to Mersenne, was the presupposed and fundamental notion behind mechanics and consequently of all of Creation. Music, Dear continues, “provided the paradigm of harmony by which the rest could be developed and judged.” Dear, Mersenne and the learning of the schools, quotes on 117 and 139 respectively. On the use of material objects in the science of mechanics, Domenico Bertoloni Meli, Thinking with objects: The transformation of mechanics in the seventeenth century (Baltimore: The Johns Hopkins University Press, 2006).

46 François Lesure, “La facture instrumentale à Paris au seizième siècle,” The Galpin Society Journal 7 (1954), 11-52. For twenty sous tournois, for instance, one could buy either a violin or a lute with its case in the middle of the sixteenth century. These prices were found throughout the first half of the seventeenth century as well for cheap instruments. See Madeleine Jurgens, Documents du Minutier central concernant l’histoire de la musique (1600-1650), 2 vols. (Paris: S.E.V.P.E.N., 1967; La Documentation Française, 1974), ii:84-93. Another good indication of the widespread distribution of lutes in the beginning of the seventeenth century is given by Jean Titelouze, a famous Rouen organist and one of Mersenne’s first correspondents. In Titelouze’s youth (he was born in 1563), everyone admired “un homme qui touchoit le lut et assez mal pourtant; et maintenant j’en voy cent plus habilles gens que luy mille fois, que l’on ne

31

Organ Making: Mersenne’s Musical Instruments

speaking musical instruments (from the mechanical arts) were still not treated equally as

the human voice (the natural organ of sound production) by the early 1600s, as I will

briefly explain in the first section below. It was one thing for musicians to delight and

entertain crowds with popular and courtly airs and chants—some instrument players

being so skillful they could transform within minutes the mood of their listeners.47 It was,

on the other hand, completely different to assert that musical instruments could make

original contributions to the study of music. Mersenne, however, did uphold such a

position from the mid 1620s onwards. The first section of this chapter, which may appear

a long digression, addresses this problem by contextualizing the rising significance of

musical instruments in the late cinquecento as legitimate producer of knowledge and

sound. The core problem rested on an art-nature debate between the artificial musical

instrument and the natural human voice, best examplified by the heated discussion in

daigne pas presque escouter.” Titelouze to Mersenne, 2 March 1622, CM I, 76. On the rising influence of the lute in sixteenth-century France, see the excellent book by Jean-Michel Vaccaro, La Musique de luth en France au XVIe siècle (Paris: Éditions du Centre National de la Recherche Scientifique, 1981).

47 One story, well known, tells of a lute player called at the court of Denmark to demonstrate his prowess on that matter. Unwilling at first to perform in front of the king and his suite, he finally obliged them, but asked that all weapons were removed from the royal chamber and that a few courtiers stayed in the antechamber so they could enter the chamber on his request, if anything were to happen. He then started to play soft melodies, which had the king and all present sad and melancholic; next the lute player changed the song for an air more vibrant and gaillard, and all of a sudden everyone was happy and joyful. Finally, the musician played a Phrygian air, striking hard on the lute’s strings, which had the king and his suite utterly enraged. The musician gave the signal at that moment and the courtiers from the antechamber came in, broke the lute on the player’s head (on his demand) and rushed over to the king to restrain him. When the king finally came back to his senses, he filled the musician with praise, comparing him to Timothy, who had showed similar skills in the presence of Alexander the Great. The story is taken from Pierre Trichet, Traité des instruments de musique (vers 1640), ed. by François Lesure (Neuilly-sur-Seine: Société de musique d’autrefois, 1957), 150-151. A Latin version of this story was written by Albert Krantz, a German who visited Danemark and later wrote a chronicle, Chronica regnorum aquilonarium Daniæ, Sueciæ, et Norvagiæ (Strassburg, 1546), published posthumously. According to Lesure, however, Trichet probably took the information from a certain P. Loyer. See Daniel P. Walker, “Musical humanism in the 16th and early 17th centuries,” Music Review (1941), 111-112. Mersenne knew this anecdote as well, see his “Traitez des consonances, des dissonances, des Genres, des Modes, & de la Composition,” book 6, “L’Art de bien chanter,” part III, “De la Musique Accentuelle,” 365, in Harmonie universelle, contenant la théorie et la pratique de la musique, 3 vols. (Paris: Centre national de la recherche scientifique, 1963), vol. 2 (hereafter cited as HU1, HU2 or HU3).

32

Organ Making: Mersenne’s Musical Instruments

print opposing Gioseffo Zarlino to Vincenzo Galilei. That artificial instruments, argued

Galilei, were as good, if sometimes not better, than the human voice in producing

knowledge about music was of fundamental importance to Mersenne. In fact, this

assertation became the foundation on which his subsequent study of sound rested.

As Mersenne explained in the dedicatory epistle of the “Traité des instrvmens a

chordes” addressed to Monsieur Henri de Refuge, theory reduced to practice and objects

should not be despised as it so often was by ancient authorities. In these four books, de

Refuge would see rare experiments describing the properties of air and movement in

general, “which ought always to be considered in the mechanics of art as well as of

nature, when one wishes to find the true reason for the difficulties which are there

encountered.”48 Mersenne dedicated other books to de Refuge, like the Traité de

l’Harmonie universelle (1627) and Les Mechaniques de Galilée (1634), in which

experiments and the material culture of natural philosophy were underscored.

What Mersenne stressed in this new dedication to de Refuge was the following: to

fully understand the production of sound, it had to be studied from all possible sources,

whether natural or artificial. Mersenne’s books on instruments, therefore, attempted to

demonstrate how important it was to investigate the manufacturing of all musical

instruments in order to shed some light on the theoretical study of sound. A few books

later, Mersenne’s dedication of the treatise on the organ to Etienne Pascal went far

beyond the simple understanding of the mechanical arts. There he explained that Pascal

père was probably the best intellectually-prepared savant to discover the causes of some

48 Mersenne, “Traité des instrvmens à chordes,” book 1, Epitre, n.p. (HU3). Mersenne, The books on instruments, 11.

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of the experiments Mersenne described, considering he so fruitfully married the practice

of science to its theory.49 As will be explained below, this marriage between instruments,

practice and theory was exactly what Mersenne tried to convey from the detailed exposé

he wrote on the most influential and majestic early modern musical instruments of all.

In addition, and of significance to my argument, musical instruments in general

were perhaps the best and most perfect Christian tools of knowledge-production since

they could be employed with much effect to praise the Lord—as Mersenne emphasized to

de Refuge in referring to the familiar Psalm 150.50 As I will demonstrate in section three,

the organ—more than any other musical instrument—held a special religious status in

early modern Europe, a distinction that was fully understood by Mersenne and his

contemporaries, whether Catholics or Protestants. This powerful Church symbol, as I will

then show in section four, became in Mersenne’s writing on the organ the best material

representation of natural philosophy—the perfect combination of artisanal knowledge,

experiments and theory. Spending a third of his books on instruments on the organum

organorum, Mersenne claimed—without having to put it into word—that carefully

49 Mersenne, “Traité de l’orgue,” book VI, Epitre, n.p. (HU3). The Epitre is dated 1 November 1635: “Car soit que l’on considere la Pratique des Mechaniques, ou leurs Raisons, & particulierement celles de l’Harmonie, il seroit tres-difficile de trouuer vn homme qui les entende mieux que vous: & peut-estre qu’il n’y en a point de si sçauant, qui ne tint à faueur d’apprendre ce que vous auez medité sur ce suiet. … I’espere que les rares experiences que vous rencontrerez dans ce liure, vous conuieront à en rechercher les raisons, car elles meritent l’estude des meilleurs esprits; ioint que vous possedez à vn haut point tous les Ressorts de la plus subtile Analyse, qui découure tout ce qui peut tomber dans vne imagination bien reglée, que vous ne pouuez apporter aucune excuse receuable. C’est pourquoy i’ose promettre à tous ceux qui cherissent les Muses, que vous mettrés bien tost la derniere main à cette partie de la Philosophie, afin qu’elle ne craigne plus desormais de paroistre deuant les plus sçauans dans la compagnie des autres sciences, & qu’elle confesse hautement qu’elle vous est plus obligée qu’à nul autre, à raison du mariage tres-excellent que vous auez fait de la Pratique auec la Theorie.”

50 The first verse of Psalm 150 reads thus: Praise Him with sound of trumpet; Praise Him with nablium [psaltery] and harp. / Praise Him with timbrel [tambourine] and pipe; Praise Him with strings and organ. / Praise Him with cymbals of sound; Praise Him with cymbals of shouting. / Let every thing that breatheth praise God. Hallelujah.

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studying the manufacturing of organs could be of assistance in becoming a “modern”

natural philosopher as well as a devoted Christian.

This chapter, in short, is about the transformation of the theoretically-inclined

Medieval musicus to the early modern “parfait musicien,” an individual in touch not only

with the theory of music, but also with its material culture. Except perhaps for Galileo,

Mersenne demonstrated better than most contemporary savants how and why doing

science was an enterprise involving everything but armchair natural philosophy.

Mersenne’s books on musical instruments—and especially the organ—epitomized like

none other in the first half of the seventeenth century the new mechanical natural

philosophy, which was ultimately grounded on theory, experiments and a thorough

understanding of the mechanical arts. This happened decades before the so-called English

empiricist turn was inaugurated in the mid seventeenth century.

GIVING A “VOICE” AND MEANING TO MUSICAL INSTRUMENTS IN THE RENAISSANCE

The popularity of instrumental music during the Renaissance breached a few dogmatic

walls regarding the use and virtue of musical instruments. It is essential to remember that

musical instruments were virtually ubiquitous in Renaissance Europe, and served several

functions in sixteenth-century parochial, urban and court cultures. Just consider

Rabelais’s descriptions of popular fêtes and festivals, French elaborate royal entries in

cities, or even Girolamo Cardano’s youthful habit of wandering all night through Milan,

dripping with perspiration at daybreak from the physical exertion of serenading on his

lute.51 Not only did scholars begin to pay attention to the manufacture of musical

51 On Rabelais, see his Gargantua and Pantagruel, and Mikhail Bakhtin, Rabelais and his world,

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instruments—like Henri Arnaut de Zwolle’s famous treatise (ca. 1440) on the organ and

lute52—European courts found a renewed interest and special opportunities for

instrumental music. At the court of Mantua, for example, the Marchesa Isabella d’Este

Gonzaga enrolled the service of the instrument maker and virtuoso instrumentalist

Lorenzo da Pavia to make a variety of musical instruments, such as viols, clavichords,

harpsichords, and lutes.53 And in France, François I had numerous joueurs d’instruments

in ensembles called musique de l’Écurie and musique de chambre as well as chantres

who sang in the king’s Grande Chapelle.54

On a larger sociological scale, music had an overall striking impact on the early

modern French court. In fact, it was not by any means fortuitous that the ballet de cour,

air de cour, and musique mesurée were introduced at court during the Wars of Religion.

Music and dance, according to Kate van Orden, participated in the “broad process of

transl. by Helene Iswolsky (Bloomington: Indiana University Press, 1984). On French Royal entries and other “outdoor” events in streets, cemeteries and fields or during hunting parties and military campaigns, Isabelle Cazeaux, French music in the fifteenth and sixteenth centuries (Oxford: Basil Blackwell, 1975), chap. 7. On Cardano’s epic all-nighters, Clement A. Miller, transl. and ed., Hieronymus Cardanus (1501-1576): Writings on music ([n. p.]: American Institute of Musicology, 1973), 17.

52 G. Le Cerf, ed. (with the collaboration of E. R. Labande), Les Traités d’Henri-Arnaut de Zwolle et de divers anonymes (ms B.N. Latin 7295) (Paris, 1932). Arnaut was a professor of medicine to Monseigneur le duc de Bourgogne. He was also interested in astronomy and even received monetary rewards for making astronomical instruments. His treatise on music is one of the firsts to study and describe the manufacture of organs, lutes, and other keyboards instruments like the clavisimbalum. See also Edward L. Kottick, “Building a 15th-century lute,” The Galpin Society Journal 26 (1973), 72-83. Edwin M. Ripin, “The early clavichord,” The Musical Quarterly 53 (1967), 518-538.

53 William F. Prizer, “Isabella d’Este and Lorenzo da Paria, ‘master instrument-maker’,” Early Music History 2 (1982), 87-127. See also Iain Fenlon, “Isabella d’Este e i suoi contemporanei. Musica e mecenatismo presso le corti dell’Italia settentrionale,” in Bernardo Clesio e il suo tempo, ed. by Paolo Prodi (Rome: Bulzoni, 1986), 607-637. On women and musical instruments in general, Lujza Tari, “Women, musical instruments and instrumental music,” Studia Musicologica Academiæ Scientiarum Hungaricæ 40 (1999), 95-143.

54 Christelle Cazaux, La Musique à la cour de François Ier (Paris: École Nationale des Chartes, 2002), 69-160. On royal chapels in general, Juan José Carreras and Bernardo García García, eds., The Royal Chapel in the time of the Habsburgs: Music and ceremony in early modern European court, transl. by Yolanda Acker with English edition by Tess Knighton (Woodbridge, UK: Boydell Press, 2005).

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behavioral and cultural disciplining that the French aristocracy underwent beginning in

the sixteenth century.” Court music and dance performances were deployed not so much

to quench violent behavior (as one might think) as to make sure the notorious aristocratic

excess of bloodshed was forced out in an orderly and organized way—in the pyrrhic

dances or ballets à cheval, for instance. Music became a royal instrument of social order

at many levels, whether during royal balls, royal entries or sacred Te Deum ceremonies.

“Through the action of music,” argues van Orden, “social bodies cohered.”55

Although music contributed to religious, courtly and popular activities, the value

and significance of musical instruments continually led to artistic, epistemological, and

theological disagreements in the Christian West. Up until the Renaissance, and through

most of it actually, a distinctive religious and scholarly consensus considered the human

voice as the purest of “instruments,” allowing any well-trained individual to sing in

accordance with the strictest of principles (or consonances) derived from ancient music

theory. This idea went back primarily to Boethius’s early sixth-century De institutione

musica, in which Boethius classified vox in three categories—reciting a prose oration

(emphasis on words spoken), singing a sequence of intervals (emphasis on sung voices),

and doing both at the same time, or the intermediate voice. The notion of vox meant for

55 Kate van Orden, Music, discipline and arms in early modern France (Chicago: The University of Chicago Press, 2005), quotes on pp. 7 and 36 respectively. On dance, see Sarah R. Cohen, Art, dance, and the body in French culture of ancien régime (Cambridge: Cambridge University Press, 2000). A similar approach is found in Robert M. Isherwood, Music in the service of the king: France in the seventeenth century (Ithaca: Cornell University Press, 1973). To a philosopher like Cardano, who played the lute as did more and more men and women (educated or not) during the mid to late Renaissance, musical instruments could be used not only to manipulate others behavior, but also as an effective source of self-development. Cardano was arguing for a style of music called monody (or monophony), which involves only one melodic voice, in contrast to polyphony (involving two or more melodic voices, generally used today). Monodic music meant anyone could learn for his or herself how to sing or play an instrument to change, in Cardano’s words, one’s own “morals, moods, or actions.” Miller, Hieronymus Cardanus (1501-1576): Writings on Music, “On the value of music,” 198-199.

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Boethius the spoken or sung voice as well as the abstract tone. In contrast to the abstract

or perfect mathematical tone, the human voice was clearly limited though remained the

best musical instrument of all. Boethius acknowledged that fact early in his treatise,

insisting that human nature was the one and only limitation to the boundlessness of vox.56

In the West the epitome of singing voices came from the Gregorian chants, or

more specifically from the origins of the Christian liturgical plainchant (cantus planus).

In order to establish the Roman ecclesiastical reform and discipline Pippin the Short and

his descendants emphasized singing as a way to further the development of uniformity in

worship, and consequently unity in religious devotion. Through singing, the ancestors of

early modern French kings aimed to replace the diverse Gallican traditions by a single

rite, later known as Roman Catholicism. Singing Church liturgical texts became above all

a way to celebrate God’s greatness. Far into the Renaissance, in fact, disciplined singing

was believed to be the surest and most adequate method to properly praise the Lord.57

Dissenting (one might say discordant) voices, however, were heard in the early

sixteenth century. In 1511 Sebastian Virdung, a German priest, published the first treatise

in the West on musical instruments, entitled Musica getutscht. This book illustrates

primarily the coming into prominence of instrumental music and the amateur

instrumentalist in the early Renaissance. Virdung composed his treatise as a “self-help”

method, and saw himself as a “silent master” leading the reader step-by-step through the

56 “The voice [vox] which is continuous and that with which we run through song are inherently boundless. For by consideration generally agreed upon, no limit is placed either on flowing through words or on rising to high pitches or sinking to low ones. But human nature imposes its own limitation on both of these kinds of voice.” Anicius Manlius Severinus Boethius, Fundamentals of music, transl. by Calvin M. Bower (New Haven: Yale University Press, 1989), §12-13, 20-21, quote on p. 21.

57 Kenneth Levy and John A. Emerson, “Plainchant,” Grove Music Online, ed. by L. Macy (Accessed via Harvard College Libraries, 22 March 2006), <http://www.grovemusic.com>.

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era’s two most important German instrumental notation systems, the tablatures for

keyboards and lutes. (See Figure 1.1.) In a similar fashion, the book also guided the

music novice through the fingerings of three sizes of recorders.58 Yet Virdung’s main

focus was not about musical instruments per se, nor was it in explaining the finer points

of abstract music theory. Virdung’s initial motivation for publishing it was chiefly the

FIGURE 1.1: GERMAN INTABULATION SYSTEM Above is a musical piece in what was called “vocal notation.” The upper right illustration is the tablature symbols found on a lute according to Virdung’s German system. To the right, the same song as above but intabulated so it can be played on the lute. From Bullard, Musica getutscht, 146, 165, 167.

advancement of Christianity. Enough evidence is found in the Scriptures, according to

Virdung, to trust that “we are bidden and commanded in so many [Biblical] passages to

rejoice in God the Lord actively, that is with instruments.” This is the reason why, he

continued, “I have begun a brief little treatise, writing a small amount about these

58 Beth Bullard, transl. and ed., Musica getutscht: A treatise on musical instruments (1511) by Sebastian Virdung (Cambridge: Cambridge University Press, 1993). Another important study, which sometimes hold opposing views to Bullard’s, particularly on the role and significance of the printed woodcuts of instruments, is Edwin M. Ripin, “A reevaluation of Virdung’s ‘Musica getutscht,’” Journal of the American Musicological Society 29 (1976), 189-223.

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instruments, from which those who wish to share in such promised blessedness may take

some small or tiny bit as a foundation or introduction to the instrument with which to

learn [it], thereby gaining the promised eternal blessedness.”59

Although Virdung’s book generated adaptations in Latin and Dutch, as well as a

direct translation of the Dutch edition into French, it is particularly recognizable in

Martin Agricola’s Musica instrumentalis deudsch.60 First published in 1529, Agricola’s

text and engravings are often strikingly similar to Virdung’s Musica getutsch and its

technical purpose was also the same: to instruct in the tablatures of stringed, wind and

keyboard instruments.61 In the second edition of 1545 (the first one was printed in 1529,

1530, 1532 and 1542) the skilled instrumentalists who objected to disclose their practice

were no longer Agricola’s principal targets. Although the new edition originated from the

view that the 1529 edition was in some places “too obscure and difficult to understand”

59 Bullard, Musica getutscht, quotes on p. 99. To Virdung, the musical instruments described in the Psalms had more than a symbolical value: they ought not be treated as allegories—as prescribed by the Church Fathers—but rather as objects worthy of God’s worship. The rationale behind the publication of his little book on instrumental music, in fact, was that its use would ultimately increase the number of blessed people. Furthermore, in writing his treatise in German—including important Biblical passages that supported his claims—he anticipated the Lutheran reform, demonstrating that the vernacular language could be used to address matters of faith. Virdung’s book thus aimed at breaking two old dichotomies pertaining to how one should praise God: voice vs. musical instruments for music; Latin vs. vernacular languages in relation to the Scriptures.

60 William E. Hettrick, transl. and ed., The ‘Musica instrumentalis deudsch’ of Martin Agricola: A treatise on musical instruments, 1529-1545 (Cambridge: Cambridge University Press, 1994). On the offspring of Virdung’s treatise, see Bullard, Musica getutscht, 61-88.

61 Ibid, Appendix 1, 145-146 for a table of Agricola’s woodcut illustrations derived from Virdung’s Musica getutscht. The thrust behind Agricola’s treatise, however, is somewhat distinct from Virdung’s, that is Agricola’s chief reason to publish in 1529 was to “democratize” instrumental music, not to demonstrate how one could praise the Lord. Agricola was hostile to the fact that those skilled in the art of instrumental music sought to keep their practice a secret following the proverb that said “Art must be held back, so that art will endure.” Agricola believed it was a truly unchristian demeanor, and hoped that his treatise would present “to people who are highly celebrated and greatly learned in this art, a Christian example and model for helping young people…” Thus instrumental music should be perceived as a bona fide liberal art, fit to be taught in schools; it was not a vulgar craft that needed to be kept secret, but a noble art that had to be passed on and celebrated. Ibid, 1529 edition, sig. A3v-A4, 4.

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for schoolchildren,62 the focus was turned toward those who blatantly opposed

instrumental music. To educate “boys” in the “noble art” of instrumental music meant

that “much useless speculation, fantasy and ideas from the mind” had to be eliminated.

Instrumental music was indeed a “noble art,” because it was not only “the source of

remarkable recreation and diversion (as I have experienced)” but, above all, it taught how

to “praise God, who has given this delightful and joyful art—with which the Holy Angels

will also praise Him without ceasing and laud Him to eternity…”63 As Agricola

explained in the preface of the 1545 edition,

Although, my dear lord Georg Rhau [his patron, friend, and publisher], several people who have shamefully scorned the Instrumental [Music] and me on account of it, might almost have discouraged me from my intended and useful writing, I reasoned finally that, indeed, because they speak about the subject so monastically (as in a monastery, where one lives quite meditatively and sings only plainsong without any musical instruments) and perhaps do not understand anything in particular of this noble art, you might therefore excuse them this time; you will not follow them, but rather Moses, David and many other excellent people who have thought very highly of it (as the Psalter etc. indicates) and have presented and bequeathed us examples of how to praise God in various ways.64

For Agricola, as well as for Virdung before him, the voice was not the flawless

“instrument” classical and contemporary authors declared it to be—and hence the most

sublime instrument in praising God. Musical instruments were valuable instruments of

worship, sanctioned in numerous sacred texts.65 The so-called dichotomy between voice

62 Quote from Agricola’s 1545 edition, sig. A3, 63. To this new edition, however, was added copious marginal notes and numerous Latin quotations to enhance the erudition of the work. This may be in response to the critics who noted the lack of classical scholarship in the previous edition. (Mathematical ratios with examples are also discussed, which is not the case in the first edition.) The work reflects, according to Hettrick, the general educational and religious environment of Saxony in the 1540s, as is also illustrated by the several references to Luther and the passionate attacks against the Roman Catholic Church. Ibid., xvi.

63 Ibid., 1545 edition, sig. A3, 63. 64 Ibid, 1545 edition, sig. A4-A4v, 64-65. 65 Agricola, interestingly enough, was a music teacher in a Magdeburg’s Lateinschule (he was

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and instruments appeared in the end artificial and dogmatic to at least a few early

cinquecento instrumental musicians and theorists.66

In the late Renaissance such a version of the art-nature debate took a natural

philosophical turn. Not only did it challenge the classical dichotomy between the

concepts of Art (musical instruments) and Nature (voice), it confronted as well (and most

importantly) the authority of ancient learning in arguing that musical instruments,

supported by careful sense experiments, contradicted longstanding assumptions. The

debate was essentially polarized between two giants of the latter cinquecento Italy,

Giuseffo Zarlino and Vincenzo Galilei. It got center stage with the publication of

Zarlino’s Sopplimenti musicali in 1588 and, the following year, Galilei’s Discorso

intorno all’opere di messer Gioseffo Zarlino da Chioggia.

Zarlino spent the first few chapters of the Sopplimenti discussing in an

Aristotelian style the perfection of nature over that of the arts. Since the publication of his

Istitutioni harmoniche in 1558, Zarlino maintained that only the human voice could sing

the vere forme of the Syntono di Tolomeo, or Ptolemy’s syntonic diatonic system of pure

named choirmaster in 1525), and in all likelihood the era’s only German music theorist to consider musica instrumentalis as important as cantus planus (plainchant). Latin schools in Germany, following Luther’s wishes, incorporated music as a central component of Protestant education. However, as was the case in Nuremberg, there is not much evidence that instrumental music was taught or generally held in high regards by Latin schoolteachers. Nuremberg’s music theorists, especially Sebald Heyden, published virtually all of their works in Latin in the 1530s and 1540s. These were essentially textbooks destined to the cities’ Latin schools, textbooks with which students learned the rudiments of music theory, plainchant and polyphony. Singing—whether in Latin or in German—not instrument playing was taught in Latin schools as part of the liberal arts curriculum. Agricola’s idiosyncratic approach emphasizing instrumental music was the exception, not the rule in early Renaissance Germany. Anna Maria Busse Berger, “Agricola [Sore], Martin,” Grove Music Online (Accessed on 12 February 2006). On music theory and Latin School in Nuremberg, Cristle Collins Judd, Reading Renaissance music theory, 82-114. The meaning and function of plainchant vs. polyphony clashed more here than did singing vs. instrument playing.

66 Jean-Michel Vaccaro, ed., Le Concert des voix et des instruments à la Renaissance (Paris: CNRS-Editions, 1995). With the help of several case studies, the chief aim of this book is to demonstrate that indeed, the classic viewpoint regarding the division of vocal and instrumental music in the Renaissance is more an artifact of history than anything else. On Agricola and other like-minded individuals, see Howard Mayer Brown, “The instrumentalist’s repertory in the sixteenth century,” in ibid., 21-32.

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mathematical consonances.67 Even though the mathematically determined true forms of

musical intervals were found on a mechanical monochord, it would be a mistake to think

all modern musical instruments could produce the pure consonances of Ptolemy’s system.

The heart of the matter rested on the fact that the addition of multiple strings on a string

instrument, for instance, did not ultimately produce the consonant true forms of the

syntonic diatonic; only a close approximation, given by a fine-tuning or temperament,

could be achieved on musical instruments. Such temperament, according to Zarlino, was

not derived from a scholarly study of musical intervals, but rather by chance (“che tal

Temperamento, o Participatione sia stata introdutta a caso, & non studiosamente”). In

three dense pages of text, Zarlino thus explained how the combination of multiple strings

on a musical instrument necessitated the use of comma, or minute differences that exist

between two relatively large, nearly identical intervals, in order to attain the consonances’

vere forme. To Zarlino, the whole art of temperament was to fiddle with a musical

instrument until (by chance) it got hold of the syntone of Ptolemy to the closest comma.

It was completely different for the human voice, which (making the necessary

adjustments) “naturally” sang the just intonation of the consonances. Because musical

instruments were above all the result of art, merely imitating nature,68 they were

inherently flawed, thus unable to “sing” perfectly. Only an “instrument of nature,”

67 On the traditional meaning of vox see Rossetti, Libellus de rudimentis musices, ed. by Albert Seay, Critical Texts, no. 12 (Colorado Springs: Colorado College Music Press, 1981), 1-60, quote on p. 5. Taken from the Thesavrvs mvsicarvm latinarvm, Center for the History of Music and Literature, University of Indiana <http://www.music.indiana.edu/tml/14th/ZAMLAM_TEXT.html> (Accessed on 13 April 2006).

68 “percioche non è fuor di ragione il dire, che gli Huomini incominciassero da principio ad osseruare I canti uarij de gli Vccelli, & ad imitar quelli con le Voci, & dopoi s’insegnassero di trouare & arteficiosamente fare alcune sorti d’Istrumenti, co i quali potessero imitar non solamente cotali canti, ma etiando quelli de gli huomini.” Gioseffo Zarlino, Sopplimenti musicali del rev. M. Gioseffo Zarlino da Chioggia… (Venice, 1588), book I, chap. 2, 13.

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faultless by definition, could.69

As a loyal student under Zarlino in the 1560s, Galilei first accepted this point of

view. When Galilei began a correspondence on matter of Greek music with the humanist

Girolamo Mei, however, he was exposed to another sort of thinking, one that was

established to some extent in experiments. Mei rejected Zarlino’s theory-laden use of

nature’s just intonation as true to reality. According to him, moderns did not sing in the

syntonic diatonic vere forme Zarlino suggested. But instead of entering into a long

dialectical proof he suggested to Galilei a simple experiment:

Stretch out over a lute (the larger it is the more obvious will what we wish to prove be to the ear) two … strings of equal length and width and measure out the frets under them accurately according to the distribution of the intervals in each of the two species of tuning—syntonic and di[a]tonic—and then, taking the notes of the tetrachord one by one by means of the frets of each string, observe which of the two strings gives the notes that correspond to what is sung today. So without any further doubt the answer will remain clear to anyone, even if what I have often fancied on my own, more as a matter of opinion than judgment, is not proved true.70

Mei was perhaps the first modern scholar to make a sharp distinction between pure and

applied knowledge. As Mei explained to Galilei, the science of arithmetic, for example,

69 Gioseffo Zarlino, Le Istitutioni harmoniche (Venice, 1561; facsimile of the second edition, Arnaldo Forni Editore, 1999), book II, chaps. 41 & 42, 125-127. On the dichotomy between art and nature, Zarlino writes: “Et benche ne i detti istrumenti temperati in tal maniera, non si poßino vsare le consonanze nella sua perfettione, cioè nella loro vera, & naturale forme; è nondimeno poßibile di poterle vsare, quando le loro chorde si volesero tirare sotto la ragione delle loro proportioni vere, & naturali. Et questo io dico, perche molte volte ne hò fatto la esperienza sopra vno istrumento, il quale feci fabricare a que sto proposito… Ma se cotali incouenienti (dirò cosi) si trouano ne gli Istrumenti arteficiali, nondimeno tra le Voci, come altre volte diremo, non si trouano tali rispetti: conciosia che riducono ogni cosa nella sua perfettione, come è il douere: essendo che la Natura, nel fare le cose, è molto superiore all’Arte: & questa nello imitare fa ogni cosa imperfetta, & quella (rimoßi gli impedimenti) ogni cosa riduce a perfettione.” (p. 127)

70 Mei to Galilei, 17 January 1578, in Girolamo Mei, Letters on ancient and modern music to Vincenzo Galilei and Giovanni Bardi, annotated by Claude V. Palisca ([n. p.]: American Institute of Musicology, 1960), 140 for the Italian text; p. 67 for the English translation. On the role of experiments, Palisca mentions the school of Padua to which Mei had an opportunity to know. Jacopo Zarabella was the chief representative of this school. See, for instance, Charles B. Schmitt, “Experience and experiment: A comparison of Zarabella’s view with Galileo’s De Motu,” Studies in the Renaissance 16 (1969), 80-138.

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was about the properties of numbers “considered for themselves as well as with reference

to other numbers, … which considerations do not serve the practical art of keeping

accounts.” It was similar with the science and practice of music. The science of music

was the investigation of musical tones for themselves with “no other aim than to come to

know the truth itself”; art should then be free to explore in any way it deemed fit “those

tones about which science has learned the truth.”71

It is in large part due to its correspondence with Mei that Galilei’s Dialogo della

musica antica et della moderna (1581) sprang to life. The dialogue between Piero Strozzi

and Giovanni Bardi, Galilei’s interlocutors, was a long response to Zarlino’s doctrine

exposed in the Istitutioni harmoniche. Following Mei’s inquiry, the book’s goal was to

determine which scale tuning was actually used by modern musicians, vocalists and

instrumentalists. Galilei’s chief finding was that none of the ancient tuning, neither

Ptolemy’s syntonic diatonic nor any other specific one, could explain what our ears liked

to hear and what our reason found to be just and accurate. In the voice of Bardi, Galilei

declared in his Dialogo: “After long observation, I find that natural voices and artfully

made instruments in this modern musical practice really do not sing and play any of the

nine ancient species of diatonic in their simple form but rather three of them variously

mixed by practitioners inadvertently.”72 Galilei did not start with an abstract idea of a

perfect mathematical scale, but turned his attention instead toward the actual tuning of

musical instruments. Not only did he find that none of the instrument’s temperament

71 Mei to Galilei, 8 May 1572, in Mei, Letters on ancient and modern music, 103 for the Italian text; p. 65 for the English translation.

72 Vincenzo Galilei, Dialogue on ancient and modern music, transl. by Claude V. Palisca (New Haven: Yale University Press, 2003), 77. The three tuning scales were that of Aristoxenus, the ancient ditonic diatonic, and the syntonic of Ptolemy.

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fitted ancient tunings, each type of instrument had identifiable tuning scales as well.73

In the Discorso, Galilei reiterated the argument that, contrary to what Zarlino

believed, modern musicians did not sing or play according to the naturally occurring

syntone of Ptolemy. Galilei even refuted Zarlino’s claim that the proof came simply from

the study of tempered instruments. According to Galilei, the evidence was found in the

syntone of Ptolemy itself: “Moreover the intervals sung today are not sung in their natural

true forms, because the syntone I say has its fifth and fourth consonant and dissonant,

whereas those sung and played today are all consonances; therefore the syntone is not

sung nor played [today].”74 Galilei brashly declared that no one endowed with the faculty

of reason would be so “thick” to adopt Zarlino’s point of view.75

Perhaps more significantly, the syntone of Ptolemy was no more or no less natural

than any other tuning scale, whether devised mathematically by the ancients or artfully by

modern instrumentalists. As a matter of fact, the syntonic diatonic scale—like any other

tuning scale—was not natural at all but solo tutto artifiziale in Galilei’s words, created by

73 Moyer, Musica scientia, 241-263 for a very good analysis of Galilei’s works. On Zarlino and Mei, see ibid., 202-225 and 225-241 respectively. See also, Palisca, Humanism in Italian Renaissance musical thought (New Haven: Yale University Press, 1985), 265-279.

74 “Le ragioni che io adduco che non si ca[n]ti ne si suoni il Sintono della maniera che lui ce lo disegna, le cauo come si è veduto, non d’altroue che dal medesimo Sintono. Soggiugne appresso che io dico che gli interualli che si cantano hoggi, non si cantano nelle vere forme loro naturali. Anzi il contrario; per che il Sintono dico io, ha delle quinte & delle quarte consonanti, & delle dissonanti, & quelle che si cantano e suonano hoggi son tutte consonanti, adunque non si canta ne si suona il Sintono.” Galilei, Discorso di Vincentio Galilei, nobile Fiorentino intorno all’opere di messer Gioseffo Zarlino da Chioggia (Florence, 1589), 33-34. For Zarlino’s critique, Sopplimenti, book IV, chap. 4 and chap. 10.

75 “ma che realmente egli sia tale, son sicuro che non si trouerà huomo tanto grosso (pur che ci sia capace di ragione) che lo creda.” Galilei, Discorso, 9. Mei wrote to Galilei a decade before that anyone who accepted and followed Zarlino’s senario as a proof of the syntone of Ptolemy were “simpletons.” Mei to Galilei, 17 January 1578, in Mei, Letters on ancient and modern music, 138. Galilei describes Zarlino’s senario as “impertinent”: “il numero Senario, o altre Zarlinesche impertinenti inouationi…” Galilei, Discorso, 98.

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Organ Making: Mersenne’s Musical Instruments

Ptolemy’s artifice.76 Zarlino agreed somewhat with this assertion, calling Ptolemy’s scale

in his Sopplimenti the “sintono artifiziale” and the just intonation only sang by voices the

“sintono naturale.”77 For Galilei, however, this dichotomy between musica naturalis

(vocal music) and musica artificialis (instrumental music) was specious: only natural

sounds existed since they were all produced by natural materia. Consonances were no

doubt natural phenomena, but they were not naturally reproduced by the voice in their

vere forme. Singing well and accurately was an art requiring practice, just as the art of

instrumental music was—or for that matter, medicine, agriculture and animal husbandry,

emphasized Galilei.78

Art, in other words, did not need inexorably to imitate nature. It was one of the

book’s major conclusions. Taking into account the lengthy argument on the valuable

disposition of art, after establishing that the syntonic diatonic scale—or any other tuning

scale for that matter—was not natural but an artifice of man, Galilei could finally affirm

76 Galilei, Discorso, 31-32. 77 Zarlino, Sopplimenti, book IV, chaps. 6-8. Daniel P. Walker, Studies in musical science in the

late Renaissance (London: The Warburg Institute; Leiden: E.J. Brill, 1978), chap. 2. 78 Galilei, Discorso, 70-78, 92-94, 82-84. Descartes said somewhat the same thing to Isaac

Beeckman when, at the very beginning of the Compendium musicæ, he emphasized the significance of sense experience, establishing a clear distinction between affectiones (characteristics of sound) and affectus (passions). Descartes explained that only the pitch and duration of sounds should matter to musicians, while how sounds were produced should be left to physici. It did not make a difference therefore whether sounds were formed by singers or instrumentalists: both used the two chief properties of sound to convey affectus. The new Cartesian estheticism thus did not rely on two different kinds of music, musica naturalis and musical artificialis, the former being more perfect than the latter. Estheticism (affectus) was completely separated from the actual properties of sound (affectiones), which were explained according to Descartes’s (and Mersenne’s) mechanistic interpretation of nature. Philippe Vendrix, “La dichotomie vocal/instrumental dans la théorie musicale aux confins de la Renaissance et du Baroque,” in Le Concert des voix et des instruments à la Renaissance, 71-81. See also Raymond Court, Sagesse de l’art (arts plastiques, musique, philosophie) (Paris: Méridiens Klincksieck, 1987), chap. 6, and Brigitte van Wymeersch, Descartes et l’évolution de l’esthétique musicale (Sprimont: Mardaga, 1999). René Descartes, Abrégé de musique, transl. and ed. by Frédéric de Buzon (Paris: Presses universitaires de France, 1987). On the dichotomy between object and subject, see also Jairo Moreno, Musical representations, subjects, and objects: The construction of musical thought in Zarlino, Descartes, Rameau, and Weber (Bloomington: Indiana University Press, 2004), chap. 2.

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that musical instruments were not improved by the human voice, as Zarlino forcefully

argued, but that most likely the reverse was true.79 It was precisely what Mersenne

acknowledged and welcomed as a fundamental principle in the beginning of his books on

instruments.80

MERSENNE’S SEVEN BOOKS ON INSTRUMENTS IN THE HARMONIE UNIVERSELLE

The scholarly dispute that erupted between Galilei and Zarlino concerning the epistemic

value of musical instruments was so consequential to Mersenne’s overall conceptual

system that he mentioned it right at the outset in his books on instruments. In the third

proposition of book one dedicated to string instruments, Mersenne—siding all along with

Galileo’s father—stated that

Actually if one tunes instruments according to the perfection of the theory, there is no doubt that they will have no need of the perfection of the voice, which can be corrected and adjusted by their means, for one can show whether the voices are singing exactly only by showing that they conform to the perfect instrument. This Zarlino should have acknowledged, had he considered it attentively.81

79 “Non è vero adunque che non si possa render ragione esatta degli interualli de’ suoni degli strumenti artifiziali senz’applicargli alle voci naturali; ma è ben vero per il contrario, che no[n] si può render ragione dell’esatto degli interualli delle voci, senza applicarle a’ suoni degli strumenti artifiziali.” Galilei, Discorso, 83. In his Dialogo, Galilei says that today’s way of singing originated in Greek unfretted instruments. Galilei, Dialogue on ancient and modern music, 317. For a discussion of Galilei’s “modern” understanding of nature, Daniel K. L. Chua, “Vincenzo Galilei, modernity and the division of nature,” in Music theory and natural order from the Renaissance to the early twentieth century, ed. by Suzannah Clark and Alexander Rehding (Cambridge: Cambridge University Press, 2001), 17-29.

80 Trichet follows Mersenne in the preface to his treatise on musical instruments: “mais enfin j’ay jugé que les instruments de musique debvoient emporter la préférence sur la pluspart des raisons qu’on allegue pour la musique vocale, d’autant qu’ils ont des attraits particuliers et des opérations plus efficaces qu’elle.” Musicians themselves, Trichet heard, were “beaucoup plus ravis et satisfaicts de leur jeu que de leur chant: et la raison me semble estre fondée sur ce qu’ils ne peuvent démonstrer qu’ils chantent justement qu’en faisant apparoir que leurs voix sont conformes a un instrument parfaict.” Trichet, Traité des instruments de musique (vers 1640), 14. Claude V. Palisca, “Mersenne pro Galilei contra Zarlino,” Nuova civiltà della macchine 16 (1998), 74-80.

81 Mersenne, “Traité des instrvmens a chordes,” book I, prop. III, 8 (HU3). English translation in Mersenne, Harmonie universelle: The books on instruments, transl. by Roger E. Chapman (The Hague: M. Nijhoff, 1957), 22. (hereafter cited as Mersenne, The books on instruments).

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According to Mersenne (and somewhat to Aristotle82) the craftsmanship of musical

instruments—if perfected by theory—was superior to the naturally created organs of the

human voice, and therefore the latter should be tuned to the former. Objects of art, in

other words, were not always predestined to becoming poor imitations of nature—

Aristotle’s ars imitatur naturam.83 It was exactly what argued Galilei against Zarlino

several decades before Mersenne. The latter in fact pushed even further the Renaissance

argument that musical instruments played a significant role to our understanding of

music. In Mersenne’s writings, the material culture of music became nothing short of a

key element to the study of music—and consequently to our understanding of universal

harmony.

Mersenne’s books on instruments are well known in the field of music. Published

in 1636 as part of the much larger Harmonie universelle, these books, along with book

two of Michael Prætorius’s 1619 Syntagma musicum, are the most important

contributions to our knowledge of early modern musical instruments. Indeed, several

historians of music (and modern instrument makers) have used Mersenne’s and

Prætorius’s detailed descriptions to explore the history and technology of individual

82 See Aristotle, Problems*, book 19, §918a29-918a34, in The complete works of Aristotle, ed. by Jonathan Barnes, 2 vols. (Princeton: Princeton University Press, 1984-1985), ii:1431: “Why, if the human voice is more pleasant than an instrument, is the voice of a man singing without words—as, for example, when singing nonny-noes—not so pleasant as a flute or lyre? Or is it true that even in the case of an instrument we get less pleasure if it is not expressive of meaning? The instrument, however, has an advantage even in its actual effect; for while the human voice is pleasanter, instruments strike the note better than the human mouth, which is why they are pleasanter to hear than nonny-noes.” This reference was taken from Past Masters internet resource <http://library.nlx.com> (Accessed via Harvard College Libraries, 22 April 2007).

83 Mersenne, “Traité des instrvmens a chordes,” book I, prop. III, 9 (HU3): “Certes il me semble que l’Art peut estre dit superieur à la Nature ou surpasser la Nature, lorsqu’il donne quelque degré de perfection à vn sujet, auquel elle ne le peut donner: ce qui n’empesche pas qu’elle ne surmonte l’Art en plusieurs autres choses.”

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musical instruments. Few scholars, however, have attempted to outline the

epistemological meaning of these same musical instruments. This is what I will

demonstrate in the section below on Mersenne’s organ. In this one I want to concentrate

rather on a general description of Mersenne’s books on instruments, what were they and

how they came into being.

It is difficult to identify exactly when Mersenne decided to add a treatise—a

compendium—on musical instruments to his overall study of music. In his Questiones in

genesim of 1623, Mersenne was interested primarily with Antiquity’s musical thought,

devoting several columns to the perfection of ancient Greek music and to the more

contemporary musique mesurée of Jean-Antoine de Baïf’s Académie de poésie et de

musique. His approach was then a humanist one, established on the study of rhetoric,

dialectic, classical writings and recent works by Pierre de Ronsard, Pontus de Tyard and

Baïf himself.84 Four years later, when Mersenne published the Traité de l’Harmonie

universelle, music had become more than a pure intellectual pursuit derived exclusively

from ancient learning. Music, through the idea of a universal harmony, could teach a new

method of learning, one not faithfully restricted to the “tyranny of opinions.” Ancient

writings, Mersenne stressed, should not be blindly received before one has done his own

sense experiments.85 Although Mersenne’s natural philosophy did not completely stir

84 David Allen Duncan, The tyranny of opinions undermined: Science, pseudo-science and scepticism in the musical thought of Marin Mersenne (Ph.D. dissertation, Vanderbilt University, 1981), esp. chapter 3. On the Académie de musique et de poésie the classic work remains Frances Yates, The French academies of the sixteenth century (London: Warburg Institute, 1947; reprinted in London: Routledge, 1988).

85 Mersenne, Traité de l’Harmonie universelle (Paris, 1627), book II, préface au lecteur, n.p., where he says: “Or ie demande vne chose aux Musiciens, & à tous les sçauans, qu'ils ne me peuuent honnestement refuser; à sçauoir qu'ils ne croyent à nulle histoire de celles que les anciens rapportent des effets de la Musique, ou de la maniere qu'elle a esté inuentée, &c. qu'ils n'en ayent premierement fait l'experience, ou qu'ils n'y soient forcez par la demonstration, car c'est chose étrange que nous embrassons si

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clear from the “learning of the schools,” as convincingly shown by Peter Dear, there was

nevertheless in the Traité de l’Harmonie universelle a fairly unusual emphasis given to

experiments and the material culture of music.86 From the mid 1620s—a full decade

before he finally published his books on instruments—Mersenne did deem significant to

start investigating, ascertaining and rationalizing the role of instruments and experiments

with regard to his new natural philosophy.

The 1636 printed books on instruments, printed before any other from the

Harmonie universelle, are divided according to the traditional Boethian system of string

(books 1-4), wind (books 5-6), and percussion (book 7) instruments. One of their avowed

and most apparent purposes was to serve as an encyclopedia of all instruments that ever

existed in the history of humanity. To this end, Mersenne’s vast network of

correspondents proved to be of a tremendous assistance. He received, for example, an

account and a drawing of a South Asian instrument that had just arrived in London from

China during the summer of 1634.87 From Italy, where most of Mersenne’s research on

facilement les opinions erronées de nos ancestres, encore qu'ils n'ayent eu nulle puissance, ny mesme le plus souuent nulle volonté de nous obliger à suiure ce qu'ils ont dit, & ce qu'ils ont écrit. Ie desire donc qu'on se tire de la captiuité qui a accoustumé de lier les hommes, & qu'on ne s'assujettisse plus à la tyrannie des opinions...”

86 Mersenne, Traité de l’Harmonie universelle, book I, préface au lecteur, n.p., where he describes the content of book IX, never printed but heralding the later books on instruments: “Le Neufiéme traite de toutes sortes d’Instrumens de Musique; esplique leur matiere, leur fabrique, leurs temperamens, leurs accords, leurs tablatures; enseigne à faire des Instrumens parfaits pour les trois genres de Musique, & pour leurs especes, sans qu’il soit besoin d’aucun temperament; comme il faut faire des Epinettes qui tiennent leur son auβi long temps que les Orgues; des Orgues qui prononcent auβi bien les syllabes, les paroles, & toutes sortes de discours comme font les hommes, & des testes qui parlent, comme celle qu’on attribuë à Albert le Grand.”

87 It was an Indian vina, though Mersenne did not know its exact name and was not even sure whether it came originally from China or India. As soon as he could, he had an engraving made and included it with a short (second-hand) description to a section on Indian and Turk musical instruments. Mersenne to Peiresc, 2 July 1634, CM IV, 230; Peiresc to Mersenne, 16 July 1634, ibid., 244 in which Peiresc tells Mersenne he should get in contact with Sr. Langlois dit Chartres, wonderful musette and flute player, and someone who could discover the owner of this instrument and arrange for an engraving. Mersenne to Peiresc, 2 February 1635, CM V, 46, in which he says that Claude Hardy brought back a

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Organ Making: Mersenne’s Musical Instruments

ancient musical instruments was focused, “Messieurs Gaffarel & Naudé” sent engravings

depicting instruments used by Greeks, Romans and Egyptians as found on several marble

artworks and medals.88 (See Figure 1.2.) In Rome, moreover, Giambattista Doni was

actively seeking information on ancient musical instruments toward the preparation of a

book on Greek music. Not only did Doni share some of this knowledge with Mersenne

(who waited in vain for the published work89), he also looked for drawings of unusual

Italian contemporary instruments. In addition, he sent to Mersenne a detailed sketch and a

brief account of his newly invented instrument, the Lyra Barberina (dedicated to Pope

Urbain VIII, Maffeo Barberini), a sort of lyra (though resembling a lute) on which gut

strings were affixed to one side and metal strings to the other.90

drawing of the said instrument. Mersenne, “Traité des instrvmens a chordes,” book IV, prop. XX (sic, XVIII), 227-228 (HU3). Mersenne to Doni, 2 February 1635, CM V, 35. In the Harmonicorum libri XII Mersenne writes: “Placet autem hîc Sinense vel Indicum Instrumentum describere, cuius figuram beneficio atque diligentiâ summi viri domini Hardy ex Anglia accepi.” Harmonicorum libri XII, vol. 2, book II, prop. XXI, 111. On the vina, Claudie Marcel-Dubois, Les Instruments de musique de l’Inde ancienne (Paris: Presses Universitaires de France, 1941), 79-80.

88 Jacques Gaffarel to Mersenne, (June 1633?), CM III, 443-444. Gabriel Naudé also sent to Mersenne an engraving taken from an Antiquity marble artwork representing Orpheus with his lyra, which was also added to the Harmonie universelle on the verso of the title page. See Naudé to Pierre Gassendi, 6 March 1632, CM III, 266-267. See also Naudé to Mersenne, 12 November 1633, CM III, 533-536 for more of Naudé’s efforts in securing images from ancient instruments.

89 Mersenne to Peiresc, 14 May 1634, CM IV, 136, where Mersenne writes: “Il m’escrivit il y a tres longtemps qu’il y metteroit quantité de choses de la musique et des instruments antiques. Dieu veuille que je puise voir son livre avant que de mettre fin au mien, affin de luy donner la louange qu’il meritera, comme je luy ay mandé.”

90 Doni to Mersenne, 15 October 1633, CM III, 508-509, where it says that “Au reste, l’instrument est reussy, d’un ton fort doux, de façon qu’il surpasse le lut et la harpe encore qu’il participe de tous deux. Je n’ay point pretendu pourtant de renouveller l’ancienne Lire tout ainsi qu’elle estoit (encore que cest instrument y approche fort, comme vous pouvez voir par ce peu de crayon que je vous envoye), mais de l’enrichir des nouvelles inventions. Le costé qui a les cordes d’airain (qui est celuy qui se voit dans ce dessein), a les touches immobiles dans la [sic] manche, comme le cistre, mais chaque ton divisé en quattre dieses enarmoniques. Il y a de plus une petite harpe de huict chordes au costé des cordes de lut, dont apparoissent les chevilles au costé gauche.” See also Doni to Mersenne, 8 April 1634, CM IV, 90. Mersenne mentions Doni’s lyra in his Harmonie universelle, “Traité des instrvmens a chordes,” book II, prop. 6, 100 (HU3). However, Mersenne omits to mention it in the Latin version, the Harmonicorum libri XII, which earned him a minor reproach from Doni (who as an excuse for Mersenne blamed the quality of the drawing), Doni to Mersenne, [May 1636], CM VI, 71-72. On the lyra barberina, see Claude V. Palisca, G.B. Doni’s Lyra Barberina (Bologna: A.M.I.S., 1981), which is a facsimile with a commentary of Doni’s

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Organ Making: Mersenne’s Musical Instruments

FIGURE 1.2: MERSENNE’S FOREIGN AND ANCIENT MUSICAL INSTRUMENTS REPRESENTATION On the left, the Indian instrument from China (with the two decorated pear-shape resonance gourds), which found its way to London in 1634. On the right, a compilation of ancient instruments described by two of Mersenne’s faithful correspondents in Italy: “Since many desire to know the customs of antiquity, I wish not to omit the instruments the Greeks, Romans, and the Egyptians used, if the old marbles of Italy and the medallions do not mislead us. The following figures have been taken from them and have been sent [to] me by Mr. Gaffarel and Mr. Naudé, both excellent persons.” Mersenne, “Traité des instrvmens a chordes,” book III, prop. XXV [sic, XIV], 172. Mersenne, The books on instruments, 221. Images are taken from Mersenne, “Traité des instrvmens a chordes,” book IV, prop. XX [sic, XVIII], 228; book III, prop. XXV [sic, XIV], 173. Closer to home, in France, Christophe de Villiers, a physician of Sens and one of

Mersenne’s most prolific correspondents on music and demonology, was the first to draw

the Minim’s attention toward an uncommon musical instrument: the trompette marine, a

one-string instrument that sounds like a brass trumpet.91 After de Villiers sent a drawing

and a complete physical description of the instrument he had examined, it still took

book published posthumously. 91 On the history, music and construction of this instrument, see Cecil Adkins, “Trumpet marine,”

Grove Music Online (Accessed on 9 August 2006). It was known since the fifteenth century.

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Mersenne several more months before he heard it play in Paris. The account Mersenne

ultimately gave in the Harmonie universelle was completely different from de Villiers’s

basic physical description—reminiscent instead of Pierre Trichet’s and Descartes’s. The

account focused rather on the instrument’s production of sound and how one could and

should play it. It was essentially theoretical, and because the instrument only had one

string (in general), Mersenne stressed its theoretical likeness to the monochord.92

Although all these correspondents and their particular exposés on ancient, foreign,

strange and modern musical instruments were useful, one person, owing to his own vast

network of relationships, did more than anyone else in trying to secure musical

knowledge for Mersenne: Nicolas-Claude Fabri de Peiresc, the celebrated gentleman

from Provence and Mersenne’s most important patron.

Toward the end of 1632, Peiresc—with the assistance of Pierre Gassendi—began

to recognize the worth of Mersenne’s music project and instrument compendium. As

regards uncommon musical instruments, Peiresc then only knew about one Sanbucca (or

Sambuca), a kind of harp of Greek origin that had been built in Rome, though he had

never received a good account of how it sounded. On foreign music from the Levant,

92 Christophe de Villiers to Mersenne, 3 March 1634, CM IV, 59-60: “J’oubliois encor à vous dire que l’on m’a fait part d’un instrument qui n’est pas connu, qui s’appelle Trompette marine. Si n’en avez entendre parler, je vous en envoyeray un pourtraict, tel qu’on me l’a representee. Et s’il arrive que je la voye, comme j’espere, je vous en donneray encore plus particuliere intelligence. Elle n’est pas maintenant au pays. Celuy qui m’en a parlé, l’a ouy trompetter et dit qu’elle se fait entendre aussi loin que les trompettes de guerre. Et neantmoins n’est que boys, le corps triangulaire, avec une corde tendue (comme à vostre viole), laquelle se touche avecque l’arcelet et rend le son susdit. Mais qui est plus merveilleux, c’est que le corps par en bas n’est large que de 8 poulces au plus, tant en boys que en cavité; et par en hault, prez du manche, d’un poulce seullement. Si n’en avez ouy parler, ne vous en travaillez daventage. Je vous en ay mandé cecy, parce que je n’ay veu le pourtrait de tel instrument dans les vostres que vous m’avez envoyé.” See also de Villiers to Mersenne, 17 August 1634, ibid., 319-322; de Villiers to Mersenne, 20 October 1634, ibid., 370-371, where he says that he is happy Mersenne could finally hear it, since it is the only way to believe what people say about it. Mersenne’s description is found in “Traité des instrvmens a chordes,” book IV, prop. XIV [sic, XII], 217-222 (HU3). On Trichet and Descartes, François Lesure, “Pierre Trichet’s Traité des instruments de musique: supplément,” The Galpin Society Journal 15 (1962), 70-81, on pp. 78-80; Descartes to Mersenne, [15 September 1634?], CM V, 360-361.

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however, Peiresc told Gassendi he would send a small mémoire to several non-Western

locations to assist with Mersenne’s research.93 Peiresc had developed over the years a

vast network of correspondents in the Middle East and in North Africa, which he used at

length, for instance, toward his study of geography and cartography.94

Mersenne was quick in thanking Gassendi for the good words put on his behalf,

while reminding the Provence savant at the same time of his promise to deliver a small

drawing of the type of cymbals played in that part of France.95 After an early May 1633

letter to Peiresc, in which Mersenne explained his desire to know every detail of music

theory and musical instruments from the Arabs, Turks and Persians—so that “nothing

was omitted to please the curious”—scores of letters followed between them and between

Peiresc and several other correspondents in Tunis, Alep (Syria), Cairo, Jerusalem, and

Constantinople.96 One particular Arab manuscript appeared promising on those matters,

93 Peiresc to Gassendi, 21 December 1632, CM III, 351-352. 94 Peiresc’s correspondents depended overwhelmingly on French collaborators, including

ambassadors, secretaries of French ambassadors, consuls and vice-consuls, merchants, ship captains travelling in the Mediterranean and missionaries. See Sonja Brentjes, Peiresc’s interests in the Middle East and Northern Africa in respect to geography and cartography (Berlin: Max Planck Institute for the History of Science [preprint 269], 2004). See also Sydney Aufrère, La Momie et la tempête: Nicolas-Claude Fabri de Peiresc et la curiosité égyptienne en Provence au début du XVIIe siècle (Avignon: Editions A. Barthélemy, c1990). I would like to thank Sonja Brentjes for this last reference and for providing me with a copy of her preprint.

95 Mersenne to Gassendi, 5 January 1633, CM IV, 355, where Mersenne writes: “Vous m’aves promis un petit crayon des cymbales usitees en Provence. Je n’attendz plus que cela avec les instructions de l’Orient, car je peux maintenant dire que nous chanterons in omni genere musicorum instrumentorum. Je vous remercie de la faveur que vous m’avez faicte auprez de M. de Peiresc. S’il en reussit quelque response favorable, j’augmenteray mes actions de graces.” Mersenne received the drawing more than a year later, after many other epistolary exchanges with Peiresc himself. Mersenne to Peiresc, 1 May 1633, CM III, 394; Peiresc to Mersenne, 1 May 1634, CM IV, 109 and Mersenne to Peiresc, 14 May 1634, ibid., 135. Mersenne described them in his Harmonie universelle, “Des instrumens de percvssion,” book VII, prop. 26, 53 (HU3).

96 Peiresc to Thomas d’Arcos, (end of January or beginning of February 1633), CM III, 373-374; Peiresc to Father Théophile Minuti, 12 October 1633, ibid., 494-495; Peiresc to Father Jacques de Vendôme, [12 October 1633?], ibid, 496; Peiresc to Jean Magy, 15 May 1634, CM IV, 155; Peiresc to Henri de Gournay, comte de Marcheville, 19 March 1634, ibid., 80. For a summary of Peiresc’s efforts on behalf of Mersenne, Peiresc to Mersenne, 13-15 October 1633, CM III, 497-505. A typical request read

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until it turned into a little epistolary drama between Mersenne and Peiresc, the former

trying to find someone in Paris with the language skills to translate it, and the latter

striving a year later to pass it along to someone else who would make a better use of it.97

Despite Peiresc’s efforts, as the correspondences show, Mersenne ultimately abandoned

the idea of integrating in his Harmonie universelle any thorough knowledge of Greek and

oriental music after several years of fruitless investigation.98

Regarding ancient and foreign musical instruments, Peiresc also paid a close

attention to his cabinet de curiosités, then one of the richest in France.99 He mentioned to

thus, this one to d’Arcos: “Pour un ouvrage excellent de la musique qui se va mettre soubz presse, on desireroit d’avoir quelque cognoissance de la musique et façon de chanter dont se servent aujourd’huy les Grecs vulgaires, les Turcs, les Persans, les Aegyptiens, les Mores et autres peuples de ces pays là. Sy en tout ou en partie, vous pouvez obliger ce bon personnage, je vous asseure qu’il n’en sera pas ingrat et que c’est un homme qui le vaut bien.”

97 At first, Mersenne and Peiresc thought that this manuscript would be very useful: “[on] y trouvera des fondements et maximes principales de la plus excellente musique des anciens Grecs, à ce que nous en avons peu juger à l’ouverture du livre, et à la consideration des figures geometriquement representatives des proportions et rapportz des tons, avec des differentes couleurs pour les entredistinguer et desmesler plus commodement; ce que je n’avois jamais veu en tous les livres imprimés et mss qui m’estoient passez par les mains. Ce qui nous a faict recognoistre que, parmy ces peuples barbares, il fault qu’il y ait eu des esprits bien desliés.” Peiresc to Father Gilles de Loches, 20 May 1634, CM IV, 158-159. Nothing useful really came out from this manuscript. See Peiresc to Jean Magy, 15 May 1634, CM IV, 155; Peiresc to Mersenne, 18 June 1634, ibid., 177-178; Claude Saumaise to Peiresc, 2 September 1634, ibid., 344-345; Mersenne to Peiresc, 15 January 1635, CM V, 28; Mersenne to Doni, 2 February 1635, ibid., 41; Peiresc to Mersenne, 20 March 1635, ibid., 107-108; Peiresc to Mersenne, 5 May 1635, ibid., 162-172; Peiresc to N. Aubery, sieur du Mesnil, 8 May 1635, ibid., 173-174; Mersenne to Peiresc, 23 May 1635, ibid., 208-210; Mersenne to Peiresc, 25 May 1635, ibid., 215; Peiresc to Jacques Dupuy, 5 June 1635, ibid., 226-227; Peiresc to Dupuy, 26 June 1635, ibid., 255-256; Peiresc to Mersenne, 3 July 1635, ibid., 274-278, and many others.

98 Mersenne to Peiresc, 20 March 1634, CM IV, 82, where he wrote: “Je n’espère maintenant plus rien de la musique des Grecs, ni des Orientaux, après avoir attendu 2 ou 3 ou 4 ans après sans aucun fruit, comme vous sçavez, quoyque j’aye tenté la voye de Rome, de Venise et de Constantinople. Je croy que nous les surpassons tous en ceste matiere. C’est pourquoy je ne veux plus m’en mettre en peine.” After receiving news of the Arab manuscript, Mersenne showed a little bit more optimism, saying to Peiresc he would organize his books, especially the one on instruments, so that he could easily add anything new from those countries. Mersenne to Peiresc, 14 May 1634, CM IV, 133-134. In the end, nothing came out of this research. Surprisingly, both Peiresc and Mersenne would have gathered more information on Arabic music and musical instruments by looking at medieval Latin manuscripts on medicine, astrology and philosophy kept in European collections. Charles Burnett, “European knowledge of Arabic texts referring to music: Some new material,” Early Music History 12 (1993), 1-17.

99 On Peiresc’s cabinet in general, Agnès Bresson, “Le cabinet de Peiresc et de quelques autres,” <http://www.peiresc.org/Cabinet.html> (Accessed on 25 May 2005).

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Mersenne a few musical instruments he owned, such as an ivory horn from India, and

sent him specifics on several other instrument representations depicted on various plates,

coins and cups from China and the Middle East.100 Although Mersenne was grateful for

Peiresc’s commitment toward the goal of gathering as much information as possible on

rare and forgotten musical instruments, every so often the Minim lacked enthusiasm for

Peiresc’s discoveries and sometimes even breached the patron-client etiquette. On one

particular Middle Eastern cup, which Mersenne had had analyzed in Paris, it was

determined that the text was not written in Arabic but rather was composed of strange

words without any meaning; more importantly, however, it was believed that comparable

cups were sold all the time in markets of Arab countries, as frequently as vulgar earth

ware was in Paris. The cup, in short, was worthless. In saying such a thing, Mersenne

inadvertently harmed Peiresc’s reputation as a distinguished collector of artifacts, a fact

the Provence gentleman promptly pointed out, as courteously as possible.101 Yet the

reproach was obvious. Peiresc, actually, criticized on several other occasions Mersenne’s

lack of “written diplomacy,” something the Minim apparently had a difficult time

understanding and conforming to.102 Though remarkable, Mersenne went beyond

100 Peiresc to Mersenne, 13-15 October 1633, CM III, 503-504; Peiresc to Mersenne, 18 June 1634, CM IV, 179; Mersenne to Peiresc, 2 July 1634, ibid., 226-227; Peiresc to Mersenne, 5 May 1635, CM V, 170-171; Peiresc to Mersenne, 10 and 15 May 1635, ibid., 185-186.

101 Mersenne to Peiresc, 17 May 1735, CM V, 201-205; Mersenne to Peiresc, 25 May 1635, ibid., 212-215; Mersenne to Peiresc, 14 June 1635, ibid., 240-241; Peiresc to Mersenne, 17 July 1635, ibid., 315-318; Peiresc to Mersenne, 23 July 1635, ibid., 332. On Peiresc’s patronage and relationship to Mersenne, Lisa T. Sarasohn, “Nicolas-Claude Fabri de Peiresc and the patronage of the new science in the seventeenth century,” Isis 84 (1993), 70-90.

102 See, for instance, Peiresc to Mersenne, 13 August 1634, CM IV, 287: “Et ne feray pas de difficulté de vous dire librement mes sentimens et tout ce que me demanderés, puisque l’avés agreable, vous reiterant surtout la priere tres humble que je vous ay si devant faite, de vous abstenir de toute sorte d’aigreur et de paroles piquantes, rudes et subjetés à sinistre interpretation. Et si vous pouviés enchore retrancher la plus grande partie des contredis et refutations de propositions et opinions que vous n’approuvés pas comme les vostres, vostre ouvrage en vaudroit au centuple, et d’un lecteur vous en

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Peiresc’s cabinet of curiosities as a source of potential information. He also tried (often

indirectly) to secure drawings and descriptions of ancient and uncommon musical

instruments from other notable Italian and French cabinets owned by Francesco Gualdo,

Johannes Rosinus, Claude Menetrié and Pierre Trichet.103

Yet the vast majority of instruments described and portrayed by Mersenne in the

Harmonie universelle were familiar ones, such as the lute, the harp, the flute, the guitar,

the violin, the organ (to which we will come back in the next two sections) and bells, to

name but a few. Moreover, no musical instrument was unworthy of consideration and

study. The hurdy-gurdy (vielle-à-roue), for instance, known as organistrum in the Gothic

period, was then a large instrument found in cloisters and monastic schools to teach

music, perform religious polyphony and provide correct intonation for singers. (See

Figure 1.3.) Needing two players at first, it was redesigned in the thirteenth century for a

single player and was named afterwards chifonie or symphonia. Although its origin is

linked to liturgical music, the hurdy-gurdy slowly lost its former excellence during the

Middle Ages and early modern period owing to its association with the chansons de geste

and the low social status of its players. Depicted in the hands of poor people and blind

attireriés à milliers des plus honestes gents, qui n’ont pas de loisir pour lisre de si gros volumes et qui ne se soussient pas de sçavoir les moyens de refuter les opinions insoubstenables ou mutilés; qui, au contraire, seroient bien aises de voir en peu de discours vos plus belles et plus dignes observations bien arresonees. Si vous l’avés une foys pratiqué, vous ne voudriés pas avoir faict aultrement et benirés l’heure que vous vous serés astrainé dans ces bornes-là qui sont un peu plus à la mode du temps que ces prolixes traités des escholes que peu des gents manient hors de colleges.” Although Mersenne wrote he would change his style, it was not the end of it. See Peiresc to Jacques Dupuy, 11 July 1634, ibid., 237; Mersenne to Peiresc, 24 August 1634, ibid., 328; Peiresc to Mersenne, 3 July 1635, CM V, 277-278; Peiresc to Mersenne, 20 November 1636, CM VI, 154-156.

103 Jean-Jacques Bouchard to Mersenne, 1 January 1635, CM V, 1-4; Mersenne to Doni, 2 February 1635, ibid., 39; Mersenne to Peiresc, 2 February 1635, ibid., 46; Mersenne, “Traité des instrvmens a chordes,” book IV, prop. 4, 184-185; prop. XX [sic, XVIII], 227-228 (HU3); Mersenne to Peiresc, [ca. 1 September 1635], CM V, 377-378.

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FIGURE 1.3: MERSENNE’S HURDY-GURDY On the left, the hurdy-gurdy as depicted in Mersenne, “Traité des instrvmens a chordes,” book IV, prop. XII [sic, X], 215. On the right, Georges de la Tour’s celebrated Hurdy-gurdy player, ca. 1631-1636. Musée des Beaux-Arts, Nantes, France, taken from Web Gallery of Art (Accessed on 10 March 2006), <http://www.wga.hu>. Poems such as this one were common since the Middle Ages: “Dist Mahier de Gournay, ne vous irai celant, / Ens ou pays de France ou pays Normant / Ainsi vont li aveugles et ly Povres truant / De si fais instrumens li Bourgeois esbattant / En l’apella depuis un instrument truant: / Car ils vont d’huis en huis leur instrument portant / Et demandent leur pain.” Quoted in Corrette, La Belle vielleuse, 3. beggars (and even in hell) by Renaissance’s painters such as Brueghel and Bosch, the

hurdy-gurdy symbolized above all a connection between physical and moral blindness.104

Prætorius showed a clear disdain vis-à-vis the hurdy-gurdy, saying that this “lyre”

104 Francis Baines, Edmund A. Bowles and Robert A. Green, “Hurdy-Gurdy,” Grove Music Online (Accessed on 24 August 2006). Edmund A. Bowles, “La hiérarchie des instruments de musique dans l’Europe féodale,” Revue de musicologie 42 (1958), 155-169, on pp. 167-169. Emanuel Winternitz, Musical instruments and their symbolism in Western art (New Haven: Yale University Press, 1979), chap. 4. The hurdy-gurdy briefly gained its lettres de noblesse during the reign of Louis XV. Claude Flagel, “La vielle parisienne sous Louis XV: un modèle pour deux siècles,” in Instrumentistes et luthiers parisiens, XVIIe-XIXe siècles, ed. by Florence Gétreau (Paris: Délégation à l’Action artistique de la ville de Paris, [1988]), 117-134. Robert A. Green, The hurdy-gurdy in eighteenth-century France (Bloomington and Indianapolis: Indiana University Press, 1995). For an eighteenth-century textbook on how to play the hurdy-gurdy, Michel Corrette, La Belle vielleuse, introduction by Claude Flagel (Saint-Denis-le-Gast: J.F. Détrée, 1978).

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was only played by “peasants and traipsing old women.”105 Contrary to most music

scholars, however, Mersenne maintained that

If men of rank would ordinarily play the Symphonie, which is called the hurdy-gurdy, it would not be so scorned as it is, but because it is played on by the poor, and particularly by the indigents [the blind] who gain their livelihood with this instrument, it is held in less esteem than the others, although they do not give as much pleasure. This does not keep me from explaining it here, since science does not pertain to the rich any more than to the poor, and there is nothing so base and vile in nature or the arts that it is not worthy of consideration.106

Mersenne was after natural philosophical knowledge and against popular prejudice or

ancient authority. Understanding the production of sounds from a hurdy-gurdy, therefore,

was as useful and valuable as if it were from a “noble” violin or harpsichord.107

Mersenne’s books on instruments do not offer comprehensive historical

descriptions of ancient and modern musical instruments, like those of Galilei and Doni in

Italy and Pierre Trichet in France, over the span of several years.108 Mersenne’s books on

105 Michael Prætorius, Syntagma musicum II: De organographia, transl. and ed. by David Z. Crookes (Oxford: Clarendon Press, 1986), 56.

106 Mersenne, “Traité des instrvmens a chordes,” book IV, prop. XII [sic, X], 211 (HU3). Mersenne, The books on instruments, 271.

107 Mersenne, “Traité des instrvmens a chordes,” book IV, prop. XII [sic, X], 213 (HU3). Mersenne, The books on instruments, 273. Kircher’s description of the hurdy-gurdy is also more positive than most at that time: “Lyræ vulgaris figuram indicat, quod quamuis instrumentum sit tritum, & vulgare, & mendicis passim in vsu, est tamen structura, & chordarum, quas binas, aut quaternas habet, sectione mirum quantum ingeniosum; omnem harmoniæ varietatem exhibet; constat præterea plectris & palmulis suis, ex quarum pressione chordæ tactæ, quam volueris modulationem facilè exhibueris rotæ S circumductione terentis chordas, & in sonum incitantis, verbo nihil aliud est, quam monochordum, vel dychordum, varia sectione plectrorum in harmoniam excitatum, Verùm tempus tera[n]si in tritisissimo passim instrumento explicando immorabor, quare figuram adiunctam consule.” Athanasius Kircher, Musurgia universalis, sive Ars magna consoni et dissoni, 2 vols (Rome, 1650; facsimile Hildesheim, Zürich, New York: Georg Olms Verlag, 2004), book 6, i:487.

108 Galilei, Dialogue on ancient and modern music. Galilei probably influenced Doni’s approach to the historical research of ancient Greek musical instruments. In the case of Trichet, his well-known contemporary manuscript located at the Bibliothèque Sainte-Geneviève in Paris was with Mersenne’s books on instruments the most comprehensive treatise on the material culture of music. However, as Trichet wrote to Mersenne, his objective was quite different from the Minim’s: “Quant à moi, tout ce que je pretends en mon livre est seulement de traitter historiquement des instruments de musique sans m’amuser à des recerches qui surpassent la capacité de mon esprit. Sur quoi voulant avoir vostre jugement, je m’estois mis en chemin pour vous aller voir à Paris, durant que la contagion affligeoit la ville de Bourdeaux...”

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instruments are somewhat closer to Prætorius’s Theatrum instrumentorum as regards the

kind of detailed physical descriptions and explanations of sound production. Prætorius’s

book would have in fact been helpful to Mersenne if he only had gotten hold of a copy

before the publication of the Harmonie universelle.109 But even more than Prætorius’s

treatise on instruments—like none other before really—Mersenne’s is filled with

technical details of fabrication and theoretical methods of improving their designs.

Mersenne wanted his readers to realize above all else that to fully understand the nature

of sound, one had not only to be au fait with the “natural” producers of sounds, but most

importantly with the “artificial” ones—the man-made musical instruments. This

exceptional emphasis on “mechanics” and “craftsmanship,” which to some extent

intruded in the standard theoretical and practical study of music, held a key role in

Mersenne’s natural philosophical practice and rhetoric. Simply said, musical instruments

were transformed into emblematic tools of the new mechanical natural philosophy. And

from them all, none better than the king of all instruments to articulate that perspective:

the pneumatic organ.

Trichet to Mersenne, 9 January 1631, CM III, 4-5. Trichet, Traité des instruments de musique (vers 1640). This is not a complete edition of Trichet’s manuscript. Other excerpts were later published by Lesure in the The Galpin Society Journal.

109 Not that Mersenne did not try to get hold of a copy, looking in the Netherlands (Beeckman) and mostly in Italy (Doni). Mersenne to André Rivet, 30 October [1628], CM II, 107-108; Peiresc to Mersenne, 13-15 October 1633, CM III, 501-502; Doni to Mersenne, 8 November 1634, CM IV, 393; Mersenne to Doni, 2 February 1635, CM V, 39-40 where he says that “Peut-estre que Scapin qu’on a icy veu jouer de 40 ou 50 sortes d’instrumentz sur le theatre avoit veu ce livre…”; Doni to Mersenne, 8 September 1635, CM V, 392. Mersenne briefly discussed Prætorius’s work in his 1638 Novvelles observations physiqves et mathematiqves, XIV. Obseruation: De la multitude des Instrumens harmoniques, & particulierement des nouueaux, included at the end of HU3. Trichet could not find it either in Bordeaux. Trichet, Traité des instruments de musique (vers 1640), 15.

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THE ORGAN AS A POWERFUL SYMBOL OF CHRISTIANITY

Of all the known early modern musical instruments, the most sublime and perfect was

said to be the organ. It was for the Church as well as for most scholars the organum

organorum, i.e. the instrument of instruments. Cardano, for instance, after elaborating

nine rules by which to judge the perfection of musical instruments, declared the organ the

most perfect one:

Considering all reasons together and not individually the organ is superior to other instruments. Although all instruments are called organs in Greek, this one alone has retained the name through its superiority and the others have changed. Out of the nine conditions by which one instrument is judged better than another the organ holds the first place in all conditions except the eight [regarding the production of very small intervals], in which it is possibly surpassed by one instrument or another. But if it is divided by dieses instead of semitones, not only in place of those that are present but also those that can be formed, it is the most excellent of all, truly the instrument of kings. It is the most simple of simple instruments and the most elaborate of the elaborate. In every category, therefore, the simple organ is the most perfect, pleasant, melodious, noble, and excellent instrument.110

And to Mersenne’s contemporary Trichet, the mechanical structure of and the melody

coming from the organ let any listener wondering whether such an invention was actually

divine rather than secular.111

Organs gained a religious status that no other musical instrument came close to

reaching in Europe. They became in the course of the Middle Ages the only musical

instrument sanctioned by the Church to play during Mass. For that reason alone they

achieved a unique status in the academic, royal, and social-cultural environments of early

110 Miller, Hieronymus Cardanus (1501-1576), 56. In a Vatican manuscript, however, Cardano says that the lyra is the most elegant and perfect of instruments. Ibid., 178-182 and 199-206.

111 Mersenne, “Traité de l’orgue,” Epitre, n.p. (HU3). Prætorius, Syntagma musicum: Textes relatifs à l’orgue, comprenant aussi la basse générale ou continue, transl. and ed. by Jacques Leguy (Chatenay Malabry: Éditions Ars Musicæ, 1999), 25. Trichet, Traité des instruments de musique (vers 1640), 23-24.

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modern Europe, often celebrated in poems and scholarly works. During the Wars of

Religion, as explained below, the organ was targeted by radical reformists and Huguenots

alike as an icon of past superstition. The revival and growth of organ making in France

between 1580 and 1640, in fact, had a direct connection to the Calvinists’ acharnement

against the sublime instrument—in parallel to the Catholic counter-reformation desire to

incite the general population in praying God.112 The organ, in short, was not only the

most complex piece of machinery built in early modern Europe. It was, more importantly,

one of the dominant symbols—icons—of Christianity.

The organ, however, has not always received such esteem. James McKinnon

showed in a well-known article that since the time of the early Church Fathers, Psalm

commentaries interpreted every mention of musical instrument allegorically. To praise

God with musical instruments was an ancient and obsolete Jewish practice (the book of

Psalms is located in the Old Testament), which should be condemned in Christian

devotion. Musical instruments were deemed as something evil, compelling people away

from the sacred Word by means of earthly passions. What the Church Fathers, and

virtually all medieval commentators that followed them, did was to justify and account

for these atavistic references to instruments. According to McKinnon, the allegorical

exegesis were meant to transform the “material things of the Old Testament [into]

prophesies or types of the spiritual realities of the New Testament.” The psalterium and

kithara of Psalm 56:9, according to Pseudo-Athanasius’s commentary, stood for the soul

and the body respectively. To the Church Fathers musical instruments symbolized

112 Norbert Dufourcq, Le Livre de l’orgue français, 1589-1789, 5 vols. (Paris: Editions A. & J. Picard, 1971-1982), iii:87-88. See also Diarmaid MacCulloch, The Reformation (New York: Viking, 2003), 570-571.

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nothing more than doctrinal or ethical truths.113 In fact, “instrumental allegory [was] so

common in the Middle Ages that a medieval ecclesiastic [could] hardly speak of musical

instruments without lapsing into it.”114 Up until the thirteenth century, commentators

such as Isidore de Séville and Thomas Aquinas claimed that musical instruments,

including the organ, were simply unnecessary to the practice of worship—better adapted

to the popular theaters than the Church.115

Throughout the Middle Ages, therefore, musical instruments were forbidden in

church and little heard as a rule during the liturgical service. Writings by ecclesiastics and

music theorists such as Guido d’Arezzo, Gulielmus Durandus, Philippe de Mézières and

Gilles de Zamore despised medieval jongleurs and instrumentalists who played in public

squares during fêtes and other popular celebrations. According de Zamore’s Ars musica

(ca. 1270) only the organ was suitable for the Church, while other instruments were

“being commonly rejected because of the abuses of the jongleurs [histrionum].”116

113 James W. McKinnon, “Musical instruments in medieval Psalm commentaries and Psalters,” Journal of the American Musicological Society 21 (1968), 3-20, quote on p. 7. Musical instruments are mentioned in Psalms 32, 42, 48, 56, 67, 70, 80, 91, 97, 130, 136, 143, 147, 149, 150 (according to the numbering of the Vulgate). In another example, commenting on Psalm 80:4, Pseudo-Athanasius remarks: “‘Blow a trumpet at the new moon.’ As formerly, Israel, taking up the corporeal trumpet, blew it at the new moon, because God had commanded this to commemorate that the Israelites had been freed from the Egyptian servitude; so now the new people using the trumpet of the Gospel, whose sound has gone forth into the whole world, commands that it be blown at the new moon, that is, in the renewal of its mind, proclaiming and bearing witness that the evangelical trumpet has freed its mind from the spiritual Egypt, that is, from the power of darkness.” Quote on pp. 6-7. See also McKinnon, “The meaning of the Patristic polemic against musical instruments,” Current Musicology 1 (1965), 69-82.

114 McKinnon, “Musical instruments in medieval Psalm commentaries and Psalters,” 12. 115 Yvonne Rokseth, La Musique d’orgue au XVe siècle et au début du XVIe (Paris: Librairie E.

Droz, 1930; reprint ed., Hildesheim: Olms, 1996), 1-2. 116 The Latin quote read thus: “Organa in speciali non nominantur, quia organum est generale

nomen vasorum omnium musicorum: specialiter est appropriatum instrumento ex multis composito fistulis sive cannis, cui folles adhibentur. Et hoc solo musico instrumento utitur ecclesia in diversis cantibus, et in prosis, in sequentiis, et in hymnis, propter abusum histrionum, eiectis aliis communiter instrumentis.” Johannes Aegidius Zamorensis, Ars musica, in Scriptores ecclesiastici de musica sacra potissimum, 3 vols., ed. by Martin Gerbert (St. Blaise: Typis San-Blasianis, 1784; reprint ed., Hildesheim: Olms, 1963), ii:370-93, on p. 388. Taken from the Thesavrvs mvsicarvm latinarvm, Center for the History of Music and

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Several ecclesiastical synods and councils, such as Trier (1227), Lyons (1274), and

Vienna (1311), and the Statutes of Bourges (1407) banned all instruments from sacred

liturgy with the exception of the organ. This considered opinion vis-à-vis the organ,

which originated essentially in the late thirteenth century, derived partly from the

improvement of sound tonalities blasted out by the pneumatic machine and partly from

the concurrent decline (even decadence) of liturgical singing by Church choirs and

general assemblies. Owing to these two key events, organs found by the fourteenth

century a natural niche in most cathedrals and monasteries as an encouragement and

support to vocal worshiping.117

The Renaissance did not modify this general view on musical instruments with

respect to religious practices. Ecclesiastical authors like Biagio Rossetti still claimed that

musical instruments—except for the organ—should be banished from the divine service

altogether. In his Libellus de rudimentis musices (1529) Rossetti asserted that musical

instruments distracted the mind of churchgoers away from devotional matters and

towards sin. Organs, however, properly played, could in contrast attract the listeners’

attention to liturgical texts.118 Evidence shows, however, that instruments other than the

organ were infiltrating sixteenth-century churches as well. In Northern Europe, Erasmus

and Martin Luther complained in numerous writings about the cacophonic presence of

Literature, University of Indiana <http://www.music.indiana.edu/tml/14th/ZAMLAM_TEXT.html> (Accessed on 6 April 2006). The English quote comes from Edmund A. Bowles, “Were musical instruments used in the liturgical service during the Middle Ages?,” The Galpin Society Journal 10 (1957), 40-56, quote on p. 46.

117 Rokseth, La Musique d’orgue au XVe siècle et au début du XVIe, 3 and 150-151. 118 Moyer, Musica scientia, 149-151. Contrary criticisms were heard in mid- seventeenth-century

Germany. Although less frequent, they illustrate the “large doses” of organ music in those years. See Alexander Silbiger, “Fantasy and craft: The solo instrumentalist,” in The Cambridge history of seventeenth-century music, 426-478, on pp. 444-445.

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musical instruments during mass. Erasmus, in his Declarationes ad censuras … facultatis

theologiæ parisiensis (1532) criticized what he called the booming sounds of instruments,

“the almost warlike din of organs, straight trumpets, curved trumpets, horns and also

bombards, since these too are admitted in divine worship.” After a mass in which a bass-

voiced sacristan, who accompanied himself with a lute, sang the Kyrie and Patrem Luther

wrote ironically that “I could hardly refrain from laughing because I was not accustomed

to such organ playing…” Even Montaigne, a few decades later, was likewise

dumbfounded to hear violins accompanying the organ during a Mass he attended in

Verona.119

But what Erasmus, Luther, and the majority of Reformists and Catholic counter-

reformists fought against was not the organ per say, but the kind of music performed

during Mass. Dances and frivolous chansons were improvised on the sacred instrument

and played in churches—what Erasmus called shameful love songs (amatoria fœdæque

cantilenæ). The habit became so generalized that the Council of Sens (1528) had to

remind all organists to abstain from playing lascivious and immodest popular music in

churches. The Council of Cologne (1536) and the Council of Trent (1562) maintained

similar positions on the subject. Yet the regulation was so badly ignored that it had to be

reiterated in the Councils of Reims (1564), Cambrai (1565) and Bordeaux (1583):

“vitetur lasciva musica … moderetur organorum usus.”120

119 Leslie Korrick, “Instrumental music in the early 16th-century Mass: New evidence,” Early Music 18 (1990), 359-370, quotes on p. 360 and 362 respectively. Richard Sherr, “Questions concerning instrumental ensemble music in sacred contexts in the early sixteenth century,” in Le Concert des voix et des instruments à la Renaissance, 145-156. This new trend came later to Italy, beginning in the 1540s. Rokseth, La Musique d’orgue au XVe siècle et au début du XVIe, 152.

120 Rokseth, La Musique d’orgue au XVe siècle et au début du XVIe, 154-156. Erasmus seemed particularly upset by what he heard in the churches of England. He wrote: “We have brought into sacred

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According to Erasmus, “if polyphonic music and organ playing are not acceptable

in churches, they can be omitted without loss of piety; if they are acceptable, care must be

taken that such music is worthy of the house of God.” Erasmus strongly disapproved of

the fact that “in certain churches, because of the concord of organs and singers, important

parts of the service are omitted or curtailed.”121 This position was precisely what Luther

and the Lutherans maintained throughout the Protestant Reform. To them, when done

properly, music, singing and organ playing were an important part of the Christian

liturgy. Other Reformist movements, however, and especially radical sects condemned

either singing alone or both singing and organ playing during Mass. After the Diet of

Worms, for instance, while Luther laid low in Wartburg Castle, Andreas Karlstadt started

preaching in Wittenberg. Although he later came to accept some singing, he banished the

organ altogether from the liturgy, calling it the “celestial bagpipe.” He saw the organ as

an icon of the old papist ways, as were all sorts of other images. In Zürich, Huldrych

Zwingli muted the organs and condemned singing, “this barbarous mumbling” as he

called it. While in Geneva, John Calvin accepted singing in his Articles of 1537 since

“we know from experience that song has great force and vigor to arouse and inflame the

hearts of men to invoke and praise God with a more vehement and ardent zeal.” Organs,

on the other hand, did not fare well under Calvinism. More often than not, they were

destroyed as in Lausanne, Biberach, Frankfurt, Schönthal and Ulm, where horses were

edifices a certain elaborate and theatrical music, a confused interplay of diverse sounds, such as I do not believe was ever heard in Greek or Roman theaters. Straight trumpets, curved trumpets, pipes and sambucas resound everywhere, and vie with human voices. Amourous and shameful songs are heard, the kind to which harlots and mimes dance. People flock to church as to a theather for aural delight.” Clement A. Miller, “Erasmus on music,” The Musical Quarterly 52 (1966), 332-349, quote on p. 339.

121 Miller, “Erasmus on music,” quotes on p. 341.

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brought into the church to break and remove the largest pipes.122

In France, the Huguenots’ iconoclasm reached a level of damage perhaps

unsurpassed in the rest of Europe. From the eradication of images to the complete

obliteration of churches, Huguenots aimed chiefly at the removal of the sacred aura

surrounding a universe they thought was built around signs and symbols.123 That the

organ was likewise targeted by extremists is perhaps not surprising considering its ever

more noticeable iconographical representation in relation to music. Dating back to the

fourteenth century, organs were found on music manuscripts, churches’ frescos and

exterior cornices and decorating city doors. Music, one of the seven liberal arts, was

beginning to be depicted as a woman playing on a portative or positive organ. Lady

Music herself, St. Cecilia, was frequently personified with an organ—though not always,

see figure 1.4. In bestiaries, the organ was played by the most gentle of monsters, a siren,

whereas a sow could be seen holding a hurdy-gurdy and a man-dragon a flute. And when

an ass was depicted with its hooves on the clavier of an organ, the animal had a monk’s

tonsure, thus mocking the foolishness of the organist rather than the instrument. Angels,

lastly, were also commonly illustrated with the liturgical instrument in their hands.124

Apart from Calvinists, Huguenots and marginal extremist sects, the Protestant

122 Gordon Rupp, “Andrew Karlstadt and Reformation Puritanism,” The Journal of Theological Studies 10 (1959), 308-326. See also Karlstadt own book, Vom Abtuhung der Bilder (1522). Charles Garside, Jr., “The origins of Calvin’s theology of music: 1536-1543,” Transactions of the American Philosophical Society, New Series, 69 (1979), 1-36, quotes on pp. 11 and 17 respectively. Jean Happel, “Orgues et organistes en Alsace au XVIe siècle. Le Rôle de l’orgue dans le culte protestant à Strasbourg,” Cahiers et Mémoires de l’orgue 15-16 (1976), 3-52, on p. 38.

123 One of the best studies on the level of destruction caused by the Huguenot iconoclasm is Denis Crouzet, Les Guerriers de Dieu. La Violence au temps des troubles de religion (vers 1525-1610), 2 vols. (Seyssel: Champ Vallon, 1990), i:493-561.

124 Rokseth, La Musique d’orgue au XVe siècle et au début du XVIe, 8-9. Lady Music’s preferred musical instrument changed with the goût du jour: an organ in the fifteenth and sixteenth centuries; a lute or viola da gamba in the seventeenth century; and a harpsichord in the eighteenth century.

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Reform had actually no misgivings against the organ as a liturgical aid to worship.

Although Strasburg’s organs, for example, were muted from circa 1520 to 1560, they

were kept intact, as were most organs in the rest of Alsace; in fact, the region experienced

an uninterrupted growth in organ making during the same period.125 Lutherans even

became fervent defenders of the organ as the century progressed, opposing the Calvinists’

repeated rhetorical denunciations and physical assaults against the pneumatic machine.

FIGURE 1.4: TWO IMAGES OF ST. CECILIA On the left, Lady Music, taken from Hettrick, The ‘Musica instrumentalis deudsch’, 1545 edition, sig. Av, p. 62. On the right, Raphael’s St Cecilia (1514), taken from Web Gallery of Art (Accessed on 10 March 2006), <http://www.wga.hu>. The instruments in Lady Music’s engraving are perhaps displayed to reminisce Psalm 136:1-2, which talks about the Jewish exile from Jerusalem after Babylon conquered it: “There we sat down, by the rivers in Babylon. We cried when we remembered Zion. There we hung up our harps [instruments] on the willow trees [poplars]” since they were unable to sing and play for strangers in a strange land. As for St Cecilia’s painting, it could be an interpretation of Job 30:31, “my organ [is changed] into the voice of those who weep.” For most of the sixteenth century, Lutherans maintained a general adiaphorist

125 Happel, “Orgues et organistes en Alsace au XVIe siècle,” 8-20.

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doctrine regarding issues of worship, meaning that for the sake of “peace and good order

in the church” certain religious practices or things were labeled “indifferent matters,” or

adiaphora. These were understood as matters that were neither necessary nor contributory

to salvation.126 Organ music was one such adiaphora—until the latter part of the century.

At the 1586 colloquy of Montbéliard, the Lutherans started shifting towards an explicit

defense of instrumental music. At Montbéliard, the Calvinist spokesman, Theodore Beza,

condemned the destruction of organs—where horses were brought inside Reformed

churches to tear apart the pipes—and argued for the adiaphoric nature of the pneumatic

machine, upholding that the Reform movement “was not bound to install organs in the

churches again.” Where they still existed, however, their use was permitted. “But that it is

necessary from the instruction and commandment of God to play on the organ and in the

church,” that he disagreed. Jakob Andreae, Beza’s Lutheran counterpart, was caught off-

guard by the Calvinist’s unexpected moderate stance. Though he acknowledged Beza’s

conclusion, at some point during the conversation he asserted that music should not be

treated as a neutral matter. Music and organ playing, he charged, were “not only not

forbidden but rather expressly commanded in order that one praise God therewith, as is

written in Psalm 150.”127

What started as a discussion between Lutherans and Calvinists became a

somewhat spiteful controversy by the early seventeenth century. During a sermon

preached in 1621 at the dedication of the organ in Sommerhausen, for example,

126 Joyce L. Irwin, Neither voice nor heart alone: German Lutheran theology of music in the age of the Baroque (New York: Peter Lang, 1993), 11.

127 Irwin, Neither voice nor heart alone, 13-15, quotes on pp. 14-15. On Luther’s viewpoint on music, see Walter E. Buszin, “Luther on music,” The Musical Quarterly 32 (1946), 80-97.

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Hieronymus Theodoricus scowled the Calvinists for dubbing the organ the “trumpets by

which the Antichrist is favored and called to court.” Matthias Hoe, in his Commentary on

the Apocalypse (1611), simply labeled critics of church music “amusical hypocrites.” He

even overthrew the traditional Lutheran adiaphoric conventions to voice a straight

apology of instrumental music:

For even if the words are not understood by all, nevertheless just as soldiers are enlivened by the sound of a trumpet, so in the meetings of the church and in the spiritual army the very variety of voices and the harmony of the organs excites devout minds greatly to earnest prayers and works of grace.

In 1615, Christoph Frick surpassed them all in writing that those who scorned music such

as Karlstadt, Zwinglians and Calvinists would face divine punishment (and experience

nightmarish harmonies): “It is certain that such people will be at the place where there

will be nothing but howling and gnashing of teeth; with the hellish wolves and all the

damned in eternity they will cry out dolefully.” Lutherans’ overstatements were an

indication that Calvinists were gaining some ground in Germany. As the controversy

intensified, music in the Lutheran liturgy eventually lost its adiaphoric status; love of

music—and organ playing—increasingly became an article of faith.128

Organs received a harsh treatment as well in Puritan England. As early as 1536,

the Lower House of Convocation included music and organ playing among the eighty-

four faults and abuses of religion. In 1567, a tract entitled “The Praise of Music”

mentioned that “not so few as one hundred organs were taken down and the pipes sold to

make pewter dishes.” Just a few years later, some Puritans reaffirmed that “concerning

singing of psalms, we allow of the people’s joining with one voice in a plain tune, but not

128 Irwin, Neither voice nor heart alone, 16-22, quotes on pp. 19, 20 and 21-22.

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of tossing the psalms from one side to the other with intermingly of organs.” And in

1586, radicals asked that “all cathedral churches [were] put down where the service of

God is grievously abused by piping with organs…” At the start of the English civil war in

1642, soldiers waged a battle against the organ at Canterbury while organ pipes from

Westminster Abbey were carried away and bartered for beer. The Chichester organ was

put down with poleaxes and soldiers marched in the street of Exeter blowing into organ

pipes newly removed. It is in the midst of this conflict, moreover, that organs were

included into the category of “superstitious monuments,” thus sealing their fate for

roughly half a century.129

An anonymous work, “Printed in the yeer of Discord 1642,” is revealing of the

hostility and ill feeling surrounding the pneumatic machine. Written in the form of a

nasty yet somewhat comical dialogue between Purple and Orange-Tawny (two colors

marking disgrace and lack of honor in England), the text exposes more than a religious

rift between the supporters and opponents of the organ. Orange-Tawny, after a series of

fitting insults in reply to Purple’s, goes straight to the point: “I will hold no disputation

with thee, but jog on in my holy violence to erect a religious battery against (those pipes

of Popery & Superstition) the Organs.”130 Purple, however, wants to hear more details

regarding Orange-Tawny’s ludicrous actions:

P[urple]. You have well satisfied me; I did imagine one decent Ceremony or other was threatned [sic], you made such a holy hast about it: but why these Organs, which were well thought of, and by the judicious worthily esteemed before you

129 Yorke Bannard, “Music of the Commonwealth: A corrected chapter in musical history,” Music & Letters 3 (1922), 394-401.

130 Anonymous, Newes from Pauls: Containing A Relation of the angry Disputation betwixt the two Church-Quarrellers, Orange-Tawnie and Purple: Being A Contention about the Lawfulnesse or Unlawfulnesse of Organs and other Ceremonies (London, 1642), 2.

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were nine days old, or your untuneable nurse taught you to lap milk, should by your extravagant zeal be now refuted and opposed, is my wonder. O[range-Tawny]. I tell thee, they be the timbrels of Satan, and entice the eares of the religious to fancy sounds of vanity, whilest the smock apparelled Singing men fill the ears of our select Brethren with crotchers.131

Purple, however, is not at all convinced by his adversary’s argument. The allegations

appear so lame that Purple ridicules Orange-Tawny when the latter tried to validate a

claim made by one of his Brother-in-arms:

P. He said, the sweetnesse of the musick lull’d him into so sweet a sleep, that another by him (inspired with the spirit of providence) stole away his hat and Bible, for which disaster he verily thought Organs were ordained to no other or no better purpose, but to give assistance to pilferers, and such as come not to pray to God, but prey upon their neighbours. O. And verily, a sound reason; but short of mine; for whilest I was sleeping, one stole away my wife. P. Is that all? I would never have been so violent against the Organs for so small a cause, surely I should rather love Organs the better all the dayes of my life, that should rid me of so great a trouble.132

Above and beyond the jest of the writing, the message of the work is simple:

those who destroy organs are grunts and low lives, whereas those who are trying to save

them are of the highest quality. Compare the list of characters (and notice the humor)

provided by both protagonists:

O. In the first place here is Ananias Slie Glazier, Hotofernes Holy-Hanke Pewterer, John Judas Serjeant, Michael Meddle-much Pin-maker, Nehemiah Needlesse Tobacco-pipe-maker, Marmaduke Marre-all Gunsmith, Stephen Stare Spectacle-maker, Ralph Round-scull Button-maker, Simon Schisme Felt-maker, Richard Riot Lock-Smith, Aminadad Mercilesse Butcher, and Edmond End-all Dyer; these are the names of the men, the rest consisteth in the allowance of women and apprentices, which you shall at large heare named.

131 Ibid., 2. 132 Ibid., 3

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P. Indeed I will not sir; you have been too tedious already; if your men be no better, I guesse what your women and apprentices are: I will now name you onely fix that shall oppose your twelve, and they are these. Thomas True-heart Gentleman, Lawrence Loyall Esquire, Francis Well-borne Gentleman, Richard Royall-thought Esquire, Constantin Tryall-proofe Gentleman, Charles Good-cause Esquire, with many more as well borne, and of as noble natures, which you are not worthy to heare named, since not capable to understand…133

Organs were still very much admired by the elite of England throughout the seventeenth

century. Its music was heard often outside of churches and composers actually improved

on past harmonies. Though John Milton, for instance, compared the organ in Paradise

Lost to the House of Demons, or Pandaemonium, he was a great lover (and player) of

organ music.134 Organ music was thus healthy overall across the Channel, the chief

exception being the Church of England. Only toward the end of the century were new

organs built and their value to the Church liturgy defended with renewed vigor.135

The Netherlands is certainly where the organ was best tolerated. Though the

synods of 1574 and 1578 decreed that “the organs, which have been tolerated for a time,

must by all means be removed from the church,” very little damage were caused to these

pneumatic machines. What probably saved them from obliteration was the fact that as

religious forces worked for their banishment from the churches, town councils took over

133 Ibid., 4-5. 134 Francis Routh, Early English organ music from the Middle Ages to 1837 (London: Barrie &

Jenkins, 1973), 50-138. Gretchen L. Finney, “‘Organical musick’ and ecstasy,” Journal of the History of Ideas 8 (1947), 273-292. Helen and Peter Williams, “Milton and music; or the Pandaemonic organ,” The Musical Times 107 (1966), 760-763. Bannard, “Music of the Commonwealth,” 396-401.

135 Joseph Brookbank, The well-tuned organ, or, An exercitation wherein this question is fully and largely discussed, whether or no instrumental and organickal musick be lawful in holy publick assemblies… (London, 1660). John Reading, A sermon delivered in the Cathedral Church of Canterbury, concerning church-musick… (London, 1663). Ralph Battell, The lawfulness and expediency of church-musick asserted in a sermon preached at St. Brides-Church… (London, 1694-95). John Newte, Mr. Newte’s sermon concerning the lawfulness and use of organ in the Christian church (London, 1696). Gabriel Towerson, A sermon concerning vocal and instrumental musick in the church as it was delivered in the parish church of St. Andrew Undershaft, upon the 31th of May, 1696, being Whit-Sunday, and the day wherein the organ there erected was first made use of (London, 1696).

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the building and repair of organs, as well as the appointment of organists. Thanks to such

an arrangement, numerous organ recitals were performed in churches throughout the

Netherlands, before and after Mass. Notwithstanding this accommodement, a vociferous

opposition continued to mount against the organ. This is well illustrated by the 1634

inaugural address of Gisbertus Voetius, newly appointed Professor at the Utrecht

Gymnasium, in which he asked for nothing less than the complete ban of the organ in

churches. The social elite, as in England, counterattacked in order to shield the organ

from fanatics. Constantijn Huygens, music lover and one of the better known and most

influential aristocrats of the era, wrote an anonymous book in defense of the organ. He

clearly fought “against our irreligious and quite unedifying use of the organ,” but called

for retinue with regard to the obliteration of the mechanical machine. Huygens received a

lot of support from leading ministers and educators. And the violent response to

Huygens’s book by Jan Janszoon Calckman, considered a serious public offense,

contributed more to the acceptance of organ playing in churches than anything else in the

Low Countries.136

In the Netherlands, as in England and the rest of the European continent, the

organ provoked passionate, even zealous, reactions during the Reformation. It was

everything but an inert piece of elaborate craftsmanship. To some fanatics it symbolized

the worst of Christianity, i.e. the popish abuse of rituals and the scandalous decadence of

136 Hill, Baroque music: Music in Western Europe, 1580-1750, 154-156. Henry A. Bruinsma, “The organ controversy in the Netherlands Reformation to 1640,” Journal of the American Musicological Society 7 (1954), 205-212. Constantijn Huygens, Use and nonuse of the organ in the churches of the United Netherlands, transl. and ed. by Ericka E. Smit-Vanrotte (Brooklyn, N.Y.: Institute of Mediaeval Music, 1964). A. J. Servaas van Rooyen, “Huygens contra Calckman en vice-versa,” Tijschrift der Vereeniging voor Noord-Nederlands Muziekgeschiedenis 9 (1912), 170-173. Wouter Kalkman, “Constantijn Huygens en de Haagse orgelstrijd,” Tijschrift der Vereeniging voor Noord-Nederlands Muziekgeschiedenis 31 (1981), 167-177.

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true faith. In Catholic France, on the other hand, the organ was a truly blessed liturgical

instrument. Organ music in church, and secular devotional airs in general,137 aimed in

fact at securing the Catholic faith under attack by the Calvinist radicals. Church music in

France also had to be regulated during the Counter Reformation, during which time

several synods addressed the question without ever stipulating a universal resolution

applicable to all Catholic nations.138 In 1600 Clement VIII’s Cœremoniale first regulated

organ-playing rules for Catholics. Beside specifying when and how the organ should

sound during Mass, it is written in black and white that the organ was the only musical

instrument tolerated: “Cavendum autem ne sonus organi sit lascivus … nec alia

instrumenta musicalia praeter ipsum organum addantur.”139 At the time Mersenne wrote

the Harmonie universelle, anyone who attended church regularly in Catholic France

acknowledged that the organ was the most sacred musical instrument of them all.

The same way Lutherans and Catholics claimed organ music helped people praise

137 In the form of sung devotional airs, seventeenth-century French Church leaders also believed music could become another instrument of their Catholic campaign to convert frivolous and immoral female aristocrats into dévotes, whose newly-found devotion to God would transcend their worldly desire. Catherine Gordon-Seifert, “From impurity to piety: Mid 17th-century French devotional airs and the spiritual conversion of women,” The Journal of Musicology 22 (2005), 268-291.

138 Restrictions of instrument music in churches were attenuated as the sixteenth-century progressed. At and after the Council of Trent, for instance, no clear-cut instruction was given as to whether musical instruments should be banned from masses. In fact, out of the thirty-three synods ante 1600 consulted by Paolo Fabbri, only five dioceses in Catholic Europe appeared to have explicitly forbidden any use of musical instruments in church other than the organ. Even more striking, Fabbri discovered that in cities where secular institutions were closely linked to the organization of church life and activity, like Cremona and Udine, musical instruments played a more central role in divine celebrations than elsewhere. In a sense, late Renaissance instrumental music in church came to symbolize not only an evolution of taste and musical disposition, but most importantly the sort of sociocultural relationship (or political channels) existing between Church and State. Paolo Fabbri, “Norme et pratique du concert des voix et des instruments dans la liturgie catholique après le concile de Trente,” in Le Concert des voix et des instruments à la Renaissance, 97-103.

139 Clement VIII’s Cœremoniale is described in detail in Denise Launay, La Musique religieuse en France du Concile de Trente à 1804 (Paris: Publications de la Société française de musicologie; Editions Klincksieck, 1993), 66-80.

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the Lord, Mersenne used the detailed description of the mechanical organ to help artisans

and savants understand the production of natural philosophical knowledge. The

ecumenical virtues of the church organ were transformed, in the secular and material

world, into epistemological virtues. By keeping the organ as mechanical as possible,

without imposing on it any allegorical or religious representation, Mersenne was able to

use the organ as a most worthy secular object of knowledge, which could be studied by

Christians of all faiths. The same piece of machinery thus symbolized the best religious

(Mass) and secular (natural philosophy) practices. It is to the craftsmanship of the

mechanical machine that we now turn our attention to.

MERSENNE’S ORGAN: THEORY, EXPERIMENT AND ARTISANAL KNOWLEDGE REVEALED

To Mersenne the organ was simply one of the most admirable pneumatic machines ever

invented. (See Figure 1.5.) And strictly that. Not once in the book was he tempted by the

art of allegory, portraying the organ as a symbol of God’s creation, for instance, as

Athanasius Kircher did in his 1650 Musurgia universalis—where in book X on universal

harmony he illustrated the divine organ, in which each of the six days of creation had its

corresponding organ register.140 Although Mersenne did not try to give his mechanical

140 Kircher, Musurgia universalis, book 10, ii:366, where he describes the Deus organædus creating the world playing on his celestial organ: “Quemadmodum igitur Opifex quidam Organum fabricaturus, primum varìas substructiones, veluti prima quædam operis rudimenta ponit, deinde fistulas omnis generis co[n]ficit, canales æris ventique conductores disponit, & ad maiorem harmoniæ varietatem demonstrandam varios adaptat canones, quos Registra vulgo vocant, postea folles veluti quædam ventorum conceptacula, quorum perpetuo motu ær constrictus atque intra ventorum canales coactus suppeditatur, ordinat. Demum Clauiarium veluti vltimum artis suæ directorem disponit, tandem digitorum ope, registrorumque varia combinatione taxillos siue palmulas, quostastos vocant, feriens, eam quam in organis cum admiratione sentimus, harmoniæ varietatem producit. DEVS Opt. Max. haud absimili ratione mundanum hoc organum inexhausta quadam varietate dissono-consonum fabricaturus…” For a general discussion of celestial organs, Hans Davidsson, “The organ in seventeenth-century cosmology,” in The organ as a mirror of its time: North European reflections, 1610-2000, ed. by Keral J. Snyder (Oxford: Oxford University Press, 2002), 78-91.

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organ an allegorical meaning, any reader could tell it represented more than a simple

FIGURE 1.5: MERSENNE’S PORTATIVE ORGAN AND ROUEN’S ST. MACLOU CHURCH ORGAN Left, the portative organ depicted in Mersenne’s, “Traité de l’orgue,” book 6, prop. I, 310. Right, the organ from St Maclou Church in Rouen built in the middle of the sixteenth century. For Titelouze, the famous Rouen organ player and composer, no other musical instrument was more sublime than the organ, as we can read from one of his poems: “Cessez vos bruits, luth trop mélancolique / Aigre pandore, et violon quinteux / … / Mais le tuyau respond, sonne et persiste / Aux longs sujets que l’expert organiste / Traite en touchant le clavier marqueté / D’un vent la force en cent bouches partie / Fait animer en longue fermeté / D’un sourd métail une grande harmonie.” Quoted in Escudier, Introduction à une étude musicale de la correspondance du Père Marin Mersenne, 1:181-182. musical instrument. Reading Mersenne’s description of the organ gives indeed incredible

insights into the practice of natural philosophy, which in addition to a thorough

knowledge of theory, now involved experimental data gathering and hands-on savoir-

faire from the mechanical arts. Not that making an actual organ made a savant out of you.

(Mersenne’s description by itself was insufficient to manufacture such an intricate piece

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of machinery.141) Making the organ was less important to Mersenne than the account of

the rigorous procedure entailing its construction—seldom carried out by instrument

makers. The organ, in other words, reified the practices of the nascent mechanical

philosophy into a respected and altogether Christian early modern material entity. The

musical harmony produced by the organ within the Church context was not only a

powerful religious symbol: it epitomized and materialized the role theory, experiment,

and the mechanical arts played in Mersenne’s overall notion of harmonie universelle.

I. PIPE EXPERIMENTS AND THE PRODUCTION OF SOUNDS

Up until the late sixteenth century, Pythagoras’s and Boethius’s method based on

the mathematical theory of proportions were usually called upon in matters related to the

theory of sound.142 Numbers wholly dominated the science of music: they not only

structured musical theory, they defined music’s quintessence. This sublime power of

numbers over music was attacked by Galilei in his dispute against Zarlino. Guided by

Mei, Galilei took the path of experiments with musical instruments. As stated by Paolo

Gozza, “music in Galilei and Mei is discourse, not science of the necessary but art of the

possible. It is music from the rhetorical and anthropological perspective of

141 Actually, toward the end of the book on organs, Mersenne explicitly instructed his readers to go and visit the instrument maker’s workshops to find out more about the accurate manufacture of organs: “As to the practice which are most certain, it is fitting to consult the best makers, such as Valeran, le Pescheur, and many others, which have made the greatest part of the organs which are seen in the churches, and from whom can be learned everything that is missing in this treatise…” Mersenne, “Traité de l’orgue,” book VI, prop. XLV, 412 (HU3). Mersenne, The books on instruments, 493.

142 Virdung, for instance, wrote that “To write about these ringing instruments and also about organ pipes, I would choose Boethius, because these have to do with the mensur, that is, [with] the measurement of the tubes and the weight of the metals (like the hammer), and that is expressed through the theory of the proportions. [I have] written nothing at all about these [here], but [I am] saving [this subject] for the complete work.” Bullard, Musica getutscht, 110-111.

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communication and fruition, in contrast to music from the perspective of the opus

perfectum et absolutum.”143 Sense experience, for Galilei, had to replace the blind

following of ancient authorities. Right from the beginning of his Dialogue on ancient and

modern music, Galilei—in the voice of Strozzi—fixed the new program of musical

scholars:

I desire in those things in which the sense is involved that we always set aside (as Aristotle says in the eighth [book] of the Physics) not only authority but seemingly plausible reasoning that may be contrary to any perception of truth. For it seems to me that those who, for the sake of proving some conclusion, want us to believe simply on the basis of authority without adducing valid arguments for it are doing something laughable, not to say (with the Philosopher) acting like silly fools.144

Galilei’s anti-theoretical reaction led him later, in his Discorso, to become the first

musician ever to reveal the falsity of Pythagoras’s celebrated (and most likely

apocryphal) musical experiments in a blacksmith’s workshop. Galilei destroyed all these

with meticulous experiments of his own, which dealt over time a severe blow to number

mysticism and ancient authorities in music.145 Mersenne, drawing again on Galilei’s

investigations, just could not believe that no one since Pythagoras had bothered doing

these simple experiments to “discover the truth.”146

Claude Palisca has perhaps been the most influential and prolific historian of

143 Paolo Gozza, “Introduction,” in Number to sound: The musical way to the Scientific Revolution, ed. by idem (Dordrecht, Boston, and London: Kluwer Academic Publishers, 2000), 41.

144 Galilei, Dialogue on ancient and modern music, 12. 145 Galilei, Discorso, 103-105. See also Galilei’s unpublished manuscripts in Claude V. Palisca,

The Florentine camerata: Documentary studies and translations (New Haven and London: Yale University Press, 1989), 152-207. Palisca, Humanism in Italian Renaissance thought, 269-277.

146 Mersenne, Traité de l’Harmonie universelle, book 2, théorème XIV, 447: All these great scholars “ont esté si negligens qu'ils n'ont pas fait vne seule experience pour découurir la verité, & pour desabuser le monde. Ie ne pense pas qu'il y ait vn homme de iugement qui vueille maintenant croire ce que disent tous ces Autheurs s'ils ne l'experimentent auparauant, puis qu'ils nous ont donné des fables pour des histoires en vne chose qui est si claire & si euidente...”

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music regarding the experimental aspect of Galilei’s life. He was also the first one to

point out letters from Giovanni Battista Benedetti to the composer Cipriano de Rore, ca.

1563, in which Benedetti’s experiments with consonances led him to postulate a

relationship between musical intervals and the vibrating motion of the monochord string.

Physics here, for the first time, defined what musical consonances were, not numerology

à la Zarlino or geometry à la Kepler.147 Palisca’s research, followed closely by Stillman

Drake’s, tried to establish the likely relevance of the new experimental method in

Renaissance music to the rise of the experimental method usually associated to the

Scientific Revolution. Both Palisca and Drake agree that Vincenzo Galilei’s own

experiments with lute strings were probably accomplished with the help of his son,

Galileo, thus guiding the younger Galilei’s first steps towards the experimental path that

heralded the birth of a new era in natural philosophy.148 Such an interpretation is

attractive considering, for instance, Mersenne’s own developing experimental

practices.149 Music is certainly not the only factor here, yet it is still more plausible—on

the Continent at least—than to look at the English empiricist tradition fleshed out by

Francis Bacon.

147 Claude V. Palisca, “Scientific empiricism in musical thought,” in Seventeenth-century science and the arts, ed. by H. H. Rhys (Princeton: Princeton University Press, 1961), 91-137. Cohen, Quantifying music, 75-78. Palisca, Humanism in Italian Renaissance thought, 257-265. Benedetti’s two letters were published by de Rore in 1585 in his Diversarujm speculationum mathematicarum & physicorum liber.

148 Claude V. Palisca, “Was Galileo’s father an experimental scientist?,” in Music and science in the age of Galileo, ed. by Victor Coelho (Dordrecht: Kluwer Academic Publishers, 1992), 143-151. Idem, “Vincenzo Galilei, scienziato sperimentale, mentore del figlio Galileo,” Nuncius 15 (2000), 497-514. Stillman Drake, “Renaissance music and experimental science,” Journal of the History of Ideas 31 (1970), 483-500. Claude V. Palisca, “Music and scientific discovery,” in idem., Music and ideas in the sixteenth and seventeenth centuries (Urbana: University of Illinois Press, 2006), 131-160.

149 In a well-thought article, Daniel Garber has tried to explain how and why Mersenne began to study, appreciate, and promote Galileo’s approach to natural philosophy. It is interesting to note, however, that he never mentions the role music may have had in Mersenne’s change of heart towards Galileo. Garber, “On the frontlines of the Scientific Revolution: How Mersenne learned to love Galileo,” Perspectives on Science 12 (2004), 135-163.

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Lord Verulam’s study of music is found almost exclusively in the second and

third centuries of the Sylva sylvarum. His aim was simple: to bridge the contemplative

and active parts of music, the theory and the practice.150 Yet reading Bacon’s Sylva

sylvarum—as Mersenne and Descartes likely did—one finds that the idea of experiment

and the notion that craftsmen and instruments were essential to the reform of natural

philosophy, albeit mentioned as powerful rhetorical tools, were unsupported by concrete

evidence. Bacon’s account of sound, in fact, relied heavily on natural magic (Ficino and

Della Porta, most notably) and Aristotelian knowledge rather than tangible experimental

results. In his New Atlantis, Bacon did refer to “sound-houses, where we practise and

demonstrate all sounds, and their generation.” And also at the royal court, where he

experienced for himself that the “sweetest and best Harmony is, when every Part or

Instrument is, not heard by itself, but a conflation of them all, which requireth to stand

some distance off.”151 Besides all those observations, however, Bacon most likely never

produced any real experiments with musical instruments, as his Italian forerunners did.

Mersenne will go one step further by exemplifying what it meant to bridge the gap

between theory and practice in natural philosophy.

Mersenne’s experimental research with organ pipes is traceable to the early

1620s. With the help of Robert Cornier, Mersenne sought to have experiments done by

other parties in order to confirm his own results. To this end, Cornier employed an

150 Francis Bacon, Sylva sylvarum: or a natural history, in ten centuries (London, 1683), §100: “Musick in the Practice hath been well pursued, and in good Variety; but in the Theory, and especially in the Tielding of the Causes of the Practick, very weakly & being reduced into certain Mystical subtilties, of no use and not much truth. We shall therefore, after our manner, joyn the Contemplative and Active Part together.”

151 Bacon, New Atlantis and the Great Instauration, ed. by Jerry Weinberger, rev. ed. (Wheeling, Ill.: Harlan Davidson, Inc., 1989), 78-79. Bacon, Sylva sylvarum, §225. Gouk, Music, science, and natural magic in seventeenth-century England, 158-170.

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“organiste” known within the circle of Rouen honnêtes hommes concerned with musical

matters. This organ maker, who also dabbled with pneumatics in Cornelis Drebbel-like

submarine experiments, conducted a series of musical experiments to determine how

sounds were modified when air went through pipes of the same length but different sizes.

Although the organ maker told Cornier that the pipe’s size mattered to the production of

sound—which was well-known to members of his profession—Cornier could not give

Mersenne quantitative findings due to the organiste’s prolonged absence from Rouen; he

apparently did not leave any detailed written account. (Which may well be a disguised

excuse for secrecy, since organ makers were very jealous of this secret.) Cornier,

however, heard from M. Le Febvre—another curieux (perhaps a member of the well-

known Rouen family of organ makers) on familiar terms with the said instrument

maker—that the organiste had taken his measurements from the rectangular tin plates,

before they were rolled up into pipes, as Mersenne most likely suggested. The size,

therefore, was the width of the tin plate, or when rolled-up the circumference; size was

not measured as the diameter (or cross-section) of the pipe. Cornier assured Mersenne

that as soon as the organiste would be back, everything would be settled to his

satisfaction.152

Although this specific set of initial experiments may not have given Mersenne any

significant information, these were nevertheless the type of evidence he was relying

upon. Around the same time, Mersenne made (or had other people make for him) other

related experiments in Paris, in which the size of several different pipes was kept constant

152 Cornier to Mersenne, 23 November 1625, CM I, 310; Cornier to Mersenne, 16 March [1626], ibid., 416-417; Cornier to Mersenne, 22 March 1626, ibid., 427-430.

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whereas the length was adjusted according to the musical intervals. Mersenne reported

this set of experiments to Father Jean Chastelier, who replied he was no expert himself in

these matters, yet knew classical texts well enough to quote chapter ten of Censorinus’s

third-century De die natali, in which the Latin author mentioned Pythagoras’s own

experiments with flutes. The quote Chastelier transcribed in the letter mentioned that

flutes of identical size but of different lengths gave the consonances if, like strings, they

were cut in the right proportions, i.e. a flute of 12 fingers (digitorum) in length made a

sound an octave inferior to a six-fingers flute; and the same six-fingers flute in length was

a fifth superior in tone to the one measuring nine fingers. To Chastelier, such writing was

enough to convince him that Mersenne had erred somewhere with his experiments.

However, he did not see why he would painstakingly search for the causes of these

experimental mistakes when they were so remote from the real things, or in other words

so far from the truth of the ancients.153

What had Mersenne discovered in this set of experiments? That if one used small

diameter pipes, say of three lignes (roughly 6 mm) and a base length of half a foot,

Pythagoras’s explanation of consonances described by Chastelier was approximately

verified—i.e. if you double the length of this small pipe, it will sound an almost perfect

octave lower. But what Mersenne discovered, and Galilei before him, was that with

bigger sounding pipes this proposition did not stand anymore. In a series of numerical

examples, Mersenne demonstrated that doubling the length of a pipe while at the same

time keeping the size constant did not produce the required octave; the sound was off by

153 Father Jean Chastelier to Mersenne, 11 July 1626, CM I, 478-479, where he writes in Latin: “Hæc Censorinus. Quo fit ut facile Antiquis assentiar et experimenta de quibus scribis credam non fuisse accurata. Unde non video cur me excruciem in quærendis causis experimentorum quæ rei veritati non congruunt.”

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half a tone, a tone, or even more.154 Similarly, though the Rouen organiste most likely did

not provide Mersenne with hard evidence, the Minim was able to report numerous

experimental results proving that keeping the length of organ pipes constant while

varying the size did not produce the required consonances either. Here he used five half-

foot pipes of diameters ranging from three lines to four inches, always doubling in size

following the geometrical series. (Mersenne sometimes defined size (grosseur) as the

width of tin plates or diameter (cross-section) of pipes.) The experiments showed that it

was virtually impossible to reach an octave when keeping the pipes’ length constant

while modifying the size. Mersenne wrote that to reach a sound an octave lower, one

would have to add two inches in diameter and two feet in length to the biggest pipe.

Mersenne’s description of the pipes’ dimension was precise to make sure that if “one

encounters other intervals in pipes larger or smaller, he will have occasion for seeking the

reason.”155

Mersenne’s experimental method and results were seriously undermining the

tyranny of opinions some contemporaries, e.g. Father Chastelier, upheld. After these two

propositions, Mersenne could ascertain with good reason that “Since experience has

shown us that the pipes ought to be of different lengths and widths to make all the pitches

of the organ, these two dimensions must be joined together, so as to have sounds which

are proportional in their pitch, sweetness and harmony.”156 For someone like de Villiers,

however, there were still many hidden things (bien des choses cachées) that reason could

154 Mersenne, “Traité de l’orgue,” book 6, prop. XIII, 333-334 (HU3). 155 Mersenne, “Traité de l’orgue,” book 6, prop. XII, 331-332 (HU3), quote on p. 331. Mersenne,

The books on instruments, 416. 156 Mersenne, “Traité de l’orgue,” book 6, prop. XIV, 334 (HU3). Mersenne, The books on

instruments, 419.

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not account for regarding the rapport between length and width in pipes. De Villiers

made his own experiments with rectangular and cylindrical pipes, though they were not

organ pipes per se but simple pipes open at both ends, in which he blew with his mouth.

Using two identical tin plates, one shaped into a rectangular pipe and the other into a

cylindrical one, he found out there was a difference of a minor tone between their

respective sounds, the rectangular pipe making a re and the cylindrical one an ut. Both

were four inches (poulce du Roy) in length minus one line, whereas the cylindrical pipe

had a diameter of one inch and a half plus one line and the base diagonal of the

rectangular pipe made two inches minus three lines. Two similarly shaped pipes, but

twice in length this time, sounded on the contrary the unison. De Villiers was astonished

to find out these two pipes sounded the same even though their volume was different

(which he simply measured by filling them with water). It was strange, de Villiers

explained, because with the two smaller pipes, which sounded differently, their volume

were unequal. Why was it not the case with the pipes twice in length? De Villiers was

confused and, because of these results, concluded that a generalization regarding the

length and size of organ pipes was almost certainly impossible.157

Mersenne knew, however, that the volume of pipes did not automatically

determined how they would sound. This he probably owed to organ makers. Mersenne

discovered that there was no standardization in the size of tin plates—plates that were

later rolled-up into cylinders. To make an eight-foot organ pipe, for instance, some organ

157 De Villiers to Mersenne, 15 May 1635, CM V, 191-193. His conclusion: “Mais je ne trouve pas qu’on doive rien asseurer de ce[ci], parce que je crois autant de diversitez de hauteur et largeur ès tuyaux, il y aura toujours diversité de raison en leur tons, tellement que je crois qu’il est bien dificile de disposer la comparaison des hauteus et largeurs des tuyaux pour en faire des proportions de tons et tirer des consequences par la reigle de troys.” (p. 193) See also de Villiers to Mersenne, 25 February 1635, ibid., 63-64; de Villiers to Mersenne, 1 May 1635, ibid., 148-151.

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makers used metallic sheets eight feet tall but with a width of two fifths, a third or a

quarter its height. It thus meant that with some adjustments—using an accordoir, for

example, or cutting a slice to one or the other pipe158—two slightly different pipes would

sound exactly the same, not withstanding the fact their volume was also different. On this

specific point, artisanal practices were probably even more useful than experiments

themselves. To Mersenne, therefore, “it is of little importance in what proportion they are

made, so long as they speak well; but since that depends on the industry and opinion of

the maker [Facteur], and since pipes are met with whose height is five or six times the

width, it is not necessary to explain this more extensively.”159

Mersenne’s ultimate objective was to standardize and rationalize the production

of organ pipes. As he said, it did not really matter whether the width of the tin or lead

plates was a third, two-fifth or a quarter of its length. This proportion, however, had to

remain the same throughout the building process. Mathematical ratios of musical

intervals compelled it. From one template, therefore, it became possible to find the

precise division of the octave. Regarding how the width and length should vary,

Mersenne explained that

158 Mersenne, “Traité de l’orgue,” book 6, prop. XXX, 368 (HU3), where he says about the organ makers: “C’est pourquoy il n’est pas necessaire que les Facteurs soient bien exacts à la taille de leurs tuyaux, puis qu’il est necessaire qu’ils y touchent soit en les roignant, ou en les eslargissant & restressissant auec leurs accordoirs : quoy qu’il soit bien à propos qu’il les fassent en raison triplée de l’interualle des sons qu’ils doiuent faire, afin qu’ils facent des tons mieux proportionnez, & plus plains & nourris. Mais il n’est pas besoin de les aduertir de cecy, puis que nous experimentons qu’ils roignent souuent plusieurs tuyaux d’vn pied entier, ou de plusieurs pouces pour les mettre d’accord.”

159 Mersenne, “Traité de l’orgue,” book 6, prop. IIII, 319 (HU3). Mersenne, The books on instruments, 404. In another proposition, Mersenne mentions that “Mais il suffit de remarquer que l’on peut donner vne infinité de differentes figures aux tuyaux tant ouuerts que bouchez, suiuant les differentes inuentions de la Geometrie: par exemple, on les peut faire de parties de parabole, d’hyperbole ou d’ellipse: d’où les Facteurs peuuent tirer de nouuelles graces pour l’harmonie.” Ibid., prop. VII, 323. Mersenne makes similar claims in prop. XLIII. See also prop. XVIII, p. 346 where Mersenne says that a surveyor named Cornu was able to make a rectangular pipe sound to the unison of cylindrical one.

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Organ Making: Mersenne’s Musical Instruments

the pipes make the desired interval exactly if their height and width have the same ratio as the said interval. For example, if the diameter of a pipe a foot in length is made 15/6 of an inch wide [22 lignes], it will make the octave perfectly with the pipe half a foot in length, whose diameter is half the other. Thus it happens that if the pipes are taken as solid cylinders, they ought to be in triple ratio with the ratio of the intervals, which represent the roots, and the simple length of the pipes, as the double ratio of that of the said intervals represent the cylindrical surfaces of the pipes.160

In other words, two proportional pipes, one half the other, would have an octave between

them. This 2:1 ratio in sound was thus comparable to an 8:1 ratio in volume. Similarly, a

3:2 ratio in sound (or a fifth) between two pipes would have their ratio in volume

changed in a proportion of 27:8. Mersenne produced a table, proposed by a clever

surveyor named Cornu, which detailed the volumetric ratio of numerous other

intervals.161

Such a rationalization of organ pipe making, based on artisanal practices and

experiments, would ensure, according to Mersenne, the most accurate of sound

production in organs. The internal volume of pipe was not as much a valuable tool of

measurement as an a posteriori theoretical reasoning extrapolated from facts. Although

experiments and artisanal practice gave Mersenne useful information on the relationship

between the construction of organ pipes and how they sounded, simple mathematical

order imposed a thorough orderliness once the fundamentals had been discovered. And it

is this theoretical conclusion that could be useful to organ makers. Therefore, they “have

need of no greater understanding to make their diapason and their very exact pipes,

although all the pipes of which I have spoken may not be sufficient to give all the just

160 Mersenne, “Traité de l’orgue,” book 6, prop. XIV, 335 (HU3); Mersenne, The book on instruments, 419.

161 Ibid., 335-336.

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consonances against each key.” That is why, based on the same simple and

experimentally determined principles, Mersenne added “another diapason as general as

can be wished, as long as one does not go to infinity.”162

“[T]he table that follows contains all that can be reasonably desired on the subject

[the division of the octave], aside from which there is nothing for the makers to know.”163

(See Figure 1.6.) In this full-page table, Mersenne combined knowledge acquired from

experiments, artisanal practices and the theory of mathematical proportions. This table—

drawn to scale, the height being one foot (pied de roy)—contains eleven columns

showing the length and width of organ pipes according to several divisions of the

diapason (or octave). Column one shows the thirteen degrees of the equally tempered

diapason (twelve equal semitones). Columns two and three shows another tempered

diapason invented by Salinas, the great Spanish music theorist. Columns four and five

show thirteen pipes in their perfection, according to a meantone temperament, following

the previous proposition. Moreover, “the fourth column contains the entire four octaves,

that is to say the whole keyboard of the organ; and it has thirteen degrees in the first

octave, and fourteen in the second, so that there is seen the degree or key which is

missing in the said ordinary organ keyboard.”164 Columns six and seven shows the

nineteen pipes derived from the perfect diapason, which comprise the three genera of

music, i.e. diatonic, chromatic, and enharmonic. Next, and

because the seventh column does not comprise all of the perfect diapason of Salinas, which has twenty-five degrees or twenty-five pipes, and since it still lacks

162 Ibid., 337. Mersenne, The book on instruments, 421. 163 Mersenne, “Traité de l’orgue,” book 6, prop. XV, 338 (HU3); Mersenne, The book on

instruments, 422. 164 Ibid.

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two degrees in this one, as I have shown elsewhere, I wish here to propose the most perfect diapason of all those which have been given up to now, that is to say, the one contained in the eighth and ninth columns, for the eighth contains thirteen degrees, which are proper to it (in which the octave of the sixth and seventh columns is excluded) since it has thirty-two degrees, pitches, keys, or pipes in its octave, each of which follows the justness of the harmonic numbers.”165 (This will be useful in the section on keyboards, below.)

Columns ten contains all thirty-two intervals of the diapason “from which the makers can

take the just measure of all sorts of one-foot pipes, or that of pipes which are smaller or

larger. This can be done similarly with the other columns.”166 The last column mentions

the width to length proportions (which is somewhat arbitrary, as said earlier) given to the

two rectangular templates on which mathematical ratios were based upon: one is one-

fourth and the other one-sixth of the one-foot long template.

This table systematizes what Mersenne learned from organ makers, experiments

conducted by himself or others on organ pipes, and from the pure mathematical theory of

music. To Mersenne, such a table could (and should) become the organ maker’s

fundamental paper organon, guaranteeing—in principle at least—the perfection of organ

pipes. It was a powerful rhetorical and didactic tool as well, which illustrated to natural

philosophers and honnêtes hommes how important experiments and artisanal knowledge

really were in formulating theoretical generalizations.167

165 Ibid., 340. Mersenne, The books on instruments, 423-424. 166 Ibid. Mersenne, The books on instruments, 424. 167 On tables in general, Domenico Bertoloni Meli, “The role of numerical tables in Galileo and

Mersenne,” Perspectives on Science 12 (2004), 164-190 where he describes many of Mersenne’s tables found in the Harmonie universelle, which have mostly didactic, philosophical, and esthetic purposes. In our case, however, I believe that experimental data are embedded in this table and the way Mersenne constructed it not solely rooted in theory.

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Organ Making: Mersenne’s Musical Instruments

FIGURE 1.6: MERSENNE’S TABLE OF ORGAN PIPE DIAPASONS Above, a flue pipe showing how it should be cut to obtain the desired musical interval. On the right, the universal table with which organ makers can build the most precise and just set of organ pipes for various diapasons. Mersenne, “Traité de l’orgue,” book 6, prop. X, 328; prop. XV, 338-339. Mersenne, however, was fully aware of the material shortcomings of his

rationalization. He knew, for instance, that there was no better instrument than the ear to

tune an organ. The difficulty did not reside in his theoretical generalization, but rather in

the actual organ-pipe making. His table would be perfectly fine

Unless one is able to trim all the pipes exactly enough and adjust the wind so equally and with so much skill that all the pipes are found in tune without its being necessary to make use of the ears to tune them. This would happen always if one observed all the proportions and circumstances of which I have spoken in this book, if the material should follow the exactness of the mind and if the manual operation corresponded perfectly with science. But since this is beyond the industry of men, who cannot anticipate the great multitude of occurrences which accompany lead, tin, wood, and the other materials with which the pipes

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are made, and which are met even in the air, I assume that the ears are entirely necessary to tune the pipes.168

Reason was not enough. To achieve perfection, countless experiments on organ pipes

needed to be performed, and it was where musical instrument makers became so

indispensable. Why, for example, did organ pipes sing different intervals when air

pressure varied? What was the relationship between air pressure, musical intervals and

the material components of pipes? For Mersenne the “manufacturers can help out

Philosophy by preparing a catalogue of the pipes which rise only a semitone, or a third, or

a fourth, or a fifth, etc., for it will be easier to find the reason when one understands the

qualities of the pipes which cause the difference of these pitches…”169 Bacon’s empirical

method of data accumulation was perhaps an influence here. (Although critical of

Bacon’s brute fact gathering, Mersenne was all the same working on a translation of the

Sylvan sylvarum.170) And to accomplish such a monumental and difficult labor, who

168 Mersenne, “Traité de l’orgue,” book 6, prop. XXIX, 363 (HU3). Mersenne, The book on instruments, 446. He repeats something similar in the subsequent proposition: “Or si l’on pouuuoit tailler les tuyaux si iustes, & leur donner le vent si esgal, qu’ils se trouuassent d’accord en les mettant sur les registres, sans qu’il fust besoin de les roigner, ou de les toucher de l’accordoir, l’oreille ne seroit pas necessaire pour accorder, mais il est tres-difficile de faire les tuyaux si iustes qu’il n’y faille nullement toucher pour les eslargir, estressir, accourcir, ou alterer, soit que l’on vse de temperament, ou que l’on les tienne iustes suiuant les raisons harmoniques, d’autant qu’il est trop difficile d’obseruer toutes les proportions des bouches, des languettes & de l’ouuerture des pieds, & que la matière des differents tuyaux n’est pas semblable : ioint que les petits tuyaux proportionnez comme les grans, ne font pas les mesmes interualles, comme i’ay remarqué en parlant de ceux qui sont d’esgale hauteur & de differente largeur.” (pp. 367-368)

169 Mersenne, “Traité de l’orgue,” book 6, prop. XXIX [sic, XIX], 346-347 (HU3). Mersenne, The book on instruments, 430. Mersenne was interested in this topic since the early and mid 1620s. See Cornier to Mersenne, 18 August [1625], CM I, 263-267.

170 Cornier to Mersenne, 24 December [1627], 611-612: “Si vous pouvés achever la traduction du Sylva Sylvarum à l’ayde de vostre Anglois et le donner au public, je croy que vous feriés une chose fort aggreable à beaucoup de monde. Pour moy je vous diray que je n’estime pas tant en Bacon la curiosité de ses experiences comme les consequences qu’il en tire, et la methode, avec laquelle il s’en sert. C’est pourquoy (encor que ses observations soient fort ordinaires), je pense que ce seroit une chose fort aggreable à beaucoup de monde de congnoistre ses procedés.” On Mersenne’s criticism, found mostly in his Vérité des sciences (1625) and focused on Bacon’s Novum organum, see Lenoble, Mersenne, ou la naissance du mécanisme, 325-335.

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would be better qualified than the people building and designing organs?

II. ORGANOLOGY, OR THE ART OF MUSICAL INSTRUMENT MAKING

Organology is the “study of musical instruments in terms of their history and

social function, design, construction and relation to performance.” It is a modern

historiographical concept that deals with the scientific study of musical instruments and

the symbolism and folklore functions of the material culture of music as investigated, for

example, by ethnomusicologists.171 I want to use it here in a particular—perhaps

anachronistic—way, as an epistemic notion put forward by Mersenne to enlighten the

role and value of artisans and musical instruments (and material culture in general)

towards the aim of perfecting the mechanical arts themselves. Not only were artisans

useful in performing experiments, as described in the previous section, they were also the

sole source of hands-on knowledge, which according to most natural philosophers needed

to be rationalized. Studying and describing meticulously the art of musical instrument

making thus gave Mersenne compelling arguments against armchair natural philosophy.

Experiments had to go hand-in-hand with instrument making. The solution to the

improvement of natural philosophy was found in the workshops. This argument is not

novel, yet Mersenne’s books on instruments are probably one of the best early modern

cases in point, which has never been exploited previously.172

171 Laurence Libin, “Organology,” Grove Music Online (Accessed on 12 September 2006). On general issues, Geneviève Dournon, “Instrumentariums et classifications,” Revue de musicologie 79 (1993), 197-207.

172 The classic literature on this topic is Paolo Rossi, Philosophy, technology, and the arts in the early modern era, transl. by Salvator Attanasio (New York: Harper & Row, 1970). Jim Bennett, “The mechanic’s philosophy and the mechanical philosophy,” History of Science 24 (1986), 1-28. Pamela O. Long, “Power, patronage, and the authorship of ars: From mechanical know-how to mechanical knowledge

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Organ Making: Mersenne’s Musical Instruments

Michael Prætorius had a genuine admiration for musical instrument makers:

“When we come to describe musical instruments, we should treat them as the art-works

of outstanding, intelligent craftsmen, who have brought them into being by manual and

intellectual effort. By applying precise plans to suitable materials, they have skillfully

fashioned instruments which can be used to publish the glory of God, or—which is

perfectly legitimate—to give pleasure to mankind, with their sweet, harmonious

sounds.”173 Mersenne did not oppose the common joueurs d’instruments, who delighted

simple folks with their sweet harmonies, yet believed they were less valuable than bona

fide artisans.174 Indeed, musical instrument makers were truly central to Mersenne’s

work. As he reminded the readers of the book on organ, due to the great and multifaceted

complexity of this machine, “whatever one may say and whatever figures one can give to

explain everything that concerns the construction of the organ, it is very difficult to have

it understood when one has not seen one made, or has not considered the pieces in the

large as well as in detail.”175 To fully understand how an organ works, therefore, one had

to observe how it was actually put together. This can mean only one thing: Mersenne

in the last scribal age,” Isis 87 (1997), 1-41; Long, Openness, secrecy, authorship: Technical arts and the culture of knowledge from Antiquity to the Renaissance (Baltimore: The Johns Hopkins University Press, 2001), esp. chaps. 6-7. Paula Findlen, Possessing nature: Museums, collecting, and scientific culture in early modern Italy (Berkeley: University of California Press, 1994). Daston and Park, Wonders and the order of nature, 1150-1750. Deborah Harkness, The jewel house: Elizabethan London and the Scientific Revolution (New Haven: Yale University Press, 2007). Smith, The body of the artisan.

173 Prætorius, Syntagma musicum II: De organographia, 21. 174 On Mersenne’s view of ménestriers, see Les Prelvdes de l’Harmonie vniverselle, ov qvestions

curievses Vtiles aux Predicateurs, aux Theologiens, aux Astrologues, aux Medecins & aux Philosophes (Paris: Chez Henry Gvenon, 1634), 185: “Quant à ce que l’on obiecte de l’inutilité des Musiciens ordinaires, que l’on appelle Menestriers, dont plusieurs se seruent pourleur passe-temps, il ne sont pas blasmables, puis qu’ils se seruent de leur industrie pour entretenir leurs familles, car encore qu’ils ne soient pas si vtiles que les autres artisans, on les peut neantmoins tolerer dans les Republiques, puis qu’ils ne font tort à personne, & que chacun peut receuoir quelque partie du plaisir innocent, qui procede de leurs sons, & de leur harmonie.”

175 Mersenne, “Traité de l’orgue,” book 6, préface au lecteur, n.p. (HU3). Mersenne, The books on instruments, 392.

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regularly conferred with organ makers—and as a rule with musical instrument makers.

There is actually no other way he could have collected all the facts on the choice of

woods, metals, tools, glue, etc., and could explain how to resolve tricky technical

obstacles such as building the organ’s pipes, wind-chest and keyboard. (See Figure 1.7.)

FIGURE 1.7: MERSENNE’S ILLUSTRATIONS OF AN ORGAN WIND-CHEST AND CLAVIER MECHANISMS Both engravings show how the organ’s wind-chest and clavier are linked together. Though these engravings were copied from Salomon de Caus, they were based on artisanal knowledge. Mersenne did not use de Caus’s printed descriptions, however; he wrote his own, more detailed ones. De Caus’s Raison des forces mouuantes, book 3, 10-12. Mersenne, “Traité de l’orgue,” book 6, prop. II, 314-315. In a few instances, Mersenne did borrow from and refer to published works, such

as de Caus’s Raisons des forces mouuantes to describe the clavier, the wind-chest and

how organ pipes were molded and shaped. (Even though some of Mersenne’s friends

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thought de Caus was a rather poor music theorist and organ maker.176) He also studied

Vannoccio Biringuccio’s De la pirotechnia, originally published in 1540 but translated in

French and printed in Rouen in 1627, in order to describe the fabrication of bellows

(which blow wind into organ pipes) and most importantly to expound on how bells of

various shapes and sizes were cast-ironed and tuned. Yet most of the time book

knowledge was insufficient. On metalworking, for example,

Now if one wishes to know more, he must consult the casters and make many experiments on this matter, with sulfur, which makes red iron cast by its touch alone, and which has an admirable power over all the metals, as well as with antinomy and the other minerals. From this one can draw enough understanding to establish a particular science.177

But Mersenne was also fully aware that bell makers were not always utilizing reason in

making and tuning large bells:

Now this brochette, or rule, of the bells so follows the harmonic ratios of the tones, that one will have perfect tuning of the bells if one follows the thicknesses marked on each line. But I wish to explain here the general method of making whatever diapason one wishes, for the founders go only by guessing when they have bells to cast more weighty, thicker, and larger than those which are marked on their brochettes, which they cannot increase because they do not know the construction through a certain and infallible science which I explain here.178

176 Cornier to Mersenne, 27 January 1626, CM I, 350-351: “A la premiere [lettre de Mersenne reçue par Cornier] donc je vous diray qu’entre tous ceux que je congnois qui ont quelque intelligence de la musique, De Caux est tenu pour fort peu intelligent en ce qui concerne cete science et ay-je oüi tenir que, pour son honneur, il eust fort bien faict de ne publier pas son livre. Il me semble aussi que lors que vous estiez icy [son voyage à Rouen en mai 1625], Le Vasseur vous dict quelque chose de cela mesmes à propos de ces tuyaux d’orgues et vous tesmoigna avoir une opinion contraire à ce que dict de Caux.” De Caus’s book on music is Institutions harmoniques (Frankfurt, 1615) and on organ making, Raisons des forces mouuantes (Frankfurt, 1615). See also Cornier to Mersenne, 21 September 1625, ibid., 294.

177 Mersenne, “Des instrumens de percvssion,” book 7, prop. VI, 8 (HU3). Mersenne, The books on instruments, 507. On the generation of metals in the earth, Mersenne mentions Palissy and Agricola. On Biringuccio, Cornier to Mersenne, 16 March 1626, CM I, 417-418; Cornier to Mersenne, 29 March [1628], CM II, 50-51.

178 Mersenne, “Des instrumens de percvssion,” book 7, prop. VII, 11 (HU3). Mersenne, The books on instruments, 510. Mersenne’s correspondent in Nevers mentioned how they also went “à taston” while making bells: “Il n’y a aucun maistre fondeur en cette ville [Nevers], duquel on puisse sçavoir de combien il amoindrit chaque cloche pour chaque ton, ny combien il donne d’espesseur au diamètre et à la hauteur de la cloche, ny en quelle proportion il mesle ses matieres pour faire son metail. Bien ay-je ouy dire que les fondeurs permettent à chacun de jetter dans la fonte, qui une piece d’argent, qui un sol ou autre métail. Ce

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Organ Making: Mersenne’s Musical Instruments

Mersenne no doubt wanted to rationalize artisanal practices when possible—perhaps

more than Descartes, who told Mersenne he had never considered what would be the

most perfect shape of a bell179; and, according to Doni, musical instrument makers lacked

so much in theoretical knowledge that he found no harpsichord maker in Rome who had

ever heard of the monochord.180 Theory was one thing, which Mersenne could describe

from other books or deduce from experience. With regard to the precise description of

artisanal practices, however, Mersenne could not have done it without engaging in an

authentic workshop experience.

All in all, information gathered from printed works—or manuscripts181—is rather

small in Mersenne’s books on instruments, and thus cannot explain the incredible amount

of facts and artisanal knowledge found in the book on organs (and the other ones as well).

Take, for instance, Mersenne’s description on how to shape and weld an organ pipe:

As to the solder and the method of soldering the pipes, it must be remarked that the mixture is composed of a twelfth part of tin to the lead, and that it must be forged quite evenly on a polished anvil like that of the tinsmiths. Now after the pipes are proportioned, one takes each of them aside, and before rolling it on the mill, one rubs the sides of the tube with chalk diluted with a little water and gum, and for this one heats the mixture a little. This done, one begins to bend the side of the tube, which ought to be along the length of the mould on which it is rolled. Afterwards, one strikes all around the said mould with a rule that is completely

qui me faict croire que communement ils n’y regardent de si prez, quoy que je sçache qu’en plusieurs lieux les choches y sont fort bien d’accord, et en autres elles sonnent musicalement.” Bredeau to Mersenne, 13 July 1628, CM II, 99.

179 Descartes to Mersenne, January 1630, AT i, 111. 180 Doni to Mersenne, 8 April 1634, CM IV, 88-89: “Vous ne sçauriez croire combien regne

l’ignorance par deça en faict de teorie et vous le pouriez juger de cecy, que voulant faire un monochorde (encores que de plusieurs cordes), je n’ay trouveé personne de ces faiseurs de clavicimbles, dont il y en a de fort experts, qui en ayent ouy parler; et je suis fort estonné qu’un estude si beau et si plaisant soit si fort delaissé.”

181 I found one manuscript destined to engravers, sculptors, painters, gilders, and draughtsmen in the Bibliothèque nationale de France, département des manuscrits français, 9155. Folio 46r ff. that deals with how to decorate wood for furniture, cabinets, lutes and violins.

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flat and rather long. And then the body of the tube is removed from the mould, so that there remains the width of a feather between the ends which are to be joined together, so as to rub with the preceding mixture. And after it is dry, one takes a small knife, which is so adjusted in the hand that the length of the blade passes along the thumb and its shaft is between the little finger and the fourth. And then one places the point, pressed by the thumb, lightly upon the edge of each side, and by running along the edge of each side from one end to the other, one presses them so that being joined together they form a small channel or gutter. Now having grated it, one takes the end of a candle and rubs on it so that the solder will run along it better. This is made of a point of lead, a pound of fine tin, and a quarter of tin-glass for the lead pipes. But one makes use of two pounds of pure tin, one pound of lead and a quarter of tin-glass of those of tin. Yet this mixture depends on the judgement and pleasure of the manufacturers. To this must be added that to solder the pipes well, it is necessary to place a little solder at the two ends before having it run the length, so as to fix the two sides of the body and to straighten and adjust one with the other.182

Neither Prætorius’s celebrated organographia nor even de Caus’s engineer-like works

described in print, in so many details, the steps and techniques required to fashion an

organ pipe. (Mersenne made a similar highly-detailed description of the wind-chest.183)

The question to ask is thus obvious: Was it that unusual for Mersenne to do such a thing?

No. I believe Mersenne was accustomed to call on artisans and converse with them. He

was, for instance, so excited about a Spanish monk visiting Paris, who apparently built

organs as well as he was playing them, that two of his correspondents warned him against

his own enthusiasm.184 Although not many such examples are available to us, one is

thoroughly interesting and can serve to prove this point.

It starts with a letter from Peiresc dated early May 1634. In it, the Provence

gentilhomme told Mersenne that a young lawyer from Aix, named Mr. Gailhard, shall

182 Mersenne, “Traité de l’orgue,” book 6, prop. VI, 321-322 (HU3). Mersenne, The books on instruments, 406. See also prop. XVII, 344-345.

183 Mersenne, “Traité de l’orgue,” book 6, prop. XLIV, 400-404 (HU3). 184 Cornier to Mersenne, 16 March [1626], CM I, 417; Father Chastelier to Mersenne, 11 July

1626, ibid., 479.

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visit him on a mission: to gather every imaginable information on public and private

fountains. Peiresc wanted to know—presumably for one or both of his estates—the

“vulgar” names of all the parts (tools, machines, pipes, conduits, faucets, basins, etc.)

needed for the manufacture and ornamentation of fountains; the correct proportions of

water conduits depending on the amount of space available, and how they should be

arranged to vary the flow of water; finally all the prices and the names of the artisans who

did this kind of work. Peiresc believed that Mersenne would have more patience than the

young messenger to accomplish such a task. Perhaps related to the latter, Peiresc also

asked Mersenne to write a precise memoir on vases, in which the dimension and the

names of all common vases and their individual parts, whether in wood, terracotta, metal,

glass, or gold plated would be penned down. This should be a simple and enjoyable

undertaking spent—Peiresc indicated—browsing within the workshops of the most

intelligent and capable of artisans. Peiresc, moreover, thought that knowing these specific

matters would help to rectify (redresser) poor artisanal practices.185

Whether or not Mersenne wanted to rectify the work of the fontainiers, he

nevertheless complied with Peiresc’s request. To do so, he consulted with the overseer of

the Rougi and the Belleville-sur-Sablon fountains in the suburbs of Paris. The great

number of potential difficulties in building such an extensive work had Mersenne write to

Peiresc that the latter should send someone on site to study all there was to learn.

185 Peiresc to Mersenne, 1 May 1634, CM IV, 110-111; Peiresc to Mersenne, 18 June 1634, ibid., 182-183. Peiresc was in the habit of asking such detailed memoirs. Around the same time, he asked Father Cœlestinus to spend around ten days in the vicinity of Mount Kasios (North-East of Alep) to look at the possible remnants of the ancient cult of Jupiter Cassius, to observe the lunar eclipse of August 1635, to investigate various natural properties of the mountain, to transcribe any type of inscription he could find and back on the plain, to ask questions to the nearby peasants on vapors and fumes that ascended the mountain. Brentjes, Peiresc’s interest in the Middle East and Northern Africa, 2-3.

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Mersenne saw all the tools of the trade, and he told Peiresc that besides an overall

manager carpenters, stonecutters, plumbers, bricklayers, etc. would be needed. Mersenne

even told Peiresc that he could make experiments to better understand the flow of water

in pipes—which remained one of the major problems at that time—and to determine why

the wind caused loud noises in conduits.

Peiresc was happy with Mersenne’s first account, yet wanted to make sure the

commission did not do violence to the Minim’s natural inclination—implying here that

perhaps Mersenne could be uncomfortable in the company of artisans. Mersenne obliged

gracefully though, never complaining—which he was prone to do. On a festive day he

even went 1,500 pas underground to carefully look at water conduits; the noise of the

villagers, however, was so loud that he could not notice anything. He told Peiresc he

would go back on a working day, when less people were in the streets. This Parisian

fontainier, however, becoming less cooperative as time went by, forced Mersenne to call

on another one who worked for a gentleman in Liencourt, in the Pas-de-Calais. The latter

wrote a memoir that pleased Peiresc, but it still was not complete enough. Too many

particulars, related to the actual artisanal practice, were missing. Peiresc wanted to know

how exactly the fountain makers distributed water to different places, the specifics on

faucets made of various materials, the ornamentation of basins and fountains themselves,

etc.186 In short, Peiresc wanted a complete and comprehensive description on fountain

making, similar perhaps to the ones Mersenne gave on musical instruments.

The information Peiresc sought was simply not found in books like Salomon de

186 Mersenne to Peiresc, 2 July 1634, CM IV, 230-231; Peiresc to Mersenne, 16 July 1634, ibid., 247-249; Mersenne to Peiresc, 26 July 1634, ibid., 268; Mersenne to Peiresc, 24 August 1634, ibid., 328; Mersenne to Peiresc, 2 February 1635, CM V, 47; Peiresc to Mersenne, 8 May 1635, ibid., 175-176; Mersenne to Peiresc, 17 May 1635, ibid., 203.

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Caus’s hydraulic opus. Exact techniques and artisanal practices, unsurprisingly, were

available only from those who performed them. But what about secrecy? Artisans and

engineers like de Caus, or the well-known Girard Desargues, often petitioned for

lucrative contracts with the city of Paris to take care of the waterworks. Hence, were

Peiresc and Mersenne hindered in their fact gathering on fountains due to trade secrets?

Mersenne said so, observing that the gens mecaniques were afraid people like him

wanted to strip them of their gaigne-pain, although it was Mersenne’s remotest idea. It

was (and still is) the usual trope, also acknowledged by de Villiers’s hired organiste

pertaining to the tuning of his organ; or by Peiresc, who told Mersenne about a bell

maker that could give him helpful guidance, if it was not from the fact that, as all artisans,

this one was jealous of his practice.187

Was secrecy a predicament in Mersenne’s case a propos of musical instruments?

Was Mersenne a potential threat to artisans? Musical instrument makers (maîtres faiseurs

d’instruments de musique) were incorporated by letters patents signed by Henry IV in

1599, perhaps a mark of their ever-growing numbers toward the end of the sixteenth

century. Before the guild was established, most musicians crafted their own musical

instruments. Within the new regulation, musical instrument makers were not as free as

before, but still were allowed some leniency regarding what they could build. For

instance, they were permitted by the letters patents to manufacture and decorate cases for

187 On fountains in general and how “ordinary” they were in early modern France, Daniel Roche, Histoire des choses banales. Naissance de la consommation, XVIIe-XIXe siècle (Paris: Fayard, 1997), 169-174. See also Simon Werrett, “Wonders never cease: Descartes’s Météores and the rainbow fountain,” British Journal for the History of Science 34 (2001), 129-147. On de Caus’s and Desargues’s appointments with the city of Paris, Registres des délibérations du bureau de la ville de Paris, publiés par les soins du Service historique, 20 vols. (Paris: Imprimerie nationale, 1883-1984), 18: 58-59; 19: 275-276. De Villiers to Mersenne, 25 February 1635, CM V, 53-54; Peiresc to Mersenne, [6 September 1633], CM III, 474-475; Mersenne to Peiresc, 2 February 1635, CM V, 47.

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their instruments, which clearly stepped on the exclusive rights of leather makers

(gainiers); likewise regarding the ornamentation of instruments with inlaid work of wood

and precious metals, infringing on the cabinetmakers (ébénistes) prerogatives.188 Only

individuals who were incorporated—namely had done their six-year apprenticeship in

bonne et due forme—were allowed to build and sell musical instruments in Paris. Some

artisans may have strongly defended their right to secrecy, but scores of faiseurs

d’instruments lived in Paris in the first half of the seventeenth century, and several of

them were prosperous—and educated—enough to partake in natural philosophical

exchanges with an erudite like Mersenne.189 The harpsichord maker Jean Denis wrote

that all sorts of people came to visit him; some to discuss his work—as Mersenne likely

did numerous times—and others to play on his harpsichords, during which time he would

detect all the awkward gestures (simagrées) younger and older customers displayed in

public.190

188 René de Lespinasse, Les Métiers et corporations de la ville de Paris, 3 vols. (Paris: Imprimerie Nationale, 1886-1897), iii:593-596.

189 The number of musical instrument makers in Paris can be approximated from the official records of the minutier central. Not all of them were as well-off as, for instance, Jean Desmoulins, but still a few seems to have part of the bourgeois society. Take Thomas Le Vacher, “facteur d’instruments de musique et bourgeois de Paris,” who inhabited a house on rue de la Pelleterie. After he died in 1624, furniture worth 175 livres, cloths worth 48 livres, a library containing ten books, and musical instruments worth 264 livres were found in his house. Jurgens, Documents du Minutier central concernant l’histoire de la musique, i:772. The documents show that these instrument makers had a much nicer signature than other artisans, reflecting a better education. (Ibid., 26-28). See also Catherine Massip, “Facteurs d’instruments et maîtres à danser parisiens au XVIIe siècle,” in Instrumentistes et luthiers parisiens, XVIIe-XIXe siècles, 17-34.

190 Jean Denis, Traité de l’accord de l’espinette, new introduction by Alan Curtis (New York: Da Capo Press, 1969 [second ed. of 1650]), 39: “Estant du mestier de faiseur d’Instruments de Musique, ie suis obligé de receuoir toutes sortes de personnes en ma boutique, aucuns viennent pour voir & entendre mes Ouurages [his musical instruments], d’autres viennent pour achepter, & par ainsi j’ay le contentement de voir toucher toutes sortes de personnes, & de voir toutes les simagrées & postures qui se font, dont plusieurs personnes ne se donnent point de garde…” Mersenne mentioned Denis in the “Traité des instrvmens a chordes,” book 3, prop. XX, 159 (HU3): “Il faut seulement remarquer que l’vn des principaux secrets de l’Epinette consiste à barrer la table, dont la bonté depend de l’excellente barrure, qui a esté pratiquée en perfection par Anthoine Potin, & Emery ou Mederic, que l’on recognoist auoir esté les

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Mersenne, of course, wanted neither to build nor sell musical instruments. And

even though the information he gathered from artisans was sometimes exhaustive the

question remains: would someone be able to build an organ (or any other instrument for

that matter) solely based on Mersenne’s written descriptions? It is very doubtful.

Mersenne often referred to the artisan’s expertise in making such and such instrument’s

parts. For the spinet, its excellence depended upon “many conditions and particulars, but

especially on the braces one places under the table, inasmuch as it is difficult to brace the

spinets perfectly, and it is one of the greatest secrets of the art, the research of which I

leave to the manufacturers.”191 In another proposition on the harpsichord, Mersenne even

mentioned that at least 1,500 separate parts were necessary to build one of these clavier

instruments. He did not describe all the parts in detail, which would make it virtually

impossible for anyone without previous knowledge, experience or access to a harpsichord

maker to build a working model.192 Moreover, it appears that some kind of knowledge-

sharing between different guilds may have been more common than it is usually thought.

Organ makers, for instance, needed to get in touch with artisans from other specialized

crafts to learn the secrets of glue making, in order to experiment how organ pipes

sounded when made from a wide variety of material.193 The six-year apprenticeship to

meilleurs Facteurs de France, ausquels les meilleurs Facteurs de maintenant, à sçauoir Iean Iacquet, le Breton, & Iean Denys ont succedé, lesquels sont excellents en leur art...”

191 Mersenne, “Traité des instrvmens a chordes,” book 3, prop. I, 107 (HU3). Mersenne, The books on instruments, 159-160.

192 Mersenne, “Traité des instrvmens a chordes,” book 3, prop. XX, 159 (HU3). 193 Mersenne did not describe in detail all the possible glues “d’autant que cela ne sert de rien à

nostre suiet, & que les Facteurs d’Orgues le peuuent apprendre des artisans qui s’en seruent, s’ils sont assez curieux pour experimenter la diuersité des sons, qui se peuuent faire par des tuyaux de toutes sortes de matiere, dont ils peuuent tirer beaucoup de secrets pour l’harmonie. “Traité de l’orgue,” book 6, prop. XVII, 345 (HU3).

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enter the faiseurs d’instruments’ guild, therefore, was not for nothing: musical

instruments, most importantly the organ, were some of the most difficult early modern

pieces of technology to manufacture. The concept of secrecy may be valid between

artisans, but probably lacked any significance and consequence between an artisan and a

savant: both knew that a written text could never replace hands-on experience. Not unlike

Peiresc’s fountains, Mersenne probably believed it was essential to grasp as many aspects

as possible regarding the mechanical art of musical instrument making to understand it

and, essentially, improve it further.

Though substantial and often drawn from life, Mersenne’s descriptions of musical

instruments were nonetheless akin to theatrum mechanicorum illustrations and

Descartes’s lens-grinding machine: they were convincing, but largely insufficient to

create working models, as Jean Ferrier tried to tell Descartes in their famous epistolary

exchange (see Chapter two).194 Mersenne understood well enough the craftsmanship of

organs to recognize the important features of this technology, and in one particular

proposition he explained how to examine and judge the excellence of an organ.195 The

interesting thing here is that Mersenne’s explanation was not unlike the contract an organ

maker would put in writing to build or repair an organ. Everything from the bellows,

wind-chest, organ pipes and the choice of registration (jeux) gave indications as to the

quality and purpose of an organ.196 As those contracts show, moreover, there was no

194 On the topic of machine representations, Wolfgang Lefèvre, ed., Picturing machines, 1400-1700 (Cambridge, Mass.: The MIT Press, 2004).

195 Mersenne, “Traité de l’orgue,” book 6, prop. XXXVII, 382-384 (HU3). 196 Dufourcq, Le Livre de l’orgue français, vol. 1, for the variety of contracts. Jurgens, Documents

du Minutier central concernant l’histoire de la musique also gives good examples of contracts during the first half of the seventeenth century. For instance, the one signed on 23 December 1635, Marché pour la réparation des orgues de l’église Saint-Jean-en Grève, par Valeran de Heman (vol. 1, 814-816), one of the

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unique way to build an organ. Each organ was different, depending on the quality of the

material used and also the allocated space to set it in. There was thus no single template.

Organ makers always had to adapt the dimensions of the wind-chest and bellows to fit

them in a specific space, whether in a church or a private home. Mersenne was fully

aware of this matter, mentioning that a typical wind-chest for a principal 8’ (an eight-foot

pitch),

such as ordinarily those are in churches where there is only one organ cabinet, one can make the wind chest five or six feet in length, according to the judgment and preference of the maker, for there are some who more easily find place for their stops on a wind chest of four feet, than others do on one of five feet. That is why I do not in any way limit the size so that the cleverness of the manufacturers can decrease them [que la subtilité des Facteurs n’en puise diminuer].197

Although there were probably as many design variations of musical instruments

as there were faiseurs d’instruments, one still has the feeling reading the books on

instruments that Mersenne sought to standardize, to harmonize the different artisanal

practices; each instrument was described as a coherent and theoretical entity, a non

problematical idealtype model based on a rationalization of craftsmanship. Mersenne’s

seven books on instruments were more than an illustrated compendium: they were a

rhetorical and epistemic tool aimed at honnêtes hommes and natural philosophers, which

cogently demonstrated that improving the mechanical arts meant one had first to study

them carefully, in every possible detail. No shortcuts would ever prove to be meaningful

in achieving such a task.

two organ makers mentioned by Mersenne, and from whom he could have taken most of his information on organ building.

197 Mersenne, “Traité de l’orgue,” book 6, prop. XLIV, 400 (HU3). Mersenne, The books on instruments, 481. For the general description of the bellows, Ibid., prop. XXXIV, 378. Mersenne descriptions are in accord with Dufourcq’s comprehensive analysis of the French organ. Dufourcq, Le Livre de l’orgue français, esp. vol. 3.

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Artisans had a crucial role towards the understanding and perfecting of the

mechanical arts. The instruments they crafted and their expertise with various kinds of

materials were essential for the natural philosophical practice of experiments. As it was

demonstrated earlier experiments with organ pipes led to theoretical generalizations

regarding sound production. The reverse process, however, was not at all excluded—and

of obvious significance. Not every aspect of music called for the help of artisanal

practices.

III. THE THEORY OF ORGAN CLAVIERS

Mersenne strongly believed that the mathematical foundation of music theory

could greatly improve the practice of organ playing as well. This he showed by studying

the “science of organ claviers.” In fact, Mersenne explained that “Zarlino would not have

taken so much pains in explaining the syntone of Ptolemy, which misses many degrees, if

he had had an understanding of the keyboards that I propose in the treatise on the spinet

and the organ.”198 Mersenne, in brief, tried to relocate the complete knowledge of

musical genres into a mechanical device, i.e. the organ clavier.199

Organ claviers—all clavier instruments actually—had an obvious problem: “Since

I [Mersenne] have shown that the keyboard and the diapason, which contains the diatonic

genre, which is used now in its perfection, have 32, 27, 25, or at least 19 keys or degrees

in each octave, and since the ordinary keyboards, organ as well as spinet, have only

198 Mersenne, “Traité des instrvmens a chordes,” book I, prop. 3, 9 (HU3). Mersenne, The books on instruments, 22-23 (translation slightly modified).

199 Mersenne, “Traité de la voix, et des chants,” book 3 entitled “Des genres, des especes, des Systemes, & des Modes de la Musique.” (HU2)

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thirteen, it follows that they cannot be just, if one wants to find in them everything that is

in the nineteen degrees of the perfect keyboard [for the diatonic genre].200 Experiments

revealed how to build organ pipes that would produce the sounds of the perfect diapason;

now a clavier had to match this same perfect diapason, so that theory and practice could

ultimately work hand-in-hand.

The traditional organ clavier (or keyboard) had (and still has today) thirteen keys

(marches), which was tuned according to the meantone temperament, i.e. a tuning made

of pure major thirds and where the fifths are smaller and the fourths larger by a quarter of

the syntonic comma—hence the label 1/4-comma meantone. As quoted above by

Mersenne, this sort of tuning does not give pure consonances, but tempered ones. To

Mersenne, a good tuning had to follow the just intonation of consonances, not simply for

musical or mathematical reasons, but more importantly to fight skepticism. In La Vérité

des sciences (1625) and the Questions harmoniques (1634) Mersenne declared that

skeptics argued against music being a science owing to the fact that there existed no

certain and evident principles to provide concords based on simple mathematical ratios.

Tempered musical intervals, as found on virtually all musical instruments, only conveyed

a sense that music was established on the vagueness and ambiguity of music theorists,

musicians, and musical instrument makers. For it was well known that string instruments

were usually tuned to an equal temperament (based on twelve equal semitones) whereas

for clavier instruments, as said above, the 1/4-comma meantone was favored (though

several other irregular temperaments existed and were in use in Renaissance and Baroque

200 Mersenne, “Traité de l’orgue,” book 6, prop. XVI, 341 (HU3). Mersenne, The books on instruments, 424-425.

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music).201 To Mersenne, therefore, a new kind of keyboard (whether for organs, spinet or

harpsichord) was needed to embed the theory of just intonation into the mechanical arts

and thus, hopefully, help fight skepticism.

Proceeding methodically, Mersenne started with two thirteen-key claviers

differently tempered, neither of which displaying however perfect major and minor thirds

and sixths.202 (See Figure 1.8.) In order to produce all the just intoned consonances, these

two claviers had to be combined into a seventeen-key clavier. Yet even this keyboard was

insufficient to exhibit the just intonation of the complete diatonic genre, which needs at

least eighteen tones (hence nineteen keys). The latter, although exhibiting the three

musical genres, did not do so perfectly for the chromatic and enharmonic ones, yet would

be the best-tempered nineteen-key organ keyboard one could imagine, matching the third

column of the organ-pipe table presented below. To fully render the perfect harmonic

diapason, a clavier would need twenty-seven keys, the first row of keys for the diatonic

genre, the second row for the chromatic and the last row for the enharmonic. The table

that accompanies the clavier’s drawing was the real thing though, displaying at a glance

the perfection of the harmonic diapason, such that one (says Mersenne) could

201 Mark Lindley, “Mersenne on keyboard tuning,” Journal of Music Theory 24 (1980), 166-203. On temperament in general, see Lindley, “Temperaments,” Grove Music Online (Accessed on 12 September 2006).

202 “Or le clauier ordinaire tant des grandes Orgues que seruent aux Eglises, que des cabinets dont on vse dans les chambres particulieres, a treize marches sur chaque Octaue, & n’est nullement different de celuy des Epinettes, dont i’ay parlé dans le liure des instrumens à chordes: c’est pourquoy il n’est pas besoin de le mettre icy, si ce n’est pour faire plaisir aux Organistes & aux Facteurs, qui pourront plus aysément comparer les nouueaux clauiers que ie donne, auec le clavier ordinaire, afin de voir & de suppleer ce qui y manque pour auoir tous les accords & les interualles dans leur iuste proportion.” Mersenne, “Traité de l’orgue,” book 6, prop. XXII, 349 (HU3).

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FIGURE 1.8: MERSENNE’S ORGAN CLAVIERS Above, the common thirteen-key clavier with a meantone temperament. Upper right, the seventeen-key clavier based upon two differently tempered thirteen-key ones. To the right, one of the two nineteen-key claviers discussed by Mersenne, which display the perfect diatonic genre. Below, a table that explains how to achieve the perfect twenty-seven-key clavier encompassing all three musical genres. Lower right, the said clavier. Mersenne, “Traité de l’orgue,” book 6, prop. XXII, 349-353; prop. XXIII, 353-358.

straightforwardly extract from it this twenty-seven key clavier. (The table was supposedly

so self-explanatory that “it would be unnecessary to add the figure of the keyboard,

except that I desire to make its understanding so easy for the organists and the makers

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that they may find no difficulty.”203

Mersenne did not explain how to manufacture these very special claviers (the only

account by Mersenne on keyboard-making was a general one on the movement

mechanism of the keys, as seen in figure 1.7 above). Such distinctive claviers were not

utterly uncommon, especially in the harpsichord family of instruments, for example the

nineteen-key clavier built in 1639 by Joan Albert Ban based on Mersenne’s own,

Zarlino’s nineteen-key clavier built in 1548 by Maestro Comenico Pesarese, Doni’s

three-manual sixty keys per octave organ clavier described in his Compendio del trattato

de’ generi, e de’ modi (Rome, 1635), and the two-manual thirty-six keys per octave

clavier of Nicola Vicentino’s archicembalo, “the foremost and perfect instrument, in that

none of the keys lacks any consonances.”204 Drawn from the most exact theory of

music—which could be confirmed by the monochord, Mersenne’s twenty-seven-key

clavier had great advantages:

As for the usefulness that can be made of this keyboard, it is very great, for it shows exactly the intervals of the three genres of music, and gives a greater light on the harmony that the Greeks [and the Latins] have written of. Thus if one teaches music and the method of singing to children by means of its keys, they would be able to understand the most subtle ratios of all sorts of compositions and concerts in very little time, and to sing enharmonic airs as easily as the chromatic and diatonic ones. I am omitting many other uses that the organists can advise, if they use the keyboard on which they will make a quantity of beautiful passages and pretty touches which cannot be found on ordinary keyboards.205

203 Mersenne, “Traité de l’orgue,” book 6, prop. XXIII, 356 (HU3). Mersenne, The books on instruments, 437.

204 Lindley, “Mersenne on keyboard tuning,” 168-170. Ban’s keyboard is found in his Kort Zangh-Bericht (Amsterdam, 1643) and information are given in Mersenne’s correspondence. On Ban, Daniel P. Walker, “Joan Albert Ban and Mersenne’s musical competition of 1640,” Music and Letters 57 (1976), 233-255. On Vicentino, see his Ancient music adapted to modern practice, transl. by Maria Rika Maniates, ed. by Claude V. Palisca (New Haven: Yale University Press, 1996), quotation on p. 315. Stuart Isacoff, Temperament: the idea that solved music’s greatest riddle (New York: Alfred A. Knopf, 2001), 181. J. Murray Barbour, Tuning and temperament: A historical survey (New York: Da Capo Press, 1972), 111.

205 Mersenne, “Traité de l’orgue,” book 6, prop. XXIII, 357 (HU3). Mersenne, The books on

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And because these claviers were so perfect, nothing should stop organists using them,

even if it meant learning anew how to play the organ:

Now it is certain that these keyboards ought to be preferred to the old ones, since they contain a greater number of consonances and other intervals in their justness… For it is of no importance that the difficulty of playing them is greater, inasmuch as it is not necessary to feel pity for the pains nor to avoid the work which leads to perfection. To this I add that they will be played as easily as the others when the hands become accustomed to them, because they follow the infallible rule of reason. And there is no need for working to hide their imperfection, as happens in ordinary keyboards since they do not have them, as is seen in the two last keyboards of the preceding proposition in which all the consonances are quite just and without any temperament.206

In this case, musicians and the mechanical arts had to meet the terms of the music

theorist, for only through the latter’s scientia would a better musical instrument be

designed and built, and consequently would music approach the long lost perfection of

Antiquity.

Mersenne argued elsewhere in his Harmonie universelle that music performed on

instruments, 439. On how the organ can help one learn to sing just without a maître, “Traité des chants,” book 2, prop. XXXVII, 46-47 (HU2). Yet a maître de chant is needed to give more charm to the voice, since instruments cannot teach “certains charmes que l’on inuente tous les iours pour embellir les chants, & pour enrichir les Concerts.”

206 Mersenne, “Traité de l’orgue,” book 6, prop. XXIII, 354 (HU3). Mersenne, The books on instruments, 437. Playing skillfully was a matter of practice, not of knowledge according to Trichet: “Avant de finir ce discours j’ay voulu mettre en cet endroit pour desennuyer le lecteur une question de Saint Augustin qui concerne les joüeurs d’instruments et qui pouvoit estre placée ailleurs aussi bien qu’ici. Scavoir s’il faut attribuer cette adresse qu’aucuns ont a remuer soupplement les doigts, ou bien a la science ou bien a l’usage. Car il peut arriver que, faisant comparaison de deux joüeurs d’instruments l’un avec l’autre, le moins scavant pourra surpasser son compagnon par le doux mouvement des doigts; que si cette agilité de la main estoit inséparablement annexée a la science, chascun y excelleroit d’autant plus qu’il se seroit perfectionné en la cognoissance de la musique, ce qui néantmoings n’est pas tousjours véritable. Mais, dira-t-on, ce que font les doigts est une opération plustot de l’esprit que du corps, car l’esprit commande et les doigts obéissent; cela despend donc de la science qui est adhérante à l’âme. Certes, il faudroit nécessairement advoüer cette objection si les doigts se rendoient tousjours souples et obéïssants a nos intentions, de façon que voulant bien a propos pinser et mignarder quelque chorde les doigts y accourussent tout aussistot sans manquer aucunement. Mais, puisque nous voyons bien souvent des doctes médecins n’estre si habiles a couper quelque membre gasté qu’un simple chirurgien, il faut croire que cette manuelle opération despend plustot de l’exercice et de la pratique que de la science.” Trichet, Traité des instruments de musique (vers 1640), 84-85.

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ordinary (meaning tempered) organs, or other similar keyboard instruments, was as

barbarous, rude and unpleasant as orations mal ordonnées.207 This appears in perfect

agreement with the pure theory of musical harmony and the organ claviers he devised.

Yet it seems that Mersenne was not always specially adamant regarding the best type of

tuning for instruments. There is evidence in some of Mersenne’s writings that he could

have, or would have favored a universal diapason for all instruments, established on

equal temperament, if it were not for the strong disapproval he received from Descartes,

Doni, and the harpsichord maker Jean Denis, who was perhaps Mersenne’s best source in

Paris on keyboard instrument tuning.208 In his Traité de l’Harmonie universelle, for

instance, although Mersenne mentioned that all instruments were imperfect due to their

tempered tuning, he said that it would be impossible to tune equal tempered instruments

such as the lute and the viola in concord with meantone tempered keyboard instruments

“unless we modify the temperament of the ones or the others.”209 In the last proposition

207 Mersenne, “Traitez des consonances, des dissonances, des Genres, des Modes, & de la Composition,” book 3, prop. 7, 161 (HU2): “Et si les Compositions que l’on ioüe sur l’Orgue ou sur les autres Instrumens à Clauier, ou à touches, peuuent estre comparees aux harangues des Orateurs : l’on peut dire que les pieces que l’on joüe sur les Instrumens ordinaires sont en comparaison de celles qui se ioûroient sur des Instrumens graduez selon lesdits Systemes parfaits, ce que sont les Oraisons mal ordonnees, fort rudes, & dont la locution est barbare & malplaisante, en comparaison des Harangues tres-polies, & si excellentes, qu’on n’y peut ajoûter, ny en oster aucune lettre sans en estropier le discours, & sans le rendre plus imparfait qu’il n’estoit deuant.”

208 Lindley, “Mersenne on keyboard tuning,” esp. 179-193. Dominique Devie, Le Tempérament musical. Philosophie, histoire, théorie et pratique (Béziers: Société de musicologie de Languedoc, 1990), 79-94. Barbour, Tuning and temperament, where he says on p. 98: “Although Marin Mersenne was a zealous advocate of equal temperament in practice, he took pains to present literally dozens of tables in just intonation.” Franz Josef Ratte, Die Temperatur der Clavierinstrumente. Quellenstudien zu den theoretischen Grundlagen und praktischen Anwendungen von der Antike bis ins 17. Jahrhundert (Kassel: Bärenreiter, 1991), 228-241. Jean Denis did favor a tempered clavier for the harpsichord, but not equal temperament. To him, the most perfect temperament for a clavier was the meantone. Denis, Traité de l’accord de l’espinette, 9.

209 Mersenne, Traité de l’Harmonie universelle, book 1, théorème XXX, 301. “Il faut neantmoins remarquer que le temperament qui se fait par la seule distribution du comma est plus propre pour les instrumens à clauier, que pour ceux qu’on pince, ou dont on iouë auec l’archet, qui supposent le temperament precedent, c’est à dire l’égalité des tons, & y ajoustent l’égalité des demy-tons par la

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of the book on organ, Mersenne even described a geometrical method, devised by

Roberval, to calculate the proportional means associated with the twelve equal semitones

of equal temperament.210 A theoretical ambiguity or indecision is present here that can

also be easily connected to the crafting of organ pipes. Looking back again at the organ-

pipe table depicted above, the first column actually displays how to cut a pipe into twelve

equal semitones, as an equal tempered organ would require to play in tune with a string

instrument. To favor equal temperament would certainly necessitate a completely new

rationale, one that could still be established on mathematical ratios (as Mersenne also

makes evident), but most likely would find support in musical practice and cultural taste.

Mersenne’s twenty-seven-key organ clavier became a true mechanical

representation—an embodiment—of the most perfect musical harmony attainable by any

of God’s creation. Yet without the precise craftsmanship of organ pipes (since each of the

twenty-seven keys found on the clavier needed to be connected to a pipe), which was

brought to light by experiments on the width and height of pipes, organ claviers were

simply useless. Furthermore, musical instrument makers not only helped with

experimental researches, but provided Mersenne with enough material data to compile his

books on instruments, on which he established the foundation of the new mechanical

philosophy.

Mersenne’s compendium meant more than a simple collection of instruments: it

symbolized in Mersenne’s work the notion that natural philosophy should be understood

distribution de la Diese, comme ie montreray en parlant des luths & des violes, qui ont tous leurs tons & leurs demy-tons égaux, & par consequent leur Octaue diuisées en trois Tierces majeures, ou en six tons, ou douze demy-tons. De la vient que … tout ce qu’on iouë sur ces instrumens est imparfait, & qu’on ne les peut accorder iustement auec les orgues, ou auec l’épinette, si on ne change le temperament des uns ou des autres.”

210 Mersenne, “Traité de l’orgue,” book 6, prop. XLV, 408-412 (HU3).

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as a combination of theory, experiments, and mechanical instruments (organa), and that

all these facets of mechanical philosophy vindicated one another. No other early modern

work on natural philosophy emphasized to such an extent the value and meaning of

mechanical instruments as epistemic tools of natural philosophical knowledge-

production.

MUSICAL INSTRUMENTS AND THE “PARFAIT MUSICIEN”

Musical instruments clearly were not always thought to be indispensable to the musica

scientia. Toward the end of book one of De institutione musica Boethius, echoing

Aristotle, explained quid musicus est:

Now one should bear in mind that every art and also every discipline considers reason inherently more honorable than a skill which is practiced by the hand and the labor of an artisan. For it is much better and nobler to know about what someone else fashions than to execute that about which someone else knows; in fact, physical skill serves as slave, while reason rules like a mistress. Unless the hand acts according to the will of reason, it acts in vain. How much nobler, then, is the study of music as a rational discipline than as composition and performance! It is as much nobler as the mind is superior to the body; for devoid of reason, one remains in servitude… It follows, then, that rational speculation is not dependent on the act of making, whereas manual works are nothing unless they are guided by reason. Just how great the splendor and merit of reason are can be perceived from the fact that those people—the so-called men of physical skill—take their names not from a discipline, but rather from instruments; for instance, the kitharist is named after the kithara, the aulete after the aulos, and the others after the names of their instruments. But a musician is one who has gained knowledge of making music by weighing with the reason, not through the servitude of work, but through the sovereignty of speculation.211

Music was an integral part of the scholastic quadrivium, accompanied by arithmetic,

geometry, and astronomy. To know music meant only one thing: to understand numbers’

ratio. Mathematical intervals characterized everything about music; numbers gave music

its power over the world (musica mundana) and humanity (musica humana).

211 Boethius, Fundamentals of music, §34, 50-51.

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Things changed considerably during the Renaissance. Numbers were no longer

the unique provider of musical knowledge. Besides natural magic and Ficino’s

Neoplatonism, which lead him down the mystical path of linking music with spiritus,

scholars began to add the trivium, or grammar, rhetoric, and dialectic as basic elements of

music learning. Italian humanists, following the lead of Giovanni del Lago, began

applying classical grammar to musical composition. This move was founded on a

concern to replicate within music the structured and formal qualities of the written text.

What made a text perfect, especially its cadence and the various traditional distinctiones,

or punctuations, had to be imitated in music. The trivium had nothing to do with the

determination of music’s character—pitch, genres, modes, etc.—but everything to do

with the harmonization of verbal and musical syntax applied to both prose and poetry.

Zarlino, for instance, mentioned that the “proportioned order of words” in grammar

corresponded to that of sounds; the “proportion of syllogisms” in dialectics produced

“wonderful harmony [concento] and great pleasure to the ear”; and rhetoric called for the

application of “musical accents at the right times” as a means of giving “marvelous

delight to the hearers” during an oration or sermon.212 In France, the musique mesurée of

the Académie de poésie et de musique, a modified accentual version of classical meters,

was an effort to put into music the rational structure of the vers mesurés invented by Baïf,

thus at last reuniting music and poetry together—as the members of the Academy

claimed it had been throughout Antiquity.213 Rhetoric and poetry did not only influence

212 Palisca, Humanism in Italian Renaissance musical thought, chap. 12 for a general discussion. On Zarlino, Paolo da Col, “The tradition and science: The Institutioni harmoniche of Gioseffo Zarlino,” in Zarlino, Le Institutioni harmoniche, 41. See also Moyer, Musica scientia, 217.

213 On musique mesurée, Howard Mayer Brown and Richard Freedman, “Vers mesurés, vers mesurés à l’antique,” Grove Music Online (Accessed on 25 September 2006). See also Daniel P. Walker,

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music theory: it, for instance, played a crucial role in determining the Cartesian treatment

of mathematics so it moved from being a simple craft to a real instrument of scientia. In

Descartes’s epistemology of evident knowledge, rhetoric and poetry as cognitive

exercises helped the mind finding the clear and distinct things—intuitus—so important

for the method.214

Mersenne stood by such a humanistic viewpoint, arguing that the parfait musicien

needed all types of knowledge, not only the mathematical culture of the quadrivium. In

the Traité de l’Harmonie universelle, he described how the liberal arts and the other

sciences were valuable to fully understand and practice music. Grammar, Mersenne

explained, was used to go back to the Greek roots of the musical language (consonances,

diapason, diapente, etc.) to grasp its true meaning, as it did for languages. Verbal

rhetorical figures taught how to arrange the subject matter of music so it pleased listeners

the most. Poetry was even more necessary than rhetoric, since it was tailor-made for

singing. Logic taught how to reason (and thus how to understand music theory)—music

depended upon arithmetic and geometry; astronomy showed how to find the consonances

in the movements, sizes, intervals and distances of stars and planets. Music was

subordinated to physics, which taught the nature of sounds and its properties.

Metaphysics conveyed the relationships between sounds and all natural beings. Medicine

taught how to find the temperament of listeners, and how to adapt songs accordingly.

Morality explained how to behave at concerts, and politics demonstrated the modes and

Music, spirit, and language in the Renaissance, ed. by Penelope Gouk (London: Variorum Reprints, 1985). 214 Matthew L. Jones, The good life in the Scientific Revolution: Descartes, Pascal, Leibniz, and

the cultivation of virtue (Chicago: The University of Chicago Press, 2006), chap. 2. On rhetoric, see also Jean-Vincent Blanchard, L’Optique du discours au XVIIe siècle. De la rhétorique des jésuites au style de la raison moderne (Descartes, Pascal) (Québec: Les Presses de l’Université Laval, 2005).

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movements required to prevent the corruption of the standard of behaviors and to

preserve the virtues that made empires and republics flourish.215 Mersenne’s concept of

the perfect musician as defined here was not exactly original: it was in fact akin to

Zarlino’s Istitutioni harmoniche.216 What makes Mersenne’s description of the parfait

musicien genuinely innovative was the addition of the mechanical arts at the end of the

list. Musical instrument and musical instrument making entered musica scientia through

Mersenne’s notion that music was the best representation of universal harmony tout

court.

In the Préludes de l’Harmonie universelle Mersenne explained, echoing

Descartes, that the sciences should not be considered as separate fields of knowledge, but

rather as a unity. In Mersenne’s words, all the sciences “have created together an

unbreakable society [ont iuré entr’elles vne inuiolable societé].”217 One, however, cannot

study them all at once; but since they all “hold hands,” one should rather focus on a

particular science and from it, ascertain the others. Mersenne, of course, concentrated on

music, where he reiterated what he had said in the Traité de l’Harmonie universelle,

namely that studying music meant exploring all the rational and practical knowledge

215 Mersenne, Traité de l’Harmonie universelle, théorème V, 20-22. On rhetoric, David Allen Duncan, “Persuading the affections: Rhetorical theory and Mersenne’s advice to harmonic orators,” in French musical thought, 1600-1800, ed. by Georgia Cowart (Ann Arbor: U.M.I Research Press, 1989), 148-175.

216 Zarlino, Institutioni harmoniche, book 4, chap. 35, “Quel, che debbe hauere ciascuno, che desidera di venire a qualche perfettione nella musica.”

217 Mersenne, Les Préludes de l’Harmonie universelle, Question V, 155-156: “Les sciences ont iuré entr’elles vne inuiolable societé, il est quasi impossible de les separer, car elles souffrent plustost que l’on les déchire; & si quelqu’vn s’y opiniastre, son trauail ne luy en arrache que des lambeaux imparfaicts & confus. Elle ne viennent pourtant pas toutes ensemble, mais elles se tiennent tellement par la main, qu’elles se suiuent d’vn ordre naturel qu’il est dangereux de changer, parce qu’elles refusent d’entrer autrement où elles sont appellees.”

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available to mankind, including the design of new musical instruments.218 Mersenne said

it best in the Traité, where he explained that the making of musical instruments belonged

to the parfait musicien, who must know all the materials entering into the craftsmanship

of all instruments, “otherwise he will find neither the pleasure nor the honor that comes

from this knowledge, and thus will be deprived of the great utility he could gain from

it.”219 To Mersenne, the material culture of music was as significant as the seven liberal

arts and all the other sciences in achieving the status of the perfect musician. This, I

believe, is one of Mersenne’s foremost contributions to the study of music and, by

ricochet, to the whole field of early modern natural philosophy—since music served as

Mersenne’s paradigmatic knowledge-producing scientia.

From Mersenne onward, the role and purpose of musical instruments in musica

scientia became indisputable. A “Complete Musitian,” according to the 1653 English

edition of Descartes’s Compendium musicæ:

is required a more then superficial insight into all kinds of Humane Learning. For, He must be a Physiologist; that He may demonstrate the Creation, Nature, Proprieties, and Effects of a Natural Sound. A Philologer, to inquire into the first Invention, Institution, and succeding Propagation of an Artificial Sound, or Musick. An Arithmetician, to be able to explaine the Causes of Motions Harmonical, by Numbers, and declare the Mysteries of the new Algebraical Musick. A Geometrician; to evince, in great variety, the Original of Intervalls Consono-dissonant, by the Geometrical, Algebraical, Mechanical Division of a

218 Ibid., 138-143. Here Mersenne puts under the art of drawing the creation of musical instruments and other technological feats: “& par consequent à la Pourtraicture, tant pour cela, que pour desseigner les nouueaux instrumens que le Musicien peut inuenter en corrigeant les vns, & adioustant aux autres, & pour ordonner des grottes, & des machines hydraulique, & pneumatiques, qu’il rendra capables de toute sorte d’harmonie.” (p.143)

219 Mersenne, Traité de l’harmonie universelle, book 1, théorème II, 10-11: “I’ajouste seulement qu’elle [la musique] considere la nature des corps, & leurs proprietez, parce que la fabrique des instrumens de Musique appartient au Musicien, qui doit connoistre le bois & les autres matieres qui seruent pour faire les instrumens de Musique, comme sont les peaux, les intestins & les metaux dont on fait les orgues, les luths, les violes, les cistres, les harpes, les flûtes, les trompettes, les hauts-bois, & les autres instrumens, s’il veut estre parfait Musicien, autrement il n’aura pas le plaisir ny l’honneur qu’il peut receuoir de cette connoissance, & sera priué de la grande vtilité qu’il en pourroit tirer.”

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Monochord. A Poet; to conform his Thoughts, and Words to the Lawes of præcise Numbers, and distinguish the Euphonie of Vowells and Syllables. A Mechanique; to know the exquisite Structure of Fabrick of all Musical Instruments, Winde, Stringed, or Tympanous aliàs Pulsatile. A Metallist; to explore the different Contemperations of Barytonous and Oxytonous, or Grave and Acute toned Metalls, in order to the Casting of tuneable Bells, for Chimes, &c. An Anatomist; to satisfie concerning the Manner, and Organs of the Sense of Hearing. A Melothetick; to lay down a demonstrative method for the Composing, or Setting of all Tunes, and Ayres. And, lastly, He must be so far a Magician, as to excite Wonder, with reducing into Practice the Thaumaturgical, or admirable Secrets of Musick…220

This long passage, which includes artisanal knowledge and the material culture of music,

describes very well the new scientia of music by the mid seventeenth century.221

Kircher’s 1650 Musurgia universalis, the next great music compendium after Prætorius’s

and Mersenne’s, could not achieve its universal goal without introducing long

descriptions of musical instruments—which borrowed heavily in fact from Mersenne’s

own, engravings included. This, I believe, is an argument too often forgotten when

dealing with the meaning of harmonia universalis. Mersenne’s instrumentarium is

perhaps the best illustration that the mechanical arts and the material culture of music had

finally crossed an important early modern intellectual threshold: they were finally

included within the “universal” of the universal harmony. Mersenne’s books on musical

instruments, in other words, opened the door to a complete redefinition of the meaning of

artisans and instruments to natural philosophy. Descartes, as we will see next, reflected

on the same issues as well, assuming different though by no means trivial conclusions.

220 Lord W. Brouncker, Renatus Descartes excellent compendium of musick: with necessary and judicious animadversions therupon (London, 1653), to the reader, n.p. For an analysis of this work, Descartes, Abrégé de musique, 37-40.

221 Natural magic, since Bacon, has been more relevant in seventeenth-century England than on the Continent as regards the science of music. See Gouk, Music, science and natural magic in seventeenth-century England. Another very good discussion on the same topic is Linda Phyllis Austern, “‘’Tis Nature’s voice’: Music, natural philosophy and the hidden world in seventeenth-century England,” in Music theory and natural order from the Renaissance to the early twentieth century, 30-67.

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CHAPTER 2

LENS MAKING: ARTISANS, MACHINES, AND DESCARTES’S ORGANON ∗

ESCARTES’S WHOLE “PROJECT OF SELF-INSTRUCTION,” we learn in Part VI of the

Discours de la méthode, “is suffering because of the need for innumerable

observations which I cannot possibly make without the help of others [sans l’aide

d’autrui].”222 Scholars have investigated the epistemic role of observations and

experiments in Cartesian natural philosophy, but few have considered these “others” fit to

assist Descartes in his quest for truth.223 Yet Descartes is quite adamant as to whom he

wants help from:

D

True, as regards observations which may help in [natural philosophy], one man could not possibly make them all. But also he could not usefully employ other hands than his own, except those of artisans, or such persons as he could pay, who would be led by the hope of gain (a most effective motive) to do precisely what he ordered them to do. For voluntary helpers, who might offer to help him

∗ This chapter has been published in a slightly modified version in History of Science 44 (2006), 187-216.

222 Descartes, Discours de la méthode, AT, vi:75; CSM, i:149. All quotes from Descartes were taken from Œuvres de Descartes, ed. by Charles Adam and Paul Tannery, 11 vols (Paris: J. Vrin, 1996) [hereafter cited as AT, vi:33-45]. For the English translation I used The philosophical writings of Descartes, transl. by John Cottingham, Robert Stoothoff, and Dugald Murdoch, 3 vols (Cambridge: Cambridge University Press, 1984-1991) [hereafter cited as CSM, i:123-135].

223 On the role of observations and experiments, see Daniel Garber, “Descartes and experiment in the Discourse and Essays,” in Descartes embodied: reading Cartesian philosophy through Cartesian science, idem (Cambridge: Cambridge University Press, 2001), 85-110; Ralph M. Blake, “The rôle of experience in Descartes’ theory of method (I),” The Philosophical Review 38 (1929), 125-43; Blake, “The rôle of experience in Descartes’ theory of method (II),” The Philosophical Review 38 (1929), 201-18; Alan Gewirtz, “Experience and the non-mathematical in the Cartesian method,” Journal of the History of Ideas 2 (1941), 183-210; Desmond M. Clarke, Descartes’s philosophy of science (Manchester: Manchester University Press, c1982); Spyros Sakellariadis, “Descartes’s use of empirical data to test hypotheses,” Isis 78 (1982), 68-76.

Lens Making: Artisans, Machines, and Descartes’s Organon

from curiosity or a desire to learn, usually promise more than they achieve and make fine proposals which never come to anything. In addition, they would inevitably wish to be rewarded by having certain difficulties explained to them, or at any rate by compliments and useless conversation, which could not but waste a lot of [the natural philosopher’s] time.224

Taken literally, this quotation from the Discours de la méthode establishes the status of

artisans as a docile main d’œuvre, whose mechanical skills should help uncover, under

the tutelage of natural philosophers, nature’s deepest secrets.225 Volontaires, or honnêtes

curieux, are given even less credit here, perceived as a nuisance rather than the source

and authority of knowledge—in contrast to Robert Boyle’s conception of gentlemanly

science.226 Is it the whole story? Are Cartesian artisans coarse “invisible technicians,” the

experienced hands of natural philosophers?227 Could artisans somehow encourage or

inspire the latter?

Artisans and experimental practices have become in the last twenty years or so a

hot topic of interest to scholars of early modern natural philosophy. Hardly any, however,

have investigated what artisans really meant to rational philosophers like Marin

Mersenne—as I have attempted to show in the previous chapter—or René Descartes.228 I

224 Descartes, Discours de la méthode, AT, vi:72-73; CSM, i:148. 225 Money sometimes was not a good enough incentive to hold artisans in check. When the time

came, for instance, to engrave the plates for the Discours and Essais, Descartes and his printer made sure the engraver would not leave without address or procrastinate for too long. The only way to enforce their wish was to keep this engraver (Franz Schooten the younger) “under house arrest”: “Celui qui les taille [the plates] me contente assez, et le libraire le tient en son logis, de peur qu’il ne lui échappe.” Descartes to Constantijn Huygens, 30 October 1636, AT, i:614.

226 Steven Shapin, A social history of truth: Civility and science in seventeenth-century England (Chicago: The University of Chicago Press, 1994). I have contented elsewhere that volontaires, although unhelpful in producing knowledge per se, were Descartes’s vectors of knowledge dissemination; they were the ones who Descartes trusted would make his philosophy known. Gauvin, “Volontaires and artisans in Descartes’s natural philosophy,” unpublished manuscript presented at the History of Science Society annual meeting, Cambridge, MA, 21 November 2003.

227 Shapin, A social history of truth, chap. 8. 228 Jim Bennett, “The mechanic’s philosophy and the mechanical philosophy,” History of Science

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hope to demonstrate in the first three parts of this chapter that artisans, at least for a short

period of time, were more than rough and mindless helping hands for Descartes. I believe

they held a rather crucial epistemic function that initially supported the very foundation

of Cartesian knowledge, namely the mathesis universalis. Descartes, I explain, saw in the

early 1620s an inherent order in the practice of simple métiers. Yet such order, unveiled

in the Regulæ ad directionem ingenii, was not encountered in the hands-on practices

themselves. Method was found beyond the specific gestes of artisans—beyond the

uniqueness of each individual ars. Inspired by Pierre Bourdieu I argue that Descartes may

have seen some sort of structured discipline within artisanal habitus. He discovered the

unity of practice that explained theoretically—rationally—how artisans built machines

and manufactured goods, assuming early in life that artisans were endowed with some

sort of an âme réglée (orderly soul), an innate and orderly reason guiding manual work.

Descartes, however, started to question the artisan’s inherent structured order as

soon as he landed in Paris in the mid-1620s. Before then, never once did he team up with

artisans—although he examined how they worked. Theoretical assertions were mostly

based on dialogues with natural philosophers (inclined towards the mechanical arts like

Isaac Beeckman) and on idiosyncratic observations made during his European tour.

When Descartes arrived in Paris and began to study optics in the company of real

24 (1986), 1-28. Pamela O. Long, “Power, patronage, and the authorship of ars: From mechanical know-how to mechanical knowledge in the last scribal age,” Isis 88 (1997), 1-41; Long, Openness, secrecy, authorship: Technical arts and the culture of knowledge from Antiquity to the Renaissance (Baltimore: Johns Hopkins University Press, 2001), esp. chaps. 6-7; Paula Findlen, Possessing nature: Museums, collecting, and scientific culture in early modern Italy (Berkeley: University of California Press, 1994); Lorraine Daston and Katharine Park, Wonders and the order of nature, 1150-1750 (New York: Zone Books, 1998); Deborah Harkness, The jewel house: Elizabethan London and the Scientific Revolution (New Haven: Yale University Press, 2007); Pamela H. Smith, The body of the artisan: Art and experience in the Scientific Revolution (Chicago: The University of Chicago Press, 2004). On the latter see the essay review by Bruce T. Moran, “Knowing how and knowing that: Artisans, bodies, and natural knowledge in the Scientific Revolution,” Studies in the history and philosophy of science 36 (2005), 577-585.

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artisans, his opinion of them wavered. Artisans, including his protégé Jean Ferrier, did

not demonstrate the intrinsic âme réglée he thought he had previously contemplated. The

artisanal trope guiding hitherto the notion of mathesis had to be replaced by something

displaying even more order, i.e. machines in the form of automata. Following D. Graham

Burnett’s insightful essay, I will show in the fourth part of the chapter that the Dioptrique

was in fact a treatise written to put in order the activity of the mechanical arts. Machines,

according to Descartes, ought to resemble natural philosophical ideas; their design,

consequently, needed to be generated by the method. Systematizing the mechanical arts

thus ensured that the artisan’s âme déréglée would never misconstrue the creation of an

orderly soul.

The Discours de la méthode and its essays, I believe, sought to dominate both the

mind and the body of early modern individuals. In the ultimate section of the chapter, I

conjecture that through the trope of machinelike order, Descartes’s method became an

instrument of authority. The method aimed not only at the production of rational and

mechanical knowledge, but perhaps more importantly at fashioning a new ideal Man, one

that could serve adequately both the State and scientia. Descartes’s goal (not unlike

Francis Bacon’s) was to forge a novum organum, a new kind of “instrument” to replace

the old peripatetic one. The method was thus a conceptual organon, a multifaceted

instrument of authority created to act on the socio-cultural as well as on the natural

philosophical fields of knowledge. The method, in other words, was designed to create

honnêtes hommes; it was Descartes’s timely response to the rise of French absolutism.

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HABITUS AND DESCARTES’S LOGIC OF PRACTICE

Artisans and Cartesian rational knowledge give the impression of an unusual pair. The

first rule of the Regulæ ad directionem ingenii in fact questions the very role artisans play

in Descartes’s philosophy. Rule I opposes widening the established (and essentially

artisanal) use of habitus to the realm of scientia. Habitus, i.e. the “bodily aptitude and

practice” of artisans, first and foremost secures proficiency in individual arts; it is

connected to the uniqueness of ars, each and every art requiring a set of bodily deftness

and movements (gestes) ordinarily distinct from one artisanal practice to another.229 Yet

Aristotle developed this conception of art into a habitus scientiarum, a notion to which

Aquinas, Suárez, and Eustachius a Sancto Paulo’s philosophies adhered, fragmenting

scientia into a multiplicity of independent knowledge-components, each imposing their

own special intellectual skills and training. Akin to the various arts every science—

knowledge—is created unique and is said to possess its proper system of principles in

order to ensure logical and coherent deductive links between objects of a same genus.230

The Aristotelian model of an ideal science thus involved, by definition, a collection of

principles that were non transferable to any other science, just as habitus was exclusive to

either the farmer or the cithara player in Descartes’s well-known example.231

229 As Descartes explains, “for one man cannot turn his hand to both farming and harp-playing [cithara], or to several different tasks of this kind, as easily as he can to just one of them.” Descartes, Regulæ ad directionem ingenii, AT, x:359-360; CSM, i:9.

230 “Habituum autem varia sunt genera, alii enim sunt animi, alii vero corporis.” Eustachius a Sancto Paulo, Summa philosophica quadripartita, 2 vols (Lyon, 1609), ii:121. See Etienne Gilson, Index scolastico-cartésien (Paris, 1912), s.v. habitus. Descartes, Règles utiles et claires pour la direction de l’esprit en la recherche de la vérité, ed. and transl. by Jean-Luc Marion (The Hague: Nijhoff, 1977), 90-91.

231 “Arithmetical demonstration and the other sciences likewise possess, each of them, their own genera; so that if the demonstration is to pass from one sphere to another, the genus must be either absolutely or to some extent the same. If this is not so, transference is clearly impossible, because the extreme and the middle terms must be drawn from the same genus: otherwise, as predicated, they will not be essential and will thus be accidents.” Aristotle, Posterior analytics I.7. The Internet Classics Archives

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Descartes argued forcefully in Rule I against the generalization of habitus because

“the knowledge of one truth does not, like skill in one art, hinder us from discovering

another; on the contrary it helps us.” Descartes instead gave credence in Rule I to the

unity of scientia, i.e. to the idea of an interconnectedness of knowledge commensurate

with the universal wisdom.232 Hence, to liken the artisan’s habitus to scientia was sterile

and vain “since what makes us stray from the correct way of seeking the truth is chiefly

our ignoring the general end of universal wisdom and directing our studies towards some

particular ends.”233 Rather, it should be “acknowledged that all the sciences are so closely

interconnected that it is much easier to learn them all together than to separate one from

the other.” To seek true knowledge, therefore, one must avoid the study of particular

sciences and try instead to “increase the natural light of his reason,” which will not only

help solve this or that scholastic problem, but also show the will “what decision it ought

to make in each of life’s contingencies.”234 In contrast to the multiplicity of arts there was

only one science for Descartes, one universal knowledge guided by an all-encompassing

wisdom. In other words, habitus was to the uniqueness of ars what wisdom was to the

unity of scientia.235

Although the character of habitus is unequivocal in Rule I, I would suggest it was

<classics.mit.edu> (accessed on 3 August 2005). A very good discussion is found in Peter Dear, Discipline and experience: The mathematical way in the Scientific Revolution (Chicago: The University of Chicago Press, 1995), 36-46.

232 On the interconnectedness of knowledge as one of the central components of Descartes’s project, Daniel Garber, Descartes’s metaphysical physics (Chicago: The University of Chicago Press, 1992).

233 Descartes, Regulæ, AT, x:359-361; CSM, i:9-10 for the quotes. 234 Descartes, Regulæ, AT, x:361; CSM, i:10. 235 On the uniqueness of ars and unity of scientia, Jean-Luc Marion, Sur l’ontologie grise de

Descartes. Science cartésienne et savoir aristotélicien dans les Regulæ, 2nd edn (Paris: Vrin, 1981), 25-30.

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not utterly useless and purposeless to the Cartesian method of knowledge production.

Looking beyond the uniqueness of habitus, to the higher ground of methodology, one can

witness how artisanal practices actually bring to light Descartes’s epistemology of

rational knowledge, namely the concept of order underpinning the Cartesian method. The

method is rarely described as a bona fide logic of practice. As such the method—not yet a

metaphysics in the Regulæ—takes place prior to any theoretical or experimental activity

of natural philosophy; it lies at the foundation of all Cartesian knowledge.236 Within the

method are embedded a series of well-defined logical rules one has to learn and—more

importantly—learn to follow; being familiar with them does not guarantee success on the

path to true knowledge. Consequently one has to practice, to train in the method, because

without practice it remains a mere jeu de l’esprit. Descartes wrote that the method

consisted “more in practice than theory,” and that the ultimate aim of the Discours de la

méthode was to uncover “a practical philosophy which might replace the speculative

philosophy taught in the schools.”237 Accordingly, the four-rule method unveiled in the

Discours—summarizing the Regulæ—was not to be taught but rather was to be

continually exercised, Descartes himself being compelled to “practice [it] constantly ... in

236 Jean-Luc Marion suggests that the Regulæ contain the seeds of the Cartesian metaphysics as found in the Meditations, but it does not then unfold because Descartes was unable to properly order the intellectual simple natures with the common simple natures. Marion, “Cartesian metaphysics and the role of the simple natures,” in The Cambridge companion to Descartes, ed. by John Cottingham (Cambridge: Cambridge University Press, 1992), 115-139.

237 Descartes to Marin Mersenne, March 1637?, AT, i:349. Descartes, Discours de la méthode, AT, vi:61; CSM, i:142. In a very insightful analysis of Descartes’s famous anaclastic line, Daniel Garber shows how the programmatic statement of the method can be reconciled with a theory of practice. Following closely this example Garber explains that what the method gives is a “workable procedure for discovering an appropriate path” between the reductive steps the knower has to take from a question asked to the actual intuitus, in this case, of a potentia naturalis. From there, the constructive steps (deductions) take us back to the question asked, for which we are now in possession of certain knowledge. Garber, Descartes’s metaphysical physics, 35-36 (emphasis original). For a very helpful diagram, see Garber, “Descartes and experiment in the Discourse and Essays,” in Descartes embodied, 85-110, on p. 100.

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order to strengthen myself more and more in its use.”238

This emphasis on practice was not merely rhetorical; through such a practical

philosophy the power and action of all things would be known “as distinctly as we know

the various crafts of our artisans.”239 Although Descartes belittled habitus as a legitimate

approach of knowledge production, he found an inherent logic beyond the observable

gestures of artisans, an artisanal logic that could help natural philosophers acquiring a

universal method. Descartes explained in Rules IX and X of the Regulæ “how we can

make our employment of intuitus and deductio more skilful,” and by the same token

“how to cultivate two special mental faculties, viz. perspicacity [perspicacitas] in the

distinct intuition of particular things and discernment [sagacitas] in the methodical

deduction of one thing from another.”240 Perspicacitas is linked to intuitus, the certain

experientia of Rule III, as the natural mental ability to concentrate “upon the most

insignificant and easiest of matters” and to focus intensively “to acquire the habit of

intuiting the truth distinctly and clearly.” Descartes contended that “[s]ome people of

course are born with a much greater aptitude for this sort of insight than others; but our

minds can become much better equipped for it through method and practice.” Artisans,

for instance, “who engage in delicate operations, and are used to fixing their eyes on a

single point, acquire through practice the ability to make perfect distinctions between

238 Descartes, Discours de la méthode, AT, vi:22; CSM, i:122. Descartes emphasizes the same point a few pages later: “Moreover, I continued practising the method I had prescribed for myself. Besides taking care in general to conduct all my thoughts according to its rules, I set aside some hours now and again to apply it more particularly to mathematical problems.” (AT, vi:29; CSM, i:125) See also Descartes, Règles utiles et claires pour la direction de l’esprit, 208. A more detailed and somewhat similar analysis is given in Peter A. Schouls, Descartes and the possibility of science (Ithaca: Cornell University Press, 2000), 63-91.

239 Descartes, Discours de la méthode, AT, vi:61-62; CSM, i:142-143. 240 Descartes, Regulæ, AT, x:400; CSM, i:33.

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things, however minute and delicate.”241

Perspicacitas was not a bodily disposition acquired through time and hands-on

practice: it was rather a mental faculty innate to every thinking being. Artisans were not

the only people endowed with such a power of perception.242 However, according to

Descartes, their habitus—the ability, for instance, to fix one’s eyes on a single point—

illustrated best how to attune one’s own inherent perspicacitas. Echoing Renaissance

humanists who urged natural philosophers to enter the craftsman’s workshops and study

the practice of their trade, Descartes suggested that the capacity to distinguish the most

minute and delicate of things—to intuit the common simple natures—is strengthened by

the action of artisanal practices.243 The gestural knowledge of artisans could not by itself

produce ideas, yet it could exhibit courses of action that guided the mind towards

scientia.

Regarding sagacitas, Descartes’s other constitutive mental faculty, Rule X

stipulates that in order to acquire it one should “methodically survey even the most

insignificant products of human skill, especially those which display or presuppose

order.” In line with perspicacitas, sagacitas—the mental skill to exercise deductio—can

be aptly brought to light from the arts and crafts:

Since not all minds have such a natural disposition to puzzle things out by their own exertions, the message of this Rule is that we must not take up the more difficult and arduous issues immediately, but must first tackle the simplest and

241 Descartes, Regulæ, AT, x:400-402; CSM, i:33-34. 242 Descartes, Regulæ, AT, x:371; CSM, i:16. Descartes maintains that “the power of judging well

and of distinguishing the true from the false—which is what we properly call ‘good sense’ or ‘reason’—is naturally equal in all men.” Descartes, Discours de la méthode, AT, vi:2; CSM, i:111.

243 The classic reference remains Paolo Rossi, Philosophy, technology, and the arts in the early modern era, transl. by Salvator Attanasio (New York: Harper Torchbooks, 1970). A more sophisticated analysis has recently been published by Smith, The body of the artisan.

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least exalted arts, and especially those in which order prevails—such as weaving and carpet-making, or the more feminine arts of embroidery, in which threads are interwoven in an infinitely varied pattern. Number-games and any games involving arithmetic, and the like, belong here. It is surprising how much all these activities exercise our minds, provided of course we discover them for ourselves and not from others. For, since nothing in these activities remains hidden and they are totally adapted to human cognitive capacities, they present us in the most distinct way with innumerable instances of order, each one different from the other, yet all regular. Human discernment [sagacitas] consists almost entirely in the proper observance of such order.244

Sagacitas directly followed perspicacitas: it was the crucial mental faculty that put in

series what perspicacitas had discovered. If perspicacitas, which aimed at “attentively

noting in all things that which is absolute in the highest degree,” is truly the “whole secret

of the art,” sagacitas was indispensable in figuring out the chain of inferences from the

most absolute to the most relative of things.245 And to create flawless chains of inferences

Descartes knew no better way “than by accustoming ourselves to reflecting with some

discernment [cum quâdam sagacitate reflectere] on the minute details of the things we

have already perceived.”246 Referring once again to the most unassuming of artisans

reinforced the epistemic connection between what lied beyond habitus and the way minds

should be disciplined.247

Descartes’s artisanal knowledge-making model diverged from the scholastic

weapons of choice, syllogisms. To rid philosophy of unproven truth-producing premises,

244 Descartes, Regulæ, AT, x:404; CSM, i:35. 245 Descartes, Regulæ, AT, x:382; CSM, i:22. 246 Descartes, Regulæ, AT, x:384; CSM, i:23. 247 According to Jean-Luc Marion, Descartes would have used in French the word “adresse”—and

not “sagacité,” which is close to “perspicacité”—to designate this mental faculty, a word the natural philosopher happily applied to both mechanical and mental skills. For instance, “il faut de l’adresse et de l’habitude pour faire et pour ajuster les machines que j’ai décrites,” and “savoir joindre l’adresse de la main à celle de l’esprit.” Descartes, Discours de la méthode, AT, vi:77 and Descartes to Huygens, 1 November 1635, AT, i:330, respectively. Descartes, Règles utiles et claires pour la direction de l’esprit, 208-209.

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he created a new method inspired by a general and inherent logic of practice found within

habitus. Although the School’s training in syllogism was better than nothing (given that it

exercised the minds of the young—which without guidance “might head towards a

precipice”), Descartes refocused the scholar’s attention on the artisanal practices, on the

things that were “perfectly known and incapable of being doubted.”248 The method,

Descartes explained,

cannot go so far as to teach us how to perform the actual operations of intuitus and deductio, since these are the simplest of all and quite basic. If our intellect were not already able to perform them, it would not comprehend any of the rules of the method, however easy they might be.249

The Cartesian method did not teach how to use intuitus and deductio, both being natural

abilities. The method was rather created to instruct how mastery of these two innate

powers could be achieved. This meant the introduction, use and continual exercise of

matter-of-fact mental faculties such as perspicacitas and sagacitas, their proficiency

drawing from basic mathematics and down-to-earth artisanal practices.

Artisanal practices, however, were not to be studied for their own sake, but as

exemplary practices of the method. Take, for instance, Descartes’s example of

blacksmithing. If first deprived of all the instruments of his trade the blacksmith—like

any artisan exercising a self-supporting mechanical art—initially uses either a hard rock

or an unformed mass of iron as an anvil, a stone as a hammer, pincers made of wood, and

other rudimentary tools he might need to begin working. Of course, he will not start

making swords, helmets, and metallic artefacts immediately, but rather will fabricate an

248 Descartes, Regulæ, AT, x:362-364; CSM, i:10-11. In the Discours Descartes mentions that he did not “cease to value the exercises done in the Schools.” Descartes, Discours de la méthode, AT, vi:5; CSM, i:113.

249 Descartes, Regulæ, AT, x:372; CSM, i:16.

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anvil, all sorts of hammers, pincers and metallic tools necessary to his trade. Only then

will the blacksmith be in a position to undertake the production of commodities. This

example taken from Rule VIII teaches that unmethodical and inconsistent operations

should be proscribed to create merchandise—or to solve mathematical problems and

settle philosophical disputes.250 Here Descartes did not emphasize the blacksmith’s

bodily skills in making tools, swords or helmets—and he certainly did not try to improve

those skills per se. Rather, he focused on the blacksmith’s working method and orderly

approach towards the production of materials. The method, seen through the eyes of this

mechanical art, becomes an unbroken “mechanical” thinking process, one that is

methodical and intended for a specific goal. Nothing is left to chance, random practices

or accidental judgements.251 In this well-known example, producing Cartesian knowledge

and producing artisanal goods look as though they fundamentally came from one and the

same logic of practice, the function of an ordered thinking process.

ORDER AND THE MATHÉMATICITÉ OF MATHESIS

The question of order is undeniably one of the most important in the Regulæ and the

Discours. In fact, it underlies the Cartesian logic of practice: “The whole method consists

entirely in the ordering and arranging of the objects on which we must concentrate our

250 Descartes, Regulæ, AT, x:397; CSM, i:31. 251 The “continuous and wholly uninterrupted sweep of thought” refers to Rule VII and is part of

Descartes’s theory of order. On the mechanical thinking process, this could explain some of Descartes’s strange assertion like: “Ce qui cadre beaucoup avec ma manière de philosopher, et qui revient merveilleusement à toutes les expériences mécaniques que j’ai faites de la nature à ce sujet.” Descartes to Villebressieu, summer 1631, AT, i:217. See also Descartes to Froidmont, 3 October 1637, AT, i:420-421. Descartes, Règles utiles et claires pour la direction de l’esprit, 204.

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mind’s eye if we are to discover some truth.”252 The preceding example of the blacksmith

(forgeron in French) is by no mean random: if we cannot discern an apparent order, we

have to mentally forge one (sed tamen aliquem fingemus, or forger un ordre) by the

power of cogitatio.253 Rule IV of the Regulæ accounts for the full meaning of order,

embedded in the concept of mathesis universalis and established as the bedrock of

Descartes’s logic of practice. Since the study of Jean-Paul Weber Rule IV is often

divided into two parts.254 The rule is said to have been written at two different times and

to bear two different purposes: the question and search for certainty through a method in

IV-A (1619), and the establishment of an even more general mathesis as the universal—

and mathematical—way to certain knowledge in IV-B (1628). Jean-Luc Marion,

however, has convincingly shown that this dichotomy is merely apparent. What unites the

methodical search for certainty to the mathematical model of knowledge is the more

abstract notion of the mathématicité of mathematics, the intrinsic order of mathematics.

The Cartesian mathesis, contrary to what is generally believed, is not grounded in

mathematics per se, but rather in a universal abstraction articulated from the orderly

nature of mathematics. Descartes in Rule IV is trying to stretch truth and certainty

beyond the realm of mathematics, to the entire body of human knowledge (scientia). As

he explained in the same rule “When I considered the matter more closely, I came to see

that the exclusive concern of mathesis [ad Mathesim] is with questions of order or

252 Descartes, Regulæ, AT, x:379; CSM, i:20. 253 Descartes, Regulæ, AT, x:404; CSM, i:35, where it is translated as “to invent an order.” For a

complete discussion see Marion, Sur l’ontologie grise de Descartes, 71-78. 254 Jean-Paul Weber, La Constitution du texte des Regulæ (Paris: Société d’édition d'enseignement

supérieur, 1964). See also John Schuster, “Descartes’ mathesis universalis, 1619-1628,” in Descartes, philosophy, mathematics and physics, ed. by Stephen Gaukroger (Sussex: Harvester Press; Totowa, N.J.: Barnes & Noble Books, 1980), 41-96.

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measure and that it is irrelevant whether the measure in question involves numbers,

shapes, stars, sounds, or any other object whatever.”255 Mathematics here “merely”

served the purpose of acquiring this science of order: it did not epitomize it.256

Descartes was thus looking for a new way to establish on a solid philosophical

foundation both non-mathematical (causal) and mathematical (intellectual) objects. This

is the chief objective of Rule IV: to achieve the unity of knowledge.257 To do so he

required more than mathematics: he needed to uncover the abstract notion of

mathématicité within non-mathematical objects. Rule II makes this exact statement,

asserting that “in seeking the right path of truth we ought to concern ourselves only with

objects which admit of as much certainty as the demonstration of arithmetic and

geometry.”258 I believe Descartes found the path towards the mathématicité of non-

255 Descartes, Regulæ, AT, x:377-378; CSM, i:19. Marion, Sur l’ontologie grise de Descartes, 55-69, is perhaps the most sophisticated and persuasive analysis of the mathesis universalis.

256 This point is made in Rule XIV of the Regulæ: “For the Rules which I am about to expound are much more readily employed in the study of these sciences [arithmetic and geometry] (where they are all that is needed) than in any other sort of problem. Moreover, these Rules are so useful in the pursuit of deeper wisdom that I have no hesitation in saying that this part of our method was designed not for the sake of mathematical problems; our intention was, rather, that the mathematical problems should be studied almost exclusively for the sake of the excellent practice which they give us in the method.” Descartes, Regulæ, AT, x:442; CSM i:58-59. The science of order produced by the mathesis universalis represents Michel Foucault’s seventeenth-century shift of épistémè. Foucault acknowledges that order does not necessarily mean an all-out mathematization of knowledge. Foucault, Les Mots et les choses: une archéologie des sciences humaines (Paris: Gallimard, 1966 [2001]), 71.

257 Rule IV should be understood as Descartes’s response to the intellectual clash between the Jesuits Benito Pereira and Christopher Clavius regarding the epistemology of mathematics. Descartes’s mathesis universalis is neither Pereira’s philosophia prima nor Clavius’s attempt at defending the philosophical status of mathematics. The mathesis is a highly developed philosophical blend between two traditions found within the Society of Jesus. Edouard Mehl, Descartes en Allemagne, 1619-1620. Le contexte allemand de l’élaboration de la science cartésienne (Strasbourg: Presses Universitaires de Strasbourg, 2001), 243-261. Dear, Discipline and experience, 32-46.

258 Descartes, Regulæ, AT, x:366; CSM, i:12-13. Marion, Sur l’ontologie grise de Descartes, 42: “L’apparente contradiction ... du privilège préalablement reconnu aux seules mathématiques, plus qu’une incohérence, traduit le coup de force et l’intention profonde des Regulæ: mettre au jour, à l’encontre de la constante aristotélicienne, où certitude et ‘physique’ restent inversement proportionnelles, des objets non-mathématiques (et donc ‘physique’) propres à fournir le même degré (voire un plus grand) de certitude, que n’en fournit l’objet des mathématiques; considérer comme certain un objet non-mathématique: telle est la

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mathematical objects within the sphere of habitus.

Because Descartes wanted to deal with non-mathematical objects he could not

fully dispose of habitus. Habitus itself, for instance, meant the bodily disposition of

artisans and musicians to produce specific knowledge. Habitus and its gestural

knowledge, for Descartes, was unique to each ars. But as we have seen with the example

of the blacksmith, the contemplation of mechanical arts permitted the revelation of a

general built-in procedure, a structured discipline that was not pure rational thinking, yet

not a completely disorganized way of creation. he saw in this structured discipline orderly

systems without specific ends, yet not at all chaotic or governed by the mere fortune of

the hands.259 For example, Descartes witnessed in weavers and embroiderers something

similar to “an infinite yet strictly limited generative capacity” emanating from some

calculated regularities; as an explicit sign of order, they conditioned the artisan’s work

habits.260 Artisans’ know-how was to some extent organized because it followed a

structured discipline moulded by regulated practices. As long as it administered order—

as in the case of blacksmiths and weavers—such a structured discipline could be drawn

upon to invent a series of epistemic steps leading to the more fundamental mathesis.

These steps in the field of the mechanical arts could be understood as structural exercices,

an overall pedagogical strategy that went further than a trial and error training system.

Descartes’s close attention to object-oriented structural exercises could well explain why

tâche que se fixent les Regulæ, au terme de la seconde [règle].” 259 I follow here the theoretical idea of structures structurées et structurantes of Pierre Bourdieu,

Le Sens pratique (Paris: Les Editions de Minuit, 1980), 88-89. 260 Bourdieu, Le Sens pratique, 92. Regarding weaving and other simple arts, “they present us in

the most distinct way with innumerable instances of order, each one different from the other, yet all regular.” Descartes, Regulæ, AT, x:404; CSM, i:35.

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the Cartesian notions of perspicacitas—to find the most absolute of things—and

sagacitas—to put into series—designed to train the mind in the method were illustrated

by both the mathematical disciplines and the mechanical arts.261

What Descartes dismissed back in Rule I was not habitus per se, but rather the

uniqueness of art, the fact that specific gestes must be learned for each art. Looking

beyond the bodily dispositions of habitus, beyond the uniqueness of the artisanal

techniques, we find a structured discipline leading to one and the same internal logic of

practice. Although each art has its own techniques the structured discipline found within

habitus is based on a unity of practice, a theoretical framework suitable for all matters of

art. It is through this abstract and more general understanding of habitus—the

mathématicité of non-mathematical objects—that Descartes fashioned to a certain extent

the unity of practice found in the mathesis universalis. Ars and scientia are not as

alienated in Cartesian knowledge as they are usually thought to be.

ÂMES RÉGLÉES AND THE IDEA OF ARTISAN

In La Recherche de la verité Descartes points out that “enough truth can be known in

each subject to satisfy amply the curiosity of orderly souls [âmes réglées].”262 The

pursuit of knowledge must be guided by an orderly soul, which ought not search for

“those simple [and textual] forms of knowledge which can be acquired without any

261 On exercices structuraux Bourdieu, Le Sens pratique, 126. Interestingly enough, perspicacitas and sagacitas as exercices structuraux for the mind find a correspondence in the mechanical arts that not even Francis Bacon dared contemplate. To Lord Verulam “The human mind is misled by looking at what is done in the mechanical arts, in which bodies are entirely changed by composition and separation, into supposing that something similar also happens in the universal nature of things.” Francis Bacon, The new organon, ed. by Lisa Jardine and Michael Silverthorne (Cambridge: Cambridge University Press, 2000), aphorism LXVI, 53.

262 Descartes, La Recherche de la verité, AT, x:500; CSM, ii:402.

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process of reasoning, such as languages, history, geography and in general any subject

which rests on experience alone” but should rather inquire into “ordinary facts about

which everyone has heard”—and which artisans are thoroughly accustomed to.263 A

closer look at Descartes’s early writings shows the artisan emerging under a more

nuanced and fundamental light. In fact, I claim, the artisan in the Regulæ should not be

seen as an amenable aide but rather as a powerful epistemic model to the production of

rational knowledge. Remarkably enough, some of the most unassuming and mechanical

artisans are converted into archetypal models of rational discipline and orderly thoughts.

However, it is the concept of artisan and artisanal practices that characterizes the

Cartesian method. The artisan as genuine homo faber is transformed in Descartes’s

writings into an idealization, a disembodied epistemic metaphor compelled by order. The

body techniques, the gestural knowledge of practices are completely dropped and

superseded by an abstract rationalization, an âme réglée, which communicates a new

theoretical understanding of the practice of natural philosophy.264 The Cartesian artisan

becomes not so much “invisible” as s/he becomes “ideal.”

The chief characteristic of Cartesian artisans is unquestionably their condition of

being “properly mechanic” individuals.265 Descartes (so far as I know) always used in

263 Descartes, La Recherche de la verité, AT, x:502-03; CSM, ii:403-04. 264 The literature on this topic is rich. See, for instance, Marcel Mauss, “Body techniques,” in

Sociology and psychology: essays, ed. by Ben Brewster (London: Routledge, 1979), 97-135 and Otto Sibum, “Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England,” Studies in History and Philosophy of Science 26 (1995), 73-106.

265 Charles Loyseau, A treatise of orders and plain dignities, ed. and transl. by Howell A. Lloyd (Cambridge: Cambridge University Press, 1994 [1610]), 179-181. Some tradesmen such as “apothecaries, goldsmiths, jewellers, haberdashers, wholesalers, drapers, hosiers, and others like them,” gained some prominence because their crafts involved commerce. The latter artisans, who called themselves “honourable men” and “bourgeois,” were morally superior to other tradesmen whose métiers “consist[ed] rather in physical labour than in commercial activity or in shrewdness of mind.” Mere manual laborers were almost by definition the basest artisans of them all since “there is no worse occupation than to have no

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French, in published and unpublished texts, the word “artisan” rather than “artiste” in

identifying craftsmen. This distinction is clearly not arbitrary and denotes another

epistemic dichotomy between forms of learning and, ultimately, the nature of knowledge

ascertained. Socially and etymologically speaking artisan and artiste meant essentially the

same thing in the sixteenth and seventeenth centuries (both derived from the Latin

artifex).266 To Descartes, however, an “artiste” was and remained someone who dealt

with the Grand Art, or alchemy, one of these “false sciences” for which he knew enough

about “to be liable not to be deceived” by their promises.267 Marin Mersenne believed

that such artistes were in a position to assist natural philosophers, although his confidence

they would eventually do so was low.268 Nonetheless, behind the substantive “artisan”

Descartes recommended we look specifically at the mechanical arts and their

practitioners—not at alchemists and Paracelsians—in order to acquire an orderly soul.

The Cartesian artisan, therefore, was not guided by an “epistemology of the hunt.”

occupation.” To qualify as a honnête homme an artisan had to leave the manual labor almost entirely to others, thus transforming himself into a merchant.

266 See Jean Nicot, Thresor de la langue française (1606) where one can read under artisan: “Artisan, ou Artiste, Artifex, Opifex.” L’Académie française made the distinction we are accustomed to use today only in 1762: “artiste, celui qui travaille dans un art où le génie et la main doivent concourir (un peintre, un architecte sont des artistes); l’artisan est un ouvrier dans un art mécanique, un homme de métier.” Le Grand Robert de la langue française, ed. by Alain Rey, s.v. artisan. For a historical analysis of this significant shift, Larry Shiner, The invention of art: A cultural history (Chicago: The University of Chicago Press, 2001), 99-120. Jean de La Fontaine, for instance, in one of his fables—Le Lion abattu par l’homme—used “artisan” to describe a painter.

267 Descartes, Discours de la méthode, AT, vi:9; CSM, i:115. In the Furetière and Académie française dictionaries, “artiste” is used especially to portray alchemists. In the Middle Ages, it became common to name “artistes” (or sometimes artiens) those who studied the liberal arts—scholars en devenir—and “artifex” those who practiced the mechanical arts. Shiner, The invention of art, 30.

268 “Ce que l’on pourroit desirer d’eux [Peripateticiens] (au cas qu’ils voulussent ayder à establir la vraye Philosophie) consiste seulement à dresser des memoires fidelles des leurs obseruations, & de leurs experiences: ce qu’il ne faut pas esperer iusqu’à ce que les honnestes hommes s’employent à cet art, & iusques à ce que les Artistes & Operateurs ayent quitté l’imagination de la poudre de projection, de la Magnesie des sages, & de la pierre Philosophique.” Mersenne, Qvestions inovyes, ov recreation des sçavans (Paris, 1634; facsimile Stuttgart: F. Frommann, 1972), question xxviii, 126-127.

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Unconstrained by a pure perception of order this “venatic methodology,” as described by

William Eamon, is “a kind of practical intelligence based upon acquired skill, experience,

subtle wit, and quick judgment: in short, cunning.”269 The venatic methodology was

needed, it was believed, to chase the signs and clues, the signatures of substances and

materials, so as to pick the scent and as a result uncover these secrets—the modern

facts—“tucked snugly in under the blanket of scientia.” Cunning, or mêtis as known to

the Greeks, supplanted orderly thoughts.270 In Descartes’s judgment, artistes rather than

artisans possessed and exercised such a mêtis; one could say they were endowed with an

âme déréglée. When Descartes contemplated artisans in the early 1620s he saw

something completely different: no venatio, no conjectural knowledge, no cunning, only

a pure and uncompromising order in their logic of practice.

The “idea of artisan” is of course not original to Descartes. In the Platonic tradition the

Creator of the world and man was symbolized by a craftsman—namely a Demiurge—

imposing order onto Nature from the universal chaos. Socrates, in Plato’s dialogue

Gorgias, asserted the relevance of artisans in enlightening such a tale of creation:

The craftsmen having their eye on their task do not select and apply to it at random what they apply; rather they see to it that their work comes to have a definite form [eidos]. For instance, painters, house builders, shipwrights, and all other craftsmen whomever you wish to choose, place all things in some order and compel one part to suit another and to harmonize with it until the whole thing as they fashion it has order and beautiful organization.

269 William Eamon, Science and the secrets of nature: Books of secrets in medieval and early modern culture (Princeton: Princeton University Press, 1994), 281.

270 Eamon, Science and the secrets of nature, 284. On the concept of mêtis more generally, Marcel Detienne and Jean-Pierre Vernant, Les Ruses de l’intelligence. La mètis des Grecs (Paris: Flammarion, 1974).

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Artisans, trying to reach ideal Forms, systematized the mechanical arts as the Demiurge

did with Nature’s matter. Order was thus inherent neither in the arts nor in Nature: it was

imposed from outside, from an external cause, from a demiourgos. In the Aristotelian

tradition, conversely, Nature herself followed an orderly purpose. Nature’s own innate

craftsmanship turned into the attribute to which artisans were now referred: ars imitatur

naturam. Whereas Aristotle used the artisan as a powerful analogy to illustrate, confirm,

and justify nature’s modus operandi Plato’s Demiurge qua craftsman was a full blown

epistemic representation of nature as a machine, orderly built like any other invention

from the mechanical arts.271

For Descartes Nature could not act as a model leading to the mathesis. The

mathesis was instead at the origins of the “grande mécanique de la nature.”

Rediscovering the mathesis (suppressed “with a kind of pernicious cunning” from the

writings of the Ancients, as artisans customarily do with their own inventions272) is to

uncover how the universe was built and set in motion—the great Cartesian fables of Le

Monde and L’Homme. Art did not imitate nature; art and nature were rather guided by a

more general mathesis. According to Descartes, anyone endowed with this science of

order would not have to bodily struggle with matter and ars. Such a struggle with reality

was indicative of a disorder in knowledge-making practices. Artisans and artistes

labouring, toiling in the workshops, manipulating and transforming matter through sweat,

burns, grease, and heat “practiced knowing … that constituted a bodily engagement with

271 Friedrich Solmsen, “Nature as craftsman in Greek thought,” Journal of the History of Ideas 24 (1963), 473-496 (Plato, Gorgias, 503e, quoted on p. 484). See also Bertrand Gille, Les Mécaniciens grecs. La naissance de la technologie (Paris: Seuil, 1980). On Aristotle and his legacy, Smith, The body of the artisan.

272 Descartes, Regulæ, AT, x:375-377; CSM, i:18-19.

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nature.” To Descartes, it merely gave them the illusion of acquiring a first-hand

understanding of reality. This “artisanal epistemology,” epitomized by the practices of

alchemy, and especially by the writings of Paracelsus, went against the approach of an

orderly soul.273 The Cartesian âme réglée was only concerned with strategies inculcated

by the mathématicité of the mathesis, which was not derived from the gestural knowledge

of artisanal practices but from the inbuilt structured discipline of habitus.

Take another of Descartes’s paradigmatic examples from the Regulæ, weaving.

The choice of this craft is historically charged and once again not taken randomly. In

France, after the devastation caused by the Wars of Religion, the Bourbon economic

restoration instigated by Henry IV was wholly felt within the textile industry. In Beauvais

alone, 700 to 800 looms were continuously in operation, employing roughly half of the

city’s population in the first half the seventeenth century. Dijon was even more important

as a ville drapante, surpassed only by the several new manufactures opening at that time

in the Parisian region.274 Interestingly enough the technological design of the horizontal

loom had not changed significantly since its introduction in the twelfth century. This

technical revolution was significant for at least one medieval philosopher. Five centuries

before Descartes’s birth weaving became one of Hugh of St. Victor’s archetypes of the

mechanical arts, inspired from the trivium and quadrivium of the liberal arts. Hugh

argued in his Didascalicon for a division between ratio (wisdom, order) and

273 Smith, The body of the artisan, esp. chaps 4 and 5 (quote on p. 142). 274 Pierre Goubert, Beauvais et le Beauvaisis de 1600 à 1730: contribution à l’histoire sociale de

la France du XVIIe siècle (Paris: S. E. V. P. E. N, 1960), 281-82, 585. Pierre Deyon, “Variations de la production textile aux XVIe et XVIIe siècles,” Annales: ESC 18 (1963), 921-55. James R. Farr, Hand of honor: Artisans and their world in Dijon, 1550-1650 (Ithaca: Cornell University Press, 1988). Henri Heller, Labour, science and technology in France, 1500-1620 (Cambridge: Cambridge University Press, 1996), chap. 6.

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administratio (actual practices) in the mechanical arts, maintaining that a ratio of

mechanical origins should also be regarded as an integral part of philosophy.275

Descartes, half a millennium later, similarly saw ratio—not just the actual gestes of

administratio—behind the mechanical arts, what we associated with the structured

discipline of habitus.

Weavers on their looms actually did not bodily struggle with the machine and the fabric,

as Descartes may have himself noticed. In fact, such bodily struggles would have resulted

in a poor quality of the manufactured goods since everything about mechanical weaving

was governed by a strict order of procedure and the smooth, continuous and regular

movements of the couple man/woman-machine (mostly women until the fifteenth

century). (Notice here two fundamental concepts of the Regulæ: order [Rule IV] and

regular and uninterrupted motion [Rule VII].) To achieve the best quality of draperies

weavers had to become one with the machine, as if they were just another link in the

great chain (tela) driving the looms. (This body-machine symbiosis was so manifest that

weavers were often called telier in old French and teler in old English.) The body and

hands-on experience of weavers did not by themselves guarantee excellence; one needed

to look instead at the orderly and uninterrupted movements of the body-machine entity

taken as a whole. Weavers in Descartes’s observation and contemplation became an

abstraction of order owing to their symbiosis with a mechanical device. Their orderly

souls thus emanated naturally from the technology of weaving.276 (See figure 2.1.)

275 Roger Baron, Science et sagesse chez Hugues de Saint-Victor (Paris: Lethielleux, 1957), 60-87. 276 Dominique Cardon, La Draperie au Moyen Âge. Essor d’une grande industrie européenne

(Paris: CNRS, 1999), 416-417, 539-563. See also Giorgio Israel, “Des Regulæ à la Géométrie,” Revue d’histoire des sciences 51 (1998), 183-236, where he discusses the role of weaving in Descartes’s thinking.

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Although Descartes skillfully used the artisan as a rhetorical trope there is no

indication he himself ever dabbled with crafts or worked with artisans before his optical

days in Paris in the mid 1620s.277 We know that when he left the Collège La Flèche to

travel around Europe, to find knowledge “in the great book of the world,” he mixed “with

people of diverse temperaments and ranks [diuerses humeurs & conditions],” which no

doubt suggests some acquaintances with artisans and instrument makers.278 In Holland,

particularly, the collective embarrassment of riches and the Baconian style of natural

philosophy caught his eyes.279

There, during his well-known stay with Isaac Beeckman in 1618, he realized that

scientia and ars should not be subordinated to one another; he recognized that both were

needed in concert to reveal the true nature of the world.280As the first “physico-

mathematici” in Europe, Beeckman and Descartes claimed, they tried—in the hydrostatic

277 According to Adrien Baillet, if Descartes had been raised in a condition allowing him to become an artisan, he would have been a skillful one because, we learn, he had in his youth a particular inclination for the arts. Like so many other such claims made by Baillet this one could be utterly wrong, or at best a misinterpretation. Adrien Baillet, La Vie de Monsieur Des-Cartes, 2 vols (Paris, 1691), i:35. Geneviève Rodis-Lewis believes Baillet has his chronology wrong here. This remark should be associated to a much later phase in Descartes’s life. Rodis-Lewis, “Descartes’ life and the development of his philosophy,” in The Cambridge companion to Descartes, 21-57, on p. 26. Descartes himself often contradicts Baillet’s assertion. He said, for instance, that he was born without any manual abilities: “pour moy … i’estois venu au monde sans mains.” Descartes to ***, [Nov.-Dec. 1638?], AT, ii:452.

278 Descartes, Discours de la méthode, AT, vi:9; CSM, i:115. On the role of travel during the early modern period, see the remarkable opus by Daniel Roche, Humeurs vagabondes. De la circulation des hommes et de l’utilité des voyages (Paris: Fayard, 2003).

279 Simon Schama, The embarrassment of riches: An interpretation of Dutch culture in the Golden Age (New York: Vintage, 1997). On Dutch Baconianism, Svetlana Alpers, The art of describing: Dutch art in the seventeenth century (Chicago: The University of Chicago Press, 1983), esp. chap. 1. Smith, The body of the artisan, esp. chaps 5 and 6.

280 This is first thing Beeckman writes down in his Journal: “Quæritur cur artes inter se non sint subordinatæ…” On the importance of both scientia and ars, he also writes down on the first page of the Journal: “Ad excitandum artium studium illud maximè faceret, si immunitates alicujus vectigalis etc. ijs qui Euclidis Elementa intelligerent, promitterentur. Quibus bene intellectis, pauci cætera studia negligerent, etiam in medijs occupationibus mechanicis.” Isaac Beeckman, Journal tenu par Isaac Beeckman de 1604 à 1634, ed. by Cornélis de Waard, 4 vols (The Hague: M. Nijhoff, 1939-1953), i:1 for both quotes.

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manuscript for example—to unify the mathematical study of nature with true ontological,

corpuscular-mechanical, causes. Trained in the candle making and water-conduit laying

trades Beeckman was able to theorize his hands-on knowledge of the mechanical arts in

order to raise to the realm of concepts the operations of artisans and machines. “What

FIGURE 2.1: RATIONAL AND GEOMETRIC WEAVING PATTERNS Ellen Harlizius-Klück, a resident scholar at the Deutsches Museum, is working in 2006 on an early eighteenth-century German book on textile patterns (based on a previous book dated 1677) that demonstrates precisely the orderly fashion (and not the randomness) with which these “threads are interwoven in an infinitely varied pattern,” to quote Descartes again. Her work (and similar analyses done by computer scientists, see: www.handweaving.net) shows that these textile patterns were rationalized in such a way that simple mathematical equations can be derived from the lines and dots printed in the book and destined to guide the weavers’ hands on the mechanical looms. Textile patterns, therefore, were an artisanal form of reason, one that appears to have been noticed by Descartes. The book was by Nathanael Lumscher, Neu eingerichtetes Weber Kunst und Bild Buch… (Bayreuth, 1708). I would like to thank Dr. Harlizius-Klück for sharing her research with me. Beeckman was demanding in natural philosophy was the application of the criteria of

meaningful communication between mechanical artisans—the appeal to a pictorial or

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imaginable structure of parts whose motions are controlled within a putative theory of

mechanics.”281 Beeckman gave the initial impetus to Descartes’s later contention that the

mechanical arts could function as a methodological guideline for the purpose of

discovering the laws of nature.

Before leaving Holland Descartes invented his proportional compass, this simple

instrument that altered how he thought about mathematics.282 In Germany a few months

later, he did more than remain in his “stone-heated room” and dream about a mirabilis

scientiæ fundamenta: he sought the company of mathematicians such as Johannes

Faulhaber and Peter Roth, and most probably conferred with the instrument maker and

mathematical practitioner Benjamin Bramer and Jost Bürgi.283 Late in the 1610s

Descartes adopted a mathematical practice that was by no means strange nor unrewarding

to those searching for the foundation of a new natural philosophy. It has been for the last

twenty years Jim Bennett’s contention that the mechanical philosophy was not solely an

intellectual construction, but something that was founded with the help of “mechanics,”

281 Stephen Gaukroger and John Schuster, “The hydrodynamic paradox and the origins of Cartesian dynamics,” Studies in the History and Philosophy of Science 23 (2002), 535-572, quote on p. 552. For a general appraisal of the Beeckman-Descartes relationship, Gaukroger, Descartes: An intellectual biography (Oxford: Clarendon Press, 1995), chap. 3; Klaas van Berkel, “Descartes’ debt to Beeckman: Inspiration, cooperation, conflict,” in Descartes’ natural philosophy, ed. by Stephen Gaukroger, John Schuster, and John Sutton (London: Routledge, 2000), 46-59. The classic work on Beeckman remains Van Berkel, Isaac Beeckman (1588-1637) en de mechanisering van het wereldbeeld (Amsterdam: Rodopi, 1983), 217-235 for the role of technology in Beeckman’s thinking.

282 Gaukroger, Descartes: An intellectual biography, 92-103. John A. Schuster, Descartes and the scientific revolution, 1618-1634: An interpretation, 2 vols (Ph.D. Dissertation, Princeton University, 1977), i:117-127. Henk J. M. Bos, “On the representation of curves in Descartes’ géométrie,” Archives for the History of Exact Sciences 24 (1981), 295-338. Michel Serfati, “Les compas cartésiens,” Archives de philosophie 56 (1993), 197-230.

283 Baillet, La Vie de M. Des-cartes, i:67-70 on meeting the two mathematicians. On Bramer and his instruments, Descartes, Cogitationes privatæ, AT, x:241-242. The best analysis of Descartes in Germany and the significance of this sojourn is Mehl, Descartes en Allemagne. See also William R. Shea, The magic of numbers and motion: The scientific career of René Descartes (Canton, MA: Science History Publications, U.S.A., 1991), 103-107.

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those whose job focused on applying the mathematical sciences. Bennett demonstrates

how the practical mathematical sciences were transformed, through the use of

instruments, into legitimate natural philosophical knowledge. In describing this contract

between practice and knowledge, Bennett has recently drew on the notion of “virtue” to

encompass both integrity and effectiveness of action. As he explains, “the integrity of the

grounding of an instrument or of a practical technique in geometrical science ensures its

efficiency as well as the certainty of its results.” In this context, both instrument and

operator become grounded in the mathematical sciences. “In a sense,” Bennett continues,

“mathematics is ‘embodied,’ in instrument and operator; it is founded on a science

rendered applicable through virtuous instruments and through codes of practice mastered

by the expert practitioner.” In other words late sixteenth-century mechanics stood for an

epistemic culture that comprised mathematical practitioners, their instruments and the

scientia of geometry. Descartes’s idea of artisans endowed with orderly souls has to some

extent a foundation in this late Renaissance epistemic culture.284

Descartes employed to his advantage the trope of artisans (whether weavers or

blacksmiths) because their ratio appeared universal, reaching the mathématicité of

mathematics. Descartes’s few years spent in Paris in the mid 1620s, however, would

significantly modify this methodological point of view. He soon shifted his portrayal of

artisans; he began to see them as individuals possessing unreliable bodily dispositions, in

serious need of a rigorous rational training in the logic of practice. This change of heart

was due to Descartes’s direct dealings (at long last) with artisans.

284 Bennett, “The mechanics’ philosophy and the mechanical philosophy”; Bennett, “Geometry in context in the sixteenth century: The view from the museum,” Early Science and Medicine 7 (2002), 214-230, quotes on pp. 229-230. On epistemic culture see Karin Knorr-Cetina, Epistemic cultures: How the sciences make knowledge (Cambridge, MA: Harvard University Press, 1999).

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THE DIOPTRIQUE AND THE RATIONALIZATION OF THE MECHANICAL ARTS

Descartes’s most celebrated achievement during his Parisian sojourn in the mid 1620s

was the elaboration of the law of refraction, demonstrating that the anaclastic line was

Kepler’s hyperboloid. How he discovered the sine law has been the subject of several

conjectures over the past two decades.285 For our purpose we need only to emphasize the

fact that Descartes was lucky enough to study with possibly one of the best Parisian

géomètres and optical practitioners of the time, the bourgeois Claude Mydorge. Mersenne

thought approvingly of Mydorge as a mathematician and draughtsman, praising the latter

many times in the second book of his Questiones celeberrimæ in genesim, dedicated to

conic sections and the fabrication of mirrors.286 Optics and mirrors piqued Mydorge’s

curiosity for intellectual reasons as well as for concerns regarding his social status.

Mirrors of all kinds were a rare luxury before 1630, highly regarded and

expensive objects of self-fashioning for the aristocracy in contact with the French court.

285 The best accounts are Stephen Gaukroger, Descartes: An intellectual biography, 135-186; John A. Schuster, “Descartes opticien: The construction of the law of refraction and the manufacture of its physical rationales,” in Descartes’s natural philosophy, 258-312; Shea, The magic of numbers and motion, 149-163. See A. I. Sabra, Theories of light from Descartes to Newton (Cambridge: Cambridge University Press, 1981), 93-135 for Fermat’s criticisms.

286 Drawing accurate parabolic mirrors held no secrets to Mydorge, judging from a letter sent by Robert Cornier to Mersenne, one of the Minim’s early correspondents: “I do not know of any other means of making parabolic mirrors beyond those with which you are acquainted, especially since you have the paper of Mr. Mydorge who knows all that can be known on the matter. I can only tell you that Mr. [Guillaume] Le Vasseur says that he has found an absolutely certain way by the sines. But I cannot say more since I do not yet know how he goes about it.” Cornier to Mersenne, 18 August [1625], in Correspondance du Père Marin Mersenne, religieux minime, ed. by Cornélis de Waard, 17 vols (Paris: G. Beauchesne, 1933-1988), i:260-261. Quoted in Shea, The magic of numbers and motion, 150. This Le Vasseur was an instrument maker from Rouen, well-known in the region for his work in navigation and map making. Cornier to Mersenne, 16 January 1626: “Je vous envoie le billet tel que Le Vasseur me l’a envoyé pour responce à ce que vous me demandiés des longitudes et latitudes.” Correspondance du Père Marin Mersenne, i:332. See also ibid, 242-243. His method to draw parabolic shapes “by the sines” most likely has nothing to do with Descartes’s (and Mydorge’s) later determination of the sine law for the refraction of light. Snel (in the 1620s) and Harriot (ca. 1598) found the same law of refraction, but both were unknown to Descartes.

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It is probably no exaggeration to state that Mydorge spent as much as 100,000 écus

towards the manufacture of countless mirrors and lenses—considering it was not

uncommon to be acquainted with people who had ruined themselves buying richly

decorated mirrors of all dimensions.287 Besides natural philosophy, extravagance of that

kind served well Mydorge’s noblesse de robe’s inclination of social climbing contra blue-

blood landed gentry. In fact he became such a master at polishing mirrors that one of

Mersenne’s early correspondents asked whether the Trésorier de France would agree to

pass on the secret of his art. Although Mydorge was a genuine honnête homme—and thus

not inclined to hide his expertise as an artisan would be—a secret like this was too good

to be shared, not so much for profit as for esteem and honour.288 Whatever Mydorge’s

chief motivation his effort at producing such fancy objects of high Parisian fashion was

central to Descartes’s later formulation and proof of the sine law.289 Alongside Mydorge

was an instrument maker well known in Mersenne’s circle, and who worked with the

287 Sabine Melchior-Bonnet, Histoire du miroir (Paris: Imago, 1994), 31-39. At the end of the century mirrors became objects of common consumption for the noblesse and bourgeoisie alike. On Mydorge’s disbursement, Baillet, La Vie de Monsieur Des-Cartes, ii:326.

288 Cornier to Mersenne, 16 janvier 1626, “Ce que vous me mandés de l’excellence des miroirs de Mr Midorge, me faict souvenir de vous prier de me mander si c’est de sa façon et, si ainsi est, quelle en est la matiere et la dose.” Cornier to Mersenne, 27 janvier 1626: “Je vous remercie de toute mon affection de la peone que vous prenés à m’expliquer les miroirs de Mr Midorge et ses opinions. J’euse bien desiré scavoir son poli, mais puisqu’il se le reserve, il n’en fault point parler. J’en scay quelques uns qui sont bons et dont j’ay veu l’effect qui, je croy, se peut conduire à une grande perfection.” Correspondance du Père Marin Mersenne, i:331 and 354 respectively.

289 On Mydorge’s importance for Descartes as an instrument maker cum natural philosopher, Baillet writes: “Rien au monde ne luy fut plus utile que ces verres pour connoître & pour expliquer, comme il a fait depuis dans sa Dioptrique, la nature de la lumiére, de la vision, & de la réfraction. M. Mydorge luy en fit faire de paraboliques & d’hyperboliques, d’ovales & d’élliptiques. Et comme il avoit la main aussi sûre & aussi délicate que l’esprit subtil, il voulut décrire luy-même les hyperboles & les éllipses. C’est ce qui fut d’un secours merveilleux à M. Descartes non seulement pour mieux comprendre qu’il n’avoit fait jusqu’alors la nature de l’éllipse & de l’hyperbole, leur propriété touchant les réfractions, la maniére dont on doit les décrire; mais encore pour se confirmer dans plusieurs belles découvertes qu’il avoit déja faites auparavant touchant la lumiére, & les moyens de perfectionner la vision.” Baillet, La Vie de Monsieur Des-Cartes, i:149-150.

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premier ingénieur du roy Jacques Aleaume in the early 1620s.290 It was, naturally, Jean

Ferrier, Descartes’s most famous artisan.291

According to Adrian Baillet, Ferrier was adroit and most of all esteemed by

Parisian scholars:

This Ferrier mentioned by M. Descartes, probably introduced to him through Mydorge, was not a simple artisan who only knew how to move his hands. He understood the theory of his occupation and knew optics and mechanics as well as any Collège Royal professor. He was not totally unfamiliar with the rest of mathematics, and in spite of his status he was welcomed in the circles of savants as if he were one of their own.292

Ferrier, Descartes, and Mydorge drew, cut, and hand-polished lenses (hyperbolic

included) as early as 1626. Their endeavour was reported by Mersenne to Robert Cornier,

who replied that Ferrier’s ability as a craftsman would most certainly be tested.293 We

290 When Aleaume passed away late in 1627, Peiresc feared for his manuscripts (some of which written by Viète) and instruments. Peiresc thus suggested on 8 January 1628 that “l’instrument [the compass] que luy avoit faict Ferrier pour descrire la ligne necessaire à la convexité desdictes lunettes et miroirs convexes, et les verres et miroirs qu’il en avoit essayez ... il faudroit que cela passast par les mains de Mr Midorge, tresorier de France ... lequel seul je cognois en ce pais le plus approchant de la curiosité de feu Mr Alleaume et de sa doctrine et prattique aux mathematiques et mechaniques.” Quoted in Mersenne, Correspondance du Père Marin Mersenne, i:617. See also Cornier to Mersenne, 24 décembre [1627]: “Je croy que Mr Midorge ne se sera pas oublié dans la venduë de Mr Alleaume.” Ibid., 613.

291 Ferrier’s first name is sometimes questioned. Maurice Daumas suggests it is Guillaume, establishing his assertion on the nineteenth-century French instrument maker Camille Sébastien Nachet. Yet, Jean-Baptiste Morin in a 1634 publication refers to Ferrier as “D. Ioannes Ferrier, instrumentorum mathematicorum sollertissimus et accuratissimus fabrefactor.” I use the latter information in naming Ferrier. Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles (Paris: Presses Universitaires de France, 1953), 98. Morin is quoted in Correspondance du Père Marin Mersenne, i:516.

292 Baillet, La Vie de Monsieur Des-Cartes, i:151. 293 Cornier to Mersenne, 16 March 1626, in Mersenne, Correspondance du Père Marin Mersenne,

i:420. This part of the letter refers, according to the editors of the Correspondance, to a letter sent by Mydorge to Mersenne regarding the hyperbolic or elliptical shape of the anaclastic line. Mydorge to Mersenne, [Feb.-March, 1626?], in ibid., i:404-415. For a discussion of the dating of this letter, Gaukroger, Descartes: An intellectual biography, 438-439. Regarding Ferrier and parabolic mirrors, Cornier continues: “Il [Ferrier] dict une chose merveilleuse, qu’une si petite partie de parabole brusle avec effect si loing. Car d’ordinaire, pour brusler de loing, estant necessaire d’avoir une portion d’une grande circonference, cela est si plat en petit volume qu’il demeure avec très peu de force.” Correspondance du Père Marin Mersenne, i:420. Descartes will later say that it is impossible for a miroir ardent to burn at a distance of one ligue (lieue) unless the mirror was over twelve meters (“plus de six toises”) across, even if it had been the work of an Angel. Descartes to Mersenne, January 1630, AT, i:109-110. Mersenne discusses this topic in Qvestions inovyes, question xxxv. On the history (legend) of Archimedes great burning mirrors, D. L.

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know from a much later letter to Constantijn Huygens that Descartes, thanks to

Mydorge’s draughtsmanship and Ferrier’s technical skill, shaped around 1627 a

hyperbolic lens that provided proof of the law of refraction.294 Although Mydorge’s

drawing and mathematical proficiency were never doubted by either Mersenne or

Descartes, Ferrier’s skills as a mécanicien were, as Cornier had anticipated, thoroughly

tested and eventually questioned.

Before Descartes landed in Paris, Mersenne had already criticized in Questiones

in genesim the ability of artisans to manufacture good mirrors and lenses.295 Descartes

too became dissatisfied with the artisans’ craftsmanship, which did not meet his early

expectations. Hence he allegedly trained in the art of lens grinding a few Parisian

tourneurs, a know-how he seemed to have mastered according to Baillet.296 Following

the relationships between Descartes, Ferrier and other Dutch and French artisans in

relation to the mechanized production of hyperbolic lenses, one can identify a significant

break regarding the epistemic value previously attributed by Descartes to these same

artisans. In a recent monograph D. Graham Burnett persuasively shows that although the

project of making telescopes may have itself initiated “a new form of cooperation”

between artisans and savants, the mechanization of lens making “can be understood as an

Simms, “Archimedes and the burning mirrors of Syracuse,” Technology and Culture 18 (1977), 1-24. 294 Descartes to Huygens, [December 1635], AT, i:335-337. 295 “Quid ita, nunquid hujuscemodi operibus utilissimis caremus, quia multi, qui has lineas

repererunt, eas aeterno silentio involvunt, ne quando alicui proficiant.” Quoted in Correspondance du Père Marin Mersenne, i:299.

296 “[Descartes] devint luy-même en trés peu de têms un grand maître dans l’art de tailler les verres: & comme l’industrie des Mathématiciens se trouve souvent inutile par la faute des Ouvriers dont l’adresse ne répond pas toûjours à l’esprit des Auteurs qui les font travailler, il s’appliqua particuliérement à former la main de quelques Tourneurs qu’il trouva les plus experts, & les mieux disposez à ce travail. En quoy il eut la satisfaction de voir le succez de ses soins avant que de sortir de la France pour se retirer en Hollande.” Baillet, La Vie de Monsieur Des-Cartes, i:150.

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effort to end this new and interdependent relationship.”297 In Descartes’s mind the

artisan—including Ferrier—changed from an ideal metaphor of order to a down-to-earth

and mundane Jacques Metius, the Dutch optician described at the beginning of the

Dioptrique who stumbled upon the discovery of the telescope through sheer mêtis.

Whether Ferrier’s failure as an instrument maker was due to psychological distress or to

his ambition of

FIGURE 2.2: DESCARTES’S LENS-GRINDING MACHINE An overall view of Descartes’s lens-grinding machine. Several steps were required to cut an hyperbolic lens. The central part of the machine is the essential one, because its special conception enables the iron tools Y67 and Z89 to cut any material in an hyperbolic shape. The purpose of this section of the machine is to shape the big stone wheel that will then grind the glass into an hyperbolic lens. To achieve this, the glass is rotated on itself and is ground by the movement of the wheel. Virtually no artisanal skills are required here, only brute manual labor. Descartes, Dioptrique, AT, vi:218. becoming a honnête homme through a royal nomination at the Galerie du Louvre did not

matter to Descartes in the end. What Descartes ultimately recognized in Ferrier and

297 D. Graham Burnett, Descartes and the hyperbolic quest: Lens making machines and their significance in the seventeenth century (Philadelphia: American Philosophical Society, 2005), 36. On Descartes, Ferrier and artisans see also Shea, The magic of numbers and motion, 151-158, 191-201; Giulia Belgioioso, “Descartes e gli artigiani,” in La Biografia intellettuale di René Descartes attraverso la Correspondance, ed. by Jean-Robert Armogathe, Giulia Belgioioso, and Carlo Vinti (Naples: Vivarium, 1999), 113-165.

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others was the simple fact that artisans in general were in need of a thorough method.298

The invention and manufacture of a mechanized lens-making machine compelled

Descartes to reconsider his conviction that the artisan was an epistemic metaphor

exemplifying a logical and disciplined orderly soul: exit the inherently methodical artisan

that guided his initial notion of mathesis. (See Figure 2.2.) The “rational” artisan no

longer was prevalent in his philosophical argument. He needed a new metaphor, one that

would essentially be more structured and logical—like a machine. Burnett is here more

relevant than ever when he claims that “In Descartes’ view the shortcomings of craftsmen

lay in their being insufficiently mechanical: they were not entirely scrutable in

mechanical terms, and therefore the path to perfected lens making lay in the

mechanization of the craftsman, more automation, and the alienation of the hand of the

artisan.”299

Because it was simply unbearable to think that an invention si vtile & si admirable

as the telescope was solely due to naked cunning and hands-on experience, Descartes’s

Dioptrique, which he began writing in the early 1630s, became the rational response to

298 Descartes is not insensitive to Ferrier’s problems, which he associates to some sort of psychological unrest: “Aprés tout, ie plains fort Mr. Ferrier & voudrois bien pouuoir, sans trop d’incommodité, soulager sa mauuaise fortune; car il la merite meilleure, & je ne connois en luy de deffaut, sinon qu’il ne fait jamais son conte sur le pié des choses présentes, mais seulement de celles qu’il espere ou qui sont passées, & qu’il a vne certaine irresolution qui l’empesche d’executer ce qu’il entreprend. Ie lui ay rebattu presque la mesme chose en toutes les lettres que ie luy ai écrittes; mais vous auez plus de prudence que moy, pour sçauoir ce qu’il faut dire & conseiller.” Descartes to Mersenne, [18 March 1630], AT, i:132. Ferrier’s lack of mechanical skills may have been caused by a too strong inclination towards pure mathematics: “[L]a douceur qu’il [Ferrier] avoit trouvée dans la méditation, & dans les entretiens des Mathématiciens, avoit beaucoup diminué en luy l’habitude du travail [manuel].” Baillet, La Vie de Monsieur Des-Cartes, i:186. In a letter Ferrier sent to Descartes, he mentions indeed how much he wants to “taste” and “comprehend” the “true foundations of science” from scholars such as Descartes “tant i’ay d’ambition de me faire connoistre par quelque chose au delà du commun.” Ferrier to Descartes, 26 October 1629, AT, i:51.

299 Burnett, Descartes and the hyperbolic quest, 36.

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the artisan’s lack of method.300 Although the Dioptrique may look like a manual of

technical instruction aimed at producing telescopes, it should be considered above all as a

work edifying the method.301 The essay, furthermore, was not intended for a hypothetical

überartisan—as Bruce Eastwood argues—but was rather meant for artisans tout court, to

those âmes déréglées populating the mechanical arts.302 The Dioptrique was written in

such a way that it established precisely how the mechanical arts should be carried out; it

showed that building complex machines should no longer be a matter of one’s cunning or

hands-on experience. The Dioptrique was meant to inculcate onto the mechanical arts

Descartes’s new and universal logic—his method.

Back in 1626 Cornier believed Descartes would never find the law of refraction if

he did not reason out first how to make telescopes of all focal lengths.303 Descartes of

course thought (and said) otherwise, and the explanation of refraction is found in the

second discourse of the Dioptrique, right after the nature of light and well before the art

of telescope making. His procedure thus reflected his entire philosophy of the order of

reasons: from the nature of light to the law of refraction, he then proceeded to the

working of the eye, the ability to see in general, how to perfect the latter with artificial

lenses, and finally how to mechanically build telescope (and microscope) lenses free of

300 Descartes to Golius, [January 1632], AT, i:234-235 where Descartes mentions he will send the first part of his Dioptrique that deals with refraction, without the philosophy.

301 Philippe Hamou, La Mutation du visible. Essai sur la portée épistémologique des instruments d’optique au XVIIe siècle, 2 vols (Villeneuve D’Ascq (Nord): Presses Universitaires du Septentrion, 1999), i:239-288.

302 Bruce Stansfield Eastwood, “Descartes on refraction: scientific versus rhetorical method,” Isis 75 (1984), 481-502.

303 “Au surplus je ne croy pas que vostre mathematicien [Descartes], quelqu’habile homme qu’il soit, puisse bien donner des raisons des refractions jusques à ce qu’il ait enseigné de faire des lunetes de Hollande par raison et reglement en telle longueur que l’on vouldra. Car en cela git un des plus grands secrets des refractions à mon advis…” Cornier to Mersenne, 16 March 1626, in Correspondance du Père Marin Mersenne, i:420.

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spherical aberration. The lens-grinding machine—or any other machine for that matter—

was the very last thing an artisan should worry about; without a comprehensive

understanding of the problem at hand, artisans reverted back to a craftsmanship based on

the dreadful mêtis—back in other words to the modus operandi of the Dutch Metius.

What Descartes was trying to accomplish in the Dioptrique had nothing to do with late

Renaissance engineering, whose famous yet mostly artistic theatres of machines depicted

extravagant mechanisms and rarely offered theoretical guidelines on how to make and

study them.304 The Dioptrique—not unlike Salomon de Caus’s Les Raisons des forces

movvantes (Frankfurt, 1615)—was a contrario an effort to bring to the order of discourse

what ought to regulate and organize the artisanal practices. The telescope here became a

powerful emblem of the necessity to carry out a thorough re-examination of the

mechanical arts. The Cartesian telescope should consequently be understood as the by-

product of a methodical mechanical art put to its perfection.

At the apex of the Dioptrique the lens-grinding machine bore the burden of the

proof of the Cartesian method. If no one could make the machine work, no hyperbolic

lens could be produced; with no lenses the truthfulness of the Cartesian optical science

could not be demonstrated; and without the latter demonstration, the whole Cartesian

method was put in jeopardy. No wonder Descartes always held a defensive stance

regarding the fabrication of this machine. Already in 1630 he believed his machine was

conceptually sound and emphasized that building it came down essentially to Ferrier’s

304 It is interesting to note that the theoretical portion of Jacques Besson’s Theatrum instrumentorum machinarum (Orleans, 1569) was never published, yet developed in the manuscript version (British Library) of the work. Alex Keller, “A manuscript version of Jacques Besson’s book of machines, with his unpublished principles of mechanics,” in On the pre-modern technology and science: Studies in honour of Lynn White, Jr., ed. by B. S. Hall and D. C. West (Malibu: Undena Publications, 1976), 75-95.

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skills. In like fashion, towards the end of the Discours de la méthode he wanted his

readers to understand and remember that if “artisans are not immediately able to put into

operation the invention explained in the Dioptrique, I do not think it can on that account

be said to be defective.” A year later he was again on the defensive when he learned from

Mersenne that Girard Desargues was discussing with the Cardinal de Richelieu the

opportunity to exploit on a grand scale the part of Dioptrique pertaining to the

mechanical manufacture of hyperbolic lenses. Flattered by the idea Descartes

nevertheless worried that if the artisans assigned to this task were not under his

immediate supervision they would be unsuccessful and, in consequence, he could be held

responsible for their failing.305 He knew that if artisans did not succeed in making

hyperbolic lenses with the lens-grinding machine, this failure would not be seen as a

mere imperfection of the mechanical design: it would be acknowledged as a collapse of

the Cartesian method.

Although no other instrument in the Cartesian corpus equaled the lens-grinding

machine in authority, mechanical apparatus were never far from Descartes’s mind.306 To

Golius, for example, he described a measuring instrument of his invention to prove

experimentally the authenticity of the law of refraction, giving sufficient details (drawing

included) to build it.307 Descartes also tried over time to improve weight-driven clocks, to

305 Descartes to Ferrier, [2 December 1630], AT, i:185. Descartes, Discours de la méthode, AT, vi:77; CSM, i:150. Descartes to Mersenne, [25 January 1638?], AT, i:500-501; Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles, 99; Baillet, La Vie de Monsieur Des-Cartes, i:320-321.

306 Descartes is fully aware that precise instrument making is of the utmost importance to natural philosophy. Instruments can be used, for instance, to ascertain the number, velocity, and shape of sunspots and to know how the air refracts the light from the stars, and whether it also affects the light from the Moon. Descartes to Mersenne, January 1630, AT, i:113: “Mais ces choses là requierent des instrumens si iustes …”

307 Descartes to Golius, [2 February 1632], AT, i:236-240. “Ie ne doute point que vous ne puissiés

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assess an Archimedean screw invented by a Dutch engineer, and to perfect an apparatus

he saw in Leucheron’s (Van Etten’s) Récréations mathématiques describing a harquebus

shooting a lead ball vertically—which, after many trials, it was said, did not fall back on

earth.308 Even the study of rainbows in the essay Météores rested heavily on the material

culture of rainbow fountain making set in seventeenth-century courtly gardens.309 What

made the lens-grinding machine distinctive came from the fact that Descartes used it to

demonstrate a simple truth: the strict organization of knowledge required to build this

machine demonstrated the Cartesian method. The artisan had been supplanted by another

metaphor, encompassing this time the inbuilt order of levers and gears—the order of

mechanism. Descartes was teaching a new and universal habitus, one based on the

rational and mechanical attributes of the method. The lens-grinding machine became in

this context more than an artisan’s tool: it became an epistemological instrument; better

yet a thing knowledge, namely an object fully embodying the Cartesian mechanization of

trouuer plusieurs autres inuentions meilleures que celle cy pour faire la mesme experience, si vous prenés la peine d’en chercher; mais pource que ie scay que vous aués beaucoup d’autres occupations, i’ay creu que si vous n’y auiés pas encore pensé, ie vous soulagerois peut-estre d’autant ….” (ibid., 240)

308 Arthur H. Schrynemakers, “Descartes and the weight-driven chain-clock,” Isis 60 (1969), 233-236. On the Archimedean screw, Descartes to Huygens, 15 November 1643, AT, iv:761-766. According to Leucheron, the experiment was done many times with the same result. Descartes does not doubt the outcome per se, but still believe it is worth exploring further. Mersenne asked someone to do the experiment with an arquebuze, giving still an identical result as in the Récréations mathématiques. Descartes, however, is not convinced and does not judge it sufficient to draw certain knowledge from it (quelque chose de certain). He therefore suggests to do the experiment again with an instrument of his design, using a cannon always kept in the upright position by a system of pulleys. Descartes to Mersenne, [April 1634], AT, i:287; Descartes to Mersenne, 15 May 1634, AT, i:293-294. The choice of a cannon, which could support a cannonball of 30 to 40 pounds is better because the iron from which it is made does not melt has easily as the lead ball from the harquebus, and moreover such a big ball would be found easier if it came back on earth.

309 Descartes uses these fashionable machines to investigate the phenomenon, as well as to relocate wonder from garden engineers to natural philosophers, thus displacing a “science of miracles” from simple technical achievements to the knowledge of mathematics and mechanical philosophy. Simon Werrett, “Wonders never cease: Descartes’s Météores and the rainbow fountain,” British Journal for the History of Science 34 (2001), 129-147.

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knowledge.310

BODY, MACHINES, AND THE DISCIPLINE OF KNOWLEDGE

In a comment made on the motion of individual particles with regard to the overall

structure of celestial matter, Descartes declares to Burman that although “the entire

system [of the universe] is in a state of equilibrium,”

[it] is a very difficult thing to conceive of, because it is a mathematical and mechanical truth. We are not sufficiently accustomed to thinking of machines, and this has been the source of nearly all error in philosophy.311

By now, and for close to two decades, Descartes had abolished artisans as the epistemic

emblem of order and replaced them with the more visual and tactile mechanical order of

machines. This “mechanical turn” was so compelling that, as Graham Burnett tentatively

illustrates, a closer connection between the mechanically produced hyperbolic lenses of

the Dioptrique and the mind’s eyes’ “metaphysical lens”—or hyperbolic doubt—found in

the Meditations could be entertained without too much of a stretch.312 The machine in the

end did not only supplant the artisan; it ultimately incarnated Cartesian metaphysics and

natural philosophy. The machine became a thing knowledge.

This, I believe, should be taken literally. In the Sidereus nuncius, for instance,

Galileo did not mention the telescope by name, referring instead to “the instrument

[organum] with the benefit of which [great things of nature] make themselves manifest to

310 Davis Baird, Thing knowledge: A philosophy of scientific instruments (Berkeley: University of California Press, 2004). Burnett, Descartes and the hyperbolic quest, 132 for the association of the the lens-grinding machine to an “epistemological instrument.” On the philosophy of instrumentation, Hans Radder, ed., The philosophy of scientific experimentation (Pittsburgh: University of Pittsburgh Press, 2003).

311 Descartes to Burman, AT, v:174. English translation in John Cottingham, ed., Descartes’ conversation with Burman (New York: Oxford University Press, 1976), 44 §73.

312 Burnett, Descartes and the hyperbolic quest, 125-132.

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our sight.”313 It is not unusual here for Galileo to speak of a mechanical instrument as an

organon—a thing that serves a specific purpose—following the traditional Aristotelian

definition of the word. Where Descartes distanced himself from Galileo and other natural

philosophers, however, was in the explicit and epistemic connection he made between an

artificial and a natural organon; between a mechanical instrument and a bodily organ.314

In the Dioptrique the correlation between mechanization and organon was firmly

established. In the essay Descartes compared the same telescope to an “organe exterieur,”

an organon or instrument that could be put over another external organ, namely the

human eye.315 For Descartes it was a simple matter of joining together two mechanical

organs, the telescope and the human eye—the latter, as claimed by Kepler already, being

nothing more than another machine, a camera obscura.316 More mechanization here

meant a sure path towards perfection, in this case the perfection of vision. The telescope,

moreover, was not unlike Descartes’s compasses found in the Géométrie. Both were

mechanical extensions of corporeal organs (eye and hand) that served the purpose of

achieving a kind of knowledge otherwise unattainable—heavenly phenomena and

complex mechanical curves respectively. That knowledge could never be intuited with

any other “natural” organ; it could not be made certain without these special mechanical

313 Galileo Galilei, Sidereus nuncius, in Le opere di Galileo Galilei, ed. by Antonio Favaro, 20 vols (Florence: Tip. di G. Barbèra, 1890-1909), iii:59. For the English translation, Galileo, Sidereus nuncius or The sidereal messenger, transl. by Albert van Helden (Chicago: The University of Chicago Press, 1989), 35.

314 A very good analysis of organon qua instrument is given by Don Bates, “Machina ex Deo: William Harvey and the meaning of instrument,” Journal of the History of Ideas 61 (2000), 577-593. See also Dennis Des Chene, Spirits and clocks: Machine and organism in Descartes (Ithaca: Cornell University Press, 2001), 89-95 for an analysis of Suárez’s notion of instrument.

315 “Si bien qu’il ne nous reste a considerer que les organes exterieurs, entre lesquels ie comprens toutes les parties transparentes de l’œil, aussy bien que tous les autres cors qu’on peut mettre entre luy & l’obiet.” Descartes, Dioptrique, AT, vi:148.

316 Descartes, Dioptrique, AT, vi:114-117.

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prostheses. Instruments, or mechanical organa could therefore be added to bodily senses

in order to achieve clear and distinct knowledge.317 The telescope and compass were in

this context mechanical addenda that could be likened to Ambroise Paré’s famous

artificial hand: once attached to the body, they became whole with it—reminiscent of the

weavers and their looms previously mentioned; they were fully integrated, incorporated,

and acted as if they were an original part of the body, a “natural organon.”318 (See Figure

2.3.)

This multiplication of mechanisms—organa—was not a problem but a virtue in

Cartesian natural philosophy. When Huygens reported to Descartes in September 1637

that an Amsterdam tourneur could build the lens-grinding machine with fewer

contrivances than depicted in the Dioptrique, Descartes was left unconvinced. Although

such an outcome would be received with enthusiasm, he strongly believed his machine

did not need less but more mechanical contrivances, things omitted in the original

description but easy to discover with experience.319 Artisans’ and engineers’ habitus told

317 Matthew Jones argues somewhat similarly when he writes that Descartes’s compasses “offered the crucial heuristic, a material propaedeutic, for Descartes’[s] revised account of mathematics freed from memory and subject to a criterion of graspable unity. A simple mathematical instrument became the model and exemplar of the knowledge of Descartes’s new subject, the one supposedly so removed from the material.” Jones, “Descartes’s geometry as spiritual exercise,” Critical Inquiry 28 (2001), 40-71, quote on p. 61.

318 Ambroise Paré, Les Œuvres de M. Ambroise Paré conseiller, et premier chirurgien du roy (Paris, 1598), Chapter 22, “Des moyens & artifices d’adiouster ce qui defaut naturellement ou par accident.”

319 Huygens to Descartes, 8 September 1637, AT, i:395-396: “Mais comme il [le tourneur d’Amsterdam] est homme industrieux en matiere de mouuemens mechaniques, il presume de venir a bout de vostre inuention a beaucoup moins de façon. En effect, il produit des choses si estranges par des petites machines de deux liards, que si ce n’estoit vous, Monsieur, i’espererois qu’il abregeroit de quelque chose ce que vous auez desseigné pour arriuer a la perfection de ces verres; nous verrons ce qui arriuera, & vous en rendrons compte.” Descartes to Huygens, 5 October 1637, AT, i:433: “Mais puisqu’il vous plaist en sçauoir mon opinion, ie vous diray franchement que tant s’en faut que i’espere qu’il en viene a bout, auec des machines qui ayent moins de façon que la miene, qu’au contraire ie me persuade qu’on y doit encore adiouster diuerses choses, que i’ay omises, mais que ie croy n’estre point si difficiles a inuenter que l’vsage ne les enseigne.”

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them otherwise, however, i.e. fewer moving parts was better as regards applied

mechanics. It was, for example, Salomon de Caus’s chief assumption. He criticized late

FIGURE 2.3: ARTIFICIAL “ORGANS” Above, the telescope as an “organe exterieur,” an instrument attached to the human eye, a natural organon, which was nothing more than a camera obscura. On the right, Paré’s famous artificial hand. Once attached to the human body it acted as “naturally” as could any other extension of the hand, for instance Descartes’s geometrical compas (upper right). Descartes, Dioptrique, AT, vi:202. Paré, Les Œuvres de M. Ambroise Paré, chap. 22. Descartes, Géométrie, AT, vi:391.

Renaissance engineers like Besson and Ramelli for their overly mechanized machines:

they may look good on paper, but in reality would simply not work (or be practical)

because the operational ratio of time over the number of geared wheels had been

extended too much.320 Yet for Descartes, more mechanization meant only one thing: one

320 “[M]ais pour reuenir à ceux qui ont eu cognoissance des Machines mouuantes & Hidrauliques, peu en ont escrit de nostre temps, bien est vray, que Jacob Besson, Augustin Ramelly, & quelques autres

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was approaching Nature’s perfection. The difference between God’s machines and

human-built machines was no longer a difference in degree, but a difference in quantity;

although His machines are composed of more parts, tinier parts and more intricate parts,

the act of creation itself—and our mechanical understanding of creation—is identical to

both our and God’s machines. Only the incommensurable number of parts in God’s

machines keeps the power of the summum Artifex beyond our reach and

comprehension.321

The human body understood as a system of mechanical organa circles back to the

notion of habitus. Habitus can be translated in both French and English as disposition,

and inasmuch as reason was Descartes’s sole universal instrument, the human body as a

machine was composed and ordered according to the particular disposition des organes,

each organon properly positioned in the body and responsible for a specific task or

action.322 This instrumental conception of the human body arose in the early 1630s in

Descartes’s L’Homme, at the same time he began to repudiate the artisan as his

knowledge-making epistemic metaphor. In this treatise on man Descartes supposed our

material incarnation to be nothing else than a statue or machine—and it was how

ont mis en lumiere quelques Machines par eux inventees sur le papier, mais peu d’icelles peuuent auoir aucun effect, & ont creu, que par vne multiplication de roües dentelees, lesdites machines auroient effect, selon leur pensee, & n’ont pas consideré, que ladite multiplication est liee auec le temps, comme il sera monstré en son lieu ....” Salomon de Caus, Les Raisons des forces movvantes Auec diuerses Machines tant vtilles que plaisantes Aus quelles sont adioints plusieurs deβeings de grotes et fontaines (Frankfurt, 1615), n.p., Epistre au Lecteur. De Caus gives an example (Theoresme XVI) of a machine to raise weights made of six geared wheels of increasing size. Although, theoretically, multiplying the number of wheels can expand infinitely the load a machine can lift, in this theorem de Caus calculates that a worker would have to turn the crank 2,985,984 times to cause the sixth and biggest wheel to make a single revolution. Assuming this worker could turn the crank 10,000 times a day, it would still take 298 days for the sixth wheel to complete one revolution!

321 Des Chene, Spirits and clocks, 101-102. 322 Descartes, Discours de la méthode, AT, vi:57; CSM, i:140. See also Descartes, Règles utiles et

claires pour la direction de l’esprit, 89-91.

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Descartes meant it to be depicted.323 It was designed by God in such a way that “inside it

all the parts required to make it walk, eat, breathe, and indeed to imitate all those of our

functions which can be imagined to proceed from matter and to depend solely on the

disposition of our organs.”324 The world on which this machine lived, Descartes’s

Monde, written around the same time, was no different. All the particles were sorted out

and reorganized from the original chaos into a perfectly pre-disposed order. And the

motion of these particles, while given a rectilinear mouvemens by God, was repeatedly

curved or irregular owing to “the various dispositions of matter.”325 The disposition of

matter and organs in the world and in the human body respectively displayed the

importance of organization (from organon) in Descartes’s natural philosophy. In other

words, Descartes was organ-izing all of knowledge, scientia; he was imposing order on

the universe.

Although automata (and particularly clocks) epitomized in early modern Europe

the supreme qualities of regularity, order, and harmony, Descartes’s original impetus to

mechanize the body in imitation of his well-ordered method may not have naturally

occurred from the contemplation of automated figures in the grottoes of the Royal

gardens at Saint-Germain-en-Laye, as is usually assumed.326 One, I believe, has to look

323 On the representation of bodily parts in Descartes’s first two posthumous editions of the treatise on man, Rebecca M. Wilkin, “Figuring the dead Descartes: Claude Clerselier’s Homme de René Descartes (1664),” Representations 83 (2003), 38-66.

324 Descartes, L’Homme, AT, xi:120; CSM, i:99. 325 Descartes, Le Monde, AT, xi:34-35, 46-47; CSM, i:97 for the quote. 326 Gaukroger, Descartes: An intellectual biography, 63-64. Werrett, “Wonders never cease.” On

clocks see Otto Mayr, Authority, liberty & automatic machinery in early modern Europe (Baltimore: Johns Hopkins University Press, 1986) and Gerhard Dohrn-van Rossum, The history of the hour: Clocks and modern temporal orders, transl. by Thomas Dunlap (Chicago: The University of Chicago Press, 1996), esp. chap. 8.

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for a much broader picture, specifically the rise of French absolutism. In France, scholars

such as Jean Bodin and Charles Loyseau wrote influential treatises emphasizing the

socio-political and cultural advantages of a disciplined and well-organized state during

and after the devastating Wars of Religion. “In all things there must be order, for the sake

of decorum and for their control,” reasoned Loyseau in the very first sentence of his

treatise.327 The clergy and royal authorities strove from the late sixteenth century onward

to impose a sense of order over a chaotic popular culture by attempting to control the

mind and body of the menu peuple. Drawing on Michel Foucault’s “political technology

of the body,” Robert Muchembled describes how the state began a repression of the body

centring on sexual conducts, the social mastery of one’s own body—how to become a

honnête homme—and the penal system. Such disciplining of the body and personal

behaviour became an essential element of the early modern “civilizing process” described

in Norbert Elias’s celebrated work. The clergy, in a similar fashion, came down hard on

witchcraft, popular fêtes, and such credulous mentality as an effective way to shape and

thus control the mind of simple people. Religious morality and complete obedience to a

father figure—family patriarch, king, God—became effective means of enforcing a

measure of civil order. Mind and body were no longer the private property of beings in

ancien régime France. Individuals became social bodies, inseparable from the royal and

religious authorities of the kingdom.328

327 Loyseau, A treatise of orders and plain dignities, 5. 328 Robert Muchembled, Culture populaire et culture des élites dans la France moderne (XVe-

XVIIIe siècle), 2nd edn. (Paris: Flammarion, 1991), 225-285. Michel Foucault, Surveiller et punir. Naissance de la prison (Paris: Gallimard, 1975), esp. 159-227. Norbert Elias, The civilizing process: Sociogenetic and psychogenetic investigations, rev. edn. (Oxford and Malden, Mass.: Blackwell Publishers, 2000). An interesting criticism of Elias’s thesis is found in Hans Peter Duerr, Nudité et pudeur: le mythe du processus de civilisation, transl. by Véronique Bodin and Jacqueline Pincemin (Paris: Maison des sciences de

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In the microcosm of artisanal life a similar fashioning of body and mind took

place. One of Henry IV’s conseillers, Barthélemy Laffemas, maintained in the early

seventeenth century that order actually reigned in the French manufactures before the

disintegration of the state’s royal authority caused by the religious wars. To improve

commerce the king needed to restore “to their past perfection” the drapery and dye

manufactures.329 A discipline of labour was seen as essential to the success of any

artisanal practice. Hence the key for master guildsmen was control over skill, both its

meaning and its possession: skill had to be made synonymous with discipline and

subordination. Training apprentices was not the only task of a master: the transmission of

trade values was as important. Artisanal habitus was as much a result of hands-on

training as it was indoctrination to the specific attitude of a community. To become a

master an apprentice had to show his/her mind and body were appropriately moulded.

Skill, as James Farr insightfully notes, “was as much a cultural construct articulating

boundaries of a community defined by status and a sense of difference as an indicator of

l’homme, 1998). Such a radical rationalization of the state and social life can only be understood in light of the disorders created by the Wars of Religion. See, for instance, Denis Crouzet, Les Guerriers de Dieu: la violence au temps des troubles de religion, vers 1525-vers 1610, 2 vols (Seyssel: Champ Vallon, 1990), ii:624 and Mack P. Holt, The French wars of religion, 1562-1629 (Cambridge: Cambridge University Press, 1995), 210-216. One of the most interesting sociological studies on this topic is Pierre Bourdieu, Méditations pascaliennes, rev. edn. (Paris: Editions du Seuil, 2003), 185-234: “Les injonctions sociales les plus sérieuses s’adressent non à l’intellect mais au corps.” (p. 204)

329 Laffemas, Reiglement genéral pour dresser les manufactures en ce royaulme (1603), where he wrote: “Le defaut de nos polices a perverti l’ordre qui s’observoit, tant a la fabrique des manufactures qu’à l’effet de tout ce qui en dépend ….” Hence the king had to reestablish the “manufactures de draperie et de teintures en leur légalité, bonté et perfection anciennes.” Quoted in Emile Levasseur, Histoire des classes ouvrières et de l’industrie en France avant 1789, 2 vols (Paris: A. Rousseau, 1900-1901), ii:155. Contemporary to Laffemas, Antoine de Monchrestien comes to an identical conclusion in 1615 when he says that “Le plus Royal exercice que peuvent prendre Vos Majestés c’est de ramener à l’ordre ce qui est détraqué. De régler et distinguer les Arts tombez en une monstrueuse confusion.” Monchrestien, Traicté de l’œconomie politique, ed. by François Billacois (Geneva: Droz, 1999), 66.

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the economic capacity of a worker.”330 Discipline and subordination of skills, both for the

body and the mind, facilitated the establishment of order within guild society. This is why

the so-called “masters by letters,” individuals nominated by royal instances without

producing a masterpiece—like the Galerie du Louvre’s artisans—were scorned by master

guildsmen. Their displeasure was not so much built around the fact that masters of

letters’ skills were often questionable, but rather that their socially-constructed authority

as legitimate masters was undermined. The challenging and expensive process of creating

a chef-d’œuvre was actually about value and skill subordination of future trade masters

rather than skill credentials per se.331

An orderly soul structured around the Cartesian method required above all an

organized body, one that acted as a material instrument, a suitable organon. Through

methodical order, Descartes sought to incorporate a new (absolute) way of knowing into

early modern bodies. His organon—his method or knowledge-producing instrument—

generated a logic of practice in both natural philosophy and the mechanical arts, ordering

mental and manual skills of philosophers and artisans towards the act of creating ideas

and machines. I have argued that the method as exhibited in the Dioptrique was the key

in bringing forth a rational foundation for the mechanical arts, and therefore in building

exact instruments and machines. Owing to the method, instruments (or “bodily” parts)

could be designed and built in such a way as to enhance natural abilities, skills, and

habitus of living organs; instruments, organa, were mechanically upgrading the human

330 James R. Farr, “Cultural analysis and early modern artisans,” in The artisan and the European town, 1500-1900, ed. by Geoffrey Crossick (Aldershot: Scolar Press, 1997), 56-74, quote on p. 67.

331 For “masters of letters,” Loyseau, A treatise of orders and plain dignities, 226. For how “unfair” was the production of masterpieces, Levasseur, Histoire des classes ouvrières et de l’industrie en France avant 1789, ii:141.

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body to a higher degree of perfection.332 The method had a foot in both the realm of

rational philosophy and in the machine world. It was neither pure thought nor vile

méchanique alone: it was both at the same time.

Descartes desired to reorganize thinking and hands-on practices, and consequently

to oversee how natural philosophers created ideas and artisans manipulated matter. He

wanted to ensure, more exactly to control the acquisition of knowledge. Yet the method

was not only beneficial to natural philosophy. Matthew Jones has convincingly shown

that Descartes’s Géométrie—the essay that best epitomizes the Cartesian method—was a

sophisticated system of “spiritual exercises” aimed at cultivating one’s self, at finding a

better—and orderly—way of life through the practice of higher mathematics (to examine

oneself geometrically Mersenne would say).333 As a universal generator of orderly souls

the method thus suggested one fundamental socio-cultural outcome: based on the

inherent bon sens of mankind, Descartes’s method became a constraining yet

multifaceted pedagogical instrument, a pedagogical tool or organon that could shape any

individual into a honnête homme.334 According to Peter Dear, Descartes used the notion

of mechanization to establish the criteria of intelligibility in natural philosophy and from

the latter, to observe how it constrained bodily behaviours. Domineering one’s own

passions came down to exerting control over one’s own body. Descartes wanted in short

332 Neil M. Ribe pointedly argues that nature in the end “is not a source of standards but is itself subject to the higher standard of Cartesian rationality.” Ribe, “Cartesian optics and the mastery of nature,” Isis 88 (1997), 42-61, quote on p. 53.

333 Matthew L. Jones, “Descartes’s geometry as spiritual exercise.” Mersenne, Qvestions inovyes, question xii, 45-46.

334 Descartes’s universal bon sens is the very first assertion he makes in the Discours de la méthode. On Descartes’s philosophy of education in general, Daniel Garber, “Descartes, or the cultivation of the intellect,” in Descartes embodied, 277-295.

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to understand in mechanical terms the movement involved in the civilizing process of

absolutism.335 In this context, the man-machine concept was an attempt to embody the

Cartesian method into the emergent early modern social body.

Consonant with Francis Bacon’s novum organum, Descartes’s organon can

ultimately be understood as an instrument that “more or less equalises intellects, and

leaves little opportunity for superiority, since it achieves everything by most certain rules

and forms of proof.”336 By fully ordering and constraining knowledge-making processes

(both body and mind) anyone, embracing the right method, could become a lord and

master of Nature—in other words a honnête homme. Descartes, reaching to a wide-

ranging audience, made sure no one would be left out of his natural philosophical

civilizing process.337 In the end, Descartes’s most famous opus was, among many other

things, a universal book of civilité.

335 Peter Dear, “A mechanical microcosm: bodily passions, good manners, and Cartesian mechanism,” in Science incarnate: Historical embodiments of natural knowledge, ed. by Christopher Lawrence and Steven Shapin (Chicago: The University of Chicago Press, 1998), 51-82.

336 Bacon, The new organon, aphorism CXXII, 95. 337 On Descartes’s audience generally, Jean-Pierre Cavaillé, “Descartes stratège de la destination,”

XVIIe siècle 177 (1992), 551-559; Cavaillé, “‘Le plus éloquent philosophe des derniers temps’: les stratégies d’auteur de René Descartes,” Annales: histoire, sciences sociales (1994), 349-367.

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CHAPTER THREE

CLOCKMAKING: PASCAL’S MACHINES, ARITHMETIC,

AND THE EPISTEMOLOGY OF COUTUME

HERE IS A FAMOUS REFERENCE TO PASCAL’S ARITHMETICAL MACHINE in the

beginning of the Entretien avec M. de Sacy, which almost suggest its inventor

was in possession of some kind of magical powers:

T It was common knowledge that [Pascal] seemed able to animate copper, and to give to brass the power of thought. Little unthinking wheels, each rimmed with then ten digits, were so arranged by him that they could give accounts [rendre raison] even to the most reasonable persons, and he could in a sense make dumb machines speak.

Pascal worked so hard on this machine, it is said, that his mind was disturbed (avoir la

tête démontée) for the next three years.338 According to Pascal’s sister Gilberte, the

young savant’s exhaustion did not come from the labor he put into designing the

machine, but rather in trying to make the Rouen artisans understand what it was all

about.339 This tension between the rational mind of Pascal and the craftsmanship of

artisans is at the center of this chapter.

Pascal’s arithmetical machine, or roue Paschaline—or simply pascaline as it was

also referred to—was an early modern technical exploit that received considerable

338 Pascal, Entretien avec M. de Sacy sur Epictète et Montaigne, in Pascal, Oeuvres complètes, ed. by Jean Mesnard, 4 vols. (Paris: Desclée de Brouwer, 1964-1992), iii:124-157. [Hereafter cited as Pascal, OC, iii:124-157.] English quote from Jean Khalfa, “Pascal’s theory of knowledge,” in The Cambridge companion to Pascal, ed. by Nicholas Hammond (Cambridge: Cambridge University Press, 2003), 122-143, on p. 123.

339 Gilberte Périer, La Vie de Monsieur Pascal, seconde version, in Pascal, OC, 1:608.

Clockmaking: Pascal’s Machines, Arithmetic, and the Epistemology of Coutume

attention within the circle of French savants and gentlemen. Though most of the attention

was positive, some was unfavorable, such as the October 1648 letter from Balthasar

Gerbier to Samuel Hartlib. An English gentleman traveller, Gerbier came upon Pascal’s

“Bocks” not long after a model in wood was finished, and thought it resembled

something invented in England twenty-four years earlier. (Gerbier most likely meant

William Pratt’s 1617 arithmeticall jewel, discussed below.) Gerbier found many

problems with the pascaline. First, its user had to be knowledgeable in arithmetic, which

ran contrary to Pascal’s rhetorical stance. Multiplications and divisions were complicated

and it even took two pascalines to make a simple rule of three. It was heavy, difficult to

move, expensive (50 pistoles, or 500 livres) and useless to anyone who would like to

learn the art of arithmetic. In other words, Gerbier did not admire this mechanical

contraption supposed to “think” by itself. He ended his letter to Hartlib quoting the

former ruler of the Low Countries: “Infine a Rare Invention farre saught, and deare

baught: putt them jn the Storre house was the old Prince of Orange wont to saye and lett

us proceede on the ordinary readdy way.”340

340 Sir Balthasar Gerbier to Samuel Hartlib, 4 October 1648, Hartlib Correspondence (CD-ROM), 10/2/13A: “Heare is to be seene a rare worke Inuented by Mr Pascall Sonne to a President Off this Parlement: It is a casse with Sundry wheeles att least thirty, it serue for Arithmetike: and heere you shall haue a drauft of jt jn lue of which I should bee glad to see a drauft of a little deuise whih was jnuented jn England somme 24 yeares past beeing a little board with copper things to turne with a stick to cast accounts. This us the Instrument her att Paris [drawing] The Bocks is of Ebonne, two foot In length; 9 Inches broad; accordingly jn height: The wheeles are of Copper: and seeme as so many Dialls or watches, sett with numbers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. The two rowes aboue are copper round things, wheron appeare little white papers sett with Cifers; when the hand sturres with a Stick the wheeles belowe, those little round things aboue turne according the wheele beloowe moues, by 100/m/1., lesse, or more the Calculation desired js made suddainly: The Bocks within [deletion] thirty weeles which moue according the hand turnes the uppermost wheeles … Butt a man must first be exact jn Arithmetike before he can make use of this Instrument, which cost 50 pistols and no rulle of three can be made butt by two of these Instruments, which are not portatiue, and Infine a Rare Invention farre saught, and deare baught: putt them jn the Storre house was the old Prince of Orange wont to saye and lett us proceede on the ordinary readdy way.” See also Courrier du CIBP, 19 (1997), quoted and partly translated in French by Jacques Attali, Blaise Pascal ou le génie français (Paris: Fayard, 2000), 88-89.

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As we will see later, Gerbier was not the only one to believe the pascaline’s

rightful place was in a cabinet of curiosities, not in the hands of mathematical

practitioners, financiers, and various other number-minded dilettantes and professionals.

It is also interesting to note that less than a century after its invention, in Germany at

least, the pascaline was virtually dismissed as a significant contribution to the domain of

calculating machines. While in France the arithmetical machine found a niche in Jean-

Gaffin Gallon’s Machines et inventions approuvées par l’Académie royale des sciences

and later in the Encyclopédie, Jacob Leupold omitted Pascal’s arithmetical machine in his

Theatrum arithmetico-geometricum, though he mentioned inventions by Caspar Schott,

Grillet, Johannis Poleni, Leibniz and himself.341

This chapter aims at (re)contextualizing Pascal’s arithmetical machine into the

intellectual, artisanal, and socio-cultural milieux of its time. Though the pascaline is well

known to historians of science and technology alike, few have attempted to situate it

within the overall context of seventeenth-century France.342 What did Pascal try to

achieve with his machine? What were the problems he faced with the clockmakers and

their specific artisanal culture? To whom was the pascaline intended for? Why did it

seem so strange and incongruous to early modern honnêtes hommes?

341 Jacob Leupold, Theatrum arithmetico-geometricum, das ist: Schau-Platz der Rechen- und Mess-Kunst, darinnen enthalten dieser beyden Wissenschaften nöthige Grund-Regeln und Handgriffe so wohl, als auch die unterschiedene Instrumente und Machinen, welche theils in der Ausübung auf den Papier theils auch im Felde besonderen Vortheil geben können, in sonderheit wird hierinnen erklaärt (Leipzig, 1727 [Hannover: Th. Schäfer, 1982]). On Schott’s, Leupold’s and Grillet’s arithmetical machine based on Napier’s bones, see chap. 8, pp. 20-26; on mechanical arithmetical machines by Poleni, Leupold and Leibniz, see chaps. 9, 10, and 11, pp. 27-40.

342 Matthew Jones is currently working on a book on these types of machine, especially by Samuel Morland, Pascal, and Leibniz, entitled The matter of calculation: Early modern calculating machines, statecraft and thinking about thinking (forthcoming), chap. 1 for Morland and Pascal; chap. 2 for Leibniz. I would like to thank the author for sharing his manuscript with me.

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Before answering these questions, it was important to first situate the arithmetical

machine within the context of early modern methods of calculation. Hence the first

section deals with the technology of calculation, or the vast assortment of mathematical

instruments that facilitated calculations. Although instruments for mathematical purposes

go back to Antiquity, and were highly developped in the Islamic world (mostly

astrolabes, quadrants and sundials) and later in the Renaissance West, I focus my analysis

on two early-seventeenth-century inventions by John Napier: rabdology and logarithms.

The reason is quite simple: both techniques aimed at transforming multiplications and

divisions into additions and subtractions—Pascal’s primary rationale behind his

arithmetical machine. This first section gives a survey of the mathematical instruments

invented to comply with and facilitate these two new mathematical practices, which were

extremely successful and widespread by the time Pascal began working on the

pascaline.343 The fact that Pascal completely disregarded these two mathematical

practices and tried essentially to remain faithful to the traditional art of arithmetic is

evidence of Pascal’s intended audience for his invention: the French gentlemen and

aristocrats.

Sections 2 through 6 of this chapter address this particular point of the pascaline’s

targeted audience. Early modern English gentlemen and French honnêtes hommes were

two different sorts of users. In England, mathematical practices and instruments were

343 An overall survey of the use and significance of mathematical instruments in Western Europe was obviously impossible to accomplish here. A number of good books and articles deal with the topic. One thing, however, which is often forgotten in the latter is the tremendous importance of the Islamic tradition. I have become convinced that the study of the role and use of mathematical instruments in Renaissance Europe simply cannot be complete without a hard look at the knowledge and savoir-faire of Arabic mathematical practitioners. The best entry points on that subject are David A. King, In synchrony with the heavens: Studies in astronomical timekeeping and instrumentation in medieval Islamic civilization, 2 vols (Leiden: Brill, 2004-2005) and François Charette, Mathematical instrumentation in fourteenth-century Egypt and Syria: The illustrated treatise of Najm al-Din al-Misri (Leiden: Brill, 2003).

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more respectable to a gentleman than they were to a French honnête homme. Though

instruments were made, delivered and found in Parisian hôtels particuliers and in

princely collections (the famous and royal Galerie du Louvre hosted several

mathematical instrument makers) they did not particularly interest the upper echelons of

French society as they did in England. Pascal, of course, was well aware of this situation.

He thus adapted his invention to the taste of his intended French audience, creating a

rhetoric for the machine around polite conversation rather than detailed written

descriptions like those in contemporary fabrica et usus books produced by mathematical

practitioners. Even though Pascal invented the machine to alleviate his father’s headaches

as a royal tax collector, financiers and merchants, who tallied large amount of numbers,

were not especially in Pascal’s mind. The pascaline was more than a mechanical

contraption useful for business: used properly, it could bestow honnêteté.

The machine, however, required more than conceptualization: it had to be

produced in materiam. These same sections discuss, besides Pascal’s two principal

contributions on the subject, the socio-cultural origins of the pascaline—namely the

clockmaking industry so vital to its manufacturing. These sections show that the

production of Pascal’s machine and the granting of the privilege were directly linked to

the early modern French clockmaking industry. But the study of the pascaline also

conveys the profound impression it left on anyone carefully studying Pascal’s rhetoric.

Though savants figured at the top of Pascal’s knowledge-production hierarchy, artisans

had an essential role to play, one too often disregarded by Pascal’s contemporaries. Just

as in the case of the organ and the lens-grinding machine, I argue that Pascal’s

arithmetical machine, too, symbolized the close alliance between theoretical, practical,

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and artisanal knowledge. The arithmetical machine married theory and practice, a claim

emphasized by Pascal and essential to his theory of knowledge.

The last section deals with memory and the epistemology of the Pascalian concept

of coutume. Mathematical instruments, such as Napier’s bones or the later slide rules,

materialized abstract mathematical concepts (Pythagorean tables of multiplication and

logarithms respectively). To use these mathematical instruments, however, meant one

had to learn (though not necessarily understand) specific mathematical practices. Pascal’s

arithmetical machine went one step further: it embedded both the abstract theory and

practices of arithmetic into its geared mechanism. It was no longer necessary to

remember (memorize) how to carry out an addition or a division with the plume and

jetons. Owing to the pascaline’s design, one had only to perform with a stylus specific

and repetitive gestes on the small reckoning wheels of the machine. In the promising

seventeenth-century mechanical culture, memory was no longer strictly a concept of the

mind, the result of an intricate social structure or contained by vast and rich natural

landscapes.344 Memory, perhaps for the first time, stepped into the realm of materiality; it

became incarnated into the geared-regularity of early modern machines—which explains

why so many historians of technology push back the development of computers to

Pascal’s arithmetical machine.345 In the specific case of the pascaline, earlier mnemonic

arts (ars memoriæ) was being replaced by bodily knowledge (ars corporalis): the practice

of arithmetic was being moved from the mind to the body. Pascal, said otherwise,

344 Maurice Halbwachs, Les Cadres sociaux de la mémoire (Paris: La Haye, Mouton Editeur, 1975 [1925]). Simon Schama, Landscape and memory (New York: Vintage Books, 1996). See also the essential Paul Ricoeur, La Mémoire, l’histoire, l’oubli (Paris: Editions du Seuil, 2000).

345 See, for example, Vernon Pratt, Thinking machines: The evolution of artificial intelligence (Oxford: Basil Blackwell, 1987) and Jean Marguin, Histoire des instruments et machines à calculer. Trois siècles de mécanique pensante, 1642-1942 (Paris: Hermann, 1994).

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transformed arithmetical knowledge from a scientia to a mundane coutume. Whereas

René Descartes tried hard to get rid of the artisan’s habitus in designing his lens-grinding

machine, as demonstrated in Chapter two, Pascal, conversely, believed that bodily

coutumes could become an authoritative source of knowledge, less prone than the mind to

commit errors. Cartesian rationalism was not the best source of knowledge—Pascal

famously declared Descartes inutile et incertain.346 Only the combination of mind

(rationalism), body (coutume) and machine (pascaline) promised the greatest rewards in

domain of natural philosophy. That, in short, was the epistemic lesson of the arithmetical

machine.

This chapter is a first attempt at recreating the socio-cultural and intellectual

context of Pascal’s arithmetical machine. Like the preceding chapters on Mersenne’s

organ and Descartes’s lens-grinding machine, this chapter demonstrates how multifaceted

natural philosophy was in France in the seventeenth century. It involved not only

Cartesian rationalism, but various aspects of scientific practices and craftsmanship.

‘ARITHMETIQVE MADE EASIE’: CALCULATION TECHNIQUES AND THE PRINT CULTURE

Pascal’s Avis nécessaire, written for those desiring to see and learn how to use the

arithmetical machine, begins with what must have sounded very promising to an early

modern gentleman dabbling with numbers: the machine, it says, could perform without

any effort whatsoever all the arithmetical operations that had so often worn out one’s

346 Pascal, Pensées, ed. by Gérard Ferreyrolles (Paris: Le Livre de Poche, 2000), S445. Pascal also wrote on Descartes: “Il faut dire en gros: ‘Cela se fait par figure et mouvement,’ car cela est vrai. Mais de dire quelles et composer la machine, cela est ridicule, car cela est inutile et incertain et pénible. Et quand cela serait vrai, nous n’estimons pas que toute la philosophie vaille une heure de peine.” Ibid., S118

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mind (qui t’a souventefois fatigué l’esprit) by means of the plume and the jetons.347 The

conventional and most widely employed method to add, substract, multiply and divide

numbers used the pen (plume) to inscribe numbers on paper and a calculating table (not

unlike the old Chinese abacus) on which tokens (jetons) were used as a memory device to

help with the four basic arithmetical operations. Of the latter operations, multiplication

and division were the ones posing the biggest challenge to would-be mathematicians.

The plume and jetons illustrated the fact that multiplications (and divisions) could

be converted into series of simple additions (and subtractions). In the example of figure

3.1 (image on the right), 763 is multiplied by 46. With the help of jetons, you proceed in

four steps. First you put 763 on the left of what was called the “tree.” Each of those jetons

now represent the number 46, or a multiple of 46 (the jetons in between lines are valued

5, 50, 500, etc.); the jetons on the right are employed to add numbers in successive order.

On the first line on the left side, since we have three jetons, you begin by adding 46 + 46

+ 46 with the jetons on the right hand side of the tree. After completing this second step,

you move one line up on the left hand side. You then repeat the addition of 46s, but at the

same line-level as the jetons on the left, i.e. you move one line higher on the right side of

the tree and just add six times the number 46—which is actually 460. In other words,

rather than beginning your additions on the line labelled “i” you play this time on the line

labelled “C.” Moving one line up is equivalent to saying you are multiplying by 10 what

you are doing. Fourth and last step, and for similar reasons—multiplying by 100 this

time—you move still one line higher than the last operations on the right side of the tree

to finish the multiplication (7 times 46). In more familiar fashion, this is what you do:

347 Pascal, Avis nécessaire, OC, ii:334.

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Clockmaking: Pascal’s Machines, Arithmetic, and the Epistemology of Coutume

46 46 46 The addition so far as seen from the right side

of the engraving after the second step. 138 46x 46x The “x” symbolizes the factor 10, which

is felt by moving one line up on the right side of the tree.

46x 46x 46x 46x 2898 46xx

The addition so far as seen from the right side of the engraving after the third step.

46xx The “xx” symbolizes the factor 100, which is felt by moving two lines up on the right side of the tree.

46xx 46xx 46xx 46xx 46xx

The final result after the fourth and final step of the multiplication. It is the jetons representation you find on the right side of the tree.

35098

This method is and was much longer than performing a real multiplication, but it

had the advantage of avoiding the dreaded Pythagorean or multiplication tables—though

they were found in printed books and thus did not need to be learned by rote. Once one

learned how to perform such a task, it became a somewhat repetitive manipulation, one

that required time, care and attention but no special kind of erudition or memorization—

again, if need be, addition and subtraction tables were found in printed books.348

348 Here is how Jean Trenchant explained this particular multiplication: “Multiplier. Povr multiplier vne somme, comme 763 par 46. Premierement ie pose la somme à multiplier derriere l’arbre, comme vous voyez: puis commençant en bas, ie leue vn get, pour lequel ie pose 46 à main droicte: & ainsi ie continue de leuer tous les gets de bas contremont, l’vn apres l’autre, & tousiours pour chasque get que ie leue de derriere ie pose 46 à dextre & à vis dont ie l’ay leué, c’est à dire, si ie leue vn cent, ie pose 46 ce[n]s sçauoir est 4 sur la ligne des milliers, vn en l’espace au dessous, & vn sur la ligne des cens, ce sont 46 cens, & ainsi des autres. Ceste multiplication monte 35098.” Jean Trenchant, L’Arithmetique de Iean Trenchant, Departie en trois liures. Ensemble vn petit discours des Changes. Auec l’art de calculer aux Getons.

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FIGURE 3.1: PRATT’S ARITHMETICALL JEWEL AND THE PLUME & JETONS ARITHMETIC On the left, William Pratt’s 1617 arithmeticall jewel, a small calculating instrument that was nothing more than a variant of the common abacus. A copy of the actual instrument is found in the Department of Medieval and Later Antiquities, British Museum. See Turner, “Mathematical instruments and the education of gentlemen,” 81. On the right, an excerpt from Jean Trenchant’s art de calculer aux getons, bounded with his L’Arithmetique, which was first published in 1558 (this edition is dated from 1618). For most of the sixteenth and seventeenth centuries, the technology of plume and

jetons was, as the Jesuit Jean François said in his arithmetic treatise of 1653, “the easiest,

safest [assurées], and most common of all.”349 Some (pocket) books, such as Alexandre

Jean’s 1637 Arithmetiqve au miroir, offered pages upon pages of multiplication tables

designed to help its owner in making a variety of French currency conversions and small

commercial transactions, without him or her having to know how to multiply or do

simple rules of three.350 Others tried to improve on the conventional technique of plume

Reueuë & augmentee en ceste derniere edition, tant de plusieurs regles & articles, par l’Autheur, que d’vne Table de poids de vingt deux Prouinces, correspondans l’vne à l’autre (Paris, 1618).

349 Jean François, S.J., L’Arithmetique ov l’art de compter tovte sorte de nombres, Auec la Plume, & les Iettons (Renne, 1653), 4.

350 Alexandre Jean, Arithmetiqve au miroir. Par laquelle on peut (en quatre vaccations de demie

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Clockmaking: Pascal’s Machines, Arithmetic, and the Epistemology of Coutume

and jetons, like William Pratt who invented the arithmeticall jewel and published a book

in 1617 explaining its use. (See Figure 3.1.) According to a later account by John Aubrey,

Dr Pell told me, that one Jeremiah Grinken [a mathematical instrument maker] frequented Mr Gunters Lectures at Gresham-College: He used an Instrument called a Mathematicall Jewell, by which he did speedily performe all Operations in Arithmeticke, without writing any figures, by little Sectors of Brasse [or some Semi-Circles] that did turn every one of them upon a Center. The Doctor has the Booke … he told me, he thought his name is [William] Pratt.351

Pratt was a mathematical practitioner and a member—along with Thomas Bretnor, John

Johnson and Aaron Rathborne—of the active circle of London’s mathematical teachers

close to Gresham College.352 His arithmeticall jewel was nothing more than a

rudimentary mechanical reconfiguration of the conventional reckoning technique: a

portable, fancier and gentlemanly adaptation of the plume and jetons. With the exception

here that you did not need paper to inscribe, for instance, the carry-over numbers of an

addition; one could instead, using a small metallic stylus, “inscribe” them on the

instrument’s appropriate sectors of brasse. The reckoning method, nonetheless, was

precisely the same as the plume and jetons. Although a number of these new and

sophisticated devices might have created some excitement in the field of arithmetic, they

heure chacune) pratiquer les plus belles regles d’icelle (n.p., 1637). For instance, “Pour sçauoir à quoy se monte le sol pour liure de quelque somme que ce soit, il faut trouuer la colomne qui represente le nombre de vostre somme, & dans la premiere ligne des sols, vous trouuerez à quoy se monte ledit sol pour liure.” (p.10). A new edition of this work was published in 1649. I found it at Houghton Library, Harvard University, bounded with Sieur de Baresme, L’Arithmetique nouvelle, dans sa véritable perfection. Où l’on peut en très-peu de tems facilement, & même seul, aprendre à compter, chiffrer & calculer sans Maître toutes sortes de Sommes. Mise dans une facilité toute particuliére, qui n’a point encore parû (Paris, 1646?) Also in that same book, Anonymous, Methode facile pour apprendre l’arithmetique de soi-même, et sans maître (Auxerre, 1656).

351 Ms Aubrey, 10 f 37, Bodleian Library, Oxford University. Quoted from Anthony Turner, “Mathematical instruments and the education of gentlemen,” Annals of Science 30 (1973), 51-88, on pp. 83-84. Pratt, in association with John Harper and Jeremy Drury, received a patent on 27 March 1616 “for the sole making of a table for casting accounts.”

352 E. G. R. Taylor, The mathematical practitioners of Tudor & Stuart England (Cambridge: Cambridge Univerity Press, 1954), 204-205.

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were still founded on established century-old techniques of calculation. It was not until

two mathematical practices—rabdology and logarithm—were invented in the 1610s by

the Scottish mathematical practitioner John Napier, that the early modern science of

calculation took a genuine new turn.

I. NAPIER’S RABDOLOGY, OR RECKONING RODS

Napier published his Rabdologiæ, seu numerationis per virgulas in 1617, after

having published in 1614 his Mirifici logarithmorum canonis descriptio. We will come

back to logarithms later. These were more famous and important as a mathematical tool

but Napier used rabdology to calculate the logarithmic tables appended to his Mirifici

logarithmorum. What Napier did with this rabdology, or art of reckoning with numbered

rods,353 was to adapt and expand on an algorithm known in thirteenth-century Italy as the

Gelosia method, which had been devised in India several centuries before and later

transmitted to Europe. In both cases, the basic idea was to replace demanding

calculations, involving multiplications and divisions of long numbers, by the simpler and

better known arithmetical operations of addition and subtraction.354 Napier’s reckoning

rods, simply said, were just a clever way to use multiplication tables without having to

learn them.

353 John Napier, Rabdologiae, seu Numerationis per virgulas libri duo cum appendice de expeditissimo multiplicationis promptuario. Quibus accessit & arithmeticae localis liber vnus. Authore & inventore Ioanne Nepero, Barone Merchistonii, &c. Scoto (Edinburgh, 1617), 1: “Rabdologia est Ars Computandi per Virgulas numeratrices.”

354 Ibid., where Napier wrote that “Virgulæ autem numeratrices, sunt virgulæ quadratæ, mobiles, simplicium notarum multiplis inscriptæ, ad difficiliores Arithmaticæ vulgaris operationes facilè & expeditè perficiendas.” For an English translation of this work, the only one to my knowledge, see Napier, Rabdology, transl. by William F. Richardson (Cambridge, MA: MIT Press, 1990).

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John Dansie, in the first English vernacular account of Napier’s rabdology, thus

described the chief purpose of reckoning rods:

The vse of them is Arithmeticall aymeing chiefly at the most difficult parts of that art: viz multiplication, diuision, extraction of the square & cubique Roots whose intricate operations, these little moueables doth so facillitate, that the meanest capacity may in 2 houres learne to multiply and diuide, which are the parts indeauored in this little manuell.355

The principle behind these Napier’s bones, as they were (and still are) often dubbed when

made of ivory,356 is simple and less time-consuming than the jetons—though one needed

pen and paper to inscribe the result of the

partial sums and, if need be, the carry-over

numbers for those who did not want to

memorize them. In the following example,

let us multiply 6497 by 6. You first go to

the rod (0-9) on the far left and look at line

6. Then, going from right to left, you add

the numbers diagonally on that line. The

first number of the multiplication is 2;

FIGURE 3.2: EXAMPLE OF NAPIER’S BONES An example of how to arrange Napier’s bones.

the second is (4+4); the third is (5+4); the fourth is (2+6) and the last is 3. In other words,

the result is 38982. If you wanted to multiply that same number 6497 by 359, you would

355 John Dansie, A Mathematicall manuel: Wherein Is handled Arithmeticke, planimetry, stereometry, and the embattelling of armies. Whereby any man that can but add and subtract, may learne to multiply and divide in two houres by rabdologie, without any trouble at all to the memorie. Whereunto is annexed the measuring of superficies, solids, the gageing of caske, with inuention of proportionall numbers, fitted to the subdiuisions of gageing rods; and the embattelling of armies according to the discipline now in vse. Written by Iohn Dansie student in the mathematiques (London, 1627), 2.

356 Ibid., 1: “or as they are vulgarly called Napeirs bones.”

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repeat the same process three times with lines 3, 5 and 9 and finally add those three

partial sums, taking into account the fact that the number 3 here actually represents 300

and 5 represents 50 (meaning that when you add those three partial sums, you have to be

careful where you position the numbers, shifting one column to the left for 5 and two for

3). Divisions with reckoning rods were a little bit longer but equally simple.357

Napier’s rods rapidly became popular in England. According to Seth Partridge, a

London-based surveyor and mathematical practitioner, these reckoning rods were easy to

make in any material whasoever; they could either be manufactured by oneself or bought

in good London instrument shops:

These speaking-Rods may be made either of Silver, Brasse, Ivorie, or Wood, as the maker and user of them best pleaseth, but they are most ordinarily made of good sollid Box, and being thereof made, they are as usefull as those made of any other substance whatsoever, Nay, I hold them more light and nimble then those made of Mettall; … Every practitioner may make them himselfe by cutting the faces of every one of the printed papers of the Rods, and so placed on a square piece of wood as before; or else they are ready made in Wood, by Master John Thompson in Hosier lane neere Smithfield, who makes all kinde of Mathematicall Instruments, and also by Mr. Anthony Thompson in Gresham Colledge, and by Mr. Thomas Browne at the Globe neere Aldgate. In Silver or Brasse they are made by Mr. Elias Allen, over against St. Clements Church without Temple-Barre.358

Their success in the decades following Napier’s 1617 publication can be gauged by the

sizeable amount of existing reckoning rods in museum collections in Europe and North

America and by the several versions and alterations made to them.359

357 A short history and a précis of their use is found in D. J. Bryden, Napier’s bones: A history and instruction manual (London: Harriet Wynter Ltd., 1992).

358 Seth Partridge, Rabdologia, or, The art of numbring by rods whereby the tedious operations of multiplication, and division, and of extraction of roots, both square and cubick, are avoided, being for the most part performed by addition and subtraction: with many examples for the practice of the same: first invented by the Lord Napier, Baron of Marchiston, and since explained, and made usefull for all sorts of men (London, 1648), 2-4. On Partridge see Taylor, The mathematical practitioners, 209.

359 For the description of several of these different sorts of Napier’s bones, see D. Baxandall and Jane Pugh, Calculating machines and instruments (London: Science Museum, 1975 [1926]). See also D. J.

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They became representative as well of the kind of mathematical tools entitled to

the education of a prince. One of the best known illustrations of such a case was

Athanasius Kircher’s Organum mathematicum, a “mathematical instrument” or box—

also called cista—within which the basic principles of arithmetic, geometry, fortification,

chronology, horography, astronomy, astrology, steganography (encryption), and music

were explained. (See Figure 3.3.) For arithmetic—the primum Organi Loculamentum—

Kircher precisely chose Napier’s reckoning rods, made in paper glued on wood and

provided in three sets of ten rods.360 Like the other mathematical disciplines embodied in

the organum, these wooden rods were meant to assist its owner in making calculations

without “capitis defatigatione.” In the letter acknowledging the reception of Kircher’s

organum mathematicum, the young Archduke of Austria Joseph Karl wrote he was

pleased with such a gift that would help him better understand the rudiments of the

mathematical disciplines, which were truly worthy of a king. As a matter of fact, he wrote

Kircher that the “organum pleases me more and more.”361

Bryden, “Scientific relics: John Napier’s bones,” Bulletin of the Scientific Instrument Society 76 (March 2003), 6-9.

360 According to Gaspar Schott, who wrote the description of Kircher’s organum mathematicum, we learn that although this number could be smaller, the more tabellas arithmeticas (as he called the reckoning rods) one had, the easier it would be to calculate larger numbers: “Non opus est, ut habeantur triginta Tabellæ Arithmetiæ, quot in primo loculamento Organi Mathematici continentur, & in præsenti Iconismo II. repræsentur: sed possunt esse pauciores. Quò tamen plures sunt, eò majores numeri per ipsas fine difficultate ac defatigatione ferè ulla multiplicari ac dividi possunt. Triginta sunt abundè satis.” Schott, Organum mathematicum libris IX explicatum (Herbipoli [Würzburg], 1668), 71. For a general description of this instruments and those similar to it, Mara Miniati, “Les cistæ mathematicæ et l’organisation des connaissances au XVIIe siècle,” in Studies in the History of Scientific Instruments, ed. by Christine Blondel et al. (London: Rogers Turner Books Ltd, 1989), 43-51. A nice example in found in Florence at the Istituto e Museo di storia della scienza.

361 Archduke Joseph Karl to Kircher, 31 December 1661, where he wrote: “Placet mihi sedulitas, ut magna cum facilitate capiam disciplinas Mathematicas, quas iure merìto regias ac principe dignas appellasti. Futurium vero est, ut mihi magis magisque placeat organum…” See also the draft of the letter Kircher sent to Karl Joseph on 7 July 1661, in which he described his instrument: “Mitto per manus P. Pizzoni Serenissimae Vestrae Celsitudini, Instrumentum quoddam quod Organum mathematicum appello; in quo summa facilitate traduntur illae Artes mathematicae, ad quas Serentitatem vestram inclinari audio,

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FIGURE 3.3 KIRCHER’S ORGANUM MATHEMATICUM

Here is part of the description Schott provided for Kircher’s organum mathematicum, above: “Nempe est Cistula A B C D E F G, scalari formâ ad modum Organorum pneumaticorum, quorum in templis nostris est usus, constructa è ligno polito, auro & aliis coloribus, ad majorem ornatum, oculorumque delectationem, variè & affabrè depicta. Insistit immobiliter basi latiori B H I K D, intus cavæ, ex eadem materiâ fabricatæ, eisdemque coloribus exornatæ. Altitudines A B & G C, ac longitudines A G & B C, possunt esse majores aut minores, quàm figura exhibet; uti & latitudines A F, G E, C D, quæ in præsenti figura justò contractiores sunt, Opticæ legibus id postulantibus, quàm in prototypo.” Schott, Organum mathematicum, 54-55 (above). Below, Schott’s modification of the reckoning rods, the “Nova cistula pro tabellis Neperianis, facilisq[ue] ac jucundus illarum usus,” chap. 12 of the Organum mathematicum.

Yet Gaspar Schott, to whom we owe the printed description of Kircher’s organum

mathematicum in 1668, added his own innovation to Napier’s reckoning rods.362 Instead

of having to deal with a number of individual little rods each time one desired to perform

a multiplication, Schott designed a box (cistula) in which Napier’s rods were converted

Regibus et Principibus uti par est, nullo non tempore summo in honore habitae?” Both letters are found in the Archivio della Pontificia università Gregoriana, Rome, APUG 555, f.075r and f.098r respectively. The letters were extracted from the Athanasius Kircher Correspondence Project established by Michael John Gorman and Nick Wilding <http://193.206.220.68/kircher/index.html#0> (accessed on 24 November 2006).

362 Schott, Organum mathematicum, 133-136. A nice overview of Schott’s life and activities is found in the introductory essay of Kaspar Schott: La technica curiosa; saggio introduttivo di Michael John Gorman e Nick Wilding; con uno studio linguistico e traduzioni annotate dal latino a cura di Maurizio Sonnino; prefazione di Paolo Galluzzi (Roma: Edizioni dell'Elefante, 2000).

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“idque in hunc modum” into cylinders, each one of them incorporating the complete set

of multiples from one to nine previously found on several separate rods.363 (See Figure

3.3.) To operate the machine, one only had to turn the cylinders’ handles to the proper

figure needed to be multiplied, and it then only became a matter of following Napier’s

well-defined rules of rabdology. Moreover, to ensure the machine would be utilized by

the greatest possible number of people, a table of addition and subtraction was provided

on the inside cover of the cistula. This system was not entirely new since in the early

1620s Wilhelm Schickard used it in what is now famously known as the first arithmetical

machine. Whether Caspar Schott knew about it is unknown, and perhaps unlikely since

Schickard machine was lost to a fire and known only through two letters sent to Kepler in

1623-24. After Schott’s publication, however, this new rabdological machine was

reproduced and redesigned many times, especially in England. In France, the clockmaker

René Grillet borrowed this concept in making his machine arithmétique in the 1670s and

Claude Perrault modified it considerably for his abaque rhabdologique toward the end of

the century. In Germany, still later, Jacob Leupold adapted it to his own Rechen-

Machine.364

363 “Fiant quotquot volueris (decem sufficiunt) cylindruli, æqualis inter se omnes longitudinis & crassitiei. In convexa superficie singulorum describatur Tabela cum numeris, quam suprâ cap. 8. §. 1. ex Nepero dedi; idque in hunc modum. Totam convexam cylindrulorum superficiem divide secundùm longitudinem in decem æqualia spatiola, juxta numerum decem columnularum citatæ Tabulæ Neperianæ. Singula spatiola divide in novem quadratula, & singula quadratula in duo triangula; triangulis verò inscribe eosdem numeros, qui in citata Tabula Neperiana scripti sunt, modo & ordine eodem qui ibi.” Schott, Organum mathematicum, 134.

364 On Grillet, see his Curiositez mathematiques (Paris, 1673) and the “Novvelle machine d’arithmetiqve de l’invention du Sieur Grillet Hologeur a Paris,” Journal des sçavans, 25 April 1678, 161-164. Rabdology was also used in various other mechanical calculating machines. Samuel Morland, for instance, designed one calculating machine on Napier’s principle and so did Claude Perrault later in the century. Morland, A new and most useful instrument for adition and subtraction of pounds, shillings, pence, and farthings (London, 1672); Perrault, “Abaque rhabdologique inventé par M. Perrault, de l’Academie royale des sciences,” in Machines et inventions approuvées par l’Académie royale des sciences, depuis son établissement jusqu’à present; avec leur Description. Dessinées & publiées du consentement de

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A lesser known modification to Napier’s bones was invented in France by Pierre

Petit, king counsellor and Intendant des Fortifications, who devised what he called an

arithmetical cylinder. (See Figure 3.4.) According to Petit, people ceased using Napier’s

“beautiful invention” because “the multitude and embarasment [sic] of those sticks, filled

with numbers on all sides, proved longsom and tedious.”365 Since Petit found this method

of calculating still useful—and because it was “easier to improve on inventions than to

become an inventor”—he designed long bands or ribbons of paper each containing all the

multiples of Napier’s rabdology. Those long bands were then attached end to end and

mounted on a wooden cylinder the size of a child’s drum or a hat, and of a length which

depended on the quantity of bands one wished to have in order to make calculations with

large numbers.366 The reckoning principles were of course identical to Napier’s rods’.

Petit deemed these common enough by then that he wrote only a brief summary of how

to proceed toward making a multiplication and a division.

l’Adadémie, par M. Gallon, 7 vols (Paris, 1735-1777), i:55-58. An example is found in the Musée des arts et métiers, Paris, inv. number 00800-0000. Leopold, Theatrum arithmetico-geometricum, 25. Leupold’s machine was not unlike Pierre Petit’s arithmetical cylinder, described below.

365 Pierre Petit, Dissertations academiques sur la nature du froid et du chaud. Avec un Discours sur la construction & l’usage d’un Cylindre Arithmetique, inventé par le mesme Autheur (Paris, 1653), 6 (this pagination is separated from the previous Dissertations): “Mais parce que la multitude & l’embarras de ces petits bastons remplis de chiffres de tous costez, apportoit des longueurs à leur arrengement, & à leur usage, à cause de leur mobilité & changement de places; on a quitté la pratique de cette belle invention.” Petit’s book was reviewed in the Philosophical Transactions 6 (1671), 3043-3045, where I took the English quote (p. 3044). A French summary of this book is found in the Journal des sçavans, lundy 13. Juin 1672, 94-95.

366 Ibid., 8-9: “je m’avisay encores pour un plus grand abrégé de plier ces bandes en cercles bien égaux & de coler sur chacun d’iceux trois ou quatre petits boutons de bois de la grosseur d’une teste d’épingle, puis de les mettre sur un rouleau ou Cylindre de bois ou carton, sur lequel on les pût tourner par le moyen desdits boutons: & c’est pour cela que j’appelle cette petite machine Cylindre Arithmetique, qui est environ de la grosseur ou diametre d’un tambour d’enfant, ou d’une forme de chapeau, & de la longueur ou hauteur que l’on veut pour contenir tant de bandes ou cercles qu’on desire pour faire de grandes operations.”

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FIGURE 3.4: PETIT’S CYLINDRE ARITHMETIQUE

Each strip or ribbon in Petit’s cylindre arithmetique contains the whole set of numbers from one to nine as found on Napier’s bones. The section with Roman numerals is there to visually delimit the multiplicant, so as to avoid any confusion when multiplying. As he wrote: “I’y adjoustay une file de characteres ou chiffres romains, I, II, III, IV, V, VI, VII, VIII, IX. pour mettre à costé & vis à vis des nombres multipliants & divisants; tres-utiles, tant pour marquer le commencement & la fin desdits nombres, pour s’arrester où il faut (toutes les bandes n’estant pas employez en toutes les operations) que pour marquer le multiple dont on se veut servir en chaque no[m]bre.” Petit, Discours sur la construction & l’usage d’un Cylindre Arithmetique, 7.

II. NAPIER’S LOGARITHMS

Despite these interesting and fairly popular innovations, Napier’s rabdology was

only a procedural technique aimed at facilitating calculation. The chief prize and true

mathematical innovation was Napier’s logarithms. Published in 1614, Napier’s Mirifici

logarithmorum found a rather quick acceptance by mathematical practitioners all over

Europe, from Kepler in Prague to Aleaume in Paris. Yet the impact was perhaps best felt

in England, where a translation by Edward Wright—supplied by an appendix from Henri

Briggs—was published as early as 1616; it was followed by a series of books and

mathematical instruments that explained and facilitated their use.367 According to Napier

367 John Napier, Mirifici logarithmorum canonis descriptio, ejusque usus, in utraque

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himself, there was nothing so “troublesome” to “Calculators” than the multiplication,

division, and extraction of square and cubic roots of great numbers, “which besides the

tedious expence of time, are for the most part subiect to many slippery errors.” Not only

his invention did “cast away from the worke it selfe, euen the very numbers themselues

that are to be multiplied, diuided, and resolued into rootes, and putteth other numbers in

their place, which performe as much as they can do, onely by Addition and Subtraction,

Diuision by two, or Diuision by three…”368 The mathematical salvation of early modern

astronomers and sailors came from providing them with a method to execute the most

difficult of calculating feats using simple additions and subtractions of “artificiall”

numbers, or logarithms.

In contrast to rabdology, where one would have to perform several additions,

logarithms could give the result of such a multiplication as 124 x 764 simply by looking

at printed tables and adding two numbers. Here is how it was done. Taking, for instance,

Briggs’s Arithmetica logarithmica one first located in the mathematical tables the

logarithm of 124—which is 2,09342,16851,6224; the same was done with 764, which

gives a second 15-digit number, 2,88309,33585,7569. One then adds these two numbers,

resulting in the “artificiall” number 4,97651,50437,3793. To find the result of the initial

trigonometria, ut etiam in omni logistica mathematica, amplissimi, facillimi, & expeditissimi explicatio. Authore ac inventore, Ioanne Nepero, Barone Merchistonii, &c. Scoto. (Edinburgh, 1614). Napier, A description of the admirable table oe [sic] logarithmes with a declaration of the most plentiful, easy, and speedy vse thereof in both kindes of trigonometrie, as also in all mathematicall calculations / invented and published in Latin by that honorable L. Iohn Nepair ... ; and translated into English by the late learned and famous mathematician Edward Wright; with an addition of an instrumentall table to finde the part proportionall, inuented by the translator, and described in the end of the booke by Henry Brigs ... ; all perused and approued by the author, & published since the death of the translator (London, 1616). It was reedited in 1618.

368 Napier’s preface to A description of the admirable table oe [sic] logarithmes, sig. A5r-A5v.

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multiplication, it sufficed to return to the mathematical tables in order to revert to the

corresponding “naturall” number 94,736.369

Logarithms were often called “artificiall numbers” or “borrowed numbers”

because, as we just saw, they transformed “naturall numbers” into completely different

ones. At the root of this transformation is a simple concept, based on mathematical

proportions. As Edmund Wingate explained in his Arithmetiqve made easie,

“Logarithmes are borrowed numbers, which differ amongst themselves by Arithmeticall

proportion, as the numbers that borrow them differ by Geometricall proportion.”370 Take

the following series of numbers:

369 Henry Briggs, Arithmetica logarithmica sive Logarithmorum chiliades triginta, pro numeris naturali serie crescentibus ab unitate ad 20,000: et a 90,000 ad 100,000 Quorum ope multa perficiuntur arithmetica problemata et geometrica. Hos numeros primus invenit clarissimus vir Iohannes Neperus baro Merchistonij: eos autem ex eiusdem sententia mutavit, eorumque ortum et vsum illustravit Henricus Briggius, in celeberrima Academia Oxoniensi geometriae professor Savilianus (London, 1624), for all the numbers. Briggs published the logarithms for the numbers 1 to 20,000 and 90,000 to 100,000. Adriaen Vlacq filled the gap between 20,000 and 90,000 in Arithmetiqve logarithmetiqve ov la constrvction et vsage d’vne table contenant les Logarithmes de tous les Nombres depuis l’Vnité jusques à 100000. Et d’vne avtre table en laquelle sont comprins les Logarithmes des Sinus, Tangentes & Secantes, de tous les Degrez et Minutes du quart du Cercle, selon le Raid de 10,00000,0000 parties. Par le moyen desqvelles on resovlt tres-facilement les Problemes Arithmetiques & Geometriques. Ces nombres premierement sont inventez par Iean Neper Baron de Marchiston: Mais Henry Brigs Professeur de la Geometrie en l’Vniversité d’Oxford, les a changé, & leur Nature, Origines, & Vsage illustré selon l’intention du dit Neper (Gouda, 1628). Vlacq, however, cut the last four decimal numbers of Briggs’s logarithms.

370 Edmund Wingate, Arithmetique made easie in tvvo bookes. The former, of naturall arithmetique: containing a perfect method for the true knowledge and practice of arithmetique, according to the ancient vulgar way, without dependance vpon any other author for the grounds thereof. The other of artificiall arithmetique, discovering how to resolve all questions of arithmetique by addition and subtraction. Together with an appendix, resolving likewise by addition and subtraction all questions, that concerne equation of time, interest of money, and valuation of purchases, leases, annuities, and the like (London, 1630), 152.

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A B C D E

1 1 0 5 5

2 10 1 8 6

4 100 2 11 7

8 1,000 3 14 8

16 10,000 4 17 9

32 100,000 5 20 10

64 1,000,000 6 23 11

The first two columns, A and B, are geometrical progressions, i.e. the quotient of two

consecutive numbers is equal to any two different consecutive numbers (for instance,

2:4::8:16). The other three columns, C, D, and E are arithmetical progressions, i.e. the

difference between any two consecutive numbers is equal to the difference of any two

other consecutive numbers (for instance, 1-2=5-6). From here, one makes a one to one

correspondence between, say, column B and C such that the logarithm of 1 is equal to 0;

the logarithm of 10 is equal to 1; the logarithm of 100 is 2, etc. In modern notation one

finds log101=0; log1010=1; log10100=2, etc. or, equivalently, 1=100; 10=101; 100=102, etc.

By definition, taking the logarithm of a number (x) is finding the numerical indice (n) in

a given base (b) that will give this exact number: logbx=n or x=bn. Owing to the

properties of indices in multiplication, multiplying two numbers x=bn by y=bm is equal to

xy=bn+m, or the sum n+m of the respective logarithms: logbx=n plus logby=m. Likewise,

dividing two numbers is simply the subtraction of the numbers’ respective logarithms.

Although using and understanding the properties of logarithms was easy enough,

the truly demanding part was computing the needed logarithms. It is why books filled

with thousands of logarithmic tables were published. Only by means of these tables were

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logarithms made genuinely useful. Because, as Wingate demonstrated, finding from

scratch a simple logarithm, such as the logarithm of 2, often involved scores of protracted

calculations, especially taking the square roots of at least twelve-decimal-place numbers,

but also as divisions and multiplications by two of similar behemoth numbers and one or

multiple rules of three. No wonder Napier invented his reckoning rods as a mathematical

aid to these time-consuming calculations.371 Although some astronomers took notice of

logarithms, like Kepler who published three books on the subject, it is in the domain of

navigation that they soon became the most practical and convenient of calculating

techniques.372

Since Gerard Mercator published a chart in 1569 with the proper projection of the

earth’s sphere, taking one’s bearing on the sea had to be modified. Mercator’s chart was

371 To find the logarithm of 2, Wingate started first by calculating a series of continuall meanes. Taking the number 10, he wrote under it its square root; then he took the square root of the last number; and the square root of that number again… until he arrived (after 24 iterations) at three numbers which all have six 0 (he called them cyphers) in their first decimal places (such as 1.000000548979). Depending on the degree of accuracy desired, one would continue this process until s/he obtained the number of cyphers needed. To find the logarithm of all these numbers, he then explained that since the logarithm of 10 was 1, and since he took the successive square root of each numbers, the logarithm of each of these numbers could be found easily by dividing by two 24 times the number 1 (if x=100.5, then log10x=0.5). The basic idea behind calculating the square root so many times until one reached a number with six cyphers is because Wingate showed that at this level of accuracy, the numbers thus found became proportional to their logarithm! Hence to find the logarithm of such a similar small number, one only needed to make a rule of three. It is this property that he then used to find the logarithm of 2. First, he took again the square root of two until he found his first numbers with six cyphers (20 iterations!); using the rule of three with the other small logarithms found earlier, he calculated the logarithm for this small number. Finally, he multiplied this logarithm by two until he reached the number for the logarithm of 2. All logarithms were not as difficult to find. For instance, to find the logarithm of 5, we know that 10÷2=5, and owing to the properties of logarithms, log1010÷log102=log105, or one minus the logarithm of 2 found with much labor gives log105. And consequently, one can easily find the logarithm of all the numbers that are made by the multiplication and division of these three numbers, i.e. 2, 5, and 10. Wingate, Arithmetique made easie, 164-175.

372 On Kepler, see Charles Naux, Histoire des logarithmes de Neper à Euler, 2 vols. (Paris: Librairie scientifique et technique A. Blanchard, 1966-1971), i:128-158. It is the best overall historical account on logarithm I found so far. Before logarithms became standardized as a mathematical tool, the most common mathematical trick used in astronomy was called prostapheresis, invented by an Arabic astronomer in the eleventh century but popularized in Latin West by Tycho Brahe. What it does again is transform long multiplications with trigonometrical numbers into simple additions, most specifically of the following sort: sin a x cos b = ½ [sin (a+b) + sin (a-b)]. Ibid., 30-32.

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no “plane” chart, meaning that the distortion introduced by this novel projection—which

kept the parallel meridians—introduced the concept of spherical triangles in navigation.

Mathematicians already had instruments at their disposition to perform these more

complex calculations with sine and cosine functions, like Peter Apian’s well-known

Instrvmentvm primi mobilis later replicated in brass by Egnatio Danti in 1568.373 In order

to help seamen, however, Edmund Gunter first adapted the sector to navigation use, a

mathematical instrument recently invented and mostly used by surveyors, military

engineers and other mathematical practitioners. In his 1623 De sectore et radio, Gunter

explained how to apply to navigation the special lines he added to the instrument, like the

lines divided according to trigonometrical functions and a linear scale of the meridional

parts (especially designed to work out problems of positions and distances on a Mercator-

projected chart). In that same work, moreover, Gunter introduced a logarithmic scale or

rule he placed on a cross-staff—besides the lines of numbers, he engraved the lines of the

logarithms of sines and tangents—so that calculations with spherical triangles were

performed by means of Napier’s invention. Three years before, in 1620, Gunter had

already published the logarithmic tables for trigonometric functions; so what the

logarithmic scale did was reproducing on a seaman’s instrument the logarithmic tables

found in printed books. (See Figure 3.5.) With a simple pair of dividers, one could

perform with tools logarithmic additions and subtractions without the awkwardness of

373 Peter Apian, Instrvmentvm primi mobilis… (Nuremberg, 1534). On Danti’s instrument, found at the Istituto e Museo di storia della scienza in Florence, see Epact: Scientific instruments of Medieval and Renaissance Europe <http://www.mhs.ox.ac.uk/epact/catalogue.php?ENumber=43630&Search=primi> (Accessed on 19 March 2007).

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having to flip through the pages of a bulky book—in the rain on the deck of a rolling

ship, for instance.374

FIGURE 3.5: GUNTER’S CANON TRIANGVLORVM AND WINGATE’S LINE OF PROPORTION In the 1623 English translation of his Canon triangvlorvm, Gunter, explained that “For these Sines are not such as halfe the chords of the double arke, nor these Tangents perpendiculars at the end of the Diameter; but other numbers substituted in their place, for attaining the same end, by a more easy way, such as the Logarithmes of the Lord of Merchiston, and thereupon I call them Artificiall Sinces and Tangents.” (p. sig. A2r) The title-page here is from the original Latin 1620 edition. Below, Wingate’s engraving of a section of his line of proportion as printed in The construction, and vse of the line of proportion.

374 Gunter, Canon triangulorum, sive Tabulae sinuum et tangentium artificialium ad radium 10000.0000. & ad scrupula prima quadrantis. Per Edm: Gunter, professorem astronomiae in Collegio Greshamensi (London, 1620). An English edition was published in 1623. Gunter, De sectore & radio. The description and vse of the sector in three bookes. The description and vse of the cross-staffe in other three bookes. For such as are studious of mathematicall practise (London, 1623). James A. Bennett, The divided circle: A history of instruments for astronomy, navigation and surveying (Oxford: Phaidon and Christie’s, 1987), 60-63. On Gunter’s scale, Florian Cajori, A history of the logarithmic slide rule and allied instruments and On the history of Gunter’s scale and the slide rule during the seventeenth century (Mendham, NJ: Astragal Press, 1994). See also Anthony Turner, “‘Utile pour les calculs’: The logarithmic scale rule in France and England during the seventeenth century,” Archives internationales d’histoire des sciences 38 (1988), 252-270.

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Gunter’s scale had a successful fortune. Travelling in France as Henrietta Maria’s

tutor, daughter of the late French king Henry IV and soon to be wedded to king Charles I,

Wingate demonstrated Napier’s logarithms and Gunter’s new mathematical instrument to

a number of Parisian savants,375 which ultimately led him to write a short treatise on the

subject:

The occasion of composing this Treatise was this: In Anno 1624 I making a journey into France, had the happinesse to be the first transporter of the use of these inventions into those parts; Where as soone as I was arrived, divers Mathematicians of the chiefest note in Paris, resorting to my chamber, and I communicating unto them first the manifold uses of the Logarithmes described upon Master Gunters Crosse-staffe, they earnestly importuned mee to expresse them by some short Treactate in the French Tongue, which when I had composed, and prefixed thereunto a Preface declaring the whole History of the rare and exquisite Invention of Logarithmes … as also of Master Gunters rare invention for projecting the Logarithmes in plane, I was advised by Master Alleaume the Kings chiefe engineir to dedicate my Booke to MONSIEUR the Kings brother, whose favourable admittance thereof, encouraged mee not long after to present him with this Treatise also…376

But because a certain lawyer from Dijon, after receiving instructions from Wingate

himself, threatened to publish right away something on the logarithmic scale rule,

Wingate had to rush through the press his own account, leaving out the usus part of this

otherwise typical fabrica et usus work, namely how to employ the rule in navigation,

375 Some of these Parisian savants that may have then seen Wingate’s instrument were Etienne Flantin, Guillaume Ferrier, Claude Bidault, Etienne Raulin, Jacques Aleaume (all from the Galerie du Louvre), Denis Henrion, Pierre Dujardin, Melchior Tavernier, Claude Piquet, A. Vernier and Daniel Chorez, who at one point or another had all constructed mathematical instruments. Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles (Paris: Presses Universitaires de France, 1953), 97-98 and Anthony Turner’s more extensive list in idem, “Mathematical instrument-making in early modern Paris,” in Luxury trades and consumerism in ancien régime France. Studies in the history of the skilled workforce, ed. by Robert Fox and Anthony Turner (Aldershot: Ashgate, 1998), 63-96, on p. 88.

376 Edmund Wingate, Logarithmotechnia, or The construction, and use of the logarithmeticall tables by the help of which, multiplication is performed by addition, division by subtraction, the extraction of the square root by bipartition, and of the cube root by tripartition, &c. Finally, the golden rule, and the resolution of triangles, as well right lined, as sphericall by addition and subtraction. First published in the French tongue by Edmund Wingate, an English gentleman: and after translated into English by the same author (London, 1635), sig. A4r-A4v. The French book to which Wingate refers to is L’Usage de la reigle de proportion en l’arithmetique et geometrie (Paris, 1624). I have not seen this book yet.

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astronomy, dialling, the military arts, etc. The reigle de proportion, nevertheless, was

found in Paris in the shop of Melchior Tavernier, Graveur & Imprimeur du roy pour les

tailles douces.377

Although Wingate published in 1628 an English translation of the previous work,

The construction and vse of the line of proportion, it was only in his 1630 Arithmetiqve

made easie that Wingate fully developed the concept of this mathematical instrument.

(See Figure 3.5.) In the preface of the latter work, he mentioned that although “how

admirabl[ly] vsefull those [logarithmic] Tables might be” great benefit would arise if they

were made less bulky, portable, and inexpensive. After some thought, Wingate

“hap[pe]ned vpon this way, which, as I co[n]ceiue, is the planest and best, that can bee

inuented for abreuiating the Tables of Logarithmes.” This instrument, in fact, was “so

portable, that being rolled vp you may inclose it in a paper box no bigger then your

finger, and little more then two inches long; and as for the vse thereof, you may discouer

at one view the Logarithme of any number whatsoever vpon it…”378 Wingate saw huge

advantages in using this printed-on-paper instrument, of which the “infallibility of the

Impreßion is not the least; for it being at first perfectly engrauen, there can be no error

committed in Printing the copies thereof; whereas the Tables of Logarithmes (printed at

377 In the preface of L’Usage de la reigle de proportion, Wingate wrote: “mais un certain Bourguignon, se disait Avocat au Parlement de Dijon, à qui j’en avois aussi entr’autres en partie monstré l’usage, a tasché de rompre mon entreprise faisant imprimer ce que je luy en avois communiqué.” Cited from Turner, “‘Utile pour les calculs’,” 253. The information on Tavernier is found at the back of the title page. See Cajori, On the history of Gunter’s scale and the slide rule, 140. This was not an uncommon problem shared by mathematical practitioners. Galileo faced a similar situation with his geometrical and military compass. Quite happy to use manuscript copies of the compass’ instructional manual for his students, he was forced to publish it after hearing someone was “getting ready to appropriate” his invention. Conversely to Wingate, however, what was left out (deliberately) was the fabrica part, not the usus one. Ten months later, he accused Baldassare Capra of plagiarizing both his book and instrument. See Mario Biagioli, Galileo’s instrument of credit: Telescopes, images, secrecy (Chicago: University of Chicago Press, 2006), 4.

378 Wingate, Arithmetiqve made easie, preface, sig. A3v-A4r. (italics original)

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large in figures) are subiect to many faults, either in the Composing, Correcting, or

Imprinting, whatsoeuer care or circumspection may be vsed to preuent the same.”379 For

Wingate, the rule of proportion was a “Mechanicall Table of Logarithmes,”380 a material

incarnation of a mathematical concept tremendously helpful to all the practices of the

mixed mathematics. But moreover, epistemologically speaking, the rule of proportion as

a mathematical instrument became the one and only “material device” capable of

perfectly embodying the tables of logarithms and, consequently, the abstract

mathematical notion of logarithm. We will see later how Pascal pushed such a

mechanical conception to its limit with his arithmetical machine.

Two years after Wingate’s reigle de proportion appeared in Paris, Denis Henrion

described a similar instrument in a book entitled Logocanon, ov regle proportionnelle

(1626). (See Figure 3.6.) Henrion, never mentioning Wingate’s visit to Paris, said he

received Gunter’s lastest works on logarithms and the logarithmic scale rule published

just a few years before. As a mathematical practitioner himself, Henrion knew perfectly

well that although the sector, or compas de proportion, was a useful instrument for

practical mathematics—that same year he reedited a book on this instrument, originally

published in 1618—the regle de proportion was better suited to make calculations on

379 Ibid., sig. A5r. (italics original) According to the entry “Logarithm” in Wikipedia, for instance, “Vlacq’s table [see note 32] was later found to contain 603 errors, but ‘this cannot be regarded as a great number, when it is considered that the table was the result of an original calculation, and that more than 2,100,000 printed figures are liable to error.’ (Athenaeum, 15 June 1872. See also the Monthly Notices of the Royal Astronomical Society for May 1872.)” Wingate wrote as well, regarding the actual printed size of the line of proportion: “And lest any man should wonder, why I haue giuen it so long a forme, and not rather haue confined it within the limits of this Volume, my Answere is, that I could haue conueniently couched it, within three pages of this Booke; but then it could not haue been reduced to so portable a forme, as aforesaid; and besides being thus ordered, you may if you please pate it vpon a conuenient board, and, vsing the Compasses with it, resolue most questions of Arithmetique without help of the pen…” Ibid., sig. A4v. (italics original)

380 Ibid., 289.

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spherical triangles. To his regle, besides Gunter’s logarithmic lines of numbers, sines and

tangents, Henrion engraved other useful and conventional lines plus what he called

geometrical treillis, made of parallelograms and rectangle triangles used as a draughting

scale.381 A few years later, Henrion combined in a single instrument, the mecometre,

three mathematical instruments routinely used separately: the compas de proportion, the

regle proportionnelle and Philippe Danfrie’s graphometer. This instrument—which

looked much like Danfrie’s graphometer—could perform all the mathematical

calculations and the measuring of distances and angles that those three others did

independently, in addition one could do with it everything “without knowing anything

more than simple arithmetical numeration [i.e. additions and subtractions].”382

381 D. Henrion, Logocanon, ov regle proportionnelle svr Laquelle sont appliquées plusieurs lignes & figures, diuisées selon diuerses proportions & mesures, en faueur de ceux qui se delectent en la practique des diuines Mathematiques (Paris, 1626). In the advice to the readers, Henrion wrote: “Il y-a enuiron deux ans que le sieur Gunter, Professeur en Astronomie au College de Gresham à Londres, publia en Anglois diuers traittez de Mathematique, lesquels il m’e[n]voya, & entre autre chose digne de luy, il y-a qu’ayant appliqué sur vne regle les Logarithmes, Sinus, & Tangentes artificielles, declarées au precedent traicté, il en enseigne l’vsage: & jaçoit qu’il y-ait bien de l’embaras en diuerses operations, lesquelles on pratique fort aisément sur le Compas de proportion; si est-ce toutesfois que pour ce qui concerne les Triangles Spheriques, cette regle est plus commode qu’iceluy Compas, encore que nous y ayons adiousté quelques lignes qui rendent beaucoup d’operations plus faciles qu’elles n’estoient auparauant: C’est pourquoy ie me suis resolu d’expliquer aux François, non seulement ce que ledit sieur Gunter a enseigné aux Anglois, touchant l’vsage de ladite Regle, mais aussi de transporter sur icelle regle plusieurs autres lignes que les trois que ledit Gunter y-a appliquées, & encor quelques figures couppées selon diverses proportions par des lignes paralleles, qui constituent quantité de petits Triangles, & Quadrangles, lesquels font ensemble vne forme de treilly: au moyen desquelles lignes adioinctes, & de ces treillis Geometriques, les vtilitez de ladite Regle que nous surnommons Proportionelle, seront de beaucoup augmentées, & plusieurs operations facilitées: non toutefois que nous nous voulions maintenant arrester à toutes les operations qui se peuuent faire & pratiquer sur ladicte Regle, ains seulement aux plus belles & vtiles, delaissant les autres iusques à vne autre fois. Adieu.” See also Turner, “‘Utile pour les calculs’,” 255-256.

382 D. Henrion, L’Vsage du mecometre. Qvi est vn instrvment Geometrique, auec lequel on peut tres-facilement mesurer toutes sortes de longueurs & distances visibles; prendre & rapporter au petit pied le plan ndes villes, Chasteaux & autres places; trasser tant sur le papier que sur la terre telles figures & fortifications qu’on voudra; faire toutes sortes de Cartes tant Geographiques que Chorographiques; & pratiquer toutes les autres operations d’Arithmetique & de Geometrie, qui se pratiquent auec le Compas de proportion, la Regle proportionnelle, le Graphometre & la Boussole (Paris, 1630). In the preface to the readers Henrion wrote: “Combien que tous les instrumens de Mathematiques venus à ma cognoissance, il n’y en ait point de plus parfaict & vniuersel, ny mesme de si commode & vtile que le Compas de proportion par nous mis en lumiere: Neantmoins quelques operations de la Trigonometrie se pratique[n]t beaucoup plus facilement sur la Regle proportionnelle, que sur ledit Compas: Et en toutes les operations de

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FIGURE 3.6: HENRION’S REGLE PROPORTIONNELLE AND DELAMAIN’S MATHEMATICALL RING Above, Henrion’s regle proportionnelle. Picture taken from the Houghton Library copy at Harvard University. Right, Delamain’s Grammelogia, Or the mathematicall ring (London, 1630). An example of such a ring can be found in the Museum of the history of science, Oxford University.

In France, no mathematical practitioner or savant after Henrion appears to have

done anything new on logarithms until Jacques Buot published his treatise on the Vsage

la campagne, ie prefere & me sers plustost du demy cercle, qu’aucuns appellent Graphometre, que dudit Compas; sans toutesfois me seruir du Rapporteur, que Philippes Danfrie adjoinct audit Graphometre, ny aussi du Recipiangle mentionné au dernier Chap. du I. l[ivre] des Fortifications du sieur Errard, ains seulement de deux poincts que ie m’aduisay dés l’année 1609, de faire marquer au mesme Graphometre, sçauoir, l’vn au diametre d’iceluy, & l’autre en l’alidade: Mais ayant consideré que si on y pouuoit encore appliquer les lignes & diuisions, tant de nostre dit Compas que de la Regle de proportion, ledit Graphometre en seroit beaucoup plus parfait & vtile, i’en aurois recherché le moyen, & l’ayant trouué, i’ay fait vn abbregé & sommaire recueil des plus belles & vtiles operations dudit instrument, lequel (amy lecteur) ie te presente icy. Et iaçoit que cet Instrument soit fort simple & aisé à fabriquer, i’espere neantmoins que tu le trouueras plus vniuersel, commode & vtile qu’aucun autre qui iusques à present ait esté mis au iour, veu qu’auec iceluy tu pourras non seulement pratiquer toutes les propositions que nous auons enseignees tant au liure de l’Vsage dudit Compas de proportion, qu’en celuy de la Regle proportionnelle, mais aussi mesurer toutes sortes de longueurs & distances beaucoup plus facilement & promptement qu’auec tout autre Instrument, quant bien tu ne sçaurois autre regle d’Arithmetique que la simple numerations…”

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de la rove de proportion in 1647.383 Judging from Buot’s description of the instrument,

the rove de proportion must have looked to a mathematical practitioner strangely similar

to the English circles of proportion, or mathematicall ring as coined by Richard

Delamain. The focus of a bitter priority dispute between Delamain and William

Oughtred, these circles of proportion were more than just Gunter’s logarithmic scale rule

or Wingate’s line of proportion bent into a circle: Each circle could be rotated separately

on a central pivot so that in actual fact this instrument was the ancestor of the slide rule,

one of the most widely used mathematical instruments until the invention of the modern

computer.384

In a letter sent to Buot in September 1646, reprinted as a long foreword notice to

the book, Pierre Petit gave a short history of logarithms, including Wingate’s visit to

Paris (though he did not name him by name), and pointed out why the logarithmic scale

rule was not really a success. According to him, one did not trust the dividers’ points on

the tiny engraved number lines of the regle de proportion, so that this instrument did not

completely eliminate the need for logarithmic tables, the use of rabdology and the pen.

After mentioning his cylindre arithmetique, he came to Buot’s invention of the rotating

logarithmic circles or rouës, which avoided the use of a compas or dividers. What

383 Jacques Buot, Vsage de la rove de proportion, Sur laquelle on pratique promptement & facilement toutes les Reigles de l’Arithmetique & les Analogies de la Trigonometrie Geometrique & Astronomique. Oevvre tres-necessaire aux Marchands, Banquiers, Asseeurs des Tailles, Ingenieurs, Astronomes, &c. (Paris, 1647). We know close to nothing of Buot’s life and activities. All we know was he later became a member of the Académie royale des sciences and invented an astronomical instrument, as one can gather from the following article: “Equerre azimutale, inventée par M. Buot, de l’Academie royale des sciences,” in Machines et inventions approuvées par l’Académie royale des sciences, i:67-69.

384 On the history of the mathematicall ring and its priority dispute, Anthony Turner, “William Oughtred, Richard Delamain and the horizontal instrument in seventeenth-century England,” Annali dell’Istituto e Museo di storia della scienza di Firenze 6/2 (1981), 99-125. Turner, “Mathematical instruments and the education of gentlemen.” Cajori, On the history of Gunter’s scale and the slide rule during the seventeenth century. Katherine Hill, “‘Juglers or schollers?’: Negotiating the role of a mathematical practitioner,” British Journal for the History of Science 31 (1998), 253-274.

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surprised Petit the most was the fact that, as maintained by Buot, the idea of arranging

these circles together came neither from the regle de proportion nor from any other part,

but rather from the principle of logarithms themselves.385 Wherever Buot’s idea came

from, Petit found it most useful, exact and easy to use. Lastly, Petit gave to Buot some

recommendations regarding the dimension that the instrument should have, the

configuration of the different circles. He advised that they should form a spiral rather

than be disposed into concentric circles. He also noted the importance of a good quality

print in the book so that, if the instrument was not engraved on brass, one could use the

printed version, and called for detailed explanation focused on the instrument rather than

on its relevance to cosmography, surveying, fortifications, astronomy, etc.386

* * *

This brief survey of mathematical instruments and practices of calculation does

not do justice to the vast amount of books and instruments actually printed and built in

early modern Europe to improve computational skills and performance.387 Too often

overlooked in this context is how Pascal’s arithmetical machine fit into the overall

development of these early modern mathematical devices. According to Pierre Petit, the

385 In the body of the text, Buot mentions Wingate’s regle proportionnelle and Henrion’s mecometre, but says that this “instrument ayant pris son estre de l’habitude secrette ou des veritables rapports que les nombres on ensemble…” Buot, Vsage de la rove de proportion, 4-5.

386 Petit to Buot, 23 September 1646. Petit’s comments form part of the first section of Buot’s book, Vsage de la rove de proportion, 17-34.

387 For France, see Camille Frémontier-Murphy, Les Instruments de mathématiques, XVIe-XVIIe siècle: cadrans solaires, astrolabes, globes, nécessaires de mathématiques, instruments d’arpentage, microscopes (Paris: Réunion des musées nationaux, 2002). An important early modern survey is Nicolas Bion, Traité de la construction et des principaux usages des instrumens de mathematique. Avec les figures necessaires pour l’intelligence de ce traité… (Paris, 1709). On England and Europe in general, see the works by Gerard L’E. Turner, Anthony Turner and Jim Bennett to name but a few “instrument” scholars.

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pascaline—though imperfect—was a true advance, something as significant and

noteworthy as Napier’s own inventions. In his letter to Buot,388 Petit declared:

I find that since the invention of logarithms and rabdology, nothing of significance occurred regarding the practice of numbers other than Monsieur Pascal’s box or instrument. It is a device truly invented with as much success [bonheur] and speculation as his author has intelligence and knowledge [science]. It consists, however, in a number of wheels, springs, and movements, and one needs the head and hands of a good clockmaker to understand how it works and to manufacture it, as well as the skills and knowledge of a good arithmetician to operate it. [For all these reasons], one fears that its use will never become widespread [commun], and that instead of being employed in financial bureaux and regional administrations [Eslections] to calculate taxes [Tailles], or in merchant offices to compute their rules of discount and company, [the machine] will be stored in cabinets and librairies, there to be admired.389

Though Petit found the pascaline truly novel as regards the “practice of numbers,” its

ultimate purpose was not to aid mathematical practitioners, astronomers and mariners in

performing ever more difficult series of calculations. It was meant rather to assist

merchants and tax collectors in doing their mercantile and governmental duties.

What Petit found so interesting about the pascaline—and what also created the

machine’s imperfection and fascination—was the fact it did not come from the print

388 Petit most likely discovered Pascal’s arithmetical machine while visiting Rouen in 1646 on his way to Dieppe, where he had to report on some kind of submarine equipment. (This letter he sent to Buot was written and signed from Dieppe during that short stay.) It was on Petit’s return trip to Rouen that he then performed with the Pascals’ the famous experiment on the vacuum, memorialized in the letter Petit sent to Monsieur Chanut in November of that same year. Petit to Chanut, 19 or 26 November 1646, in Pascal, OC, ii:346-359. One of the best analysis of this experiment is found in Matthew L. Jones, “Writing and sentiment: Blaise Pascal, the vacuum, and the Pensées,” Studies in the History and Philosophy of Science 32 (2001), 139-181.

389 Petit’s letter to Buot, in ibid., 24-25: “ie trouue que depuis ce temps-là des Logarithmes & Rabdologie, il ne s’est rien produit de considerable touchant la pratique des nombres que la Boëte ou instrument de Monsieur Pascal. Piece veritablement inuentée avec autant de bonheur & de speculation que son autheur a d’esprit & de science. Mais comme elle consiste en quantité de Rouës, de Ressorts, & de mouuements, & qu’il faut la teste & la main d’vn bon Horologeur pour la comprendre & l’executer, comme l’adresse & la connoissance d’vn bon Arithmeticien pour s’en pouuoir seruir. Il est à craindre que son vsage n’en soit iamais rendu commun, & qu’on la gardera plustost dans des Cabinets & grandes Bibliotheques pour y estre admirée, que dans des Bureaux des Finances & Eslections pour départir les Tailles, ou dans les Contoirs des Marchands, pour y faire leurs Regles d’Escomptes & de Compagnies.” See also Pascal, OC, ii:344-345.

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culture, like rabdology, logarithms, and arithmetic, where books were more important

than the material devices they explained. Pascal’s device originated in contrast from the

machine world, the geared universe of clocks and watches, which involved another type

of relationship between maker and user, as Mario Biagioli recently shown.390 Privilege

was granted for the machine itself, not for the printed text explaining its construction and

use. For this reason alone, the pascaline was a distinct type of early modern mathematical

device, aimed moreover at a different sort of clientèle, one inclined towards money rather

than mathematical practices.

The following sections focus on the arithmetical machine per se in order to better

situate it within its social, cultural and material-instrumental contexts. The pascaline’s

true novelty as a mathematical instrument, it will be explained, is found equally in its

mechanism as in the overall theory of knowledge-production it created.

SITUATING PASCAL’S ARITHMETICAL MACHINE

Jacques Buot advertised his rove de proportion as an œuvre tres-necessaire to merchants,

bankers and tax collectors [asseseurs des tailles]. And for those who had to perform long

calculations, he asserted it was better to own a large rove de proportion, between two and

a half and three feet in diameter, because the instrument would bring its user significant

convenience and exactness, and would not be cumbersome since one could just leave it in

the office.391 Buot was not the only mathematical practitioner to advertise mathematical

instruments as useful tools to merchants, bankers and other kind of higher and lower

390 Mario Biagioli, “From print to patents: Living on instruments in early modern Europe,” History of Science 44 (2006), 139-186.

391 Buot, Vsage de la rove de proportion, 30-31.

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financiers. (At least one of Pascal’s contemporaries from the republic of letters thought

the pascaline would be extremely useful to merchants, bankers and businessmen.392) In

England, especially, logarithms were promoted as an aid to commercial and financial

practices. Wingate provided an appendix to his Arithmetiqve made easie aimed at

“resolving likewise by Addition and Subtraction all Questions, that concerne Equation of

Time, Interest of money, and Valuation of Purchases, Leases, Annuities, and the like.”393

In his 1635 Logarithmotechnia, Wingate also added some monetary problems that could

be solved easily with logarithms.394 Logarithms acquired such an authority in England

that in 1674, a philo-accomptant like John Mayne could publish a treatise in which the

section on compound interest was explained almost entirely in terms of “artificiall”

numbers.395

English mathematical practitioners, according to Katherine Neal, played the

rhetorical card of utility as a means to justify the value of mathematics to everyday life—

392 J. Chapelain to Christiaan Huygens, 20 August 1659, in Huygens, Oeuvres complètes, 22 vols. (The Hague: M. Nijhoff, 1888-), ii:469: “Je ne scay si estant en France vous n’avués point veu entre ses [Roberval] mains vne Machine dvne multitude estrange de rouages disposes de sorte qu’ils seruent a faire auec vne justesse et prontitude admirables les quatre regles premieres dArithmetique au grand soulagement des Marchands, Banquiers et Gens d’affaires.”

393 Wingate, Arithmetiqve made easie, title page. (emphasis original). He repeats the same thing on sig. A6r.

394 Wingate, Logarithmotechnia, 74-75, for instance problem XI: “A summe of money being forborne for a certain time, to finde how much it will be augmented at the expiration of the same time, accounting interest upon interest according to a certaine rate propounded.”

395 John Mayne, Socius mercatoris: or The merchant's companion: in three parts. The first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. The second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. The third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. By John Mayne, philo-accomptant. (London, 1674), 118-143.

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and perhaps more importantly to distance their discipline from natural magic.396 Yet at

the same time, these mathematical practitioners aimed their work and instruments at a

gentlemanly clientèle needing ever more skills in mathematics to pursue a career in trade

and government.397 In France, by contrast, reckonmasters who published books on

arithmetic had probably a greater influence on French noblesse than did the mathematical

practitioners. Denis Henrion, as a representative of the latter, most certainly sought the

help and support of the gentlemen in publishing on the compas de proportion, or in

putting out a plain mathematical text, as the following title suggests: Mémoires

mathematiqves, recueillis et dressez en favevr de la noblesse Françoise (Paris, 1623).398

But contrary to their English counterparts, Henrion and most French mathematical

practitioners were not, generally speaking, dealing with commercial arithmetic—and

when they did, they followed the conventional scholarship of reckonmasters.399 This field

had its own set of practitioners going back to the early sixteenth century.

396 Katherine Neal, “The rhetoric of utility: Avoiding occult associations for mathematics through profitability and pleasure,” History of Science 37 (1999), 151-178.

397 Turner, “Mathematical instruments and the education of gentlemen.” 398 In the reader’s preface, Henrion mentioned regarding the compas de proportion: “Mais en

l’annee 1616, voyant que les affaires ausquels sa [Alleaume] charge d’Ingenieur l’occupent, ne luy en donnoient le loisir, acquiesçant aux prieres de plusieurs de mes amis, & Gentils-hommes mes disciples, ie tiray de mesdits Memoires Mathem. & rapportay en ce liuret les plus vtiles & necessaires operations dudit Compas de proportion, & icelles expliquay le plus clairement & intelligiblement qu’il me futs possible, afin que ceux à qui plaist ledit instrument trouuassent plus aisément ce dont ils auroient besoin: au prealable desquelles operations, ie mets aussi la constrction dudit compas.” Henrion, L’Vsage dv compas de proportion, 4th ed. (Paris, 1631).

399 Denis Henrion, Collection, ou recveil de divers traictez mathematiques. A sçavoir; d’Artithmetique, d’Algebre, de la solution de diuers Problemes & questions, tant Geometriques, qu’Astronomiques. Comme außi de plusieurs moyens pour mesurer toutes sortes de quantitez, soient lignes, superficies & corps. Item, de la Sphere du monde, auec l’vsage & pratique, tant de l’Astrolabe, du Quarré Geometrique, & des Globes, que du compas de proportion: Et encore de la construction des fortifications pratiquées aux pays bas (Paris, 1621), where he explains the basic arithmetic operations plus the règle de société ou de compagnie, the règle d’alligation ou d’alliage, and the extraction of square and cubic roots, as most treatise of arithmetic did.

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Natalie Zemon Davis has shown that sixteenth-century French books on

arithmetic could be understood not only as teaching methods but as a way of justifying

business life, to demonstrate that business and financial practices ought not be judged

vulgar and vile by the nobility. To convey their rhetoric of usefulness, arithmetic books

typically discarded the moral issues about deception and the sin of avarice linked to

commerce and finance to focus instead on the reckoning techniques. Examples of

interest-bearing loans and merchandise prices, for instance, were abstracted from their

usual theological and moralist references to just price, personal needs of merchants, and

proper standard of living. Most received “decorations” in the latter sixteenth century, i.e.

poems by eminent men of letters and fancy dedications praising the author and the noble

value of arithmetics, gave to certain books on commercial arithmetics “an aura of honor.”

The incompatibility of nobility with business activity, however, is well

documented, from the French acts of dérogeance of 1540, 1561, and 1579—noblemen

caught “trafficking in merchandise” risked losing their privileges of nobility—to the

writings of clerics and individuals on the side of nobility like the Protestant jurist

Innocent Gentillet. And though a number of mathematicians such as Milles de Norry,

Jacques Chauvet and Guillaume Gosselin wrote “honorable” works on commercial

arithmetics and often addressed an aristocratic audience due to their entries at court, the

favorable rhetoric of business life probably received very little attention within the

nobility. Such books, nonetheless, produced an impact on the ever growing French

bourgeoisie, those merchants and financiers themselves who saw, within the rhetoric of

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these books, that business was a worthwhile enterprise and perhaps not worth loosing its

virtues—and monetary comfort—to more abstract and intangible non-business values.400

In what follows, I claim that Pascal’s arithmetical machine was not only meant to

ease Blaise’s father Etienne heavy workload with numbers—or any other reckoning

misery suffered by noblesse de robe gentlemen put in similar situations—but was also

designed as a genuine luxury object capable of reaching the French nobility, provided it

was pitched with a fitting rhetoric. The fact that Pascal made his machine—the notion of

machine is important here—elegant and expensive, dedicated it to the chancelier Séguier,

and did not provide a detailed written account of its use and construction, all point toward

the fact that the pascaline was aimed at least as much (if not more) at the highest elite of

French citizens, the nobility, than at the reckonmasters and other noblesse de robe clients

Pascal may have tried to win over at the same time. Pascal’s arithmetical machine

embodied better than any other mathematical instrument previously invented both the

science of arithmetic and the concept of honnêteté.

ETIENNE PASCAL’S TAX BURDEN AND THE ORIGINS OF THE PASCALINE

Etienne Pascal arrived in the city of Rouen, capital of the Normandy province, in January

1640 as the Commissaire député par sa Majesté en la Haute Normandie, or the financial

assistant to the intendant Claude de Paris. Appointed by the Cardinal de Richelieu,

400 Natalie Zemon Davis, “Sixteenth-century French arithmetics on the business life,” Journal of the History of Ideas 21 (1960), 18-48. Idem, “Mathematicians in the sixteenth-century French academies: Some further evidence,” Renaissance News 11 (1958), 3-10. For a more general aperçu, Geoffrey Poitras, The early history of financial economics, 1478-1776: From commercial arithmetic to life annuities and joint stocks (Cheltenham, UK and Northampton, MA: Edward Elgar, 2000), esp. chap. 4. On merchant treatises in general, Pierre Jeannin, “Les Manuels de pratique commerciale imprimés pour les marchands français (XVIe-XVIIIe siècle),” in Le Négoce international, XIIIe-XXe siècle, ed. by François M. Crouzet (Paris: Economica, 1989), 35-58.

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Etienne Pascal had been in self-imposed exile from Paris less than a year before he

headed north to Rouen. Pascal père had participated in a large demonstration of angry

rentiers on 24 March 1638, mostly noblesse de robe and bourgeois individuals who

displayed their great displeasure at seeing their rentes sur l’Hôtel de Ville (annuities that

pay interests) unpaid or diminished. Pascal père had invested virtually all his capital from

the sale of his house in Clermont and office of second président en la Cour des Aides de

Montferrand in this simple and supposedly safe and trustworthy state investment. The

fixed interest was 5,55% (or denier 18), enough to live on with Pascal père’s initial

investment of close to 100,000 livres. But since the declaration of war with Spain the

king of France and his ministers decided to take back a few quartiers (quarters, as four

times a year) of paid interests.

After some protesters verbally threatened the Chancelier Séguier and the Cardinal

de Richelieu during the manifestation, a number of them were emprisoned in the Bastille.

To avoid long-term resentment and retribution from the highest instances of the State,

Pascal père judged it best to disappear from Paris for a while.401 It is to his daughter

Jacqueline, Blaise’s younger sister, that Etienne Pascal ultimately owed his return to good

grace in Richelieu’s eyes—so the story goes. Known for her talent in poetry, Jacqueline

went immediately to the Cardinal after acting in a play attended by Louis XIII’s most

influential and feared minister. In front of Richelieu, the youngest Pascal then recited a

poem in which she pleaded the Cardinal to let her father come back from exile. Richelieu

loved it. He told Jacqueline to write to her father that he could return to Paris safely, and

401 André Le Gall, Pascal (Paris: Flammarion, 2000), 97-101. On Pascal’s père office of président in Clermont, see ibid., 79-93. Régine Pouzet, Chronique des Pascal: Les affaires du monde, d’Etienne Pascal à Marguerite Périer, 1588-1733 (Paris: Champion, 2001).

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that Pascal père should visit him with the whole family—because the Cardinal also

wanted to see the fort savant Pascal fils, Blaise. That encounter occurred on 3 April

1639.402

Nine months later, Etienne Pascal arrived as a royal representative to the ravaged

city of Rouen. One of the most prosperous provinces of France just a few decades earlier,

owing in large part to a strong maritime trade, Normandy was struck during Louis XIII’s

reign by natural and (most of all) human-made afflictions. Since 1623 the plague had

become an endemic disease in Rouen, reaping death (11,000 persons in 1637 alone) and

an almost complete collapse of commerce. The province would have probably faced this

ordeal better if it had not been for the escalating taxes imposed on Rouen and Normandy

to replenish the king’s ever empty coffers. New taxes on leather, wine, dyed cloth, salt

(the gabelle), paper and cardboard (cartes) as well as special commercial privileges given

to local and foreign producers of goods (like cheap English cloth) infuriated and

impoverished Rouen’s artisanal communities. Overtaxation, perhaps more than anything

else, created the rebellious armée de souffrance known as the Nu-Pieds. At its strongest,

this army of suffering had 20,000 people wrecking havoc all over the province. In Rouen,

a clockmaker named Noël Ducastel, dit Gorin, lead the three-day riot on 21-22-23 August

1639 during which time financiers’ houses were reduced to ashes, whilst the salt tax

collector, Le Tellier de Tourneville, barely escaped alive from his besieged residence.

402 Le Gall, Pascal, 125-136. Here is the poem written by Jacqueline: “Ne vous étonnez pas, incomparable Armand, / Si j’ai mal contenté vos yeux et vos oreilles. / Mon esprit, agité de frayeurs sans pareilles, / Interdit à mon corps et voix et mouvement. / Mais pour me rendre ici capable de vous plaire, / Rappelez d’exil mon misérable père.” Ibid., 134. See also Pascal, OC, ii:213, where the last three sentences read: “Sauvez cet innocent d’un péril manifeste. / Et lors vous me rendrez l’entière liberté / De l’esprit et du corps, de la voix et du geste.” Jacqueline wrote the letter to her father the following day, 4 April 1639, in which she detailed what happened. Pascal, OC, ii:210-212.

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The Parlement acted quickly enough to momentarily quench the rebellion, capturing on

the 22nd the unruly Gorin. The Rouen riot and the disorders caused in the province by the

Nu-Pieds army, however, prompted Richelieu to send to Normandy an army of 6,000

foreign mercenaries lead by a colonel Gassion. By late November Caen was disarmed

and the Nu-Pieds army was crushed in the faubourgs of Avranches. On new year’s eve

1639, Gassion entered Rouen without encountering any resistance.403

To retake political control of the province Richelieu sent one of his creatures, the

chancelier Séguier, on whom had been bestowed extraordinary powers. Séguier, for a

short period of time, became the sole master and supreme judge of Rouen and Normandy,

on top of the then dismissed Parlement. Séguier established his royal authority swiftly; on

7 January 1640 he condemned to torture and death, without trial and on a simple verbal

command, Gorin and four other accomplices for having taken part in the August riots.404

And as if the exactions of the occupying army were not bad enough (Séguier convicted a

403 Henri Fouquet, Histoire civile, politique et commerciale de Rouen depuis les temps les plus reculés jusqu’à nos jours, 2 vols. (Rouen: Chez M. Métérie, libraire and Chez M. Augé, libraire, 1876), i:528-544. René Herval, Histoire de Rouen, 2 vols. (Rouen: Maugard, 1947-49), ii:122-138. On the Nu-Pieds rebellion, see Yves-Marie Bercé, Croquants et nu-pieds: Les soulèvements paysans en France du XVIe au XIXe siècle (Paris: Gallimard, 1991). Madeleine Foisil, La Révolte des nu-pieds et les révoltes normandes de 1639 (Paris: Presses universitaires de France, 1970). On Rouen’s trade activities before the Nu-Pieds rebellion, Gayle K. Brunelle, The New World merchants of Rouen, 1559-1630 (Kirksville, MI: Sixteenth Century Journal Publishers, Inc., 1991). See also Jacques Bottin and Jochen Hook, “Structures et formes d’organisation du commerce à Rouen au début du 17e siècle: le cas de Michel van Damme,” in Le Négoce international, 59-93.

404 Here is how it is related in Séguier’s diary: “Le dict jour, dès le matin, Mgr le chancelier a envoyé, par le prévost de l’Isle, prononcer son ordonnance verbale au prisonniers détenuz, par l’ordre du Parlement, dans le vieux palais, de la roüe contre le nommé Gorrin, lequel, pendant la sedition, alloit par la ville, aveq une balle de feu ardente au bout d’un baston, marquer les maisons que l’on debvoit brusler, démolir ou piller; et de la mort, par la corde, contre [the four others] trouvez et surpris dans quelques maisons pillées, quoy que non chargéz de butin, à ce que l’on dict.” A. Floquet, Diaire ou journal du voyage du chancelier Séguier en Normandie après la sédition des nu-pieds (1639-1640) et documents relatifs à ce voyage et à la sédition (Rouen: Edouard Frère, 1842), 112. This abuse of power was not forgotten and called barbaric by some at the time of the Fronde (see documents footnoted on pp. 112-115). On this and other condemnations by Séguier, Foisil, La Révolte des nu-pieds et les révoltes normandes de 1639, 300-311.

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few soldiers to control the rest of Gassion’s mercenaries) Séguier reimposed the tax on

dyed cloth, largely responsible for the rebellion in the first place, as well as the

formidable sum of 1,055,000 livres of taxes payable by the Rouen Hôtel de Ville. When

Séguier decided it was taking too much time for the city’s bourgeois and commissaires to

come up with the hard cash, he demanded that 250,000 livres were paid immediately and

that all the inhabitants of the city, in an act of solidarity, were put to contribution.405

Although order gradually returned to Rouen, its commerce and industry were

quelled once again by the imposition of harsh taxes. In the Etats of 1643 the Normandy

representatives declared that the “city of Rouen, capital of this province, is crushed by

such prodigious taxations that only a feeble appearance is left today of its tax exemption

status [franchise], which in the past used to make its glory…” These Etats also

mentioned that the taxes levied from the Hôtel de Ville since 1640 amounted to more

than three million livres and that the tax on dyed cloth, one of Rouen’s best industries

before the rebellion of 1639, left more than 50,000 families of artisans on the city’s

pavement.406 In the midst of social disturbances, it became Etienne Pascal’s

responsibility as the royal commissaire sur les tailles to make sure the province of

Normandy would comply with its tax obligations, whatever the cost.

Pascal père was a meticulous, forthright and honest man. His probity was already

noticed as président en la Cour des Aides of Clermont many years earlier. In Rouen, for

405 “Le soir [on 4 February], mon dict seigr le chancelier a parlé sévèrement aux principaux bourgeois et commissaires pour l’administration de la ville, sur quelque retardement qu’ilz apportoient au payement des premières 250 mil # qu’ilz ont promis sur le million 55 mil livres à quoy ils ont été taxéz.” Floquet, Diaire ou journal du voyage du chancelier Séguier en Normandie, 242. Fouquet, Histoire civile, politique et commerciale de Rouen, 547-548 (he mentions the sum of 1,085,000). Foisil, La Révolte des nu-pieds et les révoltes normandes de 1639, 315 (she mentions the sum of 1,005,554).

406 Herval, Histoire de Rouen, ii:148.

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instance, he went as far as sending home his secretary, a certain M. Jolivet (a distant

family member), for accepting a bribe of one louis d’or. Owing to a reputation of

righteousness, it appears that a number of Rouennais had asked for Pascal père to become

the sole intendant of Normandy. Yet such a diligence and moral integrity, though

certainly appreciated, came at a price: it meant he fulfilled his job as best he could as tax

supervisor.407 The determination of the correct amount of taxes Rouen and each of the

1,800 communities in Normandy had to pay, required Pascal père to travel around the

province. The task of calculating enormous amounts of numbers in millions of livres,

sols, and deniers necessitated ultimately the help of his son Blaise and one of his cousins’

son, Florin Perrier, who would soon marry Blaise’s sister Gilberte. But even additional

“computers” pushed the eldest Pascal to the limit of exhaustion. In the post scriptum of a

1643 letter Blaise sent to Gilberte, Pascal père famously wrote he never in his life carried

out one-tenth the amount of work he had at that moment, hardly ever going to sleep

before two o’clock in the morning.408 When Gilberte later recounted in the Vie de

Monsieur Pascal that her brother designed the arithmetical machine at the age of nineteen

years old, she placed its invention exactly during the period of intensive work Pascal père

described in the previous post scriptum.409 The origins of the pascaline was thus deeply

embedded in the early modern financial responsibilities of Etienne Pascal’s position as

407 Le Gall, Pascal, 140-141 for Rouen and chap. 2 for Pascal’s père official activities in Clermont.

408 Blaise Pascal to Gilberte Périer, 31 January 1643, in Pascal, OC, ii:282-283, where Pascal talks about his father’s “voyage des élections” avec de Paris. The post scriptum reads: “Ma bonne fille m’excusera si je ne lui écris comme je désirerais, n’y ayant aucun loisir. Car je n’ai jamais été dans l’embarras à la dixième partie de ce que j’y suis à présent. Je ne saurais l’être davantage à moins d’en avoir trop; il y a quatre mois que je [ne] me suis couché six fois devant deux heures après minuit.”

409 Gilberte Périer, La Vie de Monsieur Pascal, in Pascal, OC, i:576.

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commissaire sur les tailles. The material culture of money in the form of tax reform and

collection, not higher mathematical rationale nor technical prowesses, provided the initial

impetus for its creation.

In Pascal’s dedicatory letter to the chancelier Séguier, the young Archimedes—as

he was sometimes called by Marin Mersenne—mentioned the difficulty of using the

common method of calculations to perform lengthy arithmetical operations such as the

determination of taxes. Only after an extensive period of meditation, Pascal wrote, did he

determine that a simpler and faster approach could actually be discovered.410 It is

interesting to note that Pascal’s moyens ordinaires to perform arithmetical operations was

the plume and jetons, nothing else. It was the only method referred to in Séguier’s

dedication, in the Avis nécessaire cited earlier in the chapter, in the privilège and in

Gilberte’s Vie de Monsieur Pascal.411 No mention whatsoever of rabdology and

logarithms, as we saw above in relation to the English context, though Pascal père and

fils were most likely aware of these two, by then well-known, mathematical practices as

regular members of Mersenne’s Parisian circle of mathematicians.

The fact that Pascal did not bring up in his discourse the newest—and sometimes

more efficient—calculating techniques developed by mathematical practitioners points to

410 Pascal, “Lettre dédicatoire à Monseigneur le Chancelier sur le sujet de la machine nouvellement inventée par le Sieur B.P. pour faire toutes sortes d’opérations d’arithmétique par un mouvement réglé sans plume ni jetons,” in Pascal, OC, ii:332 where he writes: “Les longueurs et les difficultés des moyens ordinaires dont on se sert m’ayant fait penser à quelque secours plus prompt et plus facile, pour me soulager dans les grands calculs où j’ai été occupé depuis quelques années en plusieurs affaires qui dépendent des emplois dont il vous a plus d’honorer mon père pour le service de Sa Majesté en la Haute Normandie, j’employai à cette recherche toute la connaissance que mon inclination et le travail de mes premières études m’ont fait acquérir dans les mathématiques; et après une profonde méditation, je reconnus que ce secours n’était pas impossible à trouver.”

411 See full title in ibid. Pascal, “Avis nécessaire à ceux qui auront curiosité de voir la machine arithmétique, et de s’en servir,” in Pascal, OC, ii:334. “Privilège pour la machine d’arithmétique de M. Pascal,” in Pascal, OC, ii:712. Périer, La Vie de Monsieur Pascal, 576.

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two correlated assertions, examined in the following subsection. First, rabdology and

logarithms had a marginal impact on the French milieu of reckonmasters—and by

ricochet on merchants, financiers and bankers, despite efforts by individuals such as

Henrion, Petit and Buot. Pascal, therefore, did not find his primary insight from

mathematical practitioners in developing the arithmetical machine. Pascal, in other

words, steered clear of the fabrica et usus tradition common to mathematical instrument

makers. Second, the pascaline’s rhetoric of effortless calculations was meant to convince

and meet the needs of a specially targeted clientèle, one which owned money and,

contrary to Pascal’s father, did not necessarily want to learn complex mathematical

procedures.

A MATHEMATICAL INSTRUMENT? THE RHETORICAL ARGUMENT BEHIND THE MACHINE

In his book describing the art of reckoning all kinds of numbers with the plume and

jetons, the Jesuit Jean François briefly described other methods that could facilitate

arithmetial operations, namely rabdology, a printed book filled with multiplication tables,

and the rouë Paschaline. Though the latter made all the arithmetical operations with

“confidence and swiftness by means of a local motion,” François brought up major

drawbacks to the invention: it was expensive (the pascaline sold for 100 livres), there was

a possibility that if it broke there would be no replacement parts (or wheels) to be found,

and perhaps more importantly it left its user in complete ignorance of the art of

arithmetic.412 For this last reason—and possibly because of the machine’s lack of

412 Jean François, S.J., L’Arithmetique ov l’art de compter tovte sorte de nombres, Auec la Plume, & les Iettons (Renne, 1653), 22-23. See §6 Quelques moyens d’abbreger, & de faciliter les Operations expliquées cy-dessus: “L’Instrument nommé la rouë Paschaline les fait auec asseurance & promptitude par

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commercial success—François omitted to mention the pascaline in the 1657 reedition of

his book.

It is a fact that the pascaline was not a machine designed to teach or tutor in the

art of arithmetic. But neither was it a simple machine, requiring absolutely no knowledge

of arithmetic—contrary to Gilberte’s assertion found in her Vie de Monsieur Pascal. It

would have been very difficult indeed (most likely impossible) for someone without the

most basic notions of arithmetic to make calculations with Pascal’s arithmetical machine.

Degrees of reckoning complexity increased according to the type of operation involved,

from effortless to intricate in the following order: addition, subtraction, multiplication

and division. Although Pascal claimed in the privilège that his machine could perform all

the basic arithmetical operations “as well as all the other rules of arithmetic,”413 Guy

Mourlevat has convincingly demonstrated the somewhat laborious task ahead of anyone

interested in using the pascaline. The only exception to this rule was making an addition,

which in fact was the only straightforward arithmetical operation that could be performed

on the pascaline.

To perform an addition all that was required was to enter in successive order any

number of numbers to be added. The only rule to follow was to make sure they were

vn petit mouuement local: mais la cherté de cét instrument qui se vend 100. liures, & le danger que quelque rouë ne vienne à manquer, & l’ignorance qu’il laisse de l’Arithmetique le rend bien rare.” This quote is found also in Pascal, OC, ii:1009. Tallemant de Réaux, in Les Historiettes, mentioned that the pascaline was sold 400 livres and that it was “si difficile à faire qu’il n’y a qu’un ouvrier, qui est à Rouen, qui la sache faire.” Pascal, OC, i:464.

413 Pascal, “Privilège,” 712, where he mentions the following: “il a inventé plusieurs choses, et particulièrement une machine par le moyen de laquelle on peut faire toutes sortes de supputations, additions, soustractions, multiplications, divisions, et toutes les autres règles d’arithmétique, tant en nombre entier que rompu, sans se servir de plume ni jetons, par une méthode beaucoup plus simple, plus facile à apprendre, plus prompte à l’exécution et moins pénible à l’esprit que les autres façons de calculer qui ont été en usage jusqu’à maintenant…”

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entered correctly, that is on the appropriate wheel (thousand, hundred, unit, sol, denier,

etc.). It was not even required to enter the digits of a number from right to left, in order.

One could enter them on the machine in any sequence, putting 2 before 5 and then 6 and

8 for 5,286 if one chooses. This was made possible thanks to the carry mechanism found

inside the pascaline, the most significant feature of the machine. In short, performing

additions lived up to the promise of a machine that was unproblematic required no

mathematical skills from its user. The other three arithmetical operations, however,

necessitated more work.414 (See Figure 3.7.)

Strictly speaking, the user of the pascaline did not need to know much of

arithmetic, besides being able to count from one to ten. Though the machine’s modus

operandi could be understood and carried out without grasping the finer theoretical points

414 Guy Mourlevat, Les Machines arithmétiques de Blaise Pascal (Clermont-Ferrand: La Française d’Edition et d’Imprimerie, 1988), 50-70. This essay is part of the series Mémoires de l’Académie des sciences, belles-lettres et arts de Clermont-Ferrand, vol. LI. Because the numbered-wheels on the machine were always turning in the same direction—left to right—, two sets of numbers were drawn: 0 to 9 on the bottom line, 9 to 0 on the top line. To do an addition, the movable horizontal rod covering parts of the small windows was in an up position. To perform a subtraction, the horizontal rod was in a down position. This is where it could get confusing, because to make a subtraction one needed to use the complement of nine (and 12 and 20 when dealing with deniers and sols). That is, to make the following subtraction 65 - 27, one needed first to inscribe the number 34 on the machine (3 and 4 being both the complement of nine of 6 and 5). The number inscribed, 34, is invisible since it is under the rod; what one sees on the above windows is the wanted number, 65. From here, to substract 27, one needed to inscribe 27 and the machine did the rest, showing the result of 38. But what had been done, really, was an addition, since 34 was first inscribed (to show 65) and then 27, which gives 61. But this number remains invisible, and only its complement of nine, 38, is seen in the above windows. Multiplication with the pascaline also involved a series of additions, akin to the jetons technique described in the first section above. To multiply 246 by 132, after placing the rod in its up position, one needed to inscribe 246 twice; then 246 three times, but shifting the numbers one space to the left to take into account the fact that the multiplicant was 30, not 3; lastly, shifting once again one space to the left, one would inscribe 246. The result would appear automatically, 32,472. Performing a division on the pascaline was undoubtedly the most intricate of the arithmetical operations. Like the subtraction, the rod had to be placed in its down position. To divide 157 by 32, one first inscribed the complement of nine (842) to show 157. Then one inscribed 32, which results in 125; 32 is inscribed again, resulting in 93; once more gives 61; one last time and the number seen in the windows is 29, which is smaller than 32. Therefore, the result of the division is 4, remaining 29. Yet again, this is no different than using the plume and jetons technique, and it would certainly not be that more difficult to arrive at the same result by moving around a few jetons. It gets much trickier when one decides to divide two nombres rompus, i.e. numbers in livres, sols and deniers or decimal numbers.

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of arithmetic, it would have been most difficult to calculate square and cubic roots with

the pascaline without arithmetical knowledge. These computations involved some

educated guesses multiplications, and/or complicated sequences of divisions depending

on the algorithm employed. Teaching such complex arithmetical practices, however, was

the chief aim of printed books on arithmetic—hence François’s criticism of the pascaline.

FIGURE 3.7: THE PASCALINE Engraving taken from “Machine arithmetique, de M. Pascal,” in Machines et inventions approuvées par l’Académie royale des sciences, iv:137-139, pt. 1. Below, an exemplar from the Musée des arts et métiers, Paris. The wheel on the far right is for the deniers (12 teeth), next to it is the wheel for the sols (20 teeth), next to it is the wheel for the livres (ten teeth) and the following ones are muliples of ten in livres.

From the sixteenth-century textbooks discussed earlier to François Le Gendre’s

L’Arithmétique en sa perfection, mise en pratiqve selon l’vsage des financiers, banqviers

et marchands (1663) and Jacques Savary’s Le parfait negociant ou Instruction generale

pour ce qui regarde le commerce de toute sorte de marchandises, tant de France que des

pays estrangers (1675) the chief purpose of these works was to teach the basic and finer

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points of the art of arithmetic. Once again, Pascal’s machine distanced itself from the

print culture. Its chief aim was not the understanding of mathematic, but its utility in

counting. It was a machine akin to a crane, which was meant to lift heavy things, not to

explain the theory of mechanics, or a clock, meant to tell time not to understand the

diurnal motion of the earth.

By distancing himself from these printed books, Pascal also made certain his

machine would not be viewed and mistaken for a mathematical instrument. Fabrica et

usus books written by mathematical practitioners such as Henrion, Petit, Wingate,

Delamain, Buot, Gunter, and many others devoted a large part of their works to the

description and use of new inventions. These books focused the attention of the reader on

the usefulness and replication qualities of the instrument by means of long and technical

accounts, customarily accompanied by one or several engravings. The privilege granted

to mathematical practitioners was usually aimed at the (immaterial) text of the book, not

at the (material) instrument per se; anyone following the precise explanation given by the

inventor could replicate the instrument for personal use or even for selling purposes.415

(One uncommon exception was Buot’s rove de proportion, for which the privilege was

415 On patents and paper instruments, see Biagioli, “From print to patents,” 160-166. Paper instruments have interesting lives. They were not only meant as useful and cheap mathematical devices, but were also thought as “objects” worth collecting. On this topic, see Catherine Eagleton and Boris Jardine, “Collections and projections: Henry Sutton’s paper instruments,” Journal of the History of Collections 17 (2005), 1-13. Jim Bennett has worked out a typology of sixteenth-century mathematical instruments, within which paper instruments found a natural place: “There are brass instruments, wooden instruments, paper instruments, paper instruments with moving parts within books, woodcuts within books where there are no moving paper parts but where there is an anchored thread for relating scales to each other, there are woodcuts without threads but where the accompanying text invites the reader to use the instrument on the page by applying a thread or a rule to read off the scales, and there are woodcuts where there is no such instruction but which have the scales in every detail and which could certainly be used in this way.” Jim Bennett, “Knowing and doing in the sixteenth century: What were instruments for?,” British Journal for the History of Science 36 (2003), 129-150, quote on pp. 140-141.

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granted, de graces speciales it says, to both the text and the instrument.416) Pascal,

however, did not endow his machine with this type of exposé. Such a decision on his part

cannot be explained solely by a concern with the privilege rights to the machine (see next

subsection). Pascal sought in all probability to distance himself from other contemporary

mathematical practitioners in order to access a completely different kind of clientèle, one

with larger monetary means and significantly lower interest in mathematics and technical

intricacies. In the Avis nécessaire Pascal tried hard to justify his motive not to pen down,

as did the géomètres, a fabrica et usus account of the pascaline. To the reader, Pascal

pleaded:

I hope you will approve my decision to omit such a discourse when you take the time to ponder upon, on the one hand, the ease with which the construction and use of this machine can be explained by word of mouth and with a brief discussion and, on the other hand, when you consider the trouble [embarras] and the difficulty it would have been to convey in writing the measurements, shapes, proportions, locations and all other properties of so many differents parts. You will then judge that this tenet [doctrine] is one which can only be taught viva voce, and that a written discourse on this matter would be as useless and awkward as one used to describe every parts of a watch, of which the explanation is made so simple when done by word of mouth. And apparently such a [written] discourse would produce nothing more than an infallible disgust in the mind of many, showing them a thousand difficulties were none are to be found.417

416 Buot, Vsage de la rove de proportion, 44-45, where the Privilege dv Roy mentions that “Luy auons permis & permettons de graces speciales par ces presentes de faire imprimer ladite Rouë de Proportion & le liure de son Vsage, soit à part ou ensemble, les vendre ou faire vendre par tels Libraires que bon luy semblera en toute l’estenduë de nostre Royaume … & deffences à tous autres de quelque qualité & condition qu’ils soient, de faire, contrefaire, grauer, imprimer, ou faire grauer ny imprimer, vendre ny distribuer ladite Rouë ny ledit liure de son Vsage, soit en l’estat qu’ils sont à present, ou qu’ils seront cy-apres …”

417 Pascal, Avis nécessaire, in OC, ii:334-335: “Oui, j’espère que tu approuveras que je me sois abstenu de ce discours, si tu prends la peine de faire réflexion d’une part sur la facilité qu’il y a d’expliquer de bouche et d’entendre par une brève conférence la construction et l’usage de cette machine, et, d’autre part, sur l’embarras et la difficulté qu’il y eût eu d’exprimer par écrit les mesures, les formes, les proportions, les situations et le surplus des propriétés de tant de pièces différentes; lors tu jugeras que cette doctrine est du nombre de celles qui ne peuvent être enseignées que de vive voix, et qu’un discours par écrit en cette matière serait autant ou plus inutile et embarrassant que celui qu’on emploierait à la description de toutes les parties d’une montre, dont toutefois l’explication est si facile, quand elle est faite bouche à bouche; et qu’apparemment un tel discours ne pourrait produire d’autre effet qu’un infaillible dégoût en l’esprit de plusieurs, leur faisant concevoir mille difficultés où il n’y en a point du tout.”

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Putting forward the example of the watch helped in grounding the rhetoric of the

pascaline qua machine on one of the most prestigious expressions of early modern

technology, that of clockmaking.

Pascal described the arithmetical machine as something more than a mere

mathematical tool: it was a complicated piece of machinery, so intricate in fact that

images and written words were simply inappropriate to understand and appreciate it.

Behind the metaphors of the watch qua machine and viva voce dialogue one glimpses at

the clientèle to which Pascal was addressing the pascaline, namely the honnête homme.

To appeal to this specific clientèle, Pascal crafted a clever rhetoric that compelled his

targeted audience to perceive the sophisticated mechanical device as less esoteric and

menial than a mathematical instrument—yet as exciting as a watch—and as more noble

than a book on arithmetic. The pascaline, in other words, was designed—and marketed—

as a machine embodying the virtues of honnêteté.

In sending the curieux interested by the pascaline to the Collège Royal professor

Gilles Personne de Roberval, Pascal underscored the value of conversation described

above.418 Matthew Jones has convincingly shown the importance of good conversation

for Pascal—and fellow members of the republic of letters—toward the acquisition of

knowledge and the cultivation of virtue. Good conversation, whether about poetry,

politics or mathematics, was a skill any honnête homme needed to master. Moreover, as

Jones explains, “Conversation best taught one to understand and to judge people, books,

and plays. It helped make reasoning rigorous. It best developed speaking and reasoning

418 Pascal wrote, regarding Roberval, that “[il] leur fera voir succinctement et gratuitement la facilité des opérations, en fera vendre, et en enseignera l’usage.” Pascal, Avis nécessaire, in OC, ii:341.

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without the crutches of artificial rhetorical figures and syllogisms.” Yet conversation was

only a means to an end, namely how to live one’s life. Mathematics, Jones argues,

became Pascal’s genuine and ideal instrument to cultivate the mind and to find one’s own

limits—a way to the good life: “More than mathematical practice itself, reflecting upon

mathematical thought and practice helps human beings to esteem themselves correctly

and to recognize the powers and limits of human reason. Mathematical practice serves as

a great source of empirical data on human abilities and inabilities.”419 Could the

arithmetical machine really achieve such high standards of virtuousness? Could the

pascaline be reconciled with the role mathematics and conversation played during

Pascal’s lifetime?

The pascaline, at first glance, had none of the virtuous qualities possessed by

Pascal’s arithmetical triangle. Whereas this triangle, in Pascal’s view, could train the

mind and hone skills and aptitudes, the arithmetical machine was essentially designed to

ease the pain of reckoning. It was created in order to reduce to nothing the mental

exertions caused by long and cumbersome plume and jetons calculations. Yet, if one

could muster (and stomach) the effort, the pascaline could perhaps reveal as powerful a

tool to cultivate the mind as the arithmetical triangle. Jones has shown the great

mathematical flexibility of Pascal’s triangle established in the concept of “enunciation.”

Although the triangle was a static entity, the manner in which one arranged or combined

the numbers associated with rows, columns and diagonals was not. Pascal suggested to

his reader to play with the triangle by changing the name of sets of numbers and thus

419 Matthew L. Jones, The good life in the Scientific Revolution: Descartes, Pascal, Leibniz, and the cultivation of virtue (Chicago: The University of Chicago Press, 2006), chap. 3, quote on pp. 128 and 124 respectively. On the role of conversation for the French Republic of Letters, Marc Fumaroli, La Diplomatie de l’esprit, de Montaigne à La Fontaine (Paris: Gallimard, 1998).

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formulating equivalent, but different, enunciations. A kind of linguistic game was

embedded within the arithmetical triangle, a game that forced its players to think

differently and originally about mathematical propositions. As Jones explains,

Although Pascal stressed that mathematical practice involves linguistic transformation, he did not espouse remaining at the level of linguistic transformation without attempting to develop a deeper understanding. Far from encouraging the reader mechanically to register the soundness of each deductive step, Pascal’s effort to demonstrate his discoveries ‘openly’ was supposed to help to develop the talent, the ingenium, of the reader by laying bare the insights behind the formal linguistic transformations. Changing enunciations develops a certain kind of mathematical mind, one capable of producing new relations. This practice works to develop the capacity for innovatively drawing consequences from many principles kept in mind without reducing or confusing them.420

Could someone similarly develop his or her ingenium using the pascaline? Was the

machine constrained by its mechanism? Or endowed with its own internal flexibility?

Was its user, in other words, “mechanically” limited to the prescribed algorithmic

procedures? Most likely not, and this could have been one of Roberval’s teachings.

Nothing, for instance, could stop a particularly enthusiastic user from finding an

original algorithm that would perform subtractions when the horizontal rod of the

pascaline was in its up—instead of its down—position, and vice versa. The same was true

for multiplication and division. And what about discovering original algorithms to

calculate square and cubic roots and, why not, logarithms? Nothing said one had to

“mechanically” follow the prearranged rules of calculation. Although the pascaline’s

mechanical motion was fixed and unchanging, meaning the wheels were reproducing ad

infinitum the same rotational movement, the algorithms designed to make arithmetical

operations could vary considerably. Though the primary purpose of the arithmetical

420 Jones, The good life in the Scientific Revolution, 95-103, quote on pp. 102-103.

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machine, as the rhetoric went, was to perform effortless arithmetical operations, in the

hands of resourceful and determined users this machine could have been used to sharpen

one’s mathematical mind—as the arithmetical triangle did.421 What was the latter, in fact,

if not a paper tool, a paper instrument that could, for example, give—effortlessly—the

coefficients of binomial equations? One could use the arithmetical triangle as he or she

would the arithmetical machine, that is without having to ponder upon the mathematical

principles embedded in the material device.422

Yet Pascal, as Jones explained, explicitly encouraged the reader of the treatise on

the arithmetical triangle to go beyond mere “mechanical” manipulations, while he

emphasized these very same mechanical (or bodily) manipulations as regards the

arithmetical machine. It was as if user and machine had to become one to ensure that the

pascaline would reach its full potential. Sold as a luxury item, like so many expensive

clocks, the pascaline was endowed with an aura of dignity that few mathematical

instruments ever achieved outside princely collections. Embodied within the mechanism

of the pascaline, arithmetic was ennobled like never before. The arithmetical machine, as

envisioned by Pascal, became to arithmetic what the organ was to music: the organum

organorum. Put in the hands of a skilled user the pascaline symbolized the instrumental

perfection of scientific knowledge; and as Mersenne’s organ did, it taught how to practice

natural philosophy. The pascaline was as much a gentleman’s rhetorical device as a

natural philosophical epistemic tool. In the clockwork mechanism of Pascal’s

421 On the different ways to make subtraction, Mourlevat, Les Machines arithmétiques de Blaise Pascal, 50.

422 On the concept of paper tool, see especially David Kaiser, Drawing theories apart: The dispersion of Feynman diagrams in postwar physics (Chicago: The University of Chicago Press, 2005), 7-9 for the definition and literature; chap. 10 for a concrete example.

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arithmetical machine was set up the method of natural philosophy.

CLOCKMAKING AND PASCAL’S PRIVILEGE

The arithmetical machine, despite Pascal’s effort, never was a bestseller in the Parisian

luxury trade. Pascal had better success as an entrepreneur with the later carrosses à cinq

sols, the first Parisian system of “public” (or bourgeois) transportation. Price may have

been an issue here, as Pascal himself spelled it out in the privilège. Accounts vary

significantly, from the Jesuit mathematician François’s 100 livres to Tallemant de

Réaux’s 400 livres and Balthasar Gerbier’s 50 pistoles (or 500 livres).423 Though high-

priced as a luxury item, the pascaline was not more expensive than a lavishly decorated

(and somewhat accurate) clock or watch.424 Its greatest flaw, therefore, was perhaps not

its price but the fact it had to live on the periphery of the luxury trade, despite Pascal’s

effort in linking the arithmetical machine to the more fashionable and natural

philosophical universe of clocks and clockmaking.425

423 For Tallemant de Reaux’s assertion, see Pascal, OC, i:464. On Gerbier, see note 3. On the carrosses à cinq sols, ibid., iv:1374-1437. See also on the same topic Eric Lundwall, Les Carrosses à cinq sols. Pascal entrepreneur (Paris: Science Infuse, 2000). Pascal, Privilège, 713, where he wrote: “Et parce que ledit instrument est maintenant à un prix excessif qui le rend, par sa cherté, comme inutile au public…”

424 For price examples, see E. Develle, Les Horlogers blésois au XVIe et au XVIIe siècle (Blois: Emmanuel Rivière, Editeur, 1913), 47-50. Most watches and clocks described were valued between 75 and 125 livres. 400 livres would have been a very expensive (and royal) amount to spend on such an item, since several watches valued at 300 livres each were meant to Marie de Médicis in the early 1630s.

425 Not only, as we will see shortly, did the mechanism of the machine evoke the wheels and gears of clocks and watches, the pascaline was advertised as a strong and durable instrument, capable of sustaining without alteration the hardship of travel (reminiscent to, for instance, the numerous clock experiments then made in trying to determine the longitude at sea). Pascal, Avis nécessaire, 337-338 and 340, where he wrote: “Et quant à la durée et solidité de l’instrument, la seule dureté du métal dont il est composé pouvait en donner à quelque autre la certitude; mais d’y prendre une assurance entière et la donner aux autres, je n’ai pu le faire qu’après en avoir fait l’expérience par le transport de l’instrument durant plus de deux cent cinquante lieues de chemin, sans aucune altération. … [J]’ose te donner assurance que tous les efforts qu’elle pourrait recevoir en la transportant si loin que tu voudras ne sauraient la corrompre ni lui faire souffrir la moindre altération.” The distance is roughly equivalent to a Rouen-Clermont return trip.

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What was in vogue and what defined the material culture of nobility remained in

constant flux in seventeenth-century Paris. There were between 2400 and 2500

marchands-merciers in the city by the time Pascal invented and was granted a privilege

for the arithmetical machine. They sold a wide range of goods—jewellery, tapestries,

toys, silk fabrics and ornamental metalwork—to aristocrats and to a rising bourgeoisie

with ever greater financial means. Taste for special kind of cloths, spices, or beverages

such as tea and coffee spread at different rates and new consumer trends (like Pascal’s

own carrosses à cinq sols) became fashionable on a regular basis. In a creative and

growing early modern luxury market Pascal—though he himself advertised his machine

in front of fashionable crowds—appears to have found no successful luxury niche in

which to push his invention. Unlike watches, the pascaline was much heavier and thus

not easily portable; unlike table-top clocks, it was not as ornate and could not do anything

on its own. The pascaline was a luxury item that fit no preestablished fashionable

categories and could not initiate by itself a new one. It became a rarity, and like most

rarities it found its place in cabinets of curiosities.426

This could explain in part why Christiaan Huygens had better success in selling

copies of his new pendulum clock to French aristocrats. Huygens’s achievement in clock

technology sparked a reaction too often overlooked from a number of savants and

426 Pascal entertained “duchesses” and “cordons-bleus” at the duchesse d’Aiguillon’s salon in the petit Luxembourg with his arithmetical machine and his experiments on the vacuum. Jean Loret, La Muse historique, 14 April 1652, in Pascal, OC, ii:902-903. On luxury trades, see Robert Fox and Anthony Turner, Luxury trades and consumerism in ancien régime Paris. Woodruff D. Smith, Consumption and the making of respectability, 1600-1800 (New York: Routledge, 2002). Natacha Coquery, L’Hôtel aristocratique. Le Marché du luxe à Paris au XVIIIe siècle (Paris: Editions de la Sorbonne, 1998). On commerce in general, Natacha Coquery, ed., La Boutique et la ville. Commerces, commerçants, espaces et clientèles, XVIe-XXe siècle (Tours: Publication de l’Université François Rabelais, 2000). Franco Angiolini and Daniel Roche, eds., Cultures et formations négociantes dans l’Europe moderne (Paris: Editions de l’Ecole des Hautes Etudes en Sciences Sociales, 1995).

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members of the French republic of letters, who as a result belatedly reviewed favorably

the pascaline and even sent one exemplar to the Dutch natural philosopher. It was in fact

during that period, in the Fall of 1659, that Charles Bellair penned the first full

description of the pascaline’s clocklike mechanism. (See Figure 3.8.) In a cryptic reply to

Bellair’s letter, Huygens wrote he found the drawings “very curious” and praised the

invention.427 He thought the drawings difficult to understand however, and thus replied

that he would better appreciate the mechanism after receiving the pascaline. (As Bellair

explained, the carry mechanism was without doubt the most intricate aspect of the

machine. Reading Bellair’s convoluted description, one is reminded of Pascal’s advice in

the Avis nécessaire concerning the pointless use of textual and pictural descriptions of the

pascaline.)

It would take a few more months before the arithmetical machine reached

Huygens in the Netherlands and thus could be carefully studied. To that effect, the

distinguished gentleman (possibly Pascal himself) who loaned the machine to Huygens

via Bellair had authorized the Dutch natural philosopher to make copies of it if he so

desired. (Since the pascaline’s privilege could only be enforced in France anyway, as will

be discussed below, the authorization to make copies in Holland should be understood as

a proof of admiration and high regard toward Huygens rather than an extraordinary

427 Huygens does not appear here to have known the pascaline. Yet in planning a trip to France for his son ten years earlier, Huygens father, Constantijn, received a correspondence from Mersenne telling him that “Votre Archimède verra ici l’invention dudit Pascal pour supputer sans peine et sans rien savoir,” referring to Pascal’s arithmetical machine. Mersenne to Constantijn Huygens, 17 March 1648, in Pascal, OC, ii:578. Huygens fils will visit Paris in 1655, but apparently did not come into contact with the pascaline, even though he befriended Jean Chapelain, who praised to him later Pascal’s invention (see below).

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favor.428) After having thoroughly examined and used the pascaline, Jean Chapelain was

convinced Huygens would most certainly praise the genie behind the machine “even

FIGURE 3.8: THE PASCALINE’S MECHANISM ILLUSTRATED The upper right drawing shows the small mechanism ensuring the transport movement of the wheels. As Bellair explained to Huygens, “Il ne reste plus qu’une pièce à expliquer, qui est la plus difficile de toutes. Je ne sais si je pourrai bien la faire entendre. Elle est représentée dans la feuille de la seconde figure en 2 manières: A la fait voir par le dessous, et B par le côté. Elle sert à faire passer le mouvement d’une roue à l’autre par sa pesanteur.” Bellair to Huygens, 4 July 1659, in Huygens, Oeuvres complètes, ii:428-429. Other such detailed representations of the machine’s mechanism are found in vol. 4 of Gallon’s Machines et inventions approuvées par l’Académie royale des sciences and Diderot and D’Alembert’s Encyclopédie under “Algèbre.” more so since you will find [this genie] similar to your own.” Unfortunately, no extensive

written account from Huygens is to be found. To the Court Official and mathematician

428 Du Gast to Huygens, 6 February 1660, in Huygens, Oeuvres complètes, iii:20: “Pour la personne à qui Monsieur Pascal a fait autrefois ce beau present, et qui est une des premieres en merite que nous ayons en France, je scay, Monsieur, qu’elle vous honnore parfaitement, et qu’elle a pour vous une estime toute particuliere. Elle m’a chargé de vous dire, que vous pouuez retenir cet instrument autant de temps qu’il vous plaira, soit pour le faire voir à vos amis, soit pour en faire faire de semblables; et que quand vous en aurez disposé ainsy en toute liberté, il n’y aura qu’a le renuoyer par la mesme voye de Monsieur Petit [a Parisian librarian involved in letter exchange between France and Holland].”

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Pierre de Carcavy Huygens simply observed that he thought the pascaline was worthy of

admiration and incorporated several belles pensées.429

The link between early modern arithmetical machines and clockmaking is perhaps

quite obvious. For instance, although Schickard described his device to Kepler simply as

an arithmeticum organum, it is now commonly referred to in German as a Rechenuhr, or

reckoning clock. (Rechenmaschine is also used often, clearly.)430 Looking at figure 3.8

one easily can recognize the resemblance between the pascaline’s mechanism and the

internal gearing system of a clock or watch. Pascal left no written account regarding the

manner in which he came up with the machine’s complex mechanism. The rhetoric he

used is famous, however, saying that the “lights of geometry, physics and mechanics

provided me with the design, and assured me its operation would be infallible” if only he

could find the right craftsman to build the model he had invented. Since Pascal, he said

himself, could not work with the lathe, hammer and file as well as he did with the pen

and dividers, he had to rely on the practical expertise of artisans, in this case Rouen

clockmakers, to manufacture the pascaline.431

Until the early seventeenth century, Rouen’s horlogers were part of the serrurier-

arquebusier guild, or locksmith and firearm guild. Two types of clockmakers existed

within that guild: the horlogeur en gros volume, who built the large mechanisms of

429 Bellair to Huygens, 4 July 1659, in Huygens, Oeuvres complètes, ii:426-429; Huygens to Bellair, 28 August 1659, ibid., 473; Chapelain to Huygens, 15 October 1659, ibid., 496; Du Gast to Huygens, 4 December 1659, ibid., 515; Huygens to Carcavy, 26 February 1660, ibid, iii:28. A full dossier is also found in Pascal, OC, iv:680-698.

430 The two letters on the arithmetical machine sent to Kepler are found in Schickard’s complete correspondence, Friedrich Seck, ed., Wilhelm Schickard Briefwechsel, 2 vols. (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 2002), i:135 and 141-142. Volume 2 offers a good bibliography on the topic, see pp. 522-526. See also Pratt, Thinking machines, chap. 3 titled “Calculating clocks.”

431 For the quote, Pascal, “Lettre dédicatoire,” 332. Pascal used similar argument in the Avis nécessaire.

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church and public clocks, and the horlogeur en petit volume, or simply clockmaker, who

designed and crafted tabletop clocks and watches. In 1617 the latter, fourteen of them,

solicited the king to grant them their own statutes, claiming that a great prejudice to their

craft and to the public was perpetrated by the abuse and defective items manufactured in

the city by foreigners and others. To solve the problem, they asked that they be granted

the same statutes and privileges as the Parisian clockmakers, following the letter patents

of 1544 and a règlement from 1600. The two representatives appointed by the king to

study the question believed the citizens of Rouen would not be interested in the formal

establishment of the métier d’orloger if regulated by the same rules as those introduced in

Paris. So, to accommodate the clockmakers’ request and to ensure that the other métiers

jurés from Rouen would not fall to prejudice either, new privilege articles were written

(though largely inspired by the Parisian ones). When it was time to formally register this

règlement to the Parlement, the masters from the serrurier-arquebusier guild complained

that they were also horlogers en gros volume, and thus rightfully entitled to make large

clocks. Their protest was heard and received. It was added to the règlement that the new

clockmaker maîtres jurés could not prevent any member from the locksmith and firearm

guild to compete against them for the right of making large clock mechanisms.432

When Pascal arrived in Rouen in 1642, therefore, the guild of clockmakers was

already well established within the city. Pascal thus had an easy access to several

432 Charles de Beaurepaire, Dernier recueil de notes historiques et archéologiques concernant le département de la Seine-Inférieure et plus spécialement la ville de Rouen (Rouen: Imprimerie de Espérance Cagniard, 1892), 337-340. Ch. Ouin-Lacroix, Histoire des anciennes corporations d’arts et métiers et des conféries religieuses de la capitale de la Normandie (Rouen: Lecointe Frères, 1850), 186-187, who mentions that the new corporation was established near the Saint-André-de-la-Ville church and under the patronage of Saint Eloi. For the Parisian privilege, see René de Lespinasse, Les Métiers et corporations de la ville de Paris, 3 vols. (Paris: Imprimerie Nationale, 1886-1897), iii:546-560.

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clockmakers such as Noël Hubert, Balthazar Martinot and David Thorelet—who claimed

he was le premier horloger reçu par chef-d’oeuvre à Rouen—and their apprentices, some

of whom received their mastery (maîtrise d’orloger) around the time Pascal finished the

first model of his arithmetical machine.433 Here is, briefly, how mastery was acquired.

One had to remain an apprentice for at least six years before being given the chance to

apply for a mastery title. Master clockmakers could only have one apprentice during the

first four year of the latter’s training; a second was allowed afterward. The status of

maître juré was sanctioned only after the apprentice had demonstrated he (hardly ever

she) understood the art of clockmaking par examen et essai and had created a

masterpiece—no detail is given here; in Paris, the chef-d’oeuvre was to be at least an

alarm clock (horloge à réveille-matin). (Children of master clockmakers were not

compelled to make a masterpiece if they could convince fellow masters they were

qualified for the métier.) Clockmaker’s widows could keep the workshop open and

continue to take advantage of their deceased husbands’ benefits as long as there was a

qualified clockmaker (a man, as specified) in the house. If the widow remarried with

someone who was not already a master clockmaker, the new husband would have to

produce a masterpiece before he was received as a genuine maître juré. Once the mastery

was achieved, all maîtres jurés could manufacture and sell from their shop every type of

clocks, but only there. (If an assistant [compagnon] was found making clocks outside of

433 De Beaurepaire, Dernier recueil de notes historiques et archéologiques, 342-344. Noël Ducastel, dit Gorin, the clockmaker who lead the August 1639 riot and was put to death on order from Séguier, is not mentioned in de Beaurepaire’s list. He was probably a horloger en gros volume from the serrurier-arquebusier guild.

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the master’s shop, his work and tools would be confiscated.) Clockmakers, finally, had to

engrave their name on the clocks they built.434

All these rules and regulations slowed down, but absolutely did not quench the

considerable manufacture of mediocre and fake clocks, as well as the illegal contraband

of all kinds of timekeepers. The example of Blois has been well documented and

accurately corresponds to what was happening elsewhere in France at the same time.

Inferior quality and outright defective clocks were produced by full-fledged master

clockmakers. Thirty pieces of a réveille-matin clock were seized in 1642 at the boutique

of Daniel Maupas, under the complaint of his wife who threatened and accused the jurés

of stealing a golden box.435 A greater problem still was the forgery and clandestine trade

of clocks. Compagnons as well as mediocre master clockmakers and those called sans

boutiques often reverted to making clocks in remote rooms and greniers in order to

bypass the limiting statutes of the guild. They made clocks which they sold themselves

on the “black market” or worked for unscrupulous goldsmiths or merchants who

possessed their own network of distribution. Clocks were left unsigned, or almost as

often were signed with a fictitious or a well-established clockmaker’s name (usually from

Blois or Paris). And not only timekeepers but also forged lettres de maîtrise were sold to

compagnons in search of a quick access to the trade. These were sizeable problems,

which the Blois master clockmakers feared would ruin the good name of individual

434 De Beaurepaire, Dernier recueil de notes historiques et archéologiques, 338-340. 435 Develle, Les Horlogers blésois, 63-64. The pieces taken were: “La cage et les roues du

mouvement, le barrillet avec son arbre, le rochet, la grande roue et la roue de rencontre avec le remontoir et son pignon, les deux ressorts de grande roue, le barrillet de sonnerie, le marteau du réveil, la roue du cadran avec le tourniquet et le pignon de rapport, le coq, le ballencier et les deux contrepotences, le garde corde avec son ressort, la clef et le cercle de cadran, trois cuivreaux et un arbre à tourner … toutes lesquelles pièces sont vicieuses.”

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craftsmen and the repute of the whole profession.436 Worst of all were the

goldsmiths, or orfèvres. Four of them, in four different years (1636, 1640, 1651 and

1660) were condemned by the court of Blois for violating the clockmaker statutes. They

stopped at nothing, forging names and illicitly making all types of luxurious clocks

decorated in gold and in rich enamel paintings. The 1636 lawsuit was instituted against

the orfèvre Isaac Gribelin after some thirty fraudulent clocks were found in his boutique.

All in all, these condemnations apparently were to little avail, aiding only marginally in

promoting law-abiding behavior.437

Taking into consideration what has just been said regarding the early modern

clockmaking trade, it is not surprising to discover that at least one Rouen clockmaker

tried to steal Pascal’s idea of the arithmetical machine. Pascal needed the expertise and

skills of a clockmaker given the machine’s close similarity with the internal mechanism

of a clock. In the Avis nécessaire he even said that at one point he had several ouvriers

helping him in making the machine. But since the pascaline was not a clock as such, nor

its inventor a Rouen master clockmaker, no justifiable legal recourse was available to

Pascal if someone attempted to replicate the invention for personal fame and profit. And,

as already mentioned, someone did. Pascal named no name—whether he knew it is

unknown. He only described the ouvrier or bonhomme as a talented clockmaker from

436 Ibid., 70, where after seizing some material in 1636 chez Isaac Gribelin, a goldsmith, they talked of the “grand désordre causé dans leur état,” describing the “maîtres, tellement décriés, que tous qui ont acheté des montres, ci-devant, publient hautement que lesd. maîtres orlogers sont des trompeurs.”

437 Ibid., 70-72. The Paris statutes of 1646, for instance, are quite clear vis-à-vis this division of expertise. Article 13 says: “Item, qu’il ne sera permis à aucun orfèvre ny autre, de quelque etat et mestier qu’il soit, de se mesler de travail et negocier, directement ou indirectement, d’aucune marchandise d’horlogerie grosse ou menue, vieille ny neuve, achevée ou non achevée, s’il n’est reçeu maistre dudit art d’horloger dans nostre Ville de Paris, pour obvier aux malversations dont le public reçoit un grand prejudice, à peine de confiscation de la marchandise dont ils seront trouvés saisis et d’amende arbitraire.” Lespinasse, Les Métiers et corporations de la ville de Paris, iii:555-556.

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Rouen, who made a mock machine based on the account someone had provided him of

Pascal’s first model. Pascal actually saw this travesty of an arithmetical machine. He

described it as well crafted on the outside, clean, nicely filed and polished, but

completely useless considering the fact that the internal mechanism was deficient and

unlike Pascal’s own. Yet, because of its novelty, a curieux from Rouen bought it and put

it on display in his cabinet together with other rare and unusual artefacts.438

According to Pascal’s own account, he was so disgusted by the deception that he

fired all his artisans and decided to quit the whole business. He was mostly concerned

about the numerous other artisans that would be brash enough to do the same, thus

ruining the esteem and public utility such an invention would ever acquire. Fortunately

for the young savant, the chancelier Séguier encouraged Pascal to finish the arithmetical

machine. And to dissipate any fear Pascal may have had, the chancelier decided via the

king’s (more specifically the regent’s) authority to

take out evil from the root and preventing it to spread to the detriment of my [Pascal’s] reputation and the public’s disadvantage by granting me an uncommon [qui n’est pas ordinaire] privilege that would stifle before their birth all these illegitimate abortions that could be engendered outside of the legitimate and necessary alliance between theory and the [mechanical] arts.439

438 Pascal, Avis nécessaire, 339: “Cher lecteur, j’ai sujet de te donner ce dernier avis, après avoir vu de mes yeux une fausse exécution de ma pensée faite par un ouvrier de la ville de Rouen, horloger de profession, lequel, sur le simple récit qui lui fut fait de mon premier modèle que j’avais fait quelques mois auparavant, eut assez de hardiesse pour en entreprendre un autre, et, qui plus est, par une autre espèce de mouvement; mais comme le bonhomme n’a autre talent que celui de manier adroitement ses outils, et qu’il ne sait pas seulement si la géométrie et la mécanique sont au monde, aussi (quoiqu’il soit très habile en son art, et même très industrieux en plusieurs choses qui n’en sont point) ne fit-il qu’une pièce inutile, propre véritablement, polie et très bien limée par le dehors, mais tellement imparfaite au-dedans qu’elle n’est d’aucun usage; et toutefois, à cause seulement de sa nouveauté, elle ne fut pas sans estime parmi ceux qui n’y connaissent rien, et nonobstant tous les défauts essentiels que l’épreuve y fait reconnaître, ne laissa pas de trouver place dans le cabinet d’un curieux de la même ville, rempli de plusieurs autres pièces rares et curieuses.”

439 Pascal, Avis nécessaire, 340: “Mais, quelque temps après, Monseigneur le Chancelier, ayant daigné honorer de sa vue mon premier modèle et donner le témoignage de l’estime qu’il faisait de cette invention, me fit commandement de la mettre en sa perfection; et, pour dissiper la crainte qui m’avait retenu quelque temps, il lui plut de retrancher le mal dès sa racine et d’empêcher le cours qu’il pourrait

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With such a privilege in hand, Pascal no doubt expected to protect and profit from his

invention.

The privilege Pascal received for the pascaline was actually a gift from the king of

France, which had nothing to do with the so-called inventor’s rights of today’s patent

law. It better reflected the connections one had with the privilege-granting authority—the

crown of France here—than the originality of the invention.440 Pascal’s 1649 privilège,

perhaps unsurprisingly, bore some similarity with the revised statutes granted three years

earlier by the same Louis XIV’s regency to the Parisian clockmakers’ guild. Pascal’s

privilege (and the Avis nécessaire before it) mentioned the fact that over fifty different

prototypes were produced, of assorted shapes and composed of various kinds of

mechanisms and materials, before one finally worked to Pascal’s satisfaction. Yet not

only the working model, but all fifty versions and every other possible way of producing

a calculating device were protected by the privilege.441 It was no doubt, as Mario Biagioli

argues, a strategy fashioned by Pascal to win future infringement cases. It also matched

three specific articles of the Parisian clockmakers’ statutes, which permitted the guild’s

artisans to construct their timekeepers in any form and shape they wanted, and in all

prendre au préjudice de ma réputation et au désavantage du public par la grâce qu’il me fit de m’accorder un privilège qui n’est pas ordinaire, et qui étouffe avant leur naissance tous ces avortons illégitimes qui pourraient être engendrés d’ailleurs que de la légitime et nécessaire alliance de la théorie avec l’art.”

440 Biagioli, “From print to patents,” 141-152. 441 Pascal, Privilège, 714: “De quelle machine il aurait fait plus de cinquante modèles, tous

différents, les uns composés de verges ou lamines droites, d’autres de courbes, d’autres avec des chaînes; les uns avec des rouages concentriques, d’autres avec des excentriques, les uns mouvants en ligne droite, d’autres circulairement, les uns en cônes, d’autres en cylindres, et d’autres tout différents de ceux-là, soit pour la matière, soit pour la figure, soit pour le mouvement…” The privilege prevented anyone to produce an arithmetical machine “sans le consentement dudit sieur Pascal fils ou de ceux qui auront droit de lui, sous prétexte d’augmentation, changement de matière, forme ou figure, ou diverses manières de s’en servir…”

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desired types of material, while at the same time forbidding anyone—goldsmiths

included, ça va de soi!—to make and sell in the city all types of clockwork, gros or petit

volume, old or new, complete or unfinished.442 Pascal’s privilege also prohibited anyone

who would build such an arithmetical machine outside of France to sell it anywhere

within the realm, corresponding to article 22 of the abovementioned clockmakers’

statutes.443 (This restriction was applied only to clockmakers, however. Parisian

marchans merciers-jouaillers, whose statutes granted them privilege to sell any type of

merchandise, could sell imported clocks and related goods as long as they had been

approved by the clockmakers’ guild powers that be.444) Finally, any artisan who abided

by the spirit of this privilege and built a pascaline would have to have it punched by a

special mark (decided by Pascal or the privilege’s heirs) that recognized the permission,

442 Lespinasse, Les Métiers et corporations de la ville de Paris, iii:555-556. Article 13, supra. Article 18, “Item, qu’il ne sera permis à aucuns revendeurs, revenderesses ou colporteurs, vendre ny faire vendre aucun ouvrage d’horlogerie, sur peine aux contrevenans de cent livres d’amende.” Article 19, “Item, que les maistres horlogers pourront faire ou faire faire tous leursdiz ouvrages d’horlogeries, tant les boetes qu’autres pièces de leurdit art, de telle estoffe et matières qu’ils aviseront bon estre, pour l’embelissement de leursdits ouvrages tant d’or que d’argent, et autres estoffes qu’ils voudront, sans qu’ils puissent estre empeschés ny recherchés d’autres que par Nous, sur peine de quinze cens livres d’amende…” This article follows from an arrêt of the king’s council, dated 8 May 1643. See Savary, Dictionnaire universel de commerce, ii:829-830. Biagioli, “From print to patents,” 172, n.39.

443 Lespinasse, Les Métiers et corporations de la ville de Paris, iii:557. Article 22, “Item, qu’il ne sera permis à aucun maistre horloger de nostre Ville de Paris d’acheter ny faire venir aucun ouvrage neuf d’horlogerie, tant grosse que menue, dedans ny dehors notre royaume pour raison que ce soit, attendu qu’il se vend des ouvrages qui sont mal faits, à peine de cent livres d’amende et confiscation desdiz ouvrages.”

444 Lespinasse, Les Métiers et corporations de la ville de Paris, iii:556. Article 14, “Item, que les marchans merciers-jouaillers, ayant pouvoir de trafiquer de toutes sortes de marchandises, ne pourront acheter ny vendre aucunes marchandises d’horlogerie dans nostre Ville et banlieue de Paris, ny autre ville de nostre royaulme, que premièrement ladite marchandise n’ait esté visitée, marquée et trouvée bonne par les gardes dudit art d’horloger de nostre Ville de Paris, lesquels pourront aller en visitation chez lesditz maistres marchans jouaillers pour veoir et visiter ladite marchandise d’horlogerie, dedans l’enclos et l’isle de nostre Pallais, Ville et banlieue de Paris, pour obvier aux abus et malversations qui se pourroient commettre au grand prejudice du public. Au cas que lesdits marchans exposent en vente ladite marchandise avant la visitation, elle sera confisquée, et le marchand expositaire d’icelle condamné en l’amende arbitraire.”

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craftsmanship and working legitimacy of the machine—not unlike, of course, the

conventional use of signatures on valued manufactured goods.445

This privilege was not as uncommon as Pascal claimed it was. That it applied to

the whole of France, not just Paris, Rouen, Blois or any other smaller region as most

privileges and guild’s statutes did, or that it was granted for a limitless period of time was

certainly unusual, but not overly strange. Like any other privilege of the sort, Pascal was

not restricted on the location where he could put his machine on the market—Roberval’s

Collège Royal was but one possibility—in comparison to Parisian and Rouen

clockmakers, who had the obligation to sell their merchandise from their boutique

only.446 The privilege, however, was necessary to Pascal since the Parisian guild had

acquired a virtual monopoly on the construction of all kinds of mechanisms that bore a

resemblance to a clock. And to help them achieve this objective the clockmakers had the

right to operate a furnace in their shop, being in a position thereby to fabricate key parts

of their clocks and watches (though they most likely bought small tools of the trade from

the taillandiers-ferblantiers and clock weights from the fondeurs).447 The privilege, in

445 Pascal, Privilège, 714: “Enjoignons à cet effet à tous ouvriers qui construironts ou fabriqueront lesdits instruments en vertu des présentes d’y faire apposer par ledit sieur Pascal ou par ceux qui auront son droit, telle contremarque qu’ils auront choisie, pour témoignage qu’ils auront visité lesdits instruments et qu’ils les auront reconnus sans défaut.” Furthermore, and understandably, clockmakers were not allowed to erase a name on a clock and sell it as their own. Lespinasse, Les Métiers et corporations de la ville de Paris, iii:555. Article 12, “Item, il ne sera permis à aucun maistre de nostre Ville de Paris de changer ny effacer aucuns noms qui seront taillés ou gravés sur lesditz ouvrages d’horlogerie, attendu que cela oste la bonne renommée et repputation de ceux qui les font, et aussy que c’est pour surprendre et tromper le public, à peine d’amende comme dessus.”

446 Lespinasse, Les Métiers et corporations de la ville de Paris, iii:555. Clockmakers themselves could not sell articles outside of their boutique, yet their servants and other Parisian clockmakers could do it for them. Article 11, “Item, il ne sera permis à aucun maistre dudit art d’horloger de nostredite Ville de Paris de faire travailler, revendre, ny colporter aucune marchandise hors leur boutique, synon par leurs domestiques ou par des maitres horlogers de nostre Ville de Paris, à peine de confiscation de la marchandise et d’amende applicable comme dessus.” Biagioli, “From print to patents,” 150.

447 Lespinasse, Les Métiers et corporations de la ville de Paris, iii:557. Article 24, “Item, tous

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other words, granted Pascal not only a quasi universal right of authorship, but also the

exclusive right of crafting himself any clock mechanism pertaining to the arithmetical

machine, if he chose to. (One of Pascal’s later heirs, the chevalier Durant-Pascal, claimed

that his famous relative, having found no clever enough artisan, made one of the smaller

arithmetical machines himself using some files and other tools acquired for the task.

Considering what Pascal wrote on this matter and the fact that any clockmaker was

furnished with a huge assortment of custom-made tools to accomplish similar handiwork,

this assertion in all likelihood is false—and remains unfounded to this day.448)

mouvemens ayant pignon de roue allant par ressort et contrepoids seront faits par les maistres horlogers, attendu que cela despend de leur art; et pourront aussi lesdiz maistres horlogers avoir forge et fourneau en leur boutique et lieu public, pour fondre et forger tout ce qui depend dudit art…” According to the taillandiers-ferblantiers letter patents of 1642, the guild members had the duty “Que toutes les limes douces, limes batardes, limes rudes, escoines de toute sorte de façons, tresses tant petites que grandes, filières, tarots et forets servant au mestier d’horloger, soient toutes d’acier et acier battu. Et s’il est trouvé faisant le contraire, l’amendera avec telle condamnation d’amende que de raison.” Ibid., ii:460, article 23. For the fondeurs, in was specified in the letter patents of 1572 that “Item, lesdits maistres fondeurs ne feront ne vendront aulcun ouvraige qui ne soyt bien et deuement faict, bon, loial et marchand, bien reparé et faict de bonne estoffe, sur peyne de confiscation et d’amende arbitraire, et ne vendront ouvraige venant de la fonte, si ce n’est à ung maistre dudict mestier, excepté les poix à adjouster et menu ouvraige pour les orlogeurs.” Ibid., 2:422, article 19.

448 The chevalier wrote around 1804 in a copy of Pascal’s Lettres de A. Dettonville the following: “La plus petite des deux machines qui a cinq rouës, a le mérite d’avoir éttée faite par pascal lui même; qui nayant pus trouver un ouvrier assés intelligent pour la faire, se procurat des limes et d’autres outils et fit lui même touts les rouages qui la composent.” Quoted in Mourlevat, Les Machines arithmétiques de Blaise Pascal, 40. On the tools clockmakers needed to build clocks and watches, the afterdeath inventory (1638) of the Blois clockmaker Loys Vautier gives a very good idea of the amount of tools one had to own to have success in the métier: “Un plat à dorer, une enclume en fer garnie de son billot de bois, six gros marteaux de fer a forger, un soufflet double de forge, une paire de tenailles de forge, des fers de forge, une paire de pincettes, quatre grands étaulx d’orloger, deux bigornes de fer d’estably d’orloger, cinq paires de cisouères, douze petits marteaux de fer d’estably, sept pierres à huile enchâssées de bois, sauf une, une bouillouer de cuivre rouge, douze livres de laton à ouvrer, treize paires de presses à tourner, dix-neuf arbres à tourner avec leurs bobines, et deux arbres à croiser (sic) grandes roues avec leurs bobines, plusieurs cuivreaux et arbres à plier les ressorts, deux petits compas, l’un à balancier et l’autre à calibrer, plusieurs poinçons à river, plusieurs limes à polir boîtes, trois compas de fer, cinq paires de pincettes de fer, six paires de grandes tenailles à vis, trois paires [de] presses à river, six couteaux à tailler limes emmanchés de bois, une grande lime large, dix-huit grandes limes, une râpe, neuf douzaines de limes et une petite plateforme propre à tasser deux rivetz, deux filières à tirer ressorts, garnies de douze limes, huit livres d’acier en barre, et cinq pièces d’acier forgé en forme de lames pour faire ressorts d’horlogerie.” Develle, Les Horlogers blésois, 39-40.

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Thus Pascal, owing to his privilege, did not have to resort to clockmakers; anyone

with the permission to do so could work on the internal mechanism (and the exterior

shape, appearance and decoration) of the pascaline. It is interesting to note in addition

that the Parisian clockmakers’s guild did not seem to mind this privilege that much.

There is in fact no indication that they ever manifested ire or concern regarding the

pascaline. Less than a decade later, in contrast, Huygens discovered otherwise. In 1658

the Dutch savant tried to secure such a privilege from Louis XIV for his newly invented

pendulum clock. With the help of the astronomer Ismael Boulliau, Huygens formally

requested through the chancelier Séguier that he be granted exclusive rights on French

territory for his clock. Boulliau, unfortunately, reported that the chancelier denied the

request three times and as a justification “has always replied that he did not want all the

master clockmakers of Paris crying after him, and besides there was always the

possibility that someone else had found this same way of [making] clocks.”449 As we saw

earlier, it did not prevent Huygens from selling his clocks to various members of the

French aristocracy—completely bypassing the clockmakers’ guild. Having not been

granted a privilege did not hinder Huygens from selling his pendulum clocks, but it did

449 Huygens to Boulliau, 13 June 1658, in Huygens, Oeuvres complètes, ii:183-184: “Vous scauez, puis que Monsieur l’Ambassadeur a pris la peine de vous en escrire, que je suis deuenu sollicitant en France pour obtenir Priuilege de ma nouuelle invention d’Horloge. Luy mesme nous asseura aussi avant hier que vous aviez desia formè une requeste pour ceste effect. Ce qu’ayant appris je me suis trouuè obligè de vous rendre graces de ce que vous avez la bontè de vous employer dans cette affaire, et de vous prier d’y continuer avec le mesme soin et la mesme affection: au moins si tant y a qu’il vous semble que nous y pourrions reüssir. Ce que je vous prie sur tout de me mander.” Boulliau to Huygens, 21 June 1658, in ibid., 185-186: “Je suis fort fasché que les jinstances, que j’ay faict faire aupres de Monsieur le Chancellier, pour obtenir le priuilege que vous desires, n’ayent pas reussi. Il a refusé par trois fois de l’accorder, & il a tousjours respondu qu’il ne vouloit pas faire crier apres luy tous les maistres horologeurs de Paris. & que mesme il se pouuoit faire que quelqu’un eust trouué cette mesme façon d’horologes. S’il y auoit eu le moyen de le surmonter, ceux que j’ay emploiez l’auroient faict: Vous estes fondé en exemple & en raison, mais comme cette grace depend absolument de Monsieur le Chancellier, & luy formant ces difficultez & obstacles il n’y a pas moyen pourtant d’en venir a bout.” English translation quoted from David S. Landes, Revolution in time: Clocks and the making of the modern world (Cambridge, MA and London: The Belknap Press of Harvard University Press, 1983), 117.

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not protect his invention either. It is difficult to tell whether the excuse given by Séguier

was genuine or simply a way of turning down someone who did not hold the required

royal connections to perform such a delicate assignment—after all, Huygens’s father

negotiated with Louis XIV directly so his Archimedes-son be granted a privilege in 1665

for his remontoir clock.450

Pascal, through his father and his former acquaintance with the Cardinal de

Richelieu, certainly had the ear of the chancelier, more so than Huygens did in 1658. Yet,

it also points to the fact that Pascal’s arithmetical machine was not perceived as a bona

fide threat to the Parisian clockmaking trade. Though the internal mechanism of the

pascaline strangely resembles that of a clock, Pascal’s machine never did gain the

superior prestige and authority that timekeepers retained in early modern Europe. The

pascaline’s epistemic value for natural philosophy, however, was not lost to Pascal and

those who saw the rhetoric hidden in the gears of the machine. There was indeed a

powerful rhetorical argument behind the privilege. The manner in which Pascal phrased

the Avis nécessaire and the 1649 privilège points in fact to one fundamental conclusion

regarding the practice of early modern science: the indispensable union of theory and

practice for the advancement of natural philosophy. Not unlike Mersenne’s organ,

Pascal’s arithmetical machine, taken on its innermost layer of understanding, epitomized

the role played by both artisans and savants in the pursuit of early modern knowledge.

450 Huygens, Oeuvres complètes, v:254, 256-257, 264, and 279. See Biagioli, “From print to patents,” 143.

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THE PASCALINE AND THE MARRIAGE BETWEEN THEORY AND PRACTICE

In the Lettre dédicatoire and Avis nécessaire Pascal emphasized several times that

creating and making the arithmetical machine necessitated the alliance of theory and the

mechanical arts. Taken separately, Pascal claimed, one was as deficient as the other; both

were essential to the task, whether one liked it or not. Such a stance toward the nature of

knowledge likely came from the time spent with his father at the Mersenne academy. I

have shown in Chapter one how the Minim, especially in his Traité de l’orgue,

underscored the role of theory, experiment and musical instruments in achieving a

complete understanding of the nature of sound. Pascal père, it would appear, fully

endorsed this approach to natural philosophy. Mersenne, actually, dedicated the same

Traité de l’orgue to the elder Pascal, praising Blaise’s father not only for being an

accomplished musician, but more importantly for having married his extensive

knowledge of mathematics to the practical expression of mechanics.451 To Pascal, who

was taught everything by his father, the conjunction of theory and practice must have felt

natural, allant de soi, owing to the intellectual milieu he was bathing in since the early

adolescence. Though Pascal firmly believed the artisan was subordinated to the grandeur

of the natural philosopher’s mind, the former’s mastery of the mechanical arts was

indispensable to the success of his enterprise—and on the whole of natural philosophy.452

The tension between theory and practice was already explicit in Pascal’s Lettre

dédicatoire to Séguier. Pascal pointed out that unfamiliar or unusual inventions always

451 Mersenne, “Traité de l’orgue,” book VI, Epitre, in Harmonie universelle, contenant la théorie et la pratique de la musique, 3 vols. (Paris: Centre national de la recherche scientifique, 1963), iii:n.p. The Epitre is dated 1 November 1635. See introduction to chapter one for the full quote.

452 On this grandeur of the natural philosopher vis-à-vis the artisan, see Jones, The matter of calculation, chap. 1.

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had more censors than approvers. Scholars were especially unsympathetic to novelties.

Instead of trying to understand inventions for what they were, according to Pascal, these

savants more often than not simply judged them impossible—before discarding them as

impertinent little things. (Pierre Petit used the same trope in praising Buot’s rove de

proportion.)453 In the Avis nécessaire, Pascal warned the reader about the first cloud

(vapeur) that had to be dispersed from his mind, namely that the complexity of the

pascaline could have (and should have) been scaled down. Here Pascal somewhat echoes

what Descartes said regarding the lens-grinding machine (see Chapter two). Complexity

was not a problem here, but a direct manifestation of the need to unify theory and

practice. The suggestion that the arithmetical machine was composed of too many parts

could only come from

certain minds that obviously have some knowledge of mechanics or geometry, but because they do not know how to join them together, and these last two to physics, they flatter or deceive themselves in their imaginary impressions, convinced that outcomes are probable where none are. They possess an imperfect theory of things in general, which is insufficient to predict specific problems arising from matter itself or from the particular arrangement of a machine’s parts—the movements of which having been designed appropriately so that they remain free and do not encroach on one another. Hence, when these specious savants will suggest to you that this machine could have been less intricate [composée], I pray you to give them this reply that I would offer myself if they were to ask me…454

453 Pascal, “Lettre dédicatoire,” 333. Petit’s letter to Buot in Buot, Vsage de la rove de proportion, 18-19, where he wrote: “On ne trouuera pas estrange que i’exalte les Inuenteurs, & que ie me mette en cholere contre les ignorans qui n’estans pas capables de rien produire de leur chef, ne le sont mesmes pas d’admirer & reuerer ceux à qui la nature a donné ce genie.” (p.18)

454 Pascal, Avis nécessaire, 335-336: “Cette proposition ne te peut être faite que par certains esprits qui ont véritablement quelque connaissance de la mécanique ou de la géométrie, mais qui, pour ne les savoir joindre l’une et l’autre, et toutes deux ensemble à la physique, se flattent ou se trompent dans leurs conceptions imaginaires, et se persuadent possibles beaucoup de choses qui ne le sont pas, pour ne posséder qu’une théorie imparfaite des choses en général, laquelle n’est pas suffisante de leur faire prévoir en particulier les inconvénients qui arrivent, ou de la part de la matière, ou des places que doivent occuper les pièces d’une machine dont les mouvements sont différents, afin qu’ils soient libres et qu’ils ne puissent s’empêcher l’un l’autre. Lors donc que ces savants imparfaits te proposeront que cette machine pouvait être moins composée, je te conjure de leur faire la réponse que je leur ferais moi-même s’ils me faisaient une

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Pascal acknowledged his argument seemed paradoxical, i.e. to ensure that the machine’s

operation was as easy as possible its internal mechanism had to be intricate. Yet Pascal

asked the reader of the Avis nécessaire not to judge the pascaline imperfect on account of

its internal complexity. The movement created by the small intertwined wheels, Pascal

argued, was so simple and perfect that it could move effortlessly as many as ten thousand

such wheels if one desired—adding that he was not convinced whether another

comparable principle on which he established this mechanism existed in nature. Although

Pascal did not underscore this point himself in his exposé, one could clearly reflect upon

Pascal’s claim looking at the complexity and (increasing) exactness of a good clock, or

better yet the infinite intricacy of the clockwork universe as described by the rising

mechanical philosophy of Descartes and others. Complex mechanical movements, based

on flawless principles, presented no epistemic conundrum according to Pascal; any

scholar who assumed otherwise was plainly wrong and should be challenged to

demonstrate the contrary.

Artisans alone, as one might expect, fared no better in Pascal’s presentation of his

mechanical epistemology. The second cloud the readers of the Avis nécessaire needed to

disperse would come from the poor copies of the pascaline made by presumptuous

craftsmen. Pascal beseeched his reader to look out for these imperfect reproductions

executed by the ignorance and temerity of such ouvriers. Skilled artisans were certainly

as bad as learned scholars regarding the meaning and assessment of the arithmetical

machine: What scholars put into words, artisans built in materiam. According to Pascal,

telle proposition…”

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the better artisans were in their art, the more daring was their vanity, which inclined them

to believe they could carry out any new and original work. Intoxicated by this false

conviction, artisans

operate by trial and error, that is to say with uncertainty and without proportions as determined by art; whence it happens that after a lot of time and labor they do not produce anything that bears a resemblance to what they had originally undertaken, or at best they engender a little monster to which lacks the principal limbs, the other [parts] being distorted and without any proportion. These imperfections, rendering it ridiculed, never fail to attract the scorn of all who see it, most of whom blaming without reason the first one who ever thought about this invention in lieu of trying to find enlightenment from the inventor and then blaming the presumptuousness of these artisans who, owing to a false impudence that makes them think they can do more than their peers, manufacture these useless abortions.455

The fear that savants would blame Pascal for the flawed copies of the pascaline was

identical to Descartes’s own when he learned from Desargues that the Cardinal de

Richelieu wanted artisans to build several of his lens-grinding machines in order to

develop the lens manufacture in France. The lesson Pascal wanted his reader to bear in

mind was that regarding new inventions the mechanical arts absolutely had to be assisted

by theory “until practice had caused the rules of theory to become so common they could

be reduced to art.” Moreover, Pascal believed that “continuous exercise would give

artisans the habit of following and practising these rules with assurance.”456

455 Pascal, Avis nécessaire, 338: “puis, enivrés de cette fausse persuasion, ils travaillent en tâtonnant, c’est-à-dire sans mesures certaines et sans proportions réglées par art; d’où il arrive qu’après beaucoup de temps et de travail, ou ils ne produisent rien qui revienne à ce qu’ils ont entrepris, ou, au plus, ils font paraître un petit monstre auquel manquent les principaux membres, les autres étant informes et sans aucune proportion: ces imperfections, le rendant ridicule, ne manquent jamais d’attirer le mépris de tous ceux qui le voient, desquels la plupart rejettent sans raison la faute sur celui qui, le premier, a eu la pensée d’une telle invention, au lieu de s’en éclaircir avec lui et puis blâmer la présomption de ces artisans qui, par une fausse hardiesse d’oser entreprendre plus que leurs semblables, produisent ces inutiles avortons.”

456 Ibid., 338-339.

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Theory and practice, carried out separately, were useless to Pascal and

consequently to anyone desiring to build an arithmetical machine—extrapolating the

argument, it was also true of every new invention coming from either the mind of the

savant or the hands of the artisan.457 Theory and practice, when combined, became for

Pascal and a growing number of natural philosophers the quintessential ingredient to the

recipe of a good natural philosophy. Studying the arithmetical machine’s fabrica et usus

naturally revealed the virtues of this natural philosophical approach, as the study of

Mersenne’s organ or Descartes’s lens-grinding machine did. To change one’s

predisposition against either theory or practice, Pascal needed to alter conventional habits

of thinking, one more thing the pascaline could teach through the concept of coutume.

MEMORY, COUTUME, AND THE EMBODIMENT OF KNOWLEDGE IN MACHINES

John Napier, like most mathematical practitioners did in early modern Europe, extolled

the virtues of mathematics in the dedication of his Mirifici logarithmorum canonis

descriptio (1614) to Charles I. Since no other type of study, Napier wrote, “doth more

acuate and stirre vp generous and heroicall wits to excellent and eminent affaires,” it was

to be expected that “learned and magnanimous Princes in all former ages haue taken great

delight in them,” whereas “the vnskilled and slothfull men haue alwayes pursued them

with most cruell hatred, as vtter enemies to their ignorance and sluggishnesse.” Why

457 Ibid., 339: “Et tout ainsi qu’il n’était pas en mon pouvoir, avec toute la théorie imaginable, d’exécuter moi seul mon propre dessein sans l’aide d’un ouvrier qui possédât parfaitement la pratique du tour, de la lime et du marteau, pour réduire les pièces de la machine dans les mesure et proportions que par les règles de la théorie je lui prescrivais, il est de même absolument impossible à tous les simples artisans, si habiles qu’ils soient en leur art, de mettre en perfection une pièce nouvelle qui consiste, comme celle-ci, en mouvements compliqués, sans l’aide d’une personne qui, par les règles de la théorie, lui donne les mesures et les proportions de toutes les pièces dont elle doit être composée.”

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then, Napier asked rhetorically, should not his new invention, the logarithm—“seeing it

abhorreth [by] blunt and base natures”—rightfully “seeke and flye vnto your Highnesse

most noble disposition and patronage?” Logarithms not only eliminated all the

difficulties found in mathematical calculations, “which otherwise might haue beene

distastfull to your worthy towardnesse,” stated Napier, but was “so fitted to helpe the

weaknesse of memory, that by meanes thereof it is easie to resolue most Mathematical

questions in one hours space” instead of the full day or more it would take using

conventional mathematical methods. “[W]hat can bee more delightfull and more

excellent in any kinde of learning,” asked Napier, “than to dispatch honourable and

profound matters, exactly, readily, and without losse of either time or labour”?458

Napier’s other popular invention, rabdology, was described likewise by John Dansie, who

gave the following subtitle to his 1627 A Mathematicall manuel: “whereby Any man that

can but add and substract, may learne to multiply and divide in two houres by

Rabdologie, without any trouble at all to the memorie.”459 And in a sonnet dedicated to

Pascal’s arithmetical machine, the poet Dalibray explicitly mentioned how wonderful the

“artifice” of this “wonderful genius” was in demanding no reason nor memory to help

even the “thickest minds” to calculate.460

458 Napier, A description of the admirable table oe [sic] logarithmes, sig. A4r. 459 Dansie, A Mathematicall manuel, subtitle of the book. 460 Dalibray, Les Oeuvres poétiques, in Pascal, OC, ii:692:

Cher Pascal, qui comprends par un subtil savoir Ce que la mécanique a de plus admirable, Et de qui l’artifice aujourd’hui nous fait voir D’un merveilleux génie une preuve durable, Après ton grand esprit, que sert-il d’en avoir? Compter fut l’action d’un homme raisonnable, Et voilà, maintenant ton art inimitable

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Mathematical practices like logarithm and rabdology were invented to substitute

the so-called weakness of memory with tools such as printed logarithmic tables, paper or

metallic rules (reigles de proportion), Napier’s bones and finally calculating machines.

The memory involved in making arithmetical operations like multiplication and

subtraction, said differently, was supplanted by material devices created for specific

mathematical practices. Abstract number concepts were materialized into these devices—

they were blackboxed one would say today. They no longer required to be understood nor

remembered by rote. A material object, to which was associated a prescriptive technique,

was replacing intangible memory. This trade-in of the material for the immaterial points

as well to another fundamental aspect regarding mathematical practices in general, and

the pascaline in particular. New material objects necessitated the learning of new gestural

habits, most likely distinct from conventional ones. Using Napier’s bones, for instance,

bound a mathematician to bodily movements drastically different from the plume and

jetons technique: the positioning and reading of rods had nothing to do with the jetons.

Without the proper gestural habit, multiplication with Napier’s bones would prove

impossible. Pascal’s arithmetical machine was no different than other mathematical

instruments in this respect. To use it, one required a completely new habitude, gestural

habits that ensured the proper working of the machine. With time, the concept of

Aux esprits les plus lourds en donne le pouvoir. Il ne faut pour cet art ni raison ni mémoire, Par toi chacun l’exerce et sans peine et sans gloire, Puisque chacun t’en doit et la gloire et l’effet Ton esprit est semblable à cette âme seconde Qui va s’insinuant par tout dedans le monde Et préside et supplée à tout ce qui s’y fait.

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habitude will be generalized into coutume, which became part of Pascal’s epistemology

of knowledge.

Memory was not completely obsolete or useless. In fragment 536 of the Pensées,

Pascal asserted that “memory is necessary for all the operations of reason” and in

fragment 322 he described how central was genealogy (the memory of past generations)

to the ancients’ understanding of history. Memory was also fundamentally linked to

ordinary-life customs in the writings of Epictetus, Montaigne and Salomon de Tultie—or

Pascal himself, the last name being an anagram of Amos Dettonville, Pascal’s alias.461

Yet memory became an obvious problem when dealing with arithmetic. The pascaline’s

carry mechanism, the most important mechanical feature of the machine, was meant to

alleviate the mind from such a mental exertion:

You [the reader] know as well that while using the plume one is compelled at any time to carry or borrow numbers, and how many errors slip by in these carries and borrowings, unless one has a very long habit [habitude] [in such things] and a deep concentration, which rapidly wears out the mind. This machine relieves anyone who uses it from this vexation. It suffices that one has judgment, whilst the machine take over from the failing of memory. And, with no carrying nor borrowing [to execute], the machine does by itself what its user wants, without the latter even having to think about it.462

Memory, however, was but one annoyance to those lacking the mastery of numbers.

According to Pascal, the art of arithmetic as a whole was a chore when the reckoner

lacked the habitude of the plume and jetons. Pascal invented the arithmetical machine to

curtail the superfluousness of the conventional reckoning technique. With this new

461 Pascal, Pensées, S536 and S322 and S618. 462 Pascal, Avis nécessaire, 337: “Tu sais de même comme, en opérant par la plume, on est à tous

moments obligé de retenir ou d’emprunter les nombres nécessaires, et combien d’erreurs se glissent dans ces rétentions et emprunts, à mois d’une très longue habitude et, en outre, d’une attention profonde et qui fatigue l’esprit en peu de temps. Cette machine délivre celui qui opère par elle de cette vexation; il suffit qu’il ait le jugement, elle le relève du défaut de la mémoire; et, sans rien retenir ni emprunter, elle fait d’elle-même ce qu’il désire, sans même qu’il y pense.”

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machine, the “most ignorant [calculator] will find as much advantage as the most

experienced one” because “the instrument makes up for the lack of knowledge or lack of

habitude” of its user. Pascal added that through the machine’s “necessary movements,”

the user of the pascaline could do with ease, without even thinking about it, every

possible arithmetical operations.463

The rapidity of the machine’s mechanical action (mouvements nécessaires) was

made obvious when measured up to to the motions (gestes) required by the plume and

jetons technique. In fact, as Pascal argued to his reader, “if you want a more specific

explanation of the speed of the machine’s movements, I would tell you that it is equal to

the quickness [agilité] of the hand working on it.”464 The gearing system of the machine

did not impede at all the promptitude of the hand; owing to the machine’s design the hand

working on it could become as free and as fast as if it dealt with the plume and jetons. In

contrasting the swiftness of execution of both techniques Pascal underscored one

essential facet of his invention: the necessity of learning a new gestural habitude, one that

was as efficient as the traditional method yet utterly dissimilar. This new gestural

habitude was confounding not because it required a training of the body per se, but

because this bodily accoutumance suggested a corporeal “memory” rather than an act of

memory from the mind—called for with the plume and jetons. The pascaline, in a sense,

demoted arithmetic from the realm of the mind to that of the body. It became a “mere”

addition of la machine, or Pascal’s characterization of the human body. Arithmetic was

463 Ibid., 337. 464 Ibid., 337: “Et, enfin, quant à la promptitude, elle paraît de même en la comparant avec celle

des autres deux méthodes du jeton et de la plume; et si tu veux encore une plus particulière explication de sa vitesse, je te dirai qu’elle est pareille à l’agilité de la main de celui qui opère.”

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no longer a knowledge derived from the mind, but a precise and rhythmic mechanical

action generated by a body appendage.

According to Eric Lundwall, this could very well explain the pascaline’s failure as

a consumer item. The machine, according to Pascal’s rhetoric, replaced thinking with the

plume and jetons by a complex mechanical system that was easier, simpler, faster and

surer than conventional methods. Pascal said himself in fragment 617 that his machine,

though not endowed with a will of its own, “produce[d] effects closer to genuine thought

than anything animals could do.”465 With the machine, Pascal tried to bridge the infinite

distance between body and mind referred to in fragment 339. The pascaline, in

Lundwall’s view, thus begged for a leap of imagination that was most likely too difficult

to grasp or to accept by early modern standards of reasoning. Conversely, the success of

Pascal’s next business venture, the carrosses à cinq sols, rested on the coutume of the

coches à la campagne already well established between French provincial towns. Here

Pascal stretched a familiar coutume rather than customer’s imagination. With the

relatively cheap coach rides (five sols), Pascal made sure he stayed within the same order,

l’ordre du corps, or la grandeur de la chair, in granting bourgeois of lower means the

sensation (for a short timespan) of being wealthy and eminent gentlemen. Such an

horizontal symmetry within the grandeur de la chair was the key to the success of the

carrosses à cinq sols. In contrast, the vertical leap demanded by the pascaline between the

465 Pascal, Pensées, S617: “La machine arithmétique fait des effets qui approchent plus de la pensée que tout ce que font les animaux. Mais elle ne fait rien qui puisse faire dire qu’elle a de la volonté, comme les animaux.”

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grandeur de la chair and the grandeur de l’esprit caused problems and confusion in the

material realm of early modern markets.466

Yet for Pascal it was of the utmost importance. Following a request from

Bourdelot, a Frenchman connected to the court of Sweden since 1651, Pascal sent to

queen Christina a copy of his arithmetical machine together with a remarkable essay on

the power of the natural sciences. This text offer an early formulation of Pascal’s later

idea of the three orders of grandeur: la chair, l’esprit and la charité. Here, only the first

two were invoked. Yet they were sufficient to establish the core argument of the text.

Looking at the arithmetical machine while reading Pascal’s exposé, Christina must have

understood that l’esprit could not only master corporeal bodies, but mechanical ones as

well. The arithmetical machine, as the source and reference point of Pascal’s famous

letter, became the perfect embodiment of the power and virtue of l’esprit over matter.

Something grander than mere “mechanics” lay behind the wheels and gears of the

machine; something worth the grandeur of a queen—or the chancelier Séguier, as he

liked to be called. Pascal probably believed that the machine, if advertised as a natural

grandeur de l’esprit, would be sought out, cherished and put in the cabinets of seigneurs

and royal dignitaries, themselves grandeurs de la chair. Reciprocally, savants endowed

with the grandeur de l’esprit would want Pascal’s machine because it was found in the

cabinets of seigneurs. (Hence Pascal’s dedication of his first machine to the chancelier

466 Lundwall, Les Carrosses à cinq sols, 46-47 and 110-111. The other advantage inherent to the business of the carrosses à cinq sols came from the fact that the artisans working on the coaches need not be told what to do. Again, the artisanal coutume was continued in this business venture. Pascal, in matters of coach manufacturing and repairing, did not have to intervene or to break traditional ways of doing. On this artisanal milieu, though later, see David Lussault, “Des artisans commerçants au service des élites: selliers carrossiers et charrons à Paris au milieu du XVIIIe siècle,” in La Boutique et la ville. Commerce, commerçants, espaces et clientèles, XVIe-XXe siècle, ed. by Natacha Coquery (Tours: Publication de l’université François Rabelais, 2000), 113-130.

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Séguier.) A powerful rhetorical argument was thus set into motion within the mechanism

of the machine, one by far exceeding the machine’s (overstated) utility.467 Pascal’s

arithmetical machine, I would argue, was proposed as a social status-granting device to

assert one’s own honnêteté. The machine, combining the grandeurs de l’esprit et de la

chair, could be envisioned as a material bridge between two frequently dissociated élites.

It could be understood as the perfect unifying instrument of the republic of letters.

The unification of mind and body symbolized by the arithmetical machine seemed

like it demanded a great power of abstraction, but it actually did not. The reason is

simple: Pascal relocated this apparent abstraction into the familiar notion of habitude or

coutume. Even memory, as one of the prime functions of the mind, did not escape this

move. Conventional reckoning techniques such as the plume and jetons or even Pratt’s

arithmeticall jewel proposed material devices that functioned as aide-mémoire, memory

crutches that failed at one point or another.468 An elaborate memory contraption like

Kircher’s organum mathematicum, however, suggested a more accurate and potentially

more powerful materialization of a thesaurus sapientiae, i.e. the medieval allegory of the

mind as a strongbox representing the storage as well as the internal organization of

memory. (See Figure 3.3.) The organum’s physical loculamenta in which Kircher stored

467 Bourdelot to Pascal, 14 May 1652, in Pascal, OC, ii:919. Pascal, “Lettre à la sérénissime reine de Suède,” in ibid., 923-926. On the role of the arithmetical machine on Pascal’s theory of orders see Christian Meurillon, “La Machine arithmétique à la genèse des ordres pascaliens,” Revues des sciences humaines 186-187 (1982-83), 147-158 and Haruo Nagase, “Rhétorique de la machine arithmétique: signification de son invention dans la pensée de Pascal,” Etudes de langue et de littérature françaises 72 (1998), 17-30.

468 I use aide-mémoire somewhat liberally here. A genuine one would be this late seventeenth-century English silver medallion one which is depicted on one side the solution of three special cases of quadratic equations and on the obverse a table used to for the calculation of interest in moneylending and related financial transactions. See Stephen Johnston, “An English mathematical aide-memoire of the 17th century,” <http://www.mhs.ox.ac.uk/staff/saj/aide-memoire> (Accessed on 15 March 2007).

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and organized mathematical notions of arithmetic, geometry, astronomy, music, etc. bore

a resemblance to the figurative loculamenta evoked by the medieval practitioners of the

art of memory. The metaphorical loci of the traditional Ciceronian art of memory, where

one would store in predetermined symbolic locations fragments of a text such as the

Psalms, were an important feature of the practice of the ars memoriae. Once knowledge

had been stored into a multitude of these loci—usually represented as lighted open

spaces, not too crowded and without excessive amount of details like a church or a

market place—one needed to map onto each memory space a special image, an imagine,

that would then be used to recall the knowledge found in that particular locus of the

mind. The more bizarre, vivid, unusual and evocative the image was, the easier it would

be to recall the desired knowledge from its appropriate memory space. This act of

memory-recalling was what Aristotle had called anamnesis, and it was shattered I would

argue through the utilization of early modern mathematical tools such as Kircher’s

organum mathematicum.469

Here mental images were useless and powerless in retrieving knowledge from the

instrument’s loculamenta. Once stored in Kircher’s organum, a mathematical concept

was physically recovered by the hand’s physical movement, not by a vivid imagine. Like

mathematical instruments described earlier, Kircher’s organum encompassed abstract

mathematical concepts that did not need to be memorized but were still dependent on

469 The art of memory is a fascinating topic of study which had a tremendous impact on medieval scholasticism. On this topic, see Mary Carruthers, The book of memory: A study of memory in medieval culture (Cambridge: Cambridge University Press, 1990). Two other classic books on the art of memory are Frances Yates, The art of memory (London: Pimlico, 1992 [1966]) and Paolo Rossi, Logic and the art of memory: The quest for a universal language, transl. by Stephen Clucas (Chicago: The University of Chicago Press, 2000). Though both these books discuss the medieval art of memory, they focus their arguments respectively on the Renaissance transformation of the art of memory through the hermeticism of Giordano Bruno and the rejection of the hermetic art of memory in favor of an ars memoriae concerned with questions pertinent to method and logic.

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exact mathematical practices. Pascal’s arithmetical machine, according to the rhetoric,

went even beyond that: it not only stored mathematical knowledge within its gears but the

practice of arithmetic as well. In the end, only gestural movements—or habitudes—were

left, which meant that no memorization nor mathematical practices were required in order

to operate Pascal’s machine. The pascaline became a natural and integral part of la

machine—the Pascalian definition of the human body—by way of the gestural

knowledge encompassing its use.

Habitude and coutume were not exactly identical notions in the seventeenth

century, yet were related to each other. Coutume usually meant a more collective

behavior while habitude was applied to individual actions. Usually, coutume

encompassed both the general and the individual definitions (taking for example Mme de

Sévigné’s writings, who said about various things that Je n’en ferai pas ma coutume).

Whereas coutume could stand-in for habitude, the reverse was an incorrect semantical

usage. Even though Pascal referred to both notions repeatedly, it was the more embracing

concept of coutume that held his attention. In the Pensées, for instance, Pascal mentioned

the substantive habitude only three times compared to forty-nine times for coutume.470

Therefore, to understand the gestural habitude underlined in the Avis nécessaire it is

necessary to take a closer look at Pascal’s concept of coutume.

In fragment 480 Pascal famously said that “coutume can do everything.” It is all

powerful because one cannot see it or feel it; because most of the time we are unaware of

its presence and action. “The coutume is a second nature that destroys the first.” (S159)

470 Gérard Ferreyrolles, Les Reines du monde. L’Imagination et la coutume chez Pascal (Paris: Honoré Champion Editeur, 1995), 17-19. This is the best general analysis of Pascal’s concept of coutume.

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Coutume is a major source of errors because it pulls a veil over the real nature of things.

It affects every activity of life: intellectual, social and religious. People, for instance, are

so accustomed to see kings surrounded by royal guards, officers and drummers, things

that convey respect and fear, that they believe it all comes from a natural force instead of

a coutume.471 In matters of faith, the lack of coutume made some individuals doubt

Christ’s ressurection, since the coutume of creating something that never was (childbirth)

largely supplanted the lack of coutume vis-à-vis the (re)creation of something that once

was.472 As Gérard Ferreyrolles so aptly described, the notion of coutume thus created for

Pascal social, ontological and epistemological problems that needed to be addressed.473 It

was of great consequence, because once an individual was accustomed in using false

reasonings to prove natural phenomena, he or she would not easily acknowledge the right

ones when discovered. (S617)

Coutume, furthermore, constrained the human body; it bent la machine under the

weight of habituation. (S59) As dangerous and problematical as coutume might be, it

could nonetheless become a powerful epistemological instrument.474 In matters of faith,

Pascal determined three methods of believing: reason, coutume, and divine inspiration. A

true Christian believer opened his/her mind to reasoned proofs, confirmed them by

471 Pascal, Pensées, S59. Sometimes, however, it is the other way around: “C’est l’effet de la force, non de la coutume, car ceux qui sont capables d’inventer sont rares. Les plus forts en nombre ne veulent que suivre et refusent la gloire à ces inventeurs qui la cherchent par leurs inventions. Et s’ils s’obstinent à la vouloir obtenir et à mépriser ceux qui n’inventent pas, les autres leur donneront des noms ridicules, leur donneraient des coups de bâton.” (S122)

472 Regarding atheists and coutume, Pascal writes: “Quelle raison ont-ils de dire qu’on ne peut ressusciter? Quel est plus difficile: de naître ou de ressusciter? Que ce qui n’a jamais été soit, ou que ce qui a été soit encore? Est-il plus difficile de venir en être que d’y revenir? La coutume nous rend l’un facile, le manque de coutume rend l’autre impossible. Populaire façon de juger!” (S444)

473 Ferreyrolles, Les Reines du monde, 17-37. 474 Ferreyrolles, Les Reines du monde, 65-119.

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coutume but most importantly let divine inspiration bring in the real and salutary effect of

faith. (S655) Yet the influence of coutume here was perhaps more important than

anything else. In fragment 661, Pascal referred again to matters of faith, but one can

interpret the subtle rule of coutume beyond religion. Reasoned proofs, according to

Pascal, convinced only the mind. It was coutume that actually brought the most powerful

and raw evidence of faith and secular issues. Only coutume bent the body—the

automaton—which would then drove the mind (like the gears of a machine) without the

latter ever thinking about it. Because reasoned proofs were just too difficult to always

keep in mind, one had to acquire another, easier principle like habitude, which without

violence, art or argument “persuades all of our powers to this credence, in such a way that

our soul falls in naturally.” It was not enough to have the mind believe something. Both

mind and body needed to be convinced: the former by reasoned proofs, which required to

have been seen only once in life; the latter, the automaton, by the mechanical repetition

of coutume. Hence fragment 661 outlined for matters of faith what the Avis nécessaire

had already described several years earlier with regard to the arithmetical machine: first,

visiting with Roberval, professor at the Collège Royal, to learn at least once the reasoned

proofs of arithmetic; second, allowing the power of habitude to bend the body qua

automaton into accepting the art of arithmetic as a sentiment rather than an act of the

mind.475

“What are our natural principles if not our accustomed principles?” (S158) Such

475 Habitude and sentiment act similarly, and Pascal is quite explicit about that fact: “La raison agit avec lenteur, et avec tant de vues, sur tant de principes, lesquels il faut qu’ils soient toujours présents, qu’à toute heure elle s’assoupit ou s’égare, manque d’avoir tous ses principes présents. Le sentiment n’agit pas ainsi; il agit en un instant, et toujours est prêt à agir. Il faut donc mettre notre foi dans le sentiment, autrement elle sera toujours vacillante.” Pascal, Pensées, S661.

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issues entered Pascal’s Pensées not only from a cultural or litterary perspective—Jean

Nicot’s definition of accoutumé is remarquably similar to Pascal’s476—but from an

epistemological one. To fix the instability of reason one must revert to the mechanical

character of coutume. One must, to borrow Pascal’s own expression, s’abêtir, not in the

sense of adopting pure animal instinct, but rather in embodying rational thinking in the

course of every human act. S’abêtir meant transforming the whole body into a thinking

machine, each and every part of it becoming what Pascal called a “thinking limb,” or a

membre pensant.477 Though an appendage of la machine, the arithmetical machine had

the same ontological value as any other thinking limb of the human body. Once one was

accustomed to using the pascaline through habitude, this mechanical appendage became a

“natural” extension of his or her body. No ontological difference existed any more

between the arithmetical machine and la machine’s thinking limbs. Body, mind and

machine formed one epistemic unit dedicated to the production of knowledge.

* * *

The invention of the pascaline was originally a product of social, cultural and intellectual

circumstances—tax collection in Rouen. That Pascal designed the machine (or

specifically its mechanism) to be first and foremost useful is witnessed by the assorted

models still extant today—three for decimal-system calculation only; five for financial or

business purposes (including special wheels for the sols and deniers); and finally one for

476 Jean Nicot, Thresor de la langue françoyse tant ancienne que moderne (1606), cf. Accoutumé: “Comme tu as accoutumé, c’est à dire suivant ton naturel.” There are many other definitions of interest under that entry. Taken from the ARTFL Project, The University of Chicago.

477 Pascal, Pensées, S403: “Qu’on s’imagine un corps plein de membres pensants!” See also S401. For a general discussion, Horia Lazar, “L’Habitude de penser: de la machine arithmétique à l’‘abêtissement’,” Chronique: Institut catholique de Toulouse (1995), 57-70.

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surveying purposes (including wheels for the toises, pieds, pouces and lignes). Utility

ranked high on Pascal’s list of priorities for the machine. It is too much of a stretch to

assume, however, that Pascal meant his creation to be more than simple mechanical

device, devoid of a greater end? If so, what higher purpose could such a machine be

suggesting? How could one differentiate it from “vulgar” mathematical instruments? In

England, during the acrimonious controversy between Delamain and Oughtred referred to

above, William Forster, the translator of Oughtred’s The circles of proportion (1632),

wrote in the dedicatory epistle of the same book why the Cambridge educated

mathematician did not publish the description of his circles of proportion earlier, i.e.

before Delamain. To Oughtred, Forster wrote,

the true way of Art is not by Instruments, but by Demonstration: and that it is a preposterous course of vulgar Teachers, to begin with Instruments, and not with the Sciences, and so instead of Artists, to make their Schollers only doers of tricks, and as it were Iuglers: to the despite of Art, losse of precious time, and betraying of willing and industrious wits, unto ignorance, and idelenesse. That the use of Instruments is indeed excellent, if a man be an Artist: but contemptible, being set and opposed to Art.478

Unlike Delamain, argued Oughtred, a deep knowledge of mathematics was always a

prerequisite to the use of an instrument—and to the education of a gentleman. Though

Pascal did not thoroughly support such an approach regarding his machine, he certainly

did not wish any user of the pascaline to be regarded as a paltry “Iugler” and “doer of

tricks” either. Hence Pascal tried hard, as already mentioned, to distance himself and his

machine from the mathematical practitioners. Conversations with an eminent

mathematician, who could explain the sophistication of the machine and the finer points

of arithmetic, would partly fit the bill. Yet how could the pascaline be truly distinguished

478 Quoted by Hill, “’Juglers or schollers?’,” 256-257.

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from a conventional and rather boring mathematical tools of the trade? Obviously, a

higher purpose had to be assigned to the machine. And Pascal found it, I believe, from

the social and epistemological values it conveyed: 1) in the machine’s symbolical appeal

as a bridge between the grandeurs de la chair et de l’esprit and 2) as the epitome of

natural philosophy in marrying the theoretical and artisanal systems of knowledge

production. Both these social and epistemological values embedded in the pascaline were

but a microcosm of what, a few years later, the Académie royale des sciences would

correspond to on a much larger and grander scale.

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CHAPTER 4

MANUFACTURING MACHINES: CHRISTIAAN HUYGENS

AND THE ACADÉMIE ROYALE DES SCIENCES

ERSENNE, DESCARTES AND PASCAL WORKED (AND COPED) WITH ARTISANS. To

various degrees these savants integrated some elements of artisanal knowledge

into their practice of natural philosophy. Often criticized for their lack of method and

poor working habits—Mersenne offered to standardize organ pipe making while

Descartes tried to replace deficient grinding skills with a machine—artisans nonetheless

influenced how savants looked at the production of natural philosophical knowledge. In

fact, what I suggest in this dissertation is the profound connection between theory,

practice and artisanal knowledge in seventeenth-century French natural philosophy. I

have described for Mersenne, Descartes and Pascal, who for a time were engaged in three

distinct craft traditions—musical instrument making, lens grinding and clockmaking

respectively—how theory, experiments and mechanical devices interacted together in

forming a coherent practice of natural philosophy. These savants, by and large inclined

toward the rationalization of nature, were compelled in the end to acknowledge the value

and benefits of artisanal activities to their work.

M

They were by no means the only French natural philosophers to look favorably

and rely (though sometimes reluctantly) upon such an alliance between the spheres of

intellectual and practical knowledge. Someone like Jacques Rohault, for instance, was

famous in the learned circles of Paris between the 1650s and 1670s (first at the Académie

Manufacturing Machines: Huygens and the Académie des sciences

of Henri Louis Habert de Montmor, then at Melchisédech Thévenot’s house) for his

experiments on optics, magnetism and the vacuum. He was a staunch and well-versed

Cartesian as regards theory, yet strongly emphasized the craftsmen experience (earned

from his numerous visits to Parisian workshops) in designing the right instruments and

experiments for his fashionable physics lectures.479 Christiaan Huygens, visiting Paris in

1660, saw Rohault perform experiments several times at his home and at the Montmor

Academy.480 Huygens himself might be seen as the early modern archetype of the

nouveau savant, considering how easily he communicated with his peers of the Republic

of Letters as well as with the vulgar ouvriers and the gifted and sometimes very

successful instrument makers.

Not that Huygens accomplished more than his predecessors. As an individual

savant, he also strongly emphasized that theory, experiments and instrumentation should

be working together, and he contributed as best he could to all of these aspects of early

modern scientific practices. As a “social” savant, however, Huygens had the advantage

over his precursors of being integrated into a new form of authoritative networking,

479 Trevor McClaughlin, “Was there an empirical movement in mid-seventeenth century France? Experiments in Jacques Rohault’s Traité de physique,” Revue d’histoire des sciences 49 (1996), 459-481. Rohault’s father-in-law, Claude Clerselier, mentioned that he had “un esprit tout à fait mechanique, fort propre à inventer et à imagnier toutes sortes d’Arts et de Machines.” Rohault was acquainted with several artisans through family connexions. (pp. 475-476) On Rohault’s instruments, see his inventaire après décès described by McClaughlin, “Un exemple d’utilisation du Minutier central de Paris: La bibliothèque et les instruments scientifiques du physicien Jacques Rohault selon son inventaire après décès,” Revue d’histoire des sciences 29 (1976), 3-20. Rohault’s Traité de physique (Paris, 1671) became one of the era’s most read treatise of natural philosophy. It received a favorable review in the Journal des sçavans (Monday, 22 June 1671) in which it was said that, besides the description of experiments and machines, “Et ce qui est tres-important pour perfectionner la Physique, cet Auteur a eu la curiosité d’examiner les secrets de divers Arts, par exemple ceux de la Chime, de l’Orfevrerie, de l’art des Affineurs, & de celuy des Teinturiers; & il tâche de rendre raison dans ce livre de quelques-uns de ces secrets.” (pp. 25-26).

480 Henri-L. Brugmans, Le séjour de Christian Huygens à Paris et ses relations avec les milieux scientifiques français, suivi de son Journal de voyage à Paris et à Londres (Paris: Impressions Pierre André, 1935), 130-140.

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centered around the Académie des sciences. The Academy, since its foundation in 1666,

was the focal point of the Parisian scientific life, where theories, experiments and

machines had to intersect and be judged in order to become legitimate knowledge.

Huygens, an academician à part entière, had the obligation to evaluate not only

theoretical assertions and experimental evidences, but also all sorts of instruments and

machines sent to the Academy—whether directly or through Colbert and the royal Court.

The material culture of science, though always there and playing a significant role in

early modern France, turned into an even more serious and genuine part of knowledge-

production within the walls of the Academy.

Yet most important was perhaps the new and extended networking of people the

Academy created around itself. The Academy, I hope to demonstrate, was less

“secretive” than generally thought.481 Though it is accurate to say that the internal

workings and activities of the Academy were not meant to be seen by outsiders, a lot of

people, of different social status, gravitated around and were welcomed to its assemblées.

Because the institution was sponsored by the king and was established as the

authoritative scientific voice of the land, positioned between the French Court and the

intellectual milieu, savants, gentlemen, inventors and instrument makers all converged

towards the Academy. They all tried to get the attention of the king in producing useful

knowledge and machines. The Academy became a power-broker between these

individuals and the king, the academicians the gatekeepers deciding what made it through

the door of legitimate knowledge. Owing to his role as an academician, Huygens was put

481 Alice Stroup, A company of scientists. Botany, patronage, and community at the seventeenth-century Parisian Royal Academy of Sciences (Berkeley: University of California Press, 1990), 211.

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in contact with several types of people, including dozens of instrument makers. Actually,

as will be shown below, the Academy’s life thoroughly depended on the latter.

This chapter explores this new and extended networking between savants,

academicians, gentlemen and instrument makers created by the Académie des sciences. It

is not meant to describe the “institutional etiquette” and polite discourse and behavior

that guaranteed the production of legitimate and authoritative knowledge.482 I want rather

to make evident the ties between the Academy and the Parisian activities dealing mostly

with instruments and machines. What we find is that a savant such as Huygens, owing to

his association with the Academy, was surrounded by scores of people of different trades

and statuses. Huygens, in fact, seems less the lone savant than Mersenne, Descartes and

Pascal might have appeared in the previous chapters. Huygens used this network

generated by the Academy to the fullest.

After describing Huygens’s business with carriages, to which he dedicated a good

amount of time between 1663 and 1668, I will talk about general facets of authorship

with regard to the Académie des sciences, focusing especially on machines and their

inventors—coming from various ranks of society. Afterwards, I will reintroduce Huygens

in a discussion regarding priority claims made against two of his inventions: the balance-

spring watch and a double barometer. Again, one will see how the back-and-forth

arguments were encompassed within the Academy’s extended network of people. Lastly,

I will briefly discuss how the Journal des sçavans turned into one of the preferred means

between 1670 and 1685 of claiming priority to theoretical as well as mechanical

482 On this particular aspect of the nascent scientific institutions, see Mario Biagioli, “Etiquette, interdependence, and sociability in seventeenth-century science,” Critical Inquiry 22 (1996), 193-238.

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inventions. Once again, the authors publishing their discoveries in the Journal were part

of the extended and authoritative network formed around the Academy.483

Huygens participated in an established and authoritative institutional network that

gave him access to a wide range of individuals—savants, honnêtes hommes, instrument

makers and simple ouvriers. Through some of Huygens’s work with machines, I show

how much French natural philosophy in the 1670s and 1680s organized itself around the

Académie de sciences and how much theory, experiments and machines became

entangled in the endeavor to produce useful knowledge for the king.

AN URBAN COMMODITY: HUYGENS AND CARRIAGES

During the course of his numerous journeys around Europe, Balthasar de Monconys took

note of virtually everything he saw, heard, or discussed with savants, nobles and artisans.

Instruments and machines were observed, drawn and often bought by the French tourist.

One essential machine though, the carriage, synonym of upper-class movement and

travel, was only sporadically referred to in Monconys’s Journal. Interestingly, the famous

diarist never described his own nor his distinguished companion’s carriage, presuming it

would not interest the Journal’s potential readers since they would be all-too familiar

with this means of transportation. The few descriptions of carriage-like machines found

in the Journal report a curiosity (a horseless carriage designed and built in Nuremberg for

the king of Denmark), the craftsmanship and innovation in Dutch carriages, and the

483 The Journal des sçavans, discussed here strictly from the point of view of printed authorship for machines, is only the starting point of the eighteenth-century inventors’ commercial strategies involving public shows, lecture demonstrations and exhibitions as well as printed materials of all kinds (leaflets, advertisements, posters, usu et fabrica books, etc.). This topic has received a good analysis by Liliane Hilaire-Pérez and Marie Thébaud-Sorger, “Les Techniques dans l’espace public: Publicité des inventions et littérature d’usage au XVIIIe siècle (France, Angleterre),” Revue de synthèse 127(2) (2006), 393-428.

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rudeness of the Cologne citizens based on their use of thick and full wooden wheels on

carts.484 As the last example shows, the type of cart and carriage one possessed (or not)

and drove spoke volume about his/her social status and character. Blaise Pascal’s

carrosses à cinq sols, briefly discussed in the previous chapter, was in this context more

than an early modern system of public transportation. It granted a new level of status to a

rising Parisian bourgeoisie, who could not yet afford their own.485 Carriages (carrosses,

calèches and carioles, the latter two smaller than carrosses) became an important social

status granting urban commodity in the second half of the seventeenth century, drawing

interest not only from nobles but savants as well, especially the Dutch polymath

Christiaan Huygens.

I. THE CHAISE ROULANTE AND THE BUSINESS OF PATENTS

After Huygens declined the offer from Arthur Gouffier, duc de Roannez, to seek a

privilege in Amsterdam for a Dutch version of the carrosses à cinq sols,486 his

484 Monconys, Journal de voyage, ii:194 and 266. In the streets of Cologne he noticed “combien ce Peuple est grossier iusques aux roües de leurs broüettes qui ont vn pied dépaisseur, & ne sont que d’vne piece.” So far as I know, Daniel Roche does not discuss the technology of carriage in his otherwise essential work on early modern travel. Roche, Humeurs vagabondes. De la circulation des hommes et de l’utilité des voyages (Paris: Fayard, 2003).

485 Eric Lundwall, Les Carrosses à cinq sols. Pascal entrepreneur (Paris: Science Infuse, 2000). See, especially, Jean Mesnard, Pascal et les Roannez, 2 vols. (Paris: Desclée de Brouwer, 1965), ii: 755-814.

486 The success of the carrosses à cinq sols in Paris could not be merely duplicated elsewhere, as Pascal’s foremost collaborator and friend on this project, the duc de Roannez, learned. Shortly before Pascal’s death in 1662, Roannez asked Huygens whether he would like to get a privilege for a similar venture in Amsterdam. Contrary to the French capital, however, Amsterdam’s streets were narrower and much cleaner (Paris’s smell and filthiness were notorious). Moreover, only exceptionally did individuals get to own and drive a carriage in the city—the canals were the chief mean of transportation. Above and beyond these municipal regulations, Huygens did not want to get bugged down in court with proceedings and lawsuits. As he wrote in July of 1662 to his brother Lodewijk, “One must be extremely greedy and not value his time to undertake a thing of this nature.” Huygens to his brother Lodewick, 20 July 1662, in Oeuvres complètes, 22 vols. (The Hague: M. Nijhoff, 1888-), vol. 4, no. 1036, p. 180. [Hereafter cited as OC(4), no. 1036, p. 180.]. See also P. Jansen, “Les Carrosses à cinq sols et Christiaan Huygens,” Revue

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relationship with Roannez, dating back to his 1660-1661 Parisian sojourn, got him

involved in a somewhat related project: the creation of a new type of carriage, the chaise

roulante, also known as the “machine Roanesque” or the “Crenan,” for the main co-

sponsors: Roannez and Pierre de Perrier, marquis de Crenan.487 Huygens’s participation

began in the Fall of 1663. His enthusiasm was such that his brother-in-law, very much

interested in carriage design himself, as we will see later, asked Huygens “Un poco di

disegno s’il vous plaist” of this machine Roanesque.488 (See Figure 4.1.) Huygens

obliged, though was not involved in the design and later modifications of the machine.

His chief responsibility was rather in securing a privilege from England. To this end,

Huygens drew on his personal relationship with Robert Moray and Gabriel Silvius, the

two principal intermediaries in the matter. Technical descriptions of both the original

one-seat carriage and its later alterations, in addition to summaries of the chaise’s

successful trials in the country were sent to Moray and Silvius over the next year and a

half. The asking price was 15 to16 pistoles, or 100 écus for the machine and the rights of

using it.489 Louis XIV himself tried it in one of the first tests conducted in the Bois-de-

d’histoire des sciences 4 (1951), 171-172. 487 Others were also involved, such as the marquis de Sourches and Goibaut du Bois, both names

found on legal acts. The best description of this episode is found in Mesnard, Pascal et les Roannez, ii:831-837. A brief summary is found in P. Jansen, “Une tractation commerciale au XVIIe siècle,” Revue d’histoire des sciences 4 (1951), 173-176.

488 Huygens, OC(4), Huygens to Philips Doublet, 14 December 1663, no. 1181, p. 465. See also Huygens, OC(4), Huygens to his brother Lodewick, 28 December 1663, no. 1190, p. 480.

489 Huygens, OC(5), Huygens to Robert Moray, 9 January 1664, no. 1200, pp. 6-7; ibid., 20 February 1664, no. 1213, p. 29; ibid, 12 March 1664, no. 1218, p. 40; ibid., Huygens to Gabriel Silvius, 27 April 1664, no. 1229, pp. 61-62, where Huygens wrote that “Ils [the inventors] ont trouuè bon icy dans le commencement de cet establissement de vendre ensemble la machine et le droit de s’en servir pour cent escus croiants d’y trouuer mieux leur compte qu’en prenant le droit annuel et aussi a fin que les premieres ne manquassent pas d’estre bonnes estant faites par les ouuriers qu’ils ont instruits.”

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Boulogne and found it satisfactory.490

FIGURE 4.1: THE CHAISE ROULANTE OR MACHINE ROANESQUE The chaise roulante, better known as the “machine Roanesque” or the “Crenan.” Drawing made by Huygens in OC(6), appended to a letter to his brother Constantyn, 22 July 1666, no. 1553. The measurements are given in Rhynland (or Leyden) feet.

Although the privilege was granted rapidly in France (a month after the king’s

trial), Huygens made very little progress in England, despite the fact that news from Paris

was encouraging.491 Huygens learned from Crenan about the carriage’s modifications

made over the summer and how fashionable it had become. To Moray, Huygens repeated

that the chaises roulantes were ever more à la mode in France and even that one

490 Huygens, OC(5), Huygens to his brother Lodewijk, 8 February 1664, no. 1211, pp. 25-26; ibid., Huygens to Moray, 20 February 1664, no. 1213, pp. 28-29.

491 For a summary and source of this privilege, Mesnard, Pascal et les Roannez, ii:832-834. He had promised Roannez and the other sponsors he would secure the letters patent from England three months after the privilege had been granted and approved in Paris. However, Huygens knew he would get pressure from Roannez et alii only if the chaise was doing well in France, an argument Moray used himself in early July 1664 to explain the delays in granting the patent in England—which he thought would be easy to achieve if the machine was worth it. Huygens, OC(5), Huygens to Moray, 27 June 1664, no. 1238, p. 77; ibid, Moray to Huygens, 4 July 1664, no. 1239, p. 79.

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exemplar would soon be seen in England, sent from the Duchess of Orléans to the Queen

of England (her mother).492 The timing was perfect because both Moray and Silvius were

still unconvinced they would ask for a privilege, considering that another type of chaise

roulante, completely different from the Parisian one, was being designed at the very

moment for the king. (Though eventually, Moray argued, they could be both cited in the

same privilege.493)

What accelerated the course of action was Charles II’s trial in the backyard of the

Sommerset house. Even if his Majesty found some problems with the machine

Roanesque, he said they could be easily fixed and that he would sign the letters patent

once it was ready. A figurehead was needed though, since according to England’s law

patents could not be granted to foreigners. Moray suggested it was made in Robert

Hooke’s name, the Royal Society’s well-known mechanic.494

Less than two months later, however, Huygens learned the machine Roanesque

was in reality doing poorly in England. According to Moray, everyone (including the

king) who rode in it was disgusted with the French carriage, not only for its lack of

comfort, but for its mediocre appearance as well. Nevertheless, Moray would take the

492 Huygens, OC(5), Pierre Perrier, marquis de Crenan to Huygens, 26 July 1664, no. 1246, pp. 90-91; ibid., Huygens to Moray, 8 August 1664, no. 1250, p. 102. On the earlier failed attempt to send one chaise to England, see Huygens, OC(5), Moray to Huygens, 19 June 1664, no. 1236, p. 73 and ibid., Huygens to Moray, 27 June 1664, no. 1238, p. 77.

493 Huygens, OC(5), Moray to Huygens, 15 August 1664, no. 1252, p. 106. To convince Moray, Huygens sent him the letter he received from Crenan. See ibid., Huygens to Moray, 29 August 1664, no. 1253, p. 110.

494 Huygens, OC(5), Moray to Huygens, 23 September 1664, no. 1256, p. 116. In the same letter, and for the same reason, Moray asked Huygens for the name of someone in England to which the patent should be made regarding his sea pendulum. This episode happened more than a decade before the controversy between Huygens and Hooke over the balance-spring watch. On this, see the excellent article by Rob Iliffe, “‘In the warehouse’: Privacy, property and priority in the early Royal Society,” History of Science 30 (1992), 29-68.

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patent with three or four more similar machines. He also told Huygens that a new type of

carriage (calèche), its structure being entirely made of iron, was designed for the king by

the engineer “du Son,” or d’Esson. When it was completed, and if it worked adequately,

Huygens could act as an intermediary in order to get a privilege for it in France and

Holland.495 Regarding England, Moray suggested that d’Esson’s carriage, and several

inventions of his, should in fact be added to the patent of the French chaise roulante,

since “30 different things can be added to a patent.”496

In the meantime, Huygens continued to send praises of the machine Roanesque to

Moray—the latest coming from Roannez himself—though he apparently never approved

of it himself, on account of the load put on the horse.497 Nonetheless, he doubted that

d’Esson’s carriage would be as stable as the chaise roulante and thus allow one “to ride

flat out” in bad trails, which was doable with the Parisian invention.498 Moray wrote back

mentioning that d’Esson’s calèche was likely more unstable than the machine Roanesque

495 Huygens, OC(5), Moray to Huygens, 7 November 1664, no. 1268, p. 139, where he writes: “Quand aux chaises roulantes, le Roy et tout ceux qui ont esté dans celle de la Reyne Mere et mesme ceux qui lont veue en sont tellement desgoutez, les uns blasmant le branslement qui sy trouue, dans la complication de mouuements quon y souffre à la fois, les autres sa bassesse, les autres sa figure, c’est a dire sa mauuaise mine, qu’il ny a rien a esperer de son usage. neantmoins Jen prens la patente, mais cest en y mettant trois ou 4. autres descriptions de Calesches tout a fait differentes de la chaise roulante, desquelles on ne doubte point que quelques unes ne reussissent a merueilles non pas seulement pour les Grands chemins mais aussi pour les rues. Personne ne demande apres la chaise roulante…”

496 Huygens, OC(5), Moray to Huygens, 5 December 1664, no. 1280, p. 157. As we learn in another letter from Huygens to Moray, it is the high price of letters patent granting that made the practice of juxtaposing heterogeneous things in the same patent convenient.

497 Huygens, OC(5), Huygens to Moray, 21 November 1664, no. 1274, p. 150. On the machine Roanesque prowesses, see ibid., Roannez to Huygens, 11 December 1664, no. 1284, pp. 162-164, where he also ask about the progress made on the English patent. On Huygens reply to Roannez, of which we only have a draft summary of it, ibid., Huygens to Roannez, 31 December 1664, no. 1296, p. 178. For Huygens communication of the chaise de poste praises received from Roannez, ibid., Huygens to Moray, 2 January 1665, no. 1301, p. 186.

498 Huygens, OC(5), Huygens to Moray, 2 January 1665, no. 1301, p. 186. Huygens, however, believed Moray when he said that d’Esson’s calèches were “belles et douces.” On Moray’s praises, see ibid., Moray to Huygens, 19 December 1664, no. 1287, p. 168.

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due to the higher position of the passenger’s cabin. From the drawing he sent later, we

learn that this calèche was 15 to 16 feet in length. (See Figure 4.2.) The beams (flèches)

were fixed to the axle and the body of this two-seater was situated on top of the spiraled

iron parts marked 2-2 and 3-3, which acted as suspension springs. The whole thing was

solidly attached to both sides of the horse’s saddle via 1-1, so the carriage would only be

overturned if the horse itself fell or the leather straps broke. Regarding the load put on the

horse, Moray also mentioned that the beams in d’Esson’s carriage were supporting ninety

percent of its total weight, apparently much better than the French chaise roulante.

Despite all the bad critique coming from England and France, the latter via Silvius,

Moray told Huygens the letters patent was almost ready—and not cheap: 30 Jacobus

(circa 420 English pounds). In the same patent were also found inventions of pistols and

arquebuses, one machine to whiten cloth and prepare linen for looms, and as expected

three or four other types of carriages.499

Huygens remained unimpressed with d’Esson’s calèche. First, he was skeptical

whether the small springs would provide a smooth ride on rough roads. Second, as Moray

stated, the fact the carriage was solidly attached to the horse would not prevent it from

being overturned when the horse fell down, which would never happen with the chaise

roulante. Huygens thought differently on both accounts, and time permitting he would

put together his own carriage over the summer.500 In early September, however, he still

499 Huygens, OC(5), Moray to Huygens, 30 January 1665, no. 1318, p. 214; ibid., 6 February 1665, no. 1326, p. 227.

500 Huygens, OC(5), Huygens to Moray, 27 February 1665, no. 1338, p. 249. This letter was read at the Royal Society. It is mentioned that Huygens gave “his opinion concerning Monsieur de Son’s chariot, together with his thoughts of one of his own devising.” Also, that “Col. Blount having given several good hints for improving carriage, and particularly for trying experiments about chariots by weights, should be desired to bring in, after more trials upon this subject, a model of his conceptions about

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had nothing to show. From Paris—he was still in Holland—he learned that seven or eight

carriage models had been invented since he left France, though they were all inspired by

the chaise Roanesque.501 It took more than a year before Huygens started to work

seriously on a carriage of his own, or cariole as he often called it. For the next two years,

from 1666 to 1668, Huygens spent time, money and energy in studying, discussing and

designing a carriage he could use in the city as well as on the open country roads. From

what I gather, he never asked for a privilege—perhaps, in the end, because it was not a

complete success. Yet we see how concerned he was with the whole process, from the

original design to the practical experiments (test drives) and mechanical involvement

with artisans. Huygens was done trying to secure a privilege for a machine he did not

entirely believe in. It was now time to design his own—with the help of family members,

as he often did in scientific and technical ventures.502

II. THE THEORY, PRACTICE, AND UNCERTAINTY OF MACHINE DESIGN

Philips Doublet, Huygens’s brother-in-law, became this time one of his chief

correspondents. On 6 August 1666, Huygens described to Doublet a variation to the basic

structure of the machine Roanesque. (See Figure 4.2.) To lighten the load put on the

it.” Thomas Birch, The history of the Royal society of London for improving of natural knowledge, from its first rise. In which the most considerable of those papers communicated to the society, which have hitherto not been published, are inserted in their proper order, as a supplement to the Philosophical Transactions, 4 vols. (London, 1756-57), ii:19. Moray replied to Huygens on 6 March 1665, no. 1348, p. 262, but did not add more really to the discussion.

501 Huygens, OC(5), Adrien Auzout to Huygens, 4 September 1665, no. 1453, p. 475. 502 On this topic, see Bram Stoffele, Christiaan Huygens—A family affair. Fashioning a family in

early modern court culture (Master’s thesis, Utrecht University, 2006), esp. chap. 7 on scientific instruments.

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FIGURE 4.2: VARIATIONS OF THE CHAISE ROULANTE

Above, the modification on the “machine Roanesque” or “Crenan.” From Huygens, OC(6), appended to a letter to Doublet, 6 August 1666, no. 1555. The measurements are given in Rhynland (or Leyden) feet. On the right, the engineer d’Esson’s model of a new chariot (chaise, calèche or carriole), from Huygens, OC(5), Robert Moray to Huygens, 6 February 1665, no. 1326, p. 227.

horse, the chaise’s wheels were fixed closer to the passengers. The wheels were still

attached at the extremity of the beams (flèches), but the latter were folded on themselves,

so as to retain the suppleness of the original invention. The cabin was fixed on the beams

in a different way than on Doublet’s own carriage, though it was decorated with identical

fabric, quality leather and gilded nails. It cost but 100 écus.503

Doublet, however, did not understand why this alteration to the machine

Roanesque (which was not from Huygens) would diminish the overall load on the horse.

Surprised, Huygens explained the reason in two letters. (See Figure 4.3.) The first

explanation dealt with the principle of the lever. AB is the beam, C where the wheel is

503 Huygens, OC(6), Huygens to Philips Doublet, 6 August 1666, no. 1555, pp. 71-72.

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attached and D where the passenger would be seated. In the drawing made by Huygens,

the distance AD is three times that of DE, meaning that the horse only supports one third

of the passenger’s weight, whereas the carriage supports the rest. In fact, if the part BC

was longer so it went above D, the horse would support none of the passenser’s weight.

FIGURE 4.3: HUYGENS’S MECHANICAL EXPLANATION OF THE MODIFIED CHAISE ROULANTE

Above and below, two similar drawings explaining why Huygens’s new cart would not burden the horse any more than the machine Roanesque. The principles of the lever and of similar triangles are at the foundation of Huygens’s reasoning. From Huygens, OC(6), Huygens to Philips Doublet, 3 September 1666, no. 1560, p. 80 and ibid., 5 November 1666, no. 1562, p. 84.

(This solution, however, was impractical because the passenger would be on top of the

wheels, and thus follow their up-and-down movements in rough roads—though the

beams would somewhat soften this violent motion.) Still unconvinced, Doublet received

a second letter from Huygens, which dealt this time with the principle of similar triangles.

Here, Huygens simply mentioned that if FB was twice as long as FD, the height FK

would be twice as high as FH, depending on where the wheel was fixed (at C in the case

of FH, at B in the case of FK). Huygens also told Doublet he could lift his own carriage

with a passenger seated in it as easily as he had Doublet’s when empty.504

Carriage improvements and inventions continuously caught Huygens’s attention,

504 Huygens, OC(6), Huygens to Philips Doublet, 3 September 1666, no. 1560, p. 80 and ibid., 5 November 1666, no. 1562, p. 84. In modern notation, for similar triangles, once you have shown that the angle ADG is equal to ABG, and you know that FB is twice as long as FD, than tanθ = FH/FD = FK/FB = FK/2FD, hence FK = 2FH.

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though he had yet to create his own design.505 Carriages were everywhere and received

scrutiny by all. According to Huygens, there was in fact an infinite number of chaise

roulante and calèche variations on show in Paris, although only two types were really

worth mentioning: the chaises Crenanes (or machines Roanesque) and its adaptation

mentioned above, and a four-wheel carriage named “de manses,” for its inventor. (See

Figure 4.4.) Compared to the machine Roanesque, this one had four wheels, the ones in

FIGURE 4.4: A NEW TYPE OF FOUR-WHEEL CALÈCHE IN PARIS Huygens’s drawing of a new type of calèche in Paris. From Huygens, OC(6), Huygens to Philips Doublet, 8 April 1667, no. 1585, p. 124. front attached to the main beams by two iron arcs. The chief advantage of this calèche,

compared to the larger carrosse or even the machine Roanesque, was that the front

505 Typical of Huygens’s situation, the status of an inventor mattered. When, for instance, the Prince Maurice of Nassau described a new approach to make the carriage wheels turn better, without grinding too much the axle, Huygens promptly passed the information over to Roannez as valuable. If, on the other hand, a new type of carriage—the six-door carrosse mentioned by Doublet, for instance—had not been seen by Huygens, or had not made enough noise (i.e. was not acknowledged by someone of virtue), it was not judged to be a very good invention. Huygens, OC(6), Huygens to Philips Doublet, 3 September 1666, no. 1560, p. 80 and ibid., 5 November 1666, no. 1562, p. 85; ibid., 25 February 1667, no. 1578, p. 115.

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wheels went under the arcs when turning, making sharp turns possible without taking too

much space (one problem of the machine Roanesque). Huygens did not verify for

himself, but was told that although this calèche looked like a carrosse, its weight was

actually light. Doublet seemed impressed by the design, and asked for a better drawing of

it from Huygens.506 This type of carriage became fashionable and popular in Paris by the

end of the century.507

Huygens’s study of carriages was also encouraged by another member of the

family: the lesser-known of the Huygens brothers, Lodewijk, who was also involved in

carriage design. Big brother Christiaan, however, was quick to point out that the

passenger seated above the wheel in Lodewijk’s model would (theoretically) feel the

bumps on the road twice as much as another one in which the rider would be seated

between the horse and the wheels.508 Less than a month later, Huygens came up with an

improved design he suggested to his younger brother. It consisted in having the carriage’s

beams on top of one another, both bending in such a way as to form a hyperbolic shape.

(See Figure 4.5.) Two weeks later, Huygens wrote to Doublet this time, the “brother of

Moggershill, Surintendant des Carosses,” proposing yet another idea. He recommended

that the cabin in Lodewijk’s carriage should be moved in front of the wheels (to give it

506 Huygens, OC(6), Huygens to Philips Doublet, 25 February 1667, no. 1578, p. 115; ibid., 11 March 1667, no. 1581, p. 119; ibid., 8 April 1667, no. 1585, p. 124.

507 According to Martin Lister, “To begin with the Coaches, which are very numerous here and very fine in Gilding: But there are but few, and those only of the great Nobility, which are large, and have two Seats or funds. But what they want in the largeness, beauty, and neatness of ours in London, they have infinitely in the easiness of Carriage, and the ready turning in the narrowest Streets. For this pupose, they are all Crane-Neckt, and the Wheels before very low, not above two foot and a half Diameter; which makes them easie to get into, and brings down the Coach-Box low, that you have a much better prospect out of the foremost Glass; our high seated Coachmen being ever in the point of view.” Lister, A journey to Paris in the year 1698 (London, 1699), 12.

508 Huygens, OC(6), Huygens to his brother Lodewijk, 2 December 1667, no. 1612, p. 165; ibid., 9 December 1667, no. 1616, p. 169.

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more stability) and that the two beams should actually be inverted (like a biconvex lens),

the cabin placed on the lower one while the wheel was fixed to the upper one.509

Lodewijk

FIGURE 4.5: HUYGENS’S IDEAS ABOUT CARRIAGE SUSPENSIONS

Two models of calèches with curved beams designed by Huygens. From Huygens, OC(6), Huygens to his brother Lodewijk, 6 January 1668, no. 1618, p. 172 and Huygens to Philips Doublet, 20 January 1668, no. 1619, p. 173.

went ahead with his original model, disregarding his big brother suggestions. From

Constantijn the Elder, Huygens learned that Lodewijk’s carriage was actually done and

going well. He thus asked Lodewijk to send the measurements and observations he made

on his machine, since Huygens thought he could have one made in the Spring—if nothing

better came up until then.510

More than four years after he was enrolled by Roannez to secure an English

patent for the chaise roulante, during which time numerous letters were exchanged with

family members, Huygens finally began to work on a carriage of his own. In March 1668,

Huygens told his brother he had discussed his two-seat cariole with the expert machinist

509 Huygens, OC(6), Huygens to his brother Lodewijk, 6 January 1668, no. 1618, p. 172 and Huygens to Philips Doublet, 20 January 1668, no. 1619, p. 174. (It is difficult to resist making an analogy here between Huygens’s lens-grinding work and understanding of optics and both designs of carriage suspension, one being better than the other—spherical lenses versus hyperbolic ones.)

510 Huygens, OC(6), Huygens to his brother Lodewijk, 2 February 1668, no. 1623, pp. 186-187.

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Franchine (either the fountain engineer Jean Nicolas de Franchine or his son, Pierre de

Franchine Grand-maison). The chief problem to solve was how to fasten the leather

straps that were supporting the cabin and providing suspension, so it did not shake too

much on rough roads. Experience would tell whether Lodewijk’s solution of four straps

attached in parallel to the beams would work well. Prudence was required though, since

Charles Alexandre de Carcavy, son of Pierre de Carcavy, reported he had spotted in Paris

a calèche using a system of suspension identical to Lodewijk’s. Huygens had not seen it,

and doubted the young Carcavy’s account owing to the latter’s poor mechanical abilities.

If it were true, however, the inventors of this carriage could create a lot of trouble owing

to their presumed privilege. Once again, Huygens’s experience here in these sort of

matters cautioned him. On the other hand, if his own invention was successful—and

profitable—he would not miss a chance to ask for the privilege—which, apparently, he

never did.511

The next six months probably proved to be a bigger challenge than Huygens

anticipated at first. After having talked to two cartwrights (charrons), he found out the

cariole’s frame and cabin (without any decoration) would be relatively cheap: between

22 and 24 écus (roughly 132 to 144 livres tournois). He finally settled for 20 écus with

one of these artisans.512 Huygens was still asking Lodewijk for reports on experiments

carried with his own carriage and for further explanations regarding the type of

suspension straps he was using. Huygens also appeared to have been in relatively close

contact with Franchine, who gave him novel ideas about how to make the suspension as

511 Huygens, OC(6), Huygens to his brother Lodewijk, 23 March 1668, no. 1630, pp. 200-201. 512 Huygens, OC(6), Huygens to his brother Lodewijk, 29 March 1668, no. 1632, p. 204; ibid., 6

April 1668, no. 1634, pp. 206-207.

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smooth as possible. The invention of steel springs (ressorts à lames) was made about that

time. It was the best of suspensions, but was at first little known, very expensive and only

became standard on carriages in the eighteenth century. Huygens heard about them from

his father in 1662, but never appeared to have followed this direction. He tried instead to

improve the conventional types of suspension.513

Of course, Huygens complained about the cartwright taking too much time in

doing his job—the beau temps would be gone before he could enjoy his carriage.514 In

mid May, Huygens informed Lodewijk that the frame and cabin had been completed

(albeit not decorated). We learn that the carriage’s beams had to be mounted from three

separate pieces, joined together with iron plates. French workers (ouvriers), according to

Huygens, were slow and expensive, and not very skilled when dealing with something

they were not accustomed to make. It was not, therefore, as pleasant to mechanize

(machiner) in France as it was in Holland.515

In spite of Huygens’s grievances, the calèche was ready by mid June. (See Figure

4.6.) The cabin was suspended on leather straps, and following a short street drive in

front of where Huygens lived (the Bibliothèque du Roi), he found it quite smooth

compared to a carrosse. Because the straps were so important in providing a comfortable

ride to passengers, Huygens later described the simple tool used by the artisans to bind

513 Max Terrier, “L’Invention des ressorts de voiture,” Revue d’histoire des sciences 39 (1986), 17-30. Lister saw them on several carriages in Paris during his sojourn: “Again, They are most even Fiacres or hackneys, hung with Double Springs, at the four Corners, which insensibly breaks all Jolts. This I never was so sensible of, as after having practiced the Paris Coaches for four months, I once rid in the easiest Chariot of my Lord’s, which came from England; but not a Jolt, but what affected a Man; so as to be tired more in one hour in that, than in six in these.” Lister, A journey to Paris in the year 1698, 12.

514 Huygens, OC(6), Huygens to his brother Lodewijk, 27 April 1668, no. 1637, pp. 210-211. Huygens had already voiced the same complain to Robert Moray in discussing the machine Roanesque four years earlier. Huygens, OC(5), Huygens to Robert Moray, 9 January 1664, no. 1200, p. 7.

515 Huygens, OC(6), Huygens to his brother Lodewijk, 11 May 1668, no. 1639, pp. 216-217.

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the straps on the calèche. (See Figure 4.6.) The carriage itself was nicely decorated and

cost all in all 450 livres tournois. Other tests, however, were needed, since the streets of

FIGURE 4.6: HUYGENS’S OWN CALÈCHE Above, Huygens’s two-wheel calèche as it was built and before it was transformed into a four-wheel carriage. From Huygens, OC(6), Huygens to his brother Lodewijk, 22 June 1668, no. 1644, p. 225. On the right, the simple tool used by the artisans (charrons) to tighten the leather straps used as suspension. From Huygens, OC(6), Huygens to his brother Lodewijk, 20 July 1668, no. 1652, p. 238.

Paris were more irregular and severely damaged than the ones in Holland, the former

being made of bigger stones and having to sustain the strain of a large quantity of carts

and carrosses.516

516 Huygens, OC(6), Huygens to his brother Lodewijk, 22 June 1668, no. 1644, pp. 224-225; ibid., 20 July 1668, no. 1652, p. 238. About the decoration, Huygens wrote the following description: “Elle est fort propre avec des clous dorez et un peu de dorure en dehors sur la peinture du bois. L’etoffe en dedans est d’un dams caffard a fleur de rouge sur un fond de couleur d’or.” According to Martin Lister, who traveled to Paris some thirty years later, the pavement was “all of square Stone, of about 8 or 10 Inches thick; that is, as deep in the ground as they are broad at top.” Furthermore, Lister found Paris’s streets “very narrow, and the Passengers a-foot no ways secured from the hurry and danger of Coaches, which always pass the Streets with an air of haste; and a full trot upon broad flat Stones, betwixt high and large resounding Houses, makes a sort of Musick which should seem very agreeable to the Parisians.” Lister, A journey to Paris in the year 1698, 10. Joseph Pitton de Tournefort, an Academician, died from the impact of one of these hurried carrosses in Paris. See Jean-Pierre Nicéron, Mémoires pour servir à l’histoire des hommes illustres dans la république des lettres, 44 vols. (Paris, 1727-1745), 4:363-364. Fontenelle, in his Éloges, only says Tournefort received a heavy blow to the chest, without mentioning its origins. It was in late December 1708. References found in Stroup, A company of scientists, 186-187.

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It apparently took one week of experiments before Huygens recognized his

carriage had no value whatsoever in Paris. To Doublet, and later to Lodewijk, he

explained that though it worked adequately on country roads, it did not fare well on

Paris’s paved streets, on which he had to travel half a league to get out of town through

the Faubourg Saint-Germain. Huygens also remarked that the great number of carts and

larger carrosses on the streets’ capital made it difficult to guide the calèche by oneself.

For all of these reasons, Huygens decided to change the structure of his carriage and put

it on four rather than two wheels. In order to do so, he was consulting all the likely

authorities on the matter—and asking information on Doublet’s chaise bleue, praised by

his sister.517

At the same time Huygens was redesigning his calèche and handling concrete

issues such as how to fix the suspension, the choice of materials, and the overall technical

difficulties of switching from a two-wheel to a four-wheel carriage, the Academy

discussed some aspects of the “geometry of cartage (charriage)” during the span of two

subsequent Wednesday meetings. On 4 July 1668, Roberval shared his “Traité du

chariage [sic],” a qualitative treatise focusing on two major characteristics of cartage: the

type of terrain on which it was done and the size of the cart’s wheels. Roberval argued

that on an even and hard terrain, a small or a large wheel did not appear to possess an

advantage over the other. (Even the wheel’s weight did not really matter, nor did friction

if one considered that everything was well greased.) Where the large wheel might have

an advantage over a small one was on a soft (mol) terrain and on an irregular one (from

517 Huygens, OC(6), Huygens to Philips Doublet, 29 June 1668, no. 1646, p. 227; ibid., Huygens to his brother Lodewijk, 27 July1668, no. 1652, pp. 237-238.

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hard to soft surfaces, or vice versa). Here, the wheel with the larger diameter, owing to

the principle of the lever, would appear to have a clear advantage over the smaller

diameter wheel. Yet nothing was certain.

In the end, Roberval’s main argument was that it was the geometers’ task to sort

out these questions. They needed to focus on two factors (fondements): first, whether the

principle of the lever gave a clear advantage to either a small or a large wheel when it

was sunk to a certain level; second, whether a small or a large wheel had an advantage on

an inclined plane—which was used to characterize the shift from a soft to a hard terrain,

and also to overcome a stone on the road (see below). Only after knowing these two

points will the geometers be able to ascertain the best type of wheels.518 Roberval omitted

on purpose a third factor: the advantage or disadvantage provided by the terrain. This had

nothing to do with mathematical reasoning. It was essentially about physical qualities,

better known through reckoning (l’estime). It was equally true for the sand found on the

roads and the animals pulling the cart. All these belonged to the realm of experience.519

Roberval finished his communication with the example of a wheel bumping a rock

(cahod) on the road. When simplified, it was nothing more than a geometrical analysis of

a wheel trying to overcome an inclined plane. Roberval proved that a larger wheel had a

518 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématiques, vol. 3 (1668-1669), séance du mercredi 4 Juillet 1668, 78v-92v. Here is the conclusion to which Roberval arrived: “C’est donc aux geomestres a demesler ces diuersitez; et les fondement d’un tel demeslé sont ces deux: le premier la raison du leuier a la partie enfoncée: car si cette raison se trouue egale en l’une et l’autre roüe on conclura que pour ce chef l’une n’a point daduantage par dessu l’autre: le contraire fera conclure le contraire. Le second fondement est est d’examiner l’Inclination du plan, et quelle difficulté ou facilité il apporte a la roüe d’ou on verra laquelle a l’aduantage ou le desaduantage. Enfin ayant la connoissance de ce que produit le premier fondement, et celle de ce produit le second, on composera les raisons qui viennent de l’une et de l’autre part, pour en faire une seule raison qui fera voir le veritable aduantage ou desaduantage d’une roüe par dessus l’autre.” (p. 86r)

519 Ibid., 86v-87r.

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clear advantage over a smaller one in surmounting such an obstacle.520

The following week, both Huygens and Mariotte came to the same conclusion as

Roberval’s (using different geometrical arguments).521 These two sessions of the

Academy were, to my knowledge, the only ones that ever dealt with theoretical questions

concerning carriages. They were aimed at giving sound mathematical basis to notions

that were broadly known to carters and afficionados—like Huygens’s brother-in-law

Doublet, who knew from his vast experience with carriages that larger wheels provided

more overall advantages than the drawbacks of the added weight might cause. It was

probably for a similar reason that one of the early modifications on the machine

Roanesque was the size of its wheels.522 The Academy had but a minor role in the present

story. Yet it reminds us that Huygens lived in an epistemic space encompassed by theory,

experiments and artisanal knowledge. (Whether Huygens instigated these two special

sessions at the Academy remains unknown.) Huygens studied, supervised and customized

every possible aspect surrounding the life of machines, whether it was his air pump, his

lens-grinding endeavors, or his clocks, just to name the most celebrated ones. The

carriage is but another example of a general epistemological pattern, one increasingly

familiar in early modern France.

To redesign his cariole (a term, we learn, that should only be attributed to two-

wheel carriages), Huygens employed the nephew of the abbé Ciri, named Bertholin, a

520 Ibid., 87r-92r. 521 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de

mathématiques, vol. 3 (1668-1669), séance du mercredi 11 Juillet 1668, 94r-99r. 522 Huygens, OC(6), Huygens to Philips Doublet, 3 September 1666, no. 1560, p. 80; Huygens,

OC(5), Pierre Perrier, marquis de Crenan to Huygens, 26 July 1664, no. 1246, p. 90: “Lon faict les Roües plus haultes, Elles sont de trois pieds et demy de haulteur.”

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man knowledgeable in such matters. The modifications were extensive, since one would

now be able to enter the calèche from the side (rather than from the front) and glass

windows would be added. As for the suspension, Huygens did not really understand why

Doublet’s suggestion to secure the leather straps to the arcs rather than the beams would

eliminate the cabin’s shaking. But because experience had proven to Doublet it worked,

Huygens would follow this practice blindly (sans l’examiner d’avantage).523 By the end

of August, roughly a month later, the conversion was close to completion. The new

calèche was perhaps not as good as if it had been designed all along as a four-wheeler. It

was nonetheless nice and as confortable as it could possibly be.524

Huygens owned the calèche for about three years. Owing to another bout of

sickness, he was forced to leave Paris in the early Fall of 1670. He tried to sell his

carriage to the Carcavys (father and son), asking 100 écus. The deal never came through.

Coming back to Paris in June 1671, however, Huygens found out the Carcavy duo had

exchanged his calèche for another one—thinking that this time Huygens would not

return. “Admirez l’insolence,” he wrote to his brother Lodewijk, mentioning that the

cabin’s cushions and curtains, locked in his study in the king’s library, had also been

taken away. Huygens told the whole story to Colbert, who put Charles Perrault in charge

of finding out what exactly had happened. Both father and son Carcavy were ultimately

reprimanded for their act, the son losing most of the royal functions he had held until

523 Huygens, OC(6), Huygens to Philips Doublet, 27 July 1668, no. 1655, p. 245. 524 Huygens, OC(6), Huygens to his broter Lodewijk, 10 August 1668, no. 1657, p. 248; ibid., 31

August 1668, no. 1658, p. 251 where he says: “Ma calesche est depuis aujourdhuy attachée sur le train a 4 rouës avec 2 arcs. Les glaces y sont. Et il ne reste que les ornemens de dorure. Elle sera assez jolie apres cela, quoy que non pas tout a fait de si bonne facon que si elle n’eust pas estè racommodée. Ie la fais peindre de noir, et la dessus de chifres et feuillages d’or, et tous les biseaux et la corniche. I’ay aussi des harnois noeufs qui sont fort propres.”

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then. Huygens kept the new carriage, paying the Carcavys forty livres tournois to make

up for the value of the new machine. With new horses and touches of paint, the carriage

was fairly graceful.525

For more than five years, between 1663 and 1668, Huygens examined all aspects

of carriage design, manufacturing and sponsoring. Although he essentially dealt with

theoretical and practical problems, he had been compelled to tackle some matters of

authorship as well. The carriage became more than a highly-regarded urbane commodity

for Huygens—a status-granting tool in the eye of aristocracy and upper Parisian

bourgeoisie. The carriage (cariole or calèche) symbolized within Huygens’s epistemic

space a vehicle of knowledge, crossing effortlessly between the domains of theory,

experiment and artisanal know-how. How Huygens tackled carriage making was not at

all exceptional. It was essentially no different than how the members of the Académie des

sciences—of which he was a member—dealt with new inventions and machines.

APPROVED BY THE ACADÉMIE DES SCIENCES

The origins, history, social and epistemic contexts, as well as the membership and overall

goals of the early Academy of Sciences have been analyzed more than once.526 It is not

our purpose here. In light of what has been said thus far in this dissertation, I want to

525 Huygens, OC(7), Huygens to his broter Lodewijk, 9 July 1671, no. 1832, p. 80; ibid., 23 July 1671, no. 1835, p. 84; 30 July 1671, no. 1836, p. 86; 21 August 1671, no. 1841, pp. 100-101; 15 October 1671, no. 1846, pp. 107-108.

526 The classic studies remain Roger Hahn, The anatomy of a scientific institution: The Paris Academy of Sciences, 1666-1803 (Berkeley: University of California Press, 1971). David J. Sturdy, Science and social status. The members of the Académie des sciences, 1666-1750 (Woodbridge, UK: The Boydell Press, 1995). Stroup, A company of scientists. See also Robin Briggs, “The Académie des sciences and the pursuit of utility,” Past and Present 131 (1991), 38-88. The two-volume institutional history written by Fontenelle is Histoire de l’Académie royale des sciences, 2 vols (Paris, 1733) [hereafter cited as HARS].

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convey how integrated machines were to the theoretical and experimental practices of the

French institution. Christiaan Huygens’s air pump is certainly one of the best studied and

most obvious examples.527 Despite its importance to our understanding of the nature of

natural philosophical knowledge during the Scientific Revolution, the air pump was by

no means the only machine at the academicians’ disposition.528 It had, in fact, a

somewhat marginal role in comparison to the vast array of apparatus dedicated to

astronomy and found in the newly built observatory. According to Alice Stroup, the

investment by the crown for astronomical and mathematical instruments was

considerable: over 85,500 livres tournois between 1666 and 1699 (notwithstanding the

observatory building itself, with a price tag above 713,000 livres). This number is more

than twice the disbursement for the chemical laboratory during the same period. In

contrast, the spending for the collection of mechanical models was less than 15,000

livres.529 Instruments were an integral part of the academicians’ daily business. And

although the apparatus expenditure differed greatly, depending on the nature of the study,

one thing remained unchanged: the construction and merit of instruments, machines,

mechanical models and various other tools was always overseen and judged by one or

several academicians. It made no difference whether a theoretical paper or a new

527 Alice Stroup, “Christiaan Huygens and the development of the air-pump,” Janus 68 (1981), 129-158. Stroup, A company of scientists, 159-166. Steven Shapin and Simon Schaffer, Leviathan and the air-pump. Hobbes, Boyle, and the experimental life (Princeton: Princeton University Press, 1985), chap. 6. For a description of the machine and the first experiments done at the Academy, see Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 4 (1668), over several meetings, 1r-27v.

528 After an initial month of experimentation with Huygens’s air pump, and hearing reports about Robert Boyle and the older experiments done at the Accademia del Cimento, “la Compagnie a jugé que la matiere du vuide auoit esté suffisamment examinée et qu’il falloit passer a quelque autre matiere.” Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 4 (1668), séance du samedi 19 mai 1668, 27r.

529 Stroup, A company of scientists, tables 3, 5 and 7, pp. 246-247, 250-251, and 254.

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invention was given for approval by the Academy. They were all refereed by ad hoc

committees, made responsible to report on a subsequent session so that a collective

agreement could be reached.530 This teaches us one essential thing: though the boundary

between science and technology did not completely disappear within the confine of the

Academy, it was blurred considerably.

Artisans and academicians were in frequent contact, whether directly (for special

projects, like Huygens’s air pump (with Denis Papin) or Cassini’s silver planisphere

(with Michael Butterfield)) or via a third party, through one of the élèves or commis,

when dealing with a common project investigated by the Academy. These élèves,

especially Claude-Antoine Couplet, were paid “to execute the decisions of the company,

and especially conduct any observations which required it.” Élèves more often than

academicians received the mandate to have an instrument or machine made by an artisan

for the Academy (faire faire in French).531 Examples abound in the Academy’s Procès-

verbaux, usually following this hierarchy: academician, élève, artisan.532 Couplet and the

other élèves were also responsible for setting up and carrying out experiments, whether at

530 Hahn, The anatomy of a scientific institution, 24. Hahn ascribes this similarity in procedure to a bureaucratic purpose, “where all that counted was the rendering of a considered collective judgment.”

531 Sturdy, Science and social status, 127-137, quote on p. 127. The other élèves were Antoine de Niquet, La Voye-Mignot, Pivert and Jean Richer. On the term commis, see Huygens, OC(6), Huygens to his brother Constantyn, 30 November 1668, no. 1677, p. 300.

532 See, for instance, Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 3 (1668-1669), séance du mercredi 5 septembre 1668, 132r, where it is written: La Compagnie a resolu qu’on traiteroit de cette matiere dans la 2eme assemblée, et a donné ordre a Mr Couplet de faire preparer ce qui sera necessaire pour cette experience, suivant les ordres que Mr de Roberval luy en donnera.” An early exception relates to the making of cartographic maps. After Sanson visited the Academy, it was decided that Picart and Roberval would supervise the various manners in producing geographical data, while Jacques Buot was asked to oversee the construction of a proper circumferentor, or “d’un cercle entier de 15 pouces de Diametre dans oeuure ayant une alidade garnie de deux pinulles et sur Le limbe du Cercle deux autres pinulles fixes Diametralement opposées auec vne boussolle au centre dont l’esguille soit de 4 pouces Et Mr Buot a esté commis pour prendre le soing de faire faire cet instrument.” Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 3 (1668-1669), séance du mercredi 30 mai 1668, 30r-30v.

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the Observatory, the king’s library, or out in the field (and onto sea, in the case of La

Voye-Mignot, in order to test Huygens’s pendulum clocks for longitude determination.

Jean Richer later received such assignments.)533 They could be compared, in a sense, to

the Royal Society’s curator of experiments, Robert Hooke.

The artisans in relation with the Academy were numerous. For mathematical and

astronomical instruments we can mention the armorers Sevin, Gosselin, Guerne, Tanguy

and Lagny. To these, one must add the mathematical intrument makers Ph. Le Bas,

Migon, Butterfield and Chapotot. For clocks and clock mechanisms in general Thuret

was essentially it (though Gosselin was responsible, with Thuret, of keeping the clocks

and instruments of the Academy and Observatory in good order).534 Although the

manufacture of lenses was often done by academicians themselves (Huygens, Auzout,

Borel), instrument makers such as Pasquin, Le Bas, and Hartsoëker in France, Campani

and Divini in Italy, were regularly employed.535 Regarding the construction and repair of

mechanical models, found in the chambre des machines, specialized artisans and

engineers were also hired: Danglebert, Gayon, Potel, Buirette, Cosson, Langenach,

Colson, as well as Niquet and Couplet in a few instances.536

The Academy’s dealings with expert instrument makers and skilled ouvriers,

533 Sturdy, Science and social status, 128. 534 Regarding Thuret, the Procès-verbaux say: “Monsr. Thuret oultre les Pendules qu’il fait,

reglera les autres qui sont desja faites.” Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 2 (1667-1668), séance du 30 mars 1667, 161.

535 C. Wolf, Histoire de l’Observatoire de Paris, de sa fondation à 1793 (Paris: Gauthier-Villars, 1902), 137. See also Maurice Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles (Paris: PUF, 1953).

536 Stroup, A company of scientists, table 5, pp. 250-251. For an interesting historical aperçu regarding instrument collecting, see Anthony J. Turner, “From mathematical practice to the history of science,” Journal of the History of Collections 7 (1995), 135-150.

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sometimes hard to define exactly, happened on a regular basis—if not daily.537 Auzout

suggested early that someone—Couplet was appointed—should visit the artisans’

workshops to examine their instruments and learn their needs, secrets and deceptions

(sophisteries). Carcavy thought it could be done easily by going to the king’s artisans.538

Aside from meetings focusing on pure mathematics, every facet of the Academy’s life

involved instruments, machines, and their inventors and makers. Moreover, the Academy

became the foremost arbiter of inventions. In fact, a favorable endorsement was rapidly

turning into a sine qua non condition for a royal privilege.539 Instruments and machines

were simply everywhere during the first decades of the Académie des sciences.

The number of machine projects presented to the Academy was sizeable.

Gentlemen, engineers and artisans alike were all looking to get the Academy’s seal of

approval, increasingly using informal networks—bypassing government channels—to

537 For instance, in Auzout’s “Memoire des Instrumens & autres choses necessaires dont il faudra fournir ceux qui iront à Magadascar [sic],” a long list of instruments mentions: “Deux grands quarts de Cercle,” “Vn ou deux sextans de la mesme grandeur,” “Deux ou trois boussoles de 6 ou 8 pouces,” “De grande Lunettes de 30, 40 ou 60 pieds &c, et d’autres de moindres longueur,” “Plusieurs oculaires de touttes grandeurs & foyers,” etc. However, there are no indications as to whom should be hired to make these. Some could just be bought from trustworthy makers. Others, like Huygens’s clock, Auzout’s micrometer, and Thévenot’s level would have been built other artisans working specifically for these academicians. Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 2 (1667-1668), [January 1667], 37-40. Auzout followed this mémoire with another one on how the observations needed to be done in Madagascar.

538 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 2 (1667-1668), séance du 30 mars 1667, 161. Going to the king’s artisans, living in the Galeries du Louvre, was indeed the obvious choice since they were not regulated by the all-powerful Parisian guilds. Trade secrets, in other words, had a different meaning for them (if at all). And since they were working for and paid by the king, as were the academicians, they most likely considered themselves equal to the latter. This idea of visiting the artisans’ workshop was already in the anonymour memoir Huygens received in circa 1663 about the project of an Academy: “On taschera aussi d’apprendre toutes les tromperies des Artisans et des Marchands et leurs Sophistiqueries avec les Moyens pour les decouurir, que l’on publiera pour empescher le public d’y estre trompé, et pour obliger les ouuriers a trauailler plus fidelement. Huygens, OC(4), ? to Huygens, [1663?], no. 1105, p. 326.

539 Only in the regulations of 1699 was this advisory function to the king defined in writing. On the evolution and role of the Academy as arbiter of inventions, see Liliane Hilaire-Pérez, L’Invention technique au siècle des Lumières (Paris: Albin Michel, 2000).

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place their projects under the scrutiny of the academicians.540 In the early years, for

instance, Colbert asked the Academy to examine a pump from the Sieur Douceur and a

machine to raise water by an anonymous engineer, as well as a device for the

determination of longitudes at sea invented by a German named André Reusner de

Neystett. The former two were declared common and of no significant use. They were

dismissed after one meeting.541 The latter, though ingenious, was also dismissed. It took,

however, several discussions over the span of one week to reach this final conclusion.

The inventor clung to his idea, forcing the academicians (Carcavi, Huygens, Roberval,

Auzout and Picard) to rebuff it several times before Colbert and a high naval officer

declared de Neystett’s invention inadequate to its intended task. Perhaps the most

interesting aspect of this story is that a draft of the privilege had been penned, presented

and accepted by the inventor—on the condition the invention was approuvée by the

Academy’s committee, naturally. I found no other such draft proposal between 1668 and

1690 in the procès-verbaux, suggesting that very early, whether one went directly to

Colbert or not, an invention had first to be examined and approved by an ad hoc

committee of the Academy before one ever thought of asking for a royal privilege.542

540 Hahn, The anatomy of a scientific institution, 22. 541 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de

mathématique, vol. 3 (1668-1669), séance du mercredi 11 avril 1668, 1r-1v; ibid., séance du mercredi 25 avril 1668, 7r-7v.

542 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 3 (1668-1669), over several meetings, 38r-52v. The terms of the privilege were very generous: “Sa Maiesté a bien uoulu declarer et luy donner asseurance qu’en ce cas Elle luy accordera premierement la Somme de Soixante mil Liures comptant et outre ce un droict de quatre sols pour chacun tonneau du port de tous les vaisseaux qui vouldront se seruir des instrumens necessaires pour mettre Ledit secret en practique. De plus le priuilege de faire seul lesdits Instrumens a l’exclusion de tous autres, luy fera valoir ledict droict de quatre sols pour tonneau la somme de huict mil luires [sic| par chacun an, pour Laquelle somme elle luy fera donner toutes les asseurances qu’il pourra desirer, se reservant sadicte Maiesté la faculté de pouuoir retirer Ledict droict de quatre sols pour tonneau en payant audict Reusner de Neystett la somme de Cent mil liures comptant…”

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The Academy was thus significantly changing the function of patronage regarding

matters of invention, technology, and their value to the kingdom. An expert—and

purportedly neutral—third party had been crucially positioned by Colbert between the

king (the ultimate patron) and his potential clients. In this most important role, the

Academy acted henceforth as an authoritative power-broker only in the case of bona fide

inventions. And these were relatively few (and most from academicians themselves) over

the first three decades of the Academy.543 According to Charles Perrault, Colbert was in

fact extremely pleased that individuals were rarely given certificates of approval after

having presented their invention to the Academy.544

Yet a large number of honnêtes hommes and artisans knocked at the door of the

Academy with their inventions, especially between 1677 and 1690. In a memoir sent to

Paul Pelisson, Louis XIV’s royal historian, Huygens mentioned that “inventions designed

by individuals other than academicians, and offered to the king or to Monseigneur

Colbert were frequently forwarded to the Academy in order to be examined, which was

done in all diligence and absolute integrity; though inventors sometimes complained,

being too fond of their ideas and imaginations.”545 After his hands-on experience in

carriage design, Huygens knew for a fact it was easier to criticize an invention than

invent one that would actually work. In a letter discussing his brother Lodewijk’s

carriage, for example, Huygens mentioned to Doublet that Colbert was continuously

543 The most important of these were gathered in the eighteenth century in the well-known Machines et inventions approuvées par l’Académie royale des sciences, depuis son établissement jusqu’à present; avec leur Description. Dessinées & publiées du consentement de l’Adadémie, par M. Gallon, 7 vols (Paris, 1735-1777), vol. one for the period between 1666 to 1699.

544 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du 8 mai 1677, 103r-103v.

545 Huygens, OC(8), Huygens to Paul Pelisson, 15 August 1679, no. 2185, p. 199.

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sending him inventions of large pumps operated by windmills and other mechanisms for

providing the city of Paris with water. Though he condemned most of these inventions,

Huygens confessed he could not himself come up with a better one; hence he asked his

brother-in-law to send his own design. On occasion, Huygens would endorse an invention

so its inventors would be granted their privilege, although he did not fully approve of

it.546

Besides the machines proposed by the academicians for their own scientific work,

the Academy reviewed all kinds of other devices, even agreeing to pay for having them

built if they proved feasible, as mentioned in the case of Leibniz’s arithmetical

machine.547 Again, examples abound. The clockmaker Didier l’Allemand, sent by

Colbert, presented a 4-inch steel mechanical celestial globe, showing the movement of

the sun, moon and the fixed stars. The comments must have been favorable since a

description of the machine was published less than two weeks later in the Journal des

sçavans.548 The Sieur Cartois, harpsichord maker, presented a new manner of jack

(sautereau), replacing conventional parts by metallic ones.549 The instrument maker

Hubin, after adding some elements (particularitez) of his own, demonstrated Denis

546 Huygens, OC(6), Huygens to Philips Doublet, 20 January 1668, no. 1619, pp. 173-174. The invention in question was a new mechanical system for fixing carts’ wheels. Regarding this invention, we learn that though it had indeed been granted a privilege, it was later revoked because people contested the authors’ legitimate rights to it. Ibid., Huygens to Philips Doublet, 27 July 1668, no. 1655, p. 245.

547 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 8 (1675-1679), séance du 9 janvier 1675, 2r. On this machine, see Matthew Jones, The matter of calculation: Early modern calculating machines, statecraft and thinking about thinking (forthcoming), chap. 2.

548 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 15 mai 1677, 109r. See also the Journal des sçavans, lundi le 24 mai 1677, 129-131.

549 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 4 février 1678, 136r.

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Papin’s high-pressure device to cook meat and soften bones, described in Papin’s book—

reviewed in the Journal des sçavans.550 Franchine (or Francini) demonstrated a new type

of machine to raise water, which was quickly approved.551 Monsieur Mercator also

presented the design of a hydraulic machine (which he called siphon continué) to move

water from a valley or side of a mountain over it and towards a lower location.552 The

Parisian clockmaker de Bauffre showed a watch comprising a new type of balance

assembly, which Cassini thought was well made and did not loose too much time (7-8

minutes after eight days).553 When the wooden tower of Marly was moved on the

Observatory’s ground in 1685 to make astronomical observations with large telescopes,

at least two inventors (Father Sebastien and Cusset) sent their designs on how to support

these forthcoming massive optical devices.554 (See Figure 4.7.)

550 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 10 (1679-1683), séance du mercredi 21 mai 1681, 67v; ibid., séance du mercredi 28 mai 1681, 68r. See also the Journal des sçavans, lundi le 25 août 1681, 367-373.

551 We do not appear to have the minute of the meeting in which it was done. It is only mentioned in the year’s summary, “Mémoire des Observations et traittez Mathématiques ausquels on a travaillé depuis le 15e de juin 1681 jusqu’au ~3e de juillet 1682,” Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathematique, vol. 9 (1679-1683), 171r. Several years earlier, Huygens mentioned in his correspondence another machine by Franchine. Huygens, OC(6), Huygens to his brother Lodewijk, 27 April 1668, no. 1637, p. 212. It was presented to the Academy in 1668—though I found no trace of it in the Procès-verbaux. See also the Machines et inventions approuvées par l’Académie royale des sciences, 145-148. See as well the Journal des sçavans, 10 December 1668, 144 and Ibid., 16 December 1669, 46-48. It was installed in Colbert’s garden.

552 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathematique, vol. 9 (1679-1683), séance du samedi 15 mai 1683, 218r-220r.

553 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 11 (1683-1686), séance du samedi 13 janvier 1685, 115v; ibid., séance du samedi 27 janvier 1685, 119r. Cassini also reviewed another watch by the clockmaker Felilot. Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 12 (1686-1689), séance du mercredi 29 mai 1686, 5v.

554 On the Academy’s request to Louvois for the Marly tower, see Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 11 (1683-1686), séance du samedi 20 janvier 1685, 116r. Father Sébastien’s machine (for a 100- to 160-foot long telescope) was discussed in ibid., séance du mercredi 7 février 1685, 119v and ibid., séance du samedi 10 février 1685, 119v-120v. See also Machines et inventions approuvées par l’Académie royale des sciences, 93-94. A certain Cusset from Lyons also brought a model of such a machine, which was kept in the chambre des machines. Ibid., séance

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FIGURE 4.7: SUPPORT SYSTEMS FOR LARGE TELESCOPE Above, Father Sebastien’s support for long telescope. It was also described in the Machines et inventions approuvées par l’Académie royale des sciences edited by Gallon, from which this image was taken. Right, Cusset’s support as depicted in the Journal des sçavans.

The Marly tower and its specific requirements for precision astronomy is but one

example of the various mandates tackled by the Academy and requiring novel thinking

about instrumentation. Another such illustration was the numerous hydraulic projects

around Paris, especially the planning and completion of an adequate water supply for the

fountains at Versailles. The latter project led to major leveling efforts in order to

accurately measure the relative slope (dénivellation) between distant water supplies and

Versailles’ gardens. Picard was the chief instigator of this project and his level, first

described in the Traité de la mesure de la terre (1671) and later improved—a description

of which was published posthumously in his 1684 Traité du nivellement—was a sort of

du 28 avril 1685, 126r, and samedi 27 juillet 1685, 134r-135r, and samedi 12 janvier 1686, 154r, and samedi 19 janvier 1686, 155r, which was examined by de la Chapelle, Cassini, Perrault and de la Hire. It was described in the Journal des sçavans, 28 May 1685, 216-217. Several years earlier, Couplet and Perrault from the Academy had also proposed similar supports for extra-long telescopes. Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 27 novembre 1677, 130v.

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gold-standard in surveying instruments until the end of the century.555 (See Figure 4.8.)

Picard’s chief development was to replace the level’s sighting vanes with a telescope

(lunette), increasing the precision of the instrument. Although Auzout may have been the

original discoverer, there is no concrete evidence he ever developed it. Picard, on the

other hand, had applied a telescopic sight to an astronomical quadrant before the level.

555 Picard, Traité du nivellement, in Mémoires de l’Académie royale des sciences, vi:631-713 where the use of his level the measurements he took are also described. See also HARS, ii:198-200 explaining that de la Hire was the one responsible for the posthumous editing and publishing of this treatise in 1684. Picard gave a general talk at the Academy on levels. See Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 21 mai 1678, 158v-159r. On Picard’s level and his involvement with Versailles, see Michel Kasser, “Picard et le renouvellement de l’art du nivellement à la fin du XVIIe siècle,” in Jean Picard et les débuts de l’astronomie de précision au XVIIe siècle, ed. by Guy Picolet (Paris: Editions du CNRS, 1987), 255-263 and Hubert Loriferne, “L’influence de Picard dans les travaux d’alimentation en eau du château de Versailles sous Louis XIV,” in ibid., 275-311.

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FIGURE 4.8: VARIOUS TYPES OF LEVELS Above, Butterfield’s level with a telescopic sight, three years before Huygens. Above right, Huygens’s level, which appears to have had some success. To the right, Picard’s level discussed in his Traité du nivellement. He used it at Versailles. Below, Chapotot’s level published the same year as Huygens’s in the Journal des sçavans.

Following Picard’s improvement a number of similar levels came from artisans,

honnêtes hommes and academicians alike between 1677 and 1686.556 All with a

telescopic sight. Michael Butterfield and Louis Chapotot, instrument makers well-known

in Paris, both designed two during that period.557 (See Figure 4.8.) De Hautefeuille and

the Sieur de Puyrichard, honnêtes hommes, invented one each, the former with what

appears to have been two air thermometers à la Hubin connected together (more on air

thermometers below).558 At the Academy, Cassini, Rømer, de la Hire and Huygens also

556 Other inventions, such as Thévenot’s bubble level in 1661 and Mariotte’s 1772 level, described in his own Traité du nivellement, did not use telescopic sights. They remained marginal discoveries—though the bubble level became a common commodity in the eighteenth century. Mariotte’s treatise was reviewed in the Journal des sçavans, 12 December 1672, 147-148.

557 On Butterfield, see the Journal des sçavans, 6 September 1677, 227-228; ibid., 19 September 1678, 440 and ibid., 16 December 1678, 441-443. For Chapotot, see the Journal des sçavans, 17 June 1680, 174-176 and ibid., 20 May 1686, 141-144. Chapotot also demonstrated his level at the Academy. See Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 10 (1679-1683), séance du samedi 18 mai 1680, 60r. A short general overview on the development of levels is found in Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles, 76-78.

558 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de

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said to have improved the level.559 Of all these, Huygens’s appeared to have enjoyed the

most success.560 (See Figure 4.8.) What we see here is how a specific problem (exact

leveling) raised by a special need (royal gardens) put to work not only the Academy but

the whole Parisian “scientific” community. The Academy did not work in isolation of

technical expertise. It was put by Colbert in the center of a growing “scientific”

networking encompassing all kinds of people and specialized branches of craftsmanship

and learning. Although it was the authority-granting body of the ancien régime, the

Academy was above all an umbrella institution under which innovation was somewhat

blind to social status. As the examples below will show in more details, the academicians

always had the last say, but were by no means the only ones to contribute to the

advancement of knowledge and technology.

In effect, some inventors, honnêtes hommes and artisans alike, repeatedly called

on the Academy in order to demonstrate their new inventions. Though an earlier pump by

mathématique, vol. 8 (1675-1679), séance du mercredi 17 mai 1679, 202v. Also described in the Journal des sçavans, 7 August 1679, 215-216. There is only a brief mention, with engraving, of Puyrichard’s level in the Journal des sçavans, 16 September 1680, 276.

559 For Rømer, see Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 23 mai 1676, 46r-50v; ibid., séance du samedi 28 novembre 1676, 64v. For Cassini, ibid., séance du samedi 31 juillet 1677, 117v; ibid., Registre de physique, vol. 10 (1679-1683), séance du samedi 25 novembre 1679, 2r. For Huygens, see ibid., séance du samedi 13 janvier 1680, 9v and séance du samedi 30 mars 1680, 35v-44r. Also published in the Journal des sçavans, 29 January 1680, 21-24 and ibid., 26 February 1680, 57-60. For de la Hire, see Picard’s Traité du nivellement, where are also described Rømer’s and Huygens’s levels.

560 In 1684, the instrument maker Butterfield reduced the size of Huygens’s level to a pocket level. It was advertised in the Journal des sçavans with the following preface: “La bonté du Niveau de M. Hugens a fait rechercher avec soin le moyen de le pouvoir porter commodément.” Journal des sçavans, 5 June 1684, 192. In 1686, several after Huygens had left Paris definitely, Philippe de la Hire wrote to Huygens that “Vostre niueau est celuy de tous les niueaux qui est le plus en uogue et ie croy que ce que uous uoudrez bien nous donner la dessus sera toujours tres bien receu.” Huygens, OC(9), de la Hire to Huygens, 5 December 1686, no. 2447, p. 114. There are several other correspondences mentioning Huygens’s level as well as a chapter in Huygens, OC(21), pp. 81-108. In 1686, before describing a new level by Chapotot, the author of the Journal des sçavans wrote the following: “Il semble qu’après l’exacte précision des Niveaux que nous ont donnéz feu M. Picard & M. Hugens, il soit assez difficile de porter le nivellement à un plus haut degré de perfection qu’il l’est aujourd’huy.” Journal des sçavans, 20 May 1686, 141.

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the Sieur Douceur was judged common, an ad hoc committee formed by Picard, Mariotte

and Buot was dispatched to the Arsenal several years later to examine his new

machine.561 People like Monsieur de la Brosse, Jean de Hautefeuille, Hubin, Cusset,

Jacques Rouillon and Guillaume Amontons (who later became an academician himself)

went to the Academy several times during the 1670s and 1680s to have their machines

examined and judged by the highest authority-granting institution in France. Claude

Comiers, a canon from Embrun, also developed quite a few inventions of his own,562 like

this Clepsidra noua et admirabilis, which was in truth a table-top water fountain based on

the principle of Hero of Alexandria. (See Figure 4.9.) Comiers sent the design to the

Academy in 1669, but there is no trace in the Procès-verbaux. Huygens, who had perhaps

been asked to evaluate it, rediscovered the fountain in his papers three years later.563

Comiers had originally forwarded the design, not the actual machine. So Huygens had it

made by an

561 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 8 (1675-1679), séance du mercredi 18 novembre 1676, 99r.

562 For a list of machines designed by Comiers, see Journal des sçavans, 11 May 1676, 102-103; Ibid., 22 June 1676, 138-141; Ibid., 20 July 1676, 165-167; Ibid., 3 August 1676, 175-177; Ibid., 14 September 1676, 212-214; Ibid., 21 December 1676, 242-244.

563 Huygens, OC(6), Comiers to the Académie des sciences, 16 March 1669, no. 1714, pp. 381-382.

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FIGURE 4.9: COMIERS’S HERO FOUNTAIN

The first drawing on the right is Comiers’s fountain, as drawn in the Procès-verbaux. The one to its right was drawn by Huygens and is found in his correspondence. Below, in the center, is Hubin’s adaptation of the same table-top fountain based on Hero of Alexandria’s principle. Hubin’s air thermometer is seen in the upper left corner of that same engraving.

unknown artisan. According to the Dutch natural philosopher, it was working well, better

in fact than most fountains described in books.564 What is interesting to note here is that

Comiers’s design was promptly communicated—most likely by Huygens himself—to

564 Huygens, OC(7), Huygens to his brother Lodewijk, 9 March 1672, no. 1871, p. 153; ibid., Huygens to ?, [1672], no. 1872, pp. 154-155. When the fountain was held upright, the water found in container A was going up in the upper glass vessel in the form of a jet and, after coming down, was ending in the bottom container B. Turning the fountain upside down (so that B was now in the upper position) the same hydraulic motion took place again.

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another artisan, Hubin, the royal enameller, who visited the Academy somewhat regularly

in the decade between 1673 and 1683. Hubin appears to have made several of these, large

and small, for profit. Owing to his special skills, he was (said he) the first to build the

fountain entirely of glass, as Comiers had designed it.565 (The model built at Huygens’s

request had its two water containers made of tin.)

From an honnête homme to the Academy then ultimately to an artisan familiar

with the Academy: this intellectual to material itinerary increasingly characterized the life

of early modern French machines. As long as authorship was well established and

respected, this technological itinerary—with its unexpected and necessary variations—

ensured the superiority and value of mechanical devices. Then again we see that the

manufacturing of knowledge and machines involved several kinds of authors working in

separate and sometimes clearly delineated spheres of knowledge-production. Yet what

brought them together over and over again were the tools, contraptions, mechanisms and

complex pieces of equipment that came to epitomize the Scientific Revolution and

modern science. The Academy’s role as an authority-granting institution facilitated the

emergence of this pattern of natural philosophical discovery.

HUYGENS AND THE BUSINESS OF AUTHORSHIP

Priority claims were not an unfamiliar business to the members of the Academy. The

controversy regarding the origin of vision and the discovery of a blind spot in the eye, for

example, was hotly debated between Mariotte, Pecquet and Perrault in the early years of

565 Hubin, Machines nouvellement executees, et en partie inventees Par le sieur Hvbin, Emailleur du Roy. Premiere partie, ov se trouvent une Clepsydre, deux Zymosimetres, un Peze-liqueur, & un Themometre. Avec quelques Observations faites à Orleans, sur les qualitez de l’Air, & particulierement sur sa pesanteur (Paris, 1673), chap. 1.

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the Academy. Fontenelle, in retrospect, did not perceive disgraceful belligerence in this

controversy, but recognized instead a symbol of rational thinking; he actually saw beauty

in it.566 A few years later, Cassini brought to one of the weekly meetings a machine of his

invention designed to measure distances without any calculation. Roberval raised an

objection at that same meeting, claiming he had already invented a similar device. The

following week, it was decided that Roberval’s claim was legitimate, though what he had

proposed in the past was very different. It was thus decided that both gentlemen would

bring drawings and a written account (discours raisonné) at the following meeting. They

did, and the matter appeared settled.567

Huygens, perhaps more than most academicians, was particularly mindful of

authorship issues. The aforementioned business of carriage most likely served him well

throughout his career, especially during two chief assaults against his priority in

inventing the balance-spring watch. The first one, coming from England and led by

Robert Hooke, has been masterfully analyzed by Rob Iliffe.568 The second one, closer to

my current interest and perhaps lesser known, involved the Academy and a clergyman

named Jean de Hautefeuille.

The abbé de Hautefeuille, son of a baker, was one of those honnêtes hommes

566 On the controversy, see Mirko Grmek, “Mariotte et la physiologie de la vision,” in Mariotte savant et philosophe, ed. by Pierre Costabel (Paris: Vrin, 1986), 155-185. On Mariotte’s strategy to gain credit, see Licoppe, La Formation de la pratique scientifique, 68-69. On Fontenelle’s summary and remark, HARS, i:102-103: “Il faut voir cette dispute dans toute son étenduë, pour la voir dans toute sa beauté.”

567 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 23 février 1675, 7r; ibid., séance du samedi 2 mars 1675, 7r-7v; ibid., séance du samedi 9 mars 1675, 8r; ibid., séance du samedi 16 mars 1675, 8r-8v. The Academy’s Procès-verbaux are silent as to whom won the original claim. Fontenelle, in his two-volume history of the institution (HARS), does not mention this priority. It was most likely a minor incident, of no consequence. But Fontenelle probably did not mention it on purpose, so that dissension within this august institution would not be publicized to much.

568 Iliffe, “‘In the warehouse’: Privacy, property and priority in the early Royal Society.”

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mentioned above who exhibited several machine designs in the Academy. Besides the

alleged invention of a novel balance assembly discussed here, he proposed a new type of

level, a telescope with a larger field of view, a machine to measure the evaporation of

water, and a device to observe the variation of a compass needle.569 These are but a few

examples of the numerous other inventions he penned during his lifetime.570 In 1675, de

Hautefeuille became (in)famous after he instituted proceedings against Huygens

regarding the priority claim expressed in favor of a new kind of pocket pendulum clock

(pendules de poche). In a long Factum, de Hautefeuille accused Huygens of blatantly

stealing one of his ideas for fame and profit—since Huygens had been granted a privilege

for his balance-spring watch.571 De Hautefeuille wanted Huygens’s privilege revoked and

given to him instead. It was about honor, not profit—although he had been told that such

an important privilege could be worth as much as 4,000 livres per annum. The invention

was noteworthy because it was designed to be used on board vessels to determine the

longitude at sea. The whole idea was to replace the bobbing pendulums on clocks by a

spring, the motion of which—it was assumed—would not be upset by the boat’s swaying.

569 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 8 (1675-1679), séance du mercredi 17 mai 1679, 202v; Registre de physique, vol. 7 (1675-1679), séance du samedi 14 avril 1679, 240v-242v; Registre de mathématique, vol. 8 (1675-1679), séance du mercredi 17 mai 1679, 202; ibid., Registre de physique, vol. 10 (1679-1683), séance du mercredi 25 novembre 1682, 111r-111v; ibid., Registre de mathématique, vol. 9 (1679-1683), séance du samedi 18 juillet 1682, 167r-168r.

570 Jean-Etienne Montucla, the famous Enlightenment mathematician, said about de Hautefeuille that “Cet abbé était un homme qui ne manquoit pas de génie, mais qui, à l’instar d’autres mécaniciens que j’ai connus, n’avoit pas plutôt imaginé et publié quelqu’ébauche grossière d’une invention, qu’il passoit tout de suite à un autre objet, annonçant d’ailleurs, souvent d’après des idées incomplettes et peu réfléchies, des choses qu’il eût eu sans doute grande peine à réaliser.” For this quote and more on de Hautefeuille’s inventions, see the editor’s note in Huygens, OC(7), Huygens to his brother Constantyn, 26 April 1675, no. 2023, pp. 437-438.

571 The text of the privilege is found in Huygens, OC(7), Colbert to Huygens, 15 February 1675, no. 2011, pp. 419-420. Huygens had shown a working model to the minister a couple of weeks before. See ibid., Huygens to Gallois, 11 February 1675, no. 2007, p. 407.

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Though de Hautefeuille’s and Huygens’s inventions were completely different, as we will

see shortly, the former believed the essential principle of the design had been unfairly

appropriated by Huygens. Hence the Factum and the lawsuit against the renowned

academician.

To prove his point, and Huygens’s disingenuous action, de Hautefeuille put

forward six different types of arguments in his Factum572:

First, de Hautefeuille mentioned he had discussed (one could say disclosed) his invention at a meeting of the Académie des sciences. What was important here was the date: 7 July 1674, more than six months before Huygens was granted a privilege and before he published a short summary of the balance-spring watch in the Journal des sçavans.

Second, the plaintiff exhibited the similarity of the texts—the seeming plagiarism—between his earlier memoire read at the Academy and Huygens’s later letter sent to the Journal des sçavans.

Third, the plaintiff played with semantics, arguing that though he did not explicitly mentioned the word “spiral” in describing the shape of the spring regulator employed in his invention, he had nonetheless described it as it was. While de Hautefeuille described the object itself, Huygens had simply named it.

Fourth, the plaintiff brought into play popular knowledge, stating a well-known aphorism—Difficile est invenire, facile autem inventis addere—to emphasize the fact that everything Huygens had written concerning the “secret” of the invention was already found in de Hautefeuille’s memoire. Huygens had invented nothing, he only improved the original idea. Though he did not explicitly say it, de Hautefeuille was basically saying the he was the savant, and Huygens a mere artisan.

Fifth, the plaintiff turned the lawsuit into something bigger than himself, trying to involve the Académie des sciences. De Hautefeuille argued it was important for the honor of the Academy, and to the progress of the sciences, to make sure that the glory of individuals was respected as regards their discoveries. If people are publicly allowed to steal merit and reputation from one another, it would certainly tarnish the reputation of the Academy (ce seroit une tache à l’Académie).

572 The written document, published in 1676 and 1692, is found in Huygens, OC(7), Jean de Hautefeuille, Factum, touchant les Pendules de Poche, 1675-1676, no. 2024, pp. 439-453.

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Lastly, the plaintiff went for all-out slandering, saying in so many words that Huygens had usurped the glory of Galileo regarding the invention of the pendulum clock. (He added, in fact, that the academician used the same type of tactics as the ones denounced here.) And Huygens would have also made his a new kind of barometer discovered by Descartes—mentioning that the clockmaker Grillet was complaining as well contra Huygens about a similar barometer of his invention. (More on this below.)

The Factum, signed by the lawyer Arrault, was an attempt to discredit Huygens in order

to gain a privilege that de Hautefeuille thought was rightfully his. Yet the abbé’s

invention had virtually nothing to do with Huygens’s balance-spring watch.

In order to fix pendulum clocks, so they could work on swelling seas (i.e. become

portative), de Hautefeuille suggested an alternative to the pendulum in the memoire read

at the Academy. De Hautefeuille found by chance that replacing the pendulum by a thin

strip of steel would make it work almost as well as a regular pendulum clock. But the

“secret” of the invention lay in the shape of the regulator. Here he proposed that it should

be a vibrating spring. The result was a clock that could be used in any position, and thus

could be adapted as a smaller watch. (See Figure 4.10.) Whether or not he exhibited a

model of this so-called invention to the Academy is unknown. De Hautefeuille, however,

explicitly said the clock was coarse, made with mismatched parts, and had been made

quickly. De Hautefeuille closed by noting that he left in the hands of skilled artisans the

matter of shaping the vibrating spring—actually ending the memoire with the familiar

facile est inventis addere.573

Though we only have Huygens’s word for it, it is fair to assume that the Academy

was unimpressed by de Hautefeuille’s invention. In fact, it had been attempted before—to

573 This memoir is found in Huygens, OC(7), Jean de Hautefeuille to the Académie des sciences, 7 July 1674, no. 2028, pp. 458-459.

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no avail—by savants such as Hooke, Pascal and the Duc de Roannez, and the engineer

d’Esson.574 What Huygens proposed, and was credited for with a royal privilege, was

FIGURE 4.10: DE HAUTEFEUILLE’S AND HUYGENS’S BALANCE-SPRING WATCHES The drawing on the left is de Hautefeuille’s balance assembly with the vertical spring replacing the common pendulum. On the right, Huygens’s own balance-spring watch, with the horizontal coil spring. De Hautefeuille’s drawing is taken from his Factum; Huygens’s from the Journal des sçavans. As anyone can clearly see, the dissimilarity in mechanism is unequivocal. utterly different. (See Figure 4.10.) The fact that a spring, whatever its shape, vibrates at

the same rate regardless of how much it was compressed or stretched was indeed

common knowledge. But Huygens knew the cause, having carefully studied tautochronic

oscillators a few years before. What Huygens was aiming at was an action “regulated by

a principle of equality, just as that of pendulums is corrected by the cycloid.” More than

the spiral shape of the regulator had to be taken into account here. As stated in the

privilege, and often reiterated by Huygens himself elsewhere, it was the combination of a

spiral vibrating spring with a heavy balance wheel that generated the desired motion. De

574 Huygens, OC(7), Huygens to Contesse, 6 May 1675, no. 2027, pp. 457-458. He wrote: “L’on fit peu de reflexion dans nostre assemblee sur cet escrit quand il fut presentè, tant par ce que l’inutilitè de l’invention paroissoit par l’aveu mesme de l’autheur, que parce qu’on scavoit que d’autres que luy avoient tenté la mesme chose sans succes.” See also ibid., Huygens to Contesse(?), [1675], no. 2029, pp. 460-461. Contesse was the state prosecutor appointed to the case.

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Hautefeuille, to put it bluntly, had found nothing new at all.575

An interesting note involves Thuret, the Academy’s contracted clockmaker, who

at about the same time was also engaged with Huygens in a dispute regarding the

invention of the balance-spring watch. De Hautefeuille mentioned in his Factum that he

had communicated his idea to Thuret a few days after he went to the Academy. The fact

that Thuret claimed to have applied the spiral spring to a clock, and that he himself

shared the invention with Huygens—hence the priority dispute between Thuret and

Huygens—did not change a thing to de Hautefeuille’s lawsuit against the academician.

Whether Thuret was honest or not in his assertion did not matter. De Hautefeuille was

after the privilege, and it had been granted to Huygens.576 The latter, however, thought

Thuret was the mastermind behind de Hautefeuille’s lawsuit. Unwilling to be seen

opposing a royal privilege Thuret, according to Huygens, enrolled the services of de

Hautefeuille, un petit fol d’Abbè whose ideas were whimsical and unfounded, as the

lawsuit’s figurehead.577 There is no evidence for or against Huygens regarding this

575 For a detailed technical analysis, see Michael Mahoney, “Drawing mechanics,” in Picturing machines, 1400-1700, ed. by Wolfgang Lefèvre (Cambridge, MA: The MIT Press, 2004), 281-306, esp. pp. 302-303 (p. 303 for the quote). Huygens’s privilege mentions the two essential parts of the new mechanism: “le secret consiste en un ressort tourné en spirale qui règle les tours d’un balancier équilibre, plus grand et plus pesant qu’aux ouvrages ordinaires.” in Huygens, OC(7), Colbert to Huygens, 15 February 1675, no. 2011, pp. 419. To Contesse, Huygens wrote: “L’on verra au reste en comparant sa [de Hautefeuille’s] construction que je viens d’expliquer, avec la miene qui est dans la figure du journal [des sçavans] que je vous envoie combien elles sont differentes, puisque outre un ressort tout autrement appliquè et tout autrement formè que le sien, j’employe un balancier qui tourne sur ses pivots, et que mon invention consiste en l’assemblage de ces deux choses. Huygens, OC(7), Huygens to Contesse, 6 May 1675, no. 2027, p. 458. The figure mentioned here is found in the Journal des sçavans, 25 February 1675, 6[8]-70.

576 Huygens, OC(7), Jean de Hautefeuille, Factum, touchant les Pendules de Poche, 1675-1676, no. 2024, p. 453. The text on Thuret reads thus: “Je n’ay point étably de fondement sur ce que Mr. Thuret Horloger, à qui je communiquay mon Ecrit peu de jours après l’avoir presenté à l’Academie, pretend avoir appliqué le Ressort en spirale, & avoir declaré sa pensée à Mr. Huguens, parce que cela ne me touche point & ne fait rien au Procés, & estant une chose qui dépend de la bonne foy de tous les deux, je ne prefere point le témoignage de l’un à celuy de l’autre.”

577 Huygens, OC(7), Huygens to his brother Constantyn, 9 August 1675, no. 2045, p. 484.

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specific accusation. In France, the matter was quickly settled through the patronage of

Colbert. The Academy’s role remained somewhat discreet throughout the dispute. The

Academy indirectly helped Huygens since, in addition to the royal privilege, the Dutch

natural philosopher had been able as an academician to make a public disclosure of the

watch through the Journal des sçavans, which acted at the time as an unofficial organ of

the Academy. Another one of Huygens’s publications in the Journal des sçavans resulted

in a (lesser) priority dispute. Besides Huygens, it again involved artisans, Robert Hooke

(to a certain extent), and the Academy as an authority-granting institution.

I. HUYGENS’S BAROMETER, HUBIN’S THERMOMETER AND THE TRAJECTORY OF AN INSTRUMENT

In December of 1672, Huygens published a letter in the Journal des sçavans

describing two new barometers of his invention that used water in addition to mercury.

(See Figure 4.11.) The idea behind these barometers was to increase the magnification of

their readings. Huygens mentioned that in an ordinary Torricellian tube, the height

variation of the mercury column was no greater than two (Parisian) inches. In a similar

Torricellian tube in which mercury would be replaced by water, the same variation would

be 28 inches. Of course, the tube would have to be 32 feet tall. To make the latter smaller

(mediocre & portatif), Huygens thought of joining mercury and water together in the

same tube. The first of these new barometers was akin to the classic Torricellian tube,

except for the bulge (boëtte cylindrique) in the center. Mercury was in the bottom tube

and pan up to the middle of the bulge. Water was on top of it. The chief problem with this

model was that dissolved air from the water (even if it had been carefully boiled) would

accumulate with time in the above vacuum, making this barometer behave like a

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thermometer (more on that later). The second model was similar, albeit much better. This

FIGURE 4.11: HUYGENS’S BAROMETERS

The one on the left was actually invented by Descartes; the double barometer on the right had been proposed by Hooke a few years before (1668). Images comes from the Journal des sçavans.

barometer had two equal bulge sections. In it, mercury was in contact with the vacuum in

the upper bulge, thus eliminating the water vapor. The water filled half of the lower bulge

and came up to the middle of the right tube, which was kept open so the pressure of the

atmosphere could be felt. Huygens noted that the variation in height was as much as

twenty-two inches. (This number depended on the proportion between the diameters of

the tube and bulges. In this case, it was a factor of ten.) This spread made it possible, for

instance, to measure the barometric difference between the ground and the roof of a fifty-

foot house (roughly half an inch), which would be imperceptible in common barometers.

Lastly, to make sure the water would not evaporate, Huygens suggested to pour a drop of

oil that did not thicken in the cold weather nor evaporate on hot days—such as sweet

almond oil.578

578 Huygens, “Extrait d’vne avtre lettre de M. Hugens, touchant une nouvelle maniere de

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Huygens communicated his invention to Henry Oldenburg at the Royal Society,

adding that to measure heights, it was preferable to level the double barometer with a

plumb bob fixed behind the wood plank supporting the instrument. He also pointed out

that the drop of oil poured over the water appeared superfluous since he could not

perceive any evaporation in such a narrow tube—at least during this time of the year.579

Oldenburg wrote back mentioning that Robert Boyle would build a double barometer of

Huygens’s design. He also referred to two other types of barometers: the syphon

barometer invented by Boyle and described in his Continuation of new experiments

(1669); and the wheel barometer invented by Robert Hooke and described in his

Micrographia (1665) and later in the Philosophical Transactions.580 Surprisingly,

Oldenburg did not mention (perhaps did not remember?) that Hooke had already

demonstrated a similar two-liquid barometer in 1668 during a meeting of the Royal

Society. Hooke’s idea—put forward because he was unsatisfied with the precision of his

wheel barometer—was not published but rather confined to the minutes of the Royal

Society.581

Barometre, qu’il a inventée, “ Journal des sçavans, 12 December 1672, 152-156. Mariotte, a few years later, calculated the magnification for the double barometer according to the tube and bulge diameters and the specific gravities of the two liquids. Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 10 juillet 1677, 114v-116v. See also W. E. Knowles Middleton, The history of the barometer (Baltimore: The Johns Hopkins University Press, 1964 [1994]), 88-89. A short summary of barometer designs in the seventeenth century is found in Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles, 80-81.

579 Huygens, OC(7), Huygens to Oldenburg, 14 January 1673, no. 1919, p. 242. 580 Huygens, OC(7), Oldenburg to Huygens, 23 January 1673, no. 1920, p. 247. For a description

of both barometers, see Middleton, The history of the barometer, 76-78 and 94-98. 581 Birch, The history of the Royal society of London, ii :298. Middleton, The history of the

barometer, 88. Even more surprising is the fact that roughly ten years later, in 1683, Hooke still did not mention Huygens’s name regarding the invention and manufacturing of the two-liquid barometer. He wrote in manuscript form: “This I shewed the Roy. Society. as appears by their Journall book. This way was about 6 years after viz in the year 167[3] published by Mr. Hubin. at Paris, and tis not unlikely but that he might find it by the same method as I had before made use of in that inquiry, though I know also that most

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It would be surprising that Huygens knew about Hooke’s earlier two-liquid

barometer would be surprising, even though he mentioned to Oldenburg that Boyle’s and

Hooke’s barometers were well known in France. (He most likely meant the two (printed)

barometers mentioned by Oldenburg.) That Oldenburg did not remember Hooke’s

invention is perhaps less remarkable than one would think, considering the mass amnesia

that happened at the Academy when Huygens’s presented, then published, his description

of two “new” barometers. We learn from a letter that Huygens wrote to Oldenburg that

the first type of barometer he explained had actually been invented by Descartes several

decades earlier. This information, that no one at the Academy could then recall, was

made known to Huygens fifteen days after he had published his letter in the Journal des

sçavans. A friend of Mariotte asserted that what Huygens passed as his own had been

reported in a letter from Chanut to Perier printed at the end of Pascal’s Traitez de

l’équilibre des liqueurs, published in 1663. Huygens told Oldenburg that he would

withdraw his priority claim in the next issue of the Journal des sçavans, emphasizing that

there was nothing he loathed more than claiming credit for something that was not his.582

Not all people, though, felt likewise. René Grillet, a so-called clockmaker583,

of what I had shewn to ye R. Society was not unknown to some persons in Paris…” Quoted from W. E. Knowles Middleton, “A footnote to the history of the barometer: An unpublished note by Robert Hooke, F.R.S.,” Notes and Records of the Royal Society of London 20 (1965), 145-151, on p. 147.

582 Huygens, OC(7), Huygens to Oldenburg, 10 February 1673, no. 1922, pp. 252-253. Huygens’s retraction never appeared in the Journal des sçavans, since there was a hiatus of a year in a half, beginning with the issue following the one in which Huygens discussed the two barometers. It was found though in Huygens’s papers. See Huygens, OC(7), Huygens to Gallois, February 1673, no. 1923, pp. 255-256, where Huygens wrote “je fus bien fasché de ce que cet advertissement qui estoit veritable m’avoit este donnè si tard voyant que l’on me pourroit soupconner de m’estre voulu attribuer l’invention d’autruy, qui est la chose du monde qui me semble la plus indigue et que j’ay tousjour taschè d’eviter avec plus de soin.”

583 Grillet is mostly remembered for his arithmetical machine and his criticism of Pascal’s own machine. See his “Novvelle machine d’arithmetiqve de l’invention du Sieur Grillet Hologeur a Paris,” Journal des sçavans, 25 April 1678, 161-164. He also invented an hygrometer described in the same publication, Journal des sçavans, 3 February 1681, 35-36.

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maintained he had invented the double barometer two years before Huygens did, and that

the latter stole the idea from him. Grillet even stressed he had demonstrated his invention

during a meeting of the Academy. Huygens told Oldenburg the artisan had in fact shown

a barometer to the Academy, but it had nothing particular to it. Grillet, ce fol, was known

for having visited the Academy several times with equally extravagant propositions. This

one, the double barometer, Grillet added to his Curiosités mathématiques published that

same year. And though the Intendant of Police seized the book, Huygens would not be

surprised if a copy made it to the Royal Society.584 If Grillet was right, Huygens asked,

then why did he wait more than two years before claiming priority to the invention—

notwithstanding the fact it was Grillet’s father who was known to engage in these sorts of

curiosities.585 Huygens conceded that the idea of making a barometer with a serpentine

tube, as described in Grillet’s book, was not bad, but it ought not be used with mercury,

since that liquid metal had a tendency to break up and leave wide open spaces between

droplets. Huygens tried the idea on his double barometer, but introduced it above the

bulge where the water was, that liquid showing more fluidity than mercury.586 The idea

of the serpentine tube, however, was not Grillet’s either but taken from Hubin, our

584 Huygens, OC(7), Huygens to Oldenburg, 10 February 1673, no. 1922, p. 253. It is not clear here why the book was seized in Paris. It may be well because of this barometer and Hubin’s thermometer, discussed later.

585 Grillet’s father was perhaps Jean Grillet, émailleur ordinaire de la reine. This Grillet published one book, La Beauté des plus belles dames de la cour, les actions héroyques des plus vaillans hommes de ce temps... et plusieurs autres pièces sur divers sujets gaillards et sérieux (Paris: 1648).

586 Huygens, OC(7), Huygens to Oldenburg, 10 February 1673, no. 1922, p. 254. In his retraction, Huygens said: “Je diray seulement que pour le [Grillet] convaincre il ne faut que luy demander pourquoy dans tout ce temps de 2 ans il n’avoit pas pratiquè et publiè cette invention s’il la scavoit desia alors et quelle en estoit l’utilitè? Car elle est de peu de depense et le devra estre autant moindre a luy que le mestier de son pere a ce qu’on m’a dit est de travailler a ces sortes de curiositez. Je scay bien de la pluspart d’eux qu’il y proposa en effect une facon de barometre il y a 2 ou 3 ans, mais ou il n’y avoit que le vif argent seul et qui avec raison ne fut point approuuee comme valant fort peu de chose.” Huygens, OC(7), Huygens to Gallois, February 1673, no. 1923, pp. 255-256.

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second individual caught up in the clockmaker’s web of priority claim deceptions.587

Hubin, émailleur ordinaire du roy, was perhaps one of the only instrument

makers in Paris skilled enough to make the kind of double barometers proposed by

Huygens.588 We actually learn from Hubin’s 1673 publication that he made Huygens’s

earliest double barometers. What is even more interesting here is that it took Hubin very

little time to transform the double barometer into a new type of air thermometer. The only

thing he did was add a closed bulb over the barometer’s open tube, in order to

hermetically seal the whole instrument. (See Figure 4.9.) In such a way, the atmospheric

pressure no longer influenced the water’s level inside the tube. Instead, dilatation (due to

heat) and condensation (due to cold) were the only acting forces inside the instrument—

Hubin replaced the water by an eau seconde, a green acid solution of copper nitrate

produced in the refining of gold. This transformation of a barometer into a thermometer

was done quickly, because Hubin said he tried it in his shop over the period of five to six

weeks before presenting it to the Academy on 21 January 1673—roughly six weeks after

587 We will see below that Hubin took the idea from Laurent Cassegrain. But it was already used in Italy at the Accademia del Cimento in the late 1650s. As far as I know Hubin did not know this. Some of these glass termometri a spirale are still extent and are famous representations of the quantitative experiments done in the Florentine Galilean academy. W. E. Knowles Middleton, The experimenters: A study of the Accademia del Cimento (Baltimore: The Johns Hopkins University Press, 1971). Paolo Galluzzi, ed., Scienziati a Corte. L’arte della sperimentazione nell’Accademia Galileiana del Cimento (1657-1667) (Livorno: Sillabe; Florence: Istituto e Museo di Storia della Scienza, 2001). On the role of experiments, see Luciano Boschiero, “Natural philosophical contention inside the Accademia del Cimento: The properties and effects of heat and cold,” Annals of science 60 (2003), 329-349.

588 His shop was on rue Saint-Denis, in front of the rue aux Ours, and it was mentioned in the famous Parisian chronicles of Spon and Nicolas de Blaigny. Abraham du Pradel (a.k.a. Nicolas de Blaigny), Le Livre commode des adresses de Paris pour 1692, which also mentioned the addresses of Lebas, Chapotot and Butterfield. See also Stroup, A company of scientists, 192-193. Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles, 111. Daumas says Hubin was from England, like Butterfield. Again according to Daumas, “Dès la fin du XVIIe siècle, lorsque les baromètres et thermomètres entrèrent dans la fabrication artisanale, ils furent fabriqués par des émailleurs parce que la division graduée était inscrite sur une plaque de métal émaillée.” Hubin was one of the first enamellers in Paris to manufacture barometers and thermometers. Ibid., 130.

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Huygens described his double barometer in the Journal des sçavans.589 The Academy

approved of it, saying it was more sensitive than all the air and spirit thermometers

currently in use. Huygens believed likewise.590 To claim the priority to his invention,

Hubin printed the Academy’s certificate of approval in his book. But before it was

published, Grillet made his move.

We learn from Hubin that after he demonstrated his thermometer to the Academy,

he displayed it on his shop’s window sill. On 2 February, Hubin saw Grillet looking at it

from the street. Hubin invited the onlooker inside to observe it more closely. Because

Grillet already knew how to copy the double barometer, as we saw above, it must have

been relatively easy for him to recognize Hubin’s improvement.591 After a journey to

Orléans, where he made a few thermometers and one of Huygens’s double barometer to

some of the city’s gentlemen, Hubin came back to Paris and did likewise—something

also attested by Huygens.592 It was shortly thereafter that Hubin discovered Grillet’s

fraud, found in the clockmaker’s book published before Hubin’s own. The fact that

Grillet disguised his “new intrument” by sticking together Huygens’s double barometer

589 Hubin, Machines nouvellement executees, 12. See also W. E. Knowles Middleton, A history of the thermometer and its use in meteorology (Baltimore: The Johns Hopkins University Press, 1966), 62-64.

590 Huygens, OC(7), Huygens to ?, March 1673, no. 1928, pp. 261-262, where he describes Hubin’s new thermometer (with drawing) and says: “Il paroit donc que le thermometre de Monsieur Hubin tant pour sa seuretè, que pour la sensibilitè est encore preferable a ces derniers [air and spirit thermometers], et qu’ainsi il a toutes les qualitez requises.”

591 Hubin, Machines nouvellement executees, 12. 592 Hubin, Machines nouvellement executees, 13, where he says about the thermometers he made

for a M. Toinard, fils de M. le Président d’Orléans: “A sçavoir trois verticaux, l’un de cinq à six pieds: deux de prés de huit pieds chacun, differemment chargez de liqueur pour estre plus sensibles, l’un au chaud, & l’autre au froid: & un quatrième, aussi de six pieds, que ledit Sieur Toinard me proposa de faire incliné, afin que la liqueur ayant plus d’étenduë en pareille hauteur, & estant portée sur une rampe, marquast plus distinctement les degrez: & c’est celui que represente la VI. Figure.” (See Figure 12.) Hubin also performed a series of experiments in Orléans with his thermometers. Huygens, OC(7), Huygens to his brother Lodewijk, 27 October 1673, no. 1972, p. 359, where Huygens says after describing the barometer: “On a fait quantitè de ces machines icy que l’on enchasse dans des belles bordures dorées.” This quote confirms the role and exclusivity of enamellers in making barometers, as asserted by Daumas.

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and Hubin’s thermometer, including some serpentine tubings, did not fool Hubin—nor

Huygens for that matter, as mentioned above. In pleading his case, Hubin asked the same

rhetorical question Huygens did, namely why did Grillet not mention earlier the

possibility of transforming the barometer into a thermometer if he knew about it for some

time? Hubin also said the idea of putting serpentine tubes on his instrument had been

given to him by a professor of Chartres, Laurent Cassegrain—better known for his

invention of a new type of reflecting telescope—five years before (Hubin also mentioned

it during his presentation at the Academy several months before). Lastly, after wishing

Grillet would give proper credit to inventors, so as not to tarnish his future reputation,

Hubin made the same criticism as Huygens did regarding Grillet’s simple mercury

barometer.593

While Grillet’s book seems to have been seized for privilege infringement,

Hubin’s was reviewed in the Journal des sçavans.594 Hubin no doubt understood the new

patronage system involving the Académie des sciences as a go-between, and he learned

quickly how to play it. After 1673, he visited the Academy often, becoming the official

glassblower and meteorological instrument supplier of the Academy.595 In 1677, using

the Academy as a power-broker, Hubin was even able to exhibit to the Dauphin two of

his double barometers, which the heir to the throne of France found nice (honneste).596

593 Hubin, Machines nouvellement executees, 21-22. 594 Journal des sçavans, 17 December 1674, 11-12. The review does not mention the priority

dispute with Grillet. Hubin’s book had the same publisher as the Journal. 595 Stroup, A company of scientists, 193, 317 n.3. On Hubin’s visit to the Academy, see Académie

des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 7 (1675-1679), séance du samedi 24 juillet 1677, 117v; ibid., séance du samedi 6 mars 1678, 141r; ibid., Registre de physique, vol. 10 (1679-1683), séance du mercredi 21 mai 1681, 67v; ibid., séance du mercredi 28 mai 1681, 68r; ibid., séance du mercredi 13 janvier 1683, 119v.

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Associated to Huygens in the early years of his career, Hubin became an important client

to another academician later in his life, Guillaume Amontons, who praised the enameller

for his work.597

The examples of the balance-spring watch, barometer and thermometer involving

Huygens, artisans, and the Académie des sciences remind us that the business of

manufacturing the material culture of natural philosophy was not taken lightly in France

in the last third of the seventeenth century.598 Authorship of instruments and machines

had become a serious matter, requiring the know-how, theoretical knowledge and

authority-granting system of three distinct contributors—two individuals, one

institutional. In that context, as it had always been for conventional knowledge-making,

printing turned into a powerful security blanket against priority claims and disputes over

mechanical authorship. Grillet’s error was not in manufacturing Huygens’s double

barometer (and later Hubin’s thermometer), but rather in publishing his “invention” when

Huygens had already done so. Authorship capital for mechanical inventions came ever

more from the printing world. The Journal des sçavans, unofficially associated with the

Académie des sciences, played a significant role here from the day it was founded in

596 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 8 (1675-1679), séance du samedi 20 novembre 1677, 130r; ibid., séance du samedi 11 décembre 1677, 134v.

597 Guillaume Amontons, Remarques et experiences phisiques sur la construction d’une clepsidre, sur les Barometres, Termometres, & Higrometres (Paris, 1690), Avertissement, n.p., where the author writes: “Au reste, je ne dois pas manquer de dire en cet endroit, par un juste motif de reconnoissance, & pour rendre un sincére témoignage, à la verité, que le sieur Hubin Emailleur ordinaire du Roy, si connu de tous les Sçavans, & par son merite, & par l’excellence de son travail, a si bien secondé mes intentions dans l’execution, que le public luy est redevable des nouveautez que je luy propose.” See also Journal des sçavans, 8 March 1688, 245-247, where Amontons writes: “Les Curieux en trouveront de l’une & de l’autre maniere chez le fameux Mr. Hubin qui apporte tous ses soins à favoriser les nouvelles découvertes.”

598 The best general discussion on instrument privileges and patents is Mario Biagioli, “From print to patents: Living on instruments in early modern Europe,” History of Science 44 (2006), 139-186.

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1665.

MACHINES, THE ACADEMY’S IMPRIMATUR, AND THE JOURNAL DES SÇAVANS

At a meeting of the Compagnie in January 1675, it was decided that members would

forward their contributions—after they had been read at the Academy—to the newly

appointed author of the Journal des sçavans, abbé Jean-Paul de la Roque. Abbé Gallois,

member of the Academy and previous author of the Journal, would make sure they were

printed.599 Members of the Academy were already accustomed to send letters to the abbé

Gallois to be included in the Journal. From its inception in 1665 the Journal’s mot

d’ordre had been to publish summaries of the best books coming out from the European

presses, to give eulogies of famous scholars and to report on all sorts of physical and

chemical experiments, astronomical observations, as well as machines and inventions—

the Journal’s motto later became e pluribus, unum, i.e. from several origin, one source of

knowledge.600 Yet, notwithstanding the fact that the Journal was implicated in

ecclesiastical turmoil—the tone given by its first author, Denis de Sallo, was fiercely

Gallican and critical of Jesuit ultramontanism—it did not seem at first to offer much in

matters of “science” and “technology.” Henri Justel wrote to Oldenburg in 1666: “Those

who work at our Journal are rather Historians than Philosophers, that is why you see

nothing in it concerning Physics. In time perhaps they will devote themselves to it.”601

599 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématique, vol. 8 (1675-1679), séance du mercredi 9 janvier 1675, 1r.

600 See the preface Av Lectevr in Journal des sçavans, 1665. 601 Justel to Oldenburg, 27 January 1666, quoted in Harcourt Brown, Scientific organizations in

seventeenth century France (1620-1680) (Baltimore: The Williams & Wilkins Company, 1934), 198. On the Journal in general, see David A. Kronick, A history of scientific & technical periodicals: The origins and development of the scientific and technical press, 1665-1790, 2nd ed. (Metuchen, N.J.: The Scarecrow

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And so they did. By the early 1670s, the Journal des sçavans had unofficially become the

academicians’ chief means of public expression regarding their scientific and

technological productions. It was similarly true for the Academy’s close network of

honnêtes hommes and instrument makers.

The Academy was in full control of what the Journal des sçavans published with

regard to its scientific productions. In 1691, when an anonymous writer proposed an

hydrographic problem to all Parisian mathematicians and professors of hydrography, it

was suggested that all solutions should be sent to the secretary of the Academy, the abbé

Jean-Baptiste du Hamel. All these would be examined by the academicians, s’il leur

plait, and printed in a later edition of the Journal. It did not please Cassini. In a

November meeting of the same year Cassini said he did not believe the Academy should

get involved in this public project—though he had himself found one solution and read it

to his fellow academicians. It was decided, moreover, that the author of the Journal

would be notified of the following: nothing regarding the Academy was to be published

without its explicit consent.602 The Academy was thus extremely mindful of its image as

the French supreme judge of what should count as good, useful and sound science. The

Journal was the vessel through which scientific knowledge was made public; it could not

determine the Academy’s agenda.

Everything destined for the Journal from an academician had generally been

Press, Inc., 1976). Martha Ornstein, The rôle of scientific societies in the seventeenth century (London: Archon Books, 1963 [1913]), chap. 7. Raymond Birn, Le Journal des savants sous l’ancien régime (Paris: Klincksieck, 1965). Jean-Pierre Vittu, Le Journal des savants et la République des lettres, 1665-1714 (thèse de Doctorat d'État ès Lettres, Paris I-Sorbonne, to appear in the éditions Honoré Champion). Betty Trebelle Morgan, Histoire du Journal des sçavans depuis 1665 jusqu’en 1701 (Paris, 1929).

602 Journal des sçavans, 10 September 1691, 400-402. Académie des sciences, Procès-verbaux de l’Académie royale des sciences, vol. 13 (1689-1696), séance du mercredi 14 novembre 1691, 67v-68r.

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discussed during a previous assemblée, whether it concerned an astronomical

observation, a mathematical problem or a machine, such as Huygens’s barometer already

mentioned or Roberval’s famous scale, to name but these examples.603 As any other type

of printed material, the Journal was about authorship—as its 1679 volume preface

reiterated.604 The novelty here, however, was that the Journal was printed every week or

two—or so it was intended; it was actually very irregular. If all went well, the turn around

time between a presentation at the Academy and its publication could be short, much

shorter in fact than a regular book format—sometimes a matter of only a few weeks. And

owing to its privilege, no one could reproduce a piece that had appeared in the Journal.605

Another advantage was the visibility it offered outside France, since an edition of the

Journal was published in Holland and the London Philosophical Transactions was

sometimes translating some of its articles (as did the Journal with some of the Royal

Society’s litterary organ).606

Such an advantage was not overlooked either by the honnêtes hommes and

603 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 6 (1669), séance du mercredi 21 août 1669, 158v-163r. Journal des sçavans, 10 February 1670, 9-12.

604 Journal des sçavans, 1679, 4 where it is written: “Au reste la iustice que l’on a tâché de rendre aux Inventeurs des nouvelles Machines, ou à ceux qui ont fait quelques nouvelles découvertes dans la Physique, dans la Chymie, dans l’Anatomie &c. n’invite pas peu ceux qui seront assez heureux pour enrichir de nouveau le Public par le fruit de leur Esprit & de leur Industrie de ne tarder pas à faire part de leurs Inventions à l’Auteur du Iournal, afin de ne se laisser point enlever la gloire qui suit toûjours les nouvelles découvertes, & de n’avoir pas le chagrin de voir qu’un autre se pare d’un honneur qui souvent leur a coûté bien de la peine, bien du chagrin & bien de la dépense.”

605 See, for instance, the Journal of 1681 where the abstract of the privilege reads thus: “avec defense à toutes personnes de quelque qualité ou condition qu’elles soient de contrefaire ledit Iournal, de donner leur Iujement ni d’écrire sur aucunes desdites choses & matieres sur tout dont it aura esté parlé dans le Journal sous quelque titre & pretexte que ce soit à peine de trois milles liv. d’amende, confiscation des Exemplaires contrefaits, dépens, dommage & interests, ainsi qu’il est énoncé plus au long ausdites Lettres.”

606 For instance, see “A description of an Hydraulique Engin, taken out of the Register of the Royal Academy of the Sciences of Paris, and inserted in the Journal des Scavans, 1675: Englished by the Publisher, for the better Examination of those that are skilfull in such Engins here in England,” Philosophical Transactions 11 (1676), 679-681.

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instrument makers close to the Academy. Though none of the latter were required to

receive the Academy’s imprimatur before going to print, some—if not most—sought it.

We saw, for example, that both Hubin and Franchine had shown the Academy their new

inventions before going to print—in a book and the Journal, respectively. Amontons,

prior to becoming an academician, demonstrated his new hygrometer, barometer, and

vacuum tube at the Academy before having them all mentioned in the Journal as well as

printed in a separate book a couple of years later.607 Others like Comiers, de Hautefeuille,

Grillet, and Chapotot were familiar names to the academicians, regularly presenting

original designs of instruments and machines to the Compagnie. They all published their

inventions in the Journal des sçavans, often before going on the conventional road of the

pamphlet or book. No instrument maker though was more committed to the Journal than

Butterfield. Perhaps one of the most expert instrument makers in Paris at the time,

Butterfield made several mathematical and astronomical instruments for the Academy,

frequently working with an academician. (I briefly mentioned the silver planisphere he

built with Cassini.) Whether he tried to get a formal imprimatur for his inventions from

the Academy is not clear, since the Procès-verbaux are rather mute on the subject. His

acknowledged relationship with and contribution to the Academy, however, gave him all

the credentials needed. Between 1677 and 1684 Butterfield published in the Journal a

short notice on a hygroscope invented in England, two articles on new types of levels (in

addition to having considerably reduced in size Huygens’s own level), and two more

607 Amontons was actually introduced at the Academy by Hubin in 1687. Amontons became an academician in 1690. Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 12 (1686-1689), séance du samedi 16 juillet 1687, 48r-48v and 150r-153v; ibid., séance du mercredi 27 mars 1688, 78r; ibid., séance du mercredi 8 avril 1688, 81r-82v. Journal des sçavans, 8 March 1688, 245-247; ibid., 10 May 1688, 394-396.

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articles on different models of hodometers designed for carriages.608

Butterfield’s levels were clearly meant for the savants and for professional

surveying, an important activity around Versailles and Paris at the time. The hydroscope

and hodometers, however, were destined to a type of wealthy clientèle often dubbed

curieux.609 Hence the Journal des sçavans was about authorship as well as commercial

interests. Amontons mentioned the name of Hubin, whom customers could visit to buy

Amontons’s new model of hygrometer. Jacques Ozanam, elected an academician in the

early 1700s, mentioned Chapotot in his description of a new universal instrument for

practical geometry.610 Mathion, who designed a graduated sector, sent the Journal’s

readers to the Quai de l’Horloge, “aux deux Globes,” where the Sieur le Fevre was

constructing it.611 Savants, honnêtes hommes and instrument makers were paired all the

time and used the Journal for the explicit purposes of authorship, public recognition and

profit—all together most of the time.

As expected, these motivations clashed every so often and created rivalries in

instrument making. I mentioned earlier the numerous types of levels that were invented

after Picard’s own improvement. In 1684, Chapotot briefly described a mathematical

instrument (called pantagone, “for all angles”) in an April issue of the Journal. Only two

608 Journal des sçavans, 29 March 1677, 84; ibid., 6 September 1677, 227-228; ibid., 5 December 1678, 414-416; ibid., 26 December 1678, 441-443; ibid., 4 August 1681, 353-354; ibid., 5 June 1684, 192.

609 The notice for the hygroscope reads thus: “La justesse avec laquelle le Sieur Butterfield a reüssi dans l’execution du petit Hygroscope … merite bien qu’on apprenne aux Curieux qu’on en trouvera chez luy dans la ruë des Fossez S. Germain du Fauxbourg, au Roy d’Angleterre, avec plusieurs Instruments de Mathematique fort curieux.” Journal des sçavans, 29 March 1677, 84.

610 Journal des sçavans, 11 October 1688, 319-320, where it is said: “Pour lui il s’estime heureux d’avoir rencontré le sieur Chappotot tres propre à executer son dessein…”

611 Journal des sçavans, 30 April 1691, 170-172. This le Fevre could very well be the same who was named academician in 1682. According to Daumas and others, he was excluded from the Academy circa 1701 and would have then opened a workshop of mathematical instruments at the same exact address mentioned here a decade before. Daumas, Les Instruments scientifiques aux XVIIe et XVIIIe siècles, 106.

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months later, the instrument maker Pouilly described a similar angle-measuring device,

which could perform even more operations than Chapotot’s. The interesting thing here is

that as a result of Pouilly’s advertisement, Chapotot had to disclose the “secret” of his

instrument in December, which he did not bother doing in the April issue, in order to

establish the distinction between the two instruments.612 (See Figure 4.12.) This sort of

craft quarrel happened frequently with mathematical instruments. In July of 1688, a

Parisian professor of mathematics, Mr. Tarragon, presented to the Academy a sector of

his invention designed for the trisection of angles. At the next meeting a few days later,

the academician de la Hire exhibited to the Compagnie a similar sector of his own made

ten or twelve years earlier. No priority dispute appears to have ensued, and it did not

prevent Tarragon from publishing his invention in a late September issue of the Journal,

describing how it was used and where to find it—at Nicolas Bion’s workshop on the

“quai de l’Horloge du Palais, au Quart de Cercle. A few months later, though, a certain R.

E. P. L. from Orléans wrote in the Journal that it was easy to invent several such

trisection instruments that were as geometrical and as simple as Tarragon’s—describing

one a month later.613 (See Figure 4.12.) Controversy was not restricted only to theory and

612 Journal des sçavans, 17 April 1684, 131-132; ibid., 16 June 1684, 215-216; ibid., 18 December 1684, 352 where Chapotot writes: “Le secret de cette invention que le Sr. Chapotot s’estoit reservé de dire d’abord, consiste en ce que pour que le rapporteur n’empesche de prendre toute sorte d’angles, on le redresse sur sa base par le moyen d’une charniere a laquelle il est attaché, & on le rabaisse avec facilité pour voir la valeur des angles.”

613 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 12 (1686-1689), séance du mercredi 14 juillet 1688, 94v; ibid., séance du samedi 17 juillet 1688, 94v-95r. Journal des sçavans, 20 September 1688, 261-265; ibid., 31 January 1689, 28-30; ibid., 7 February 1689, 44-48. For a general discussion of mathematics in the Journal, see P. Sergescu, “Les mathématiques dans le Journal des savants: Première période, 1666-1701,” Osiris 1 (1936), 568-583. On Bion, see Daumas Les Instruments scientifiques aux XVIIe et XVIIIe siècles, 109-110 and passim. Daumas mentions that Bion’s address “Au Quart de Cercle” was only found in 1704. We clearly see here that it was much earlier than that, likely before the other address he is known to have had, “Au soleil d’or.”

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FIGURE 4.12: VARIOUS MATHEMATICAL INSTRUMENTS Above, Chapotot’s pantagone, an instrument to measure angles. Above right, Pouilly’s version of a similar instrument. Below, Tarragon’s compas de trissection made by Nicolas Bion. Right, R. E. P. L.’s simpler trisection instrument.

experimental observations in the Journal. The material culture of science received as

much attention and scrutiny as the former two since authorship, public recognition and

profit were usually involved—when it was not triggered by chauvinistic pride, as might

be argued in the case of Newton’s versus Cassegrain’s telescopes debated in a few issues

of the 1672 Journal.

Since its beginning in 1665, the Journal was advertising itself as a source of

universal knowledge—e pluribus, unum—useful to all, including artisans, “who will find

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excellent examples and principles for their art.” In 1683, in trying to appeal to the widest

readership possible, namely the ouvriers and artisans as well as the savants and honnêtes

hommes, the author of the Journal added four little words to the subtitle: Recueil succint

et abregé.614 These disappeared in 1687, when one can thereafter see a significant drop in

the number of reviews dealing with the sciences, instruments and machines. From that

moment on, the Journal turned more “savant” with longer book reviews on history,

theology and philosophy. This drop can partly be explained by the death of Colbert in

1683 and the nomination of his successor, Michel François Le Tellier, marquis de

Louvois. From Stroup’s very useful quantitative study, we learn that the total expenditure

on instruments at the Academy fell by more than half during the reign of Louvois. (It was

even worse during the reign of Louvois’s successor, Louis Phélypeaux de Pontchartrain.)

The livres tournois spent on expeditions and special projects, which often led to the use

of a large number of instruments, dropped even more sharply. While the total sum spent

on mechanical models, stored in the chambre des machines, simply plummeted.615

Louvois’s stance on instruments and machines was at best equivocal. In 1683, just

a few months after he took office as first minister to the Sun King, he asked the Academy

to make a complete inventory of all the machines found in the king’s library. Moreover,

every instrument and machine ever made for the Academy’s use, including Rømer’s two

614 On those four little words, the preface of the 1683 Journal reads: “Au reste comme il y a bien des personnes que le seul titre du Iournal des Sçavans détourne de la lecture de cet ouvrage, se persuadant qu’il faut estre sçavant & habile pour y comprendre quelque chose, on est bien aise de les détromper & de leur faire connoistre par quatre petits mots qu’on ajoûtera desormais au titre, que les moins habiles, & les ouvriers mesme y peuvent trouver de quoy se divertir, & de quoy s’instruire aussi bien que les plus sçavans; puisque c’est un abregé de la science universelle qui comprend ce qui arrive de plus surprenant dans la nature, ce qui se fait de plus beau & de plus curieux dans la Republique des Lettres, & ce qui se découvre, ou qui s’invente de plus nouveau & de plus rare dans tous les arts.”

615 Stroup, A company of scientists, 246-251, tables 3-5.

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celestial models, were to be sent to the same library—Couplet, the fidèle commis, was put

in charge of organizing the machines and writing the memoire, and inherited the custody

of the chamber’s key. This was such a serious affair that Claude Perrault wrote to

Huygens, who was yet again in Holland for health reasons, that he should return any

mathematical instrument made for the Academy and paid by the king since “Monsieurs

de Louuoy fait faire vne perquisition fort exacte.”616 The purpose of this sudden and strict

monitoring of the Academy’s instruments and machines is not explained in the Procès-

verbaux. It may perhaps be linked to Louvois’s ambivalence toward their particular

utility. Another example is enlightening here, showing that Louvois was more concerned

about politics than attempts at generating public and academic enthusiasm for

technological virtuosity.

During the summer of 1683 a public exhibition of machines—the first one ever in

Paris—was set up in the Quartier Latin, on the rue de la Harpe, vis-à-vis the Saint Côme

church. It was organized by Jean-Baptiste Picot and sponsored by the youngest son of

Colbert, Jules Armand, marquis d’Ormoy et de Blainville, who was then Surintendant des

bâtiments du roi. This unusual exhibit, for which a catalogue was swiftly put together and

published, exhibited machine models made by famous engineers such as Jacques Besson,

Agostino Ramelli, Salomon de Caus and by more recent inventors, especially by a certain

M. L. C. D. O., who turned out to be Picot himself, Monsieur le Chevalier D’Ormes.

According to the catalogue, four new models were supposed to be added to the exhibition

every two weeks, machines that were already known or recently described in the Journal

616 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 11 (1683-1686), séance du mercredi 15 décembre 1683, 24v; ibid., séance du samedi 18 décembre 1683, 37v. Huygens, OC(8), Perrault to Huygens, 10 February 1684, no. 2328, p. 480.

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des sçavans. The marquis de Blainville, through the future academician Joseph Sauveur,

even presented a few machine designs to the Compagnie—machines that were being

built, undoubtedly, though not specifically mentioned, for the purpose of this exhibition.

But as soon as Colbert died in early September of 1683, and was replaced by Louvois, the

young marquis was forced to resign his office. Picot, losing his chief supporter, had no

other choice but to abruptly stop the exhibit. As one historian wrote, this reflected nicely

the two opposite visions of Colbert and Louvois: the progressist bourgeois versus the

narrow-minded obscurantist. Besides the exhibition catalogue, there is virtually no

contemporary trace of this event, not even in the Journal des sçavans, which was

supposed to contribute to it. Machines were not Louvois’s forte, to say the least.617

Nonetheless, Louvois got himself involved with machines as a powerful patron

would when protecting one of his clients. Thuret, perhaps the foremost expert clockmaker

of his generation, seemed to have been in the good graces of Louvois. During a meeting

of the Academy, Cassini read a note from the abbé Castelan regarding Thuret’s

experiment with a sealed barometer, which was flawed—the clockmaker asserting his

sealed barometer was working as a normal, open barometer. Castelan stated that the

instrument was not sealed properly, hence displaying the same effects as a conventional

barometer. Less than two weeks after the meeting, de la Chapelle asked, upon Louvois’s

request, that Thuret’s experiment be straightened out. De la Hire was put in charge of that

task. Climbing up the Notre Dame cathedral towers, he first discovered that Thuret’s

617 [Jean-Baptiste Picot], Explication des modeles des machines et forces mouvantes, que l’on expose à Paris dans la ruë de la Harpe vis-à-vis Saint Cosme (Paris, 1683). Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 11 (1683-1686), séance du samedi 14 août 1683, 9v. Walter G. Endrei, “The first technical exhibition,” Technology and Culture 9 (1968), 181-183. Arthur Birembaut, “L’exposition de modèles de machines à Paris en 1683,” Revue d’histoire des sciences 20 (1967), 141-158.

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barometer was actually letting air in. Once he hermetically sealed it, the academician

found out it was acting like a thermometer—the level of mercury being lower at the

bottom of the towers where the temperature was colder. (This instrument was nothing

more than a different version of Hubin’s thermometer discussed above.) This new verdict

seemed to have settled the case.618

One could even argue that Thuret was indirectly responsible for Huygens’s

informal ousting of the Académie des sciences. Owing to health problems, Huygens left

Paris once again for The Hague in late 1681. He carried with him the planetarium he had

begun designing, a project authorized by Colbert. Once in The Hague, Huygens worked

on this machine with a very skillful clockmaker, Johannes van Ceulen. What the Dutch

academician emphasized all along was how much better his machine would be compared

to Rømer’s own showing the planetary motions—which was well known in scientific

circles and presented to the king when he visited the Academy in early December 1681.

After several months of work, Huygens reported to Colbert that his planetarium was

finally done and had cost a “mere” 620 écus from the king’s treasure chest (much less

than Rømer’s). He described it at length to the minister, mentioning thirteen reasons why

it was better than the one designed by the Danish astronomer. To Gallois, following a

long silence from Colbert, Huygens declared he had been compelled to stay in The Hague

to complete the work because in Paris he would not have found a clockmaker skilled

enough to the task. There was Thuret, but considering what had happened between him

and Huygens regarding the balance-spring watch controversy, he was not a viable option.

618 Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de physique, vol. 11 (1683-1686), séance du samedi 3 juin 1684, 70v; ibid., séance du mercredi 14 juin 1684, 72r-72v.

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In fact Thuret had built Rømer’s machine and indeed was alone named in the Journal des

sçavans where both of Rømer’s machines were described. Though Huygens never

referred to the clockmaker in his correspondence, some of his criticisms of Rømer’s

machine aimed directly at the design of the clock mechanism. Thuret as much as Rømer

was the target of Huygens’s negative account.619

A few days after Louvois took office as Louis XIV’s most powerful minister,

Huygens wrote to ask for his protection and for a better treatment than the one he had

received over the last sixteen years under Colbert. Expecting good words from Louvois,

Huygens mentioned in the letter’s postscriptum that during his stay in Holland he worked

on a planetarium, once discussed with him. Louvois did write back, addressing the Dutch

savant as “Monsr. Huijgens &c. mathematicien,” which gave Constantijn the Elder the

impression that the French minister was addressing his Archimedes as he would his

fortification engineer. Months went by, however, without any indication that Huygens

would be welcomed back to Paris. Through Henri de Beringhen, “Premier écuyer du roi,”

Constantijn the Elder tried to intercede on his son’s behalf. In the father’s letter was also

mentioned the planetarium and the invention of a large telescope without a tube. Eight

months after his first letter to Louvois, Huygens wrote back to the minister to present him

a short pamphlet on the invention of large telescopes without tubes. (Reviewed in the

Journal des sçavans in the 4 December 1684 issue.) Two more letters to de Beringhen,

619 Huygens, OC(8), Huygens to Gallois, 19 February 1682, no. 2255, pp. 342-343; ibid., Huygens to Colbert, 27 August 1682, no. 2272, pp. 374-378; ibid., Huygens to Gallois, 1 October 1682, no. 2279, pp. 393-394. Description of Huygens planetarium are in ibid., Huygens to S. Alberghetti, 6 February 1683, no. 2289, pp. 408-410 and in Huygens, OC(21), pp. 111-184. See also Henry C. King, Geared to the stars: The evolution of planetariums, orreries, and astronomical clocks (Toronto: University of Toronto Press, 1978), 113-117. This planetarium still exists and can be seen at the Museum Boerhaave in Leiden. For the description in the Journal, see Journal des sçavans, 19 January 1682, 22-24. On the king’s visit to the Academy, HARS, i:319-320.

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one from Huygens and another from his father, towards the end of 1684 did not change

Louvois’s mind: Huygens would not be reinstated at the Academy. He would, in fact,

never go back to Paris.620 What inspired Colbert did not draw Louvois’s attention:

machines had virtually no appeal to the new minister. Even though chauvinism may have

played an important role as well, it cannot explain everything. Machine authorship lost

some of its luster under Louvois—and Pontchartrain, to a lesser extent. It came back in

full only in the next century.

***

The first three chapters of this dissertation illustrated how individual savants such as

Mersenne, Descartes and Pascal, before 1650, cooperated with artisans and interacted

with instruments and machines. They were rather circumscribed activities, involving one

savant, one machine (or a class of machines in Mersenne’s instance) and scientific

knowledge derived from experiments and theory. Instruments, I showed, were essential in

producing new knowledge about the world and in thinking about natural philosophy in

general. Except for Pascal’s arithmetical machine, however, instrument and machine

authorship was not a key issue to these savants. In fact, the rational process, more than

the actual material result, predominated their thinking about instruments. Mersenne,

Descartes and Pascal did not only seek natural philosophical knowledge in using

instruments, but perhaps more importantly they wanted to rationalize the process in

620 Huygens, OC(8), Huygens to Louvois, 16 September 1683, no. 2321, pp. 456-457; ibid., Constantijn Huygens père to Henri de Beringhen, 9 March 1684, no. 2331, pp. 483-484; ibid., Huygens to Louvois, 18 May 1684, no. 2334, pp. 488-489; ibid., Huygens père to de Beringhen, 2 November 1684, no. 2375, pp. 550-551; ibid., Huygens père to de Beringhen, 6 December 1684, no. 2377, pp. 552-553; ibid., Huygens to de Beringhen, 14 December 1684, no. 2378, pp. 553-554.

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making instruments and machines. They all acknowledged that theory and practice

should work together rather than separately: savants had the obligation to work out

artisanal practices whereas artisans ought to train their minds in rational thinking.

Artisans, savants and machines then formed narrowly defined networks comprising few

individuals and were limited to specific—often rational—goals.

The purpose of this chapter was to demonstrate that for someone like Christiaan

Huygens, these networks were considerably more complex and extended than before

1650. Huygens, as an individual, did nothing much different than, say, Mersenne in

dealing with artisans. He visited them, talked to them, learned from them, complained

about them, and tried to improve their reasoning skills. The chief difference here has to

do with the goal, which was frequently more material than intellectual. Huygens did have

a carriage built to his design. He did have a balance-spring watch and a barometer

made—besides the air pump and pendulum clocks. (Mersenne, to my knowledge, never

had his theorized organ claviers built and used by anyone. Nor did Descartes’s lens-

grinding machine ever work. Pascal’s arithmetical machine was more a curiosity than a

performing machine.) Huygens’s goal was not only to produce natural philosophical

knowledge, but also to build instruments and machines that would generate more of it.

Authorship had also become a major issue in the savants’ life. There was fame,

recognition and profit to be gained from designing instruments and machines that actually

worked. The king, through the newly founded Académie des sciences, desired its savants

to work for the benefit of the State. Under the umbrella of the Academy, networks

comprised of artisans, savants, gentlemen and academicians were formed and interacted

in all possible ways as inventors, makers, and judges. Huygens navigated through all

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these with an easiness that was increasingly generalized to all members of the Parisian

scientific community.

Huygens’s way of philosophizing, in short, cannot be dissociated from these

extended networks essentially centering on the Académie des sciences. The epistemic

space in which Huygens evolved naturally encompassed networks of artisans, savants and

machines. Whether it concerned the design of carriages, watches, surveying and

mathematical instruments, Huygens faced issues such as authorship that were mostly

ignored by the previous generation of savants. As an individual, Huygens did not carry

out a drastically different agenda than his forefathers. What changed was the social and

intellectual context—the epistemic space—in which he worked. This, if it had not been

said clear enough, was due to the foundation of the Académie des sciences.

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CHAPTER 5

THE ORGANUM SCIENTIAE AND THE PRODUCTION OF

NATURAL PHILOSOPHICAL KNOWLEDGE

ENTRAL METAPHORS RISE AND FALL. Conjured up as heuristic strategies by

historians, sociologists, and philosophers of science alike they steer us through the

intricacies and subtleties of scientific knowledge-making. In the last twenty years, we

have seen not only the hard collapse of some of these enduring metaphors, but also the

addition of a major variable to the equation of scientific knowledge: instruments—or,

speaking in broader terms, the material culture of science. Peter Galison voiced one of the

first and most powerful acknowledgments of this missing piece of the historical puzzle in

1988 when he wrote:

C

We need a history of the material culture of science, but one that is not the dead collection of discarded instruments. In its place we need a history of the way that scientists deploy objects to meet experimental goals whether or not these were set by high theory; a history of instrument-construction linked to the history of technology; a history that encompasses the relation of instruments to forms of demonstration; a history of the laboratory that tracks the development of the organization of scientific work; and a history of the embodiment of theory in hardware.621

Going over Galison’s argument, the editors of the Osiris issue on scientific instruments

acknowledged that “The philosophical debate over whether theory drives experiment or

experiment drives theory has tended to obscure the independent role of instruments in

621 Peter Galison, “History, philosophy, and the central metaphor,” Science in Context 2 (1988), 197-212, quote on p. 211. This article has been integrated and expanded in Galison’s Image and logic: A material culture of microphysics (Chicago: The University of Chicago Press, 1997), chap. 9.

The organum scientiæ and the Production of Natural Philosophical Knowledge

science. Instruments come and go, but not necessarily in phase with the vicissitudes of

experiment and theory. The traditional mix of experiment and theory needs a new

ingredient—instruments. It is not just a matter of getting the quantities right; we need an

entirely new recipe.”622 It is to this fresh scholarly dish that I now turn my attention to in

the final chapter of this dissertation. Using the inclusive concept of organum, I wish to

demonstrate that early modern “instruments” were indeed a key ingredient to our

understanding of a logic of practice in natural philosophy. Whether they were material or

intangible, early modern instruments played a fundamental role in determining the

interaction between theory and practice, and between savants and artisans.

What I am particularly interested in this chapter is to look at how an instrument

becomes an instrument of knowledge—an organum scientiæ—with a built-in purpose and

scientific meaning. By itself, left alone, an instrument is nothing but an elaborate idea or

a fancy tool. To produce anything, an organum requires action, training, and exercices.

These are acquired by habits—habitus. All habits are habits of knowledge, and all habits

are linked one way or another to an organum. Habitus and organum, therefore, are joined

at an epistemological level, creating material and scientific knowledge alike.

On one level stood the habitus in anima, the habits of the mind involved in

intelligence, science, wisdom and also the arts. These habits were about universal

knowledge, independent of where or who you were. They stood for a methodical scheme

and a rational mind that could generate true knowledge. As I have shown in Chapter two

in the case of Descartes’s method, such an habitus in anima required training. It was not

622 Albert van Helden and Thomas L. Hankins, eds., Instruments, in Osiris, 2nd series, 9 (1994), 1-250, quote on p. 6.

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enough to possess the organum, the instrument of knowledge: one had to be trained in

using it. Though it was considered more virtuous than the artisans’ tools and machines, it

nonetheless necessitated intellectual practice defined by habitus. On a second level stood

the habitus in corpore, the habits of the body involved in all types of physical exertions.

This type of habitus was linked to local knowledge, influenced by social, cultural and

institutional frameworks. It involved body techniques and the ways of the hand, which

were different whether one was learning to swim, to fight, to craft a clock or weave a

tapestry. The body had to be trained and constrained in various ways to accomplish the

task at hand. Whether one deals with a seventeenth-century pendulum, an eighteenth-

century electric planetarium, or a nineteenth-century atlas, the body techniques involved

in creating scientific knowledge have to be better recognized for their epistemic worth.623

It is why, I believe, the tools, the instruments, and the machines composing the

material culture of early modern natural philosophy—other than the usual suspects, i.e.

the telescope, the microscope, and the air pump—need to be examined and reflected upon

from the cultural and natural philosophical milieu within which they were actually

designed, built, and operated. In the previous four chapters, taking as a point of departure

instruments and well-known natural philosophers (and an institution in the case of the

Académie royale des sciences), I have shown that French seventeenth-century natural

philosophy was in fact the result of a co-ordination between these machines, the

623 Dusan I. Bjelic, Galileo’s pendulum. Science, sexuality, and the body-instrument link (Albany: State University of New York Press, 2003). Lorraine Daston and Peter Galison, Objectivity (New York: Zone Books, 2007), chap. 4. Simon Schaffer, “Experimenters’ techniques, dyers’s hands, and the electric planetarium,” Isis 88 (1997), 456-483. Here Schaffer says it best: “Bodily knowledge in controversy and the changing self-evidence of gestures are further focused through the reworking of experiments such as those of Faraday, Joule, and their ilk developed recently by Sibum and his colleagues. If, instead of repeating trials to show that they function reliably, historians rework them to explore the form of knowing involved in their performance, then traditional boundaries between epistemology and practice are questioned.” (p. 483)

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individuals who made them, and the savants who used them to investigate—or reflect

upon—nature. The notion of organum is, I believe, the most fitting (and historically

appropriate) concept one can think of and elaborate upon when dealing with the role

played by instruments and machines in natural philosophy. It is to this early modern

organum scientiæ that I will now turn to in the following two sections.

THE ORGANUM AS AN EARLY MODERN EPISTEMIC INSTRUMENT OF KNOWLEDGE

What was a “scientific” instrument in early modern Europe? To begin with, it was not

“scientific” per se—as terminology would have it since the nineteenth century. Secondly,

it was more diverse and wide-ranging than the telescope, microscope, thermometer,

barometer, air pump and pendulum clock—sometimes identified as “philosophical”

instruments.624 In Thinking with objects, Domenico Bertoloni Meli gives a fascinating

account of the tremendous variety of simple and commonplace objects used by natural

philosophers in their study of mechanics: “Galileo’s pendulum, inclined planes, beams,

rolling and projected balls, Benedetto Castelli’s barrel and taps, Evangelista Torricelli’s

pierced cisterns, Marin Mersenne’s vibrating strings, pendulums, and rolling spheres,

Descartes’ slings, Marcus Marci’s billiard balls, Huygens’s cycloidal and colliding

pendulums, Hooke’s springs, Newton’s pendulums and balls of wool, glass, cork and

steel” were, he claims, “just some notable examples of the engagement of scholars with

624 I leave aside for the moment the ambivalence of this conventional expression—scientific instrument—which needs some explanation, especially when dealing with early modern Europe. On this topic, Deborah J. Warner, “What is a scientific instrument, when did it become one, and why?,” British Journal for the History of Science 23 (1990), 83-93. On a related topic see also Judith V. Field, “What is scientific about a scientific instrument?,” Nuncius 3 (1988), 3-26. On the conventional notion of an early modern “scientific” instrument, Albert van Helden, “The birth of the modern scientific instrument, 1550-1700,” in The uses of science in the age of Newton, ed. by J. G. Burke (Berkeley: University of California Press, 1983), 49-84.

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the material world around them.” In the hands of the above natural philosophers and

other theory-minded individuals such as Guidobaldo dal Monte, the tools and objects of

everyday experience helped them grasp the fundamental link between theory and

practice. Where I disagree with Bertoloni Meli, however, is his reluctance to call them

“instruments” because, says he, the substantive instrument conveys the idea of something

more elaborate than mundane tools and objects of everyday life.625 By focusing our

attention here to the original etymology of instrument—instrumentum, organum—I wish

to demonstrate that in fact an early modern “instrument” embraced not only both the

mundane and elaborate objects of craftsmanship, but also the abstract instruments of

knowledge. It is thus useful to think about all types of early modern things, tools, and

mechanical devices as epistemic organa, instruments (in the broader etymological sense

of the term) that generate natural philosophical knowledge.

Take, for instance, Galileo’s instruments of credit. As Mario Biagioli explains in

his most recent book, these “instruments” of Galileo’s were not only the geometrical

compass and telescope he developed, used and built in Padua and elsewhere in Italy, but

they were also the “techniques he used to maximize the credit he could receive from

readers, students, employers, and patrons.” Here, Biagioli specifically means

the apparatus to make printable pictures out of telescopic observations, his systematic withholding of instrument-making techniques to establish a monopoly over telescopic astronomy, the bootstrapping techniques for constructing an authoritative persona, the new kinds of pictorial narratives he developed to gain assent for his discoveries, and the astute grafting of his theological arguments onto those of the theologians themselves.

625 Domenico Bertoloni Meli, Thinking with objects: The transformation of mechanics in the seventeenth century (Baltimore: The Johns Hopkins University Press, 2006), quote on p. 2. For early modern instruments and their involvement in practice and theory, Willem D. Hackmann, “Instrumentation in the theory and practice of science: Scientific instruments as evidence and as an aid to discovery,” Annali dell’Istituto e Museo di storia della scienza di Firenze 10 (1985), 87-115.

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What is mentioned here goes beyond the realm of seventeenth-century Italian material

culture. These “instruments” were rather powerful social, economic and epistemic

techniques that helped Galileo create who he was as a natural philosopher. Biagioli

demonstrates convincingly that though solid, tangible instruments fashioned Galileo’s

intellectual world in his early career, his subsequent instruments of credit became

increasingly less material, moving from brass instruments to textual devices. Galileo’s

“instruments” were undeniably the mundane inclined planes and the elaborate compass

and telescope. Yet other instruments were intangible and conceptual as well, like textual

devices, forming an integral part of his natural philosophy and self-fashioning as a natural

philosopher at the Medici court.626

So, I ask again, what was an instrument in early modern Europe? Instrument, in

both the English and French vernaculars, comes from the fourteenth-century estrument

and before that from the Latin instrumentum (provision, apparatus, furniture, tool)—itself

derived from instruere, i.e. to fit out, equip, or instruct. The primary definition of an

instrument is “That which is used by an agent in or for the performance of an action.” It

is “a thing with or through which something is done or effected.” An instrument, at its

core, is thus “anything that serves or contributes to the accomplishment of a purpose or

end.” The “thing” here mentioned is not only material, like a craftsman’s hammer, a

natural philosopher’s air pump or a musician’s viola da gamba, but it can be a person—

626 Mario Biagioli, Galileo’s instruments of credit: Telescopes, images, secrecy (Chicago: The University of Chicago Press, 2006), 1-3, quote on p. 2. In the epilogue, Biagioli emphasizes the fact that whether material or not, “epistemically productive differences can emerge from the play of unexpected social actions as much as from the play inherent in writing or in the operations of inscription apparatuses. It really does not matter if monsters are social or natural, or if the differences they enable can be easily recognized as inscriptions or if instead they look more like changes or displacements in the actors’ landscape. What matters is difference in whatever shape or form it may come.” (p. 263)

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the instrument of God—a body part—the instruments of breathing (an organ)—as well as

a formal legal document in law or an authenticated record of a transaction drawn up by a

notary-public.627 It could also mean a religious or sacred text, like Erasmus’s Novum

instrumentum (1516), which was intended to provide an authoritative text of the Greek

New Testament—the Latin translation of which, alongside the Greek original, was meant

to revitalize the Latin Vulgate.628 All of these uses of instrument were employed in early

modern Europe, which is why it makes this term so rich and so important to any analysis

of natural philosophy.

A contemporary dictionary such as Jean Nicot’s Thresor de la langue françoyse

(1606) puts under the headword “instrument” the Latin instrumentum and organum. The

latter two words are indeed very much related to one another. (In point of fact,

“instrument” in Nicot’s Thresor de la langue françoyse and “organum” in Estienne’s

Dictionarium latinogallicum (1552) have both the exact same definition: “Instrument à

faire quelque chose que ce soit.”) Etymologically speaking, instrumentum was derived

from the Greek οργανον (organon)—or organum in Latin. Though the meaning of these

627 Quotes taken from the Oxford English Dictionary Online (Oxford: Oxford University Press, 2007), s.v. instrument. (Accessed via Harvard College Libraries, 7 July 2007) The French definition for instrument is analogous, see Trésor de la langue française informatisé <http://atilf.atilf.fr/tlf.htm> (Accessed on 7 July 2007) Robert Estienne’s Dictionarium latinogallicum (1552) also offers a very similar definition when one looks under the headword instrumentum. For analogous contemporary definitions, see the first edition of the Dictionnaire de l’Académie française (1694) and Antoine Furetière, Dictionnaire universel (1690).

628 The second edition of Erasmus’s text was published in 1519 and was renamed Novum testamentum, its conventional title. It appears that the title of Novum instrumentum surprised many at the time. In a letter to Robert Aldrige in 1527, Erasmus explained that people who complained about his choice of term were overdramatizing, since he wrote it only twice in all of his writings. Yet the choice of instrumentum was certainly not wrong, used by Jerome himself and Augustin himself, who mentioned in Contra duas epistolas Pelagionorum that it was better to say Instrument than Testament. Erasmus probably knew he would draw some outrage from this title. One could explain the choice of instrumentum by Erasmus’s desire to renew with the prisca theologia and also to signify the philological intention of the work. On this topic, see Erasmus, Les Préfaces au Novum testamentum (1516), ed. by Yves Delègue, avec la collaboration de J. P. Gillet (Geneva: Labor et Fides, 1990), 21.

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two words was alike, as one can ascertain from Thomas Aquinas’s lexicon, distinctions

existed.629 For instance, in circa 400, Augustine favored the term organum to specifically

designate the pipe organ (its true Latin meaning according to him), whereas

instrumentum was to be used for all other musical instruments. In music, especially in the

medieval period, organum meant several different things besides a musical instrument

and an organ: the simple and elaborate (polyphonic) vocal ensembles (to sing in hymnis

et organis), the canonical liturgy, its chant and even the book containing the authorized

texts.630 Yet organum could also be employed to characterize a person (Pope Innocent IV

was known as Doctor Pater et Organum Veritatis) and, of course, any type of tool,

engine of war, surgical instrument and later bodily organ. Though etymologically similar

to instrumentum, organum is nonetheless more interesting as a concept owing to its clear

association with Aristotle’s Organon—or logic—and to Francis Bacon’s early modern

criticism of it, his Novum organum (1620). Perhaps more than instrumentum, organum

epitomized both the material and abstract instruments of knowledge.

In his dedication to king James I, Lord Verulam pleaded for a regeneration, a

renewal of the sciences that was long overdue. He compared James I to Solomon, and

entrusted his sovereign to “emulate that same king in another way, by taking steps to

ensure that a Natural and Experimental History be built up and completed … So that at

last, after so many ages of the world, philosophy and the sciences may no longer float in

629 See the following very useful online resource: Ludwig Schütz, Thomas-Lexikon: Sammlung, Übersetzung und Erklärung der in sämtlichen Werken des hl. Thomas von Aquin vorkommenden Kunstausdrücke und wissenschaftlichen Aussprüche <http://www.corpusthomisticum.org/tl.html> (Accessed on 8 July 2007).

630 On all these different possibilities, see Peter Williams, “The meaning of organum: some case studies,” Plainsong and Medieval Music 10 (2001), 103-120. See also the very complete definition of organ in the Oxford English Dictionary Online.

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the air, but rest upon the solid foundations of every kind of experience properly

considered.” To achieve this goal, Bacon proclaimed he had “supplied the Instrument

(Equidem Organum probui).”631 Bacon likened his “instrument” to a nautical compass of

the mind, which could be used to “sail to the more remote and secret places of nature.”632

He made full use of the material culture analogy of tools and machines from the

mechanical arts in order to describe how best to renew the use of the human intellect.

Aphorism two is famous in describing how one should think about this novum organum:

Neither the bare hand nor the unaided intellect has much power; the work is done by tools and assistance [instrumentis et auxiliis res], and the intellect needs them as much as the hand. As the hand’s tools [instrumenta manus] either prompt or guide its motions, so the mind’s tools [instrumenta mentis] either prompt or warn the intellect.633

In the preface, Bacon even went so far as to say that “from the very start the mind should

not be left to itself, but be constantly controlled; and the business done (if I may put it

this way) by machines.”634 There is a constant reminder throughout the work of the

importance of method and order, something evidently found in well-organized machines

and skilled tool-using craftsmen. To reform scientia, one ought to step in a workshop

rather than a library to discover heuristic practices that would help in making a new

instrument of knowledge.635

631 Francis Bacon, The new organon, ed. by Lisa Jardine and Michael Silverthorne (Cambridge: Cambridge University Press, 2000), book 1, dedication, 4-5. The Latin original is taken from the facsimilé of The works of Francis Bacon, ed. by James Spedding, 14 vols (Stuttgart-Bad Canstatt: Frommann-Holzboog, c1989), i:124.

632 Bacon, The new organon, book 1, preface to “The great renewal,” 10-11. 633 Bacon, The new organon, book 1, Aphorism II, 33. Bacon, The works of Francis Bacon, i:157. 634 Bacon, The new organon, book 1, preface, 28. 635 Bacon, The new organon, book 1, Aphorism LXXXV, 70, where he says that “Anyone who has

turned his attention from workshops to libraries and conceived an admiration for the immense variety of books we see around us will surely experience a stupendous change of mind once he has given the matter and content of the books themselves a careful examination and inspection. Having observed that there is no

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Bacon wanted his reader to understand how much the mechanical arts had

contributed to human civilization, and that these were simply based on a few axioms and

“the patience and the subtle, ordered movement of hand and tool.”636 Bacon was writing

for everyone, so that his new instrument of knowledge production was not solely used for

amusement or personal gain in wealth, fame and power, but rather “for the uses and

benefits of life, and to improve and conduct it in charity.”637 Bacon’s organum, therefore,

was not meant for a restrictive category of people. It was meant for all: “Our method of

discovery in the sciences is designed not to leave much to the sharpness and strength of

the individual talent; it more or less equalises talents and intellects.” The novum organum

was more than a general method of knowledge production; it was a method that anyone

could learn, notwithstanding his/her level of intellect. To drive the point home, Bacon

compared his organum to the most simple of mathematical tools: “In drawing a straight

line or a perfect circle, a good deal depends on the steadiness and practice of the hand,

but little or nothing if a ruler or a compass is used. Our method is exactly the same.”638

Bacon’s instrument was universal regarding both the method of knowledge production

and the individuals who could learn to use it to a good end. Behind the Baconian notion

of a novum organum, one discovers a broader spectrum of meanings not necessarily

found with the use of the instrumentum derivatives.

Hence, organum was perhaps endowed with an universal overtone lacking in the

end to repetitions, and how men keep on doing and saying the same things, he will pass from admiration of variety to amazement at the poverty and paucity of the things which until now have held and occupied the minds of men.”

636 Bacon, The new organon, book 1, Aphorism LXXXV, 69. 637 Bacon, The new organon, book 1, preface to “The great renewal,” 13. 638 Bacon, The new organon, book 1, LXI, 50.

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utilization of the word instrumentum. A book such as Instrumentum pacis Constantiæ

(Venice, 1497) was about a specific event, the 1183 peace treaty of Constance. Leonhard

Zubler’s Novum instrumentum geometricum (Basel, 1607) was about a specific

instrument, i.e. a triangulation instrument used for military purposes (range-finding) and

surveying. Even Erasmus’s Novum instrumentum was about a specific sacred text, the

New Testament. Organum, on the other hand, meant all styles of vocal polyphonic music.

Michael Praetorius’s De organographia (Wolfenbüttel, 1618), book two of his Syntagma

musicum, described all the known musical instruments. Similarly, Johannes Hevelius’s

Organographiam, sive, Instrumentorum astronomicorum omnium ... accuratam

delineationem ... exhibens (Gdansk, 1673) was meant as a description and representation

of all astronomical instruments. And Kircher’s Organum mathematicum was a box—a

cistula—meant to contain all knowledge of mathematics, as we saw in Chapter three.

There was thus the idea of universality behind organum, like Aristotle’s Organon was

supposed to be the sum of all knowledge about logic. And as mentioned above Bacon’s

Novum organum was written as a new universal method of knowledge production. Not

only did it stand for a material device or an abstract notion, organum connoted universal

rather than specific knowledge about an instrument (in all the inferences of the word) or a

theoretical conception.

To Aristotle, an organon was anything that mediated between the doer and the

deed. In his Physics, for instance, the Philosopher explained that movement rested on

three things: the moved (the deed), the mover (the doer), and the instrument of motion

(what mediated between the two). The moved was in motion; the mover caused motion

yet was unmoved; and finally the instrument of motion had to move something else and

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be itself in motion—for, Aristotle said, “it changes together with the moved, with which

it is in contact and continuous, as is clear in the case of things that move other things

locally, in which case the two things must up to a certain point be in contact.”639 The

instrument of motion was not therefore the cause of motion—the same way the hand that

throws a ball is not the cause of motion, but the instrument of motion.

In Generation of animals, in trying this time to explain “which part comes into

being after which,” Aristotle complicated matters further by stating that

there is a difference between the end or final cause and that which exists for the sake of it; the latter is prior in order of development, the former is prior in essence. Again, that which exists for the sake of the end admits of division into two classes, first the origin of the movement, and then that which is used by the end; I mean, for instance, that which can generate, and that which serves as an instrument to what is generated, for the one of these, that which makes, must exist first, as the teacher before the learner, and the other later, as the pipes are later than he who learns to play upon them, for it is superfluous that men who do not know how to play should have pipes. Thus there are three things: first, the end, by which we mean that for the sake of which something else exists; secondly, the principle of movement and of generation, existing for the sake of the end (for that which can make and generate, considered simply as such, exists only in relation to what is made and generated); thirdly, the useful, that is to say what the end uses.640

Though Aristotle classified instruments in two separate classes (“that which can generate,

and that which serves as an instrument to what is generated”) both existed for the sake of

the end. Whether it was material (hammer, saw, lancet) immaterial (fire, breath) or alive

(bodily organ) an organum’s raison d’être was about the action leading toward a specific

goal. Aristotle emphasized in his physics, physiology and metaphysics the effectiveness

639 Aristotle, Physics, book 8, §256b13-256b27, in The complete works of Aristotle, ed. by Jonathan Barnes, 2 vols. (Princeton: Princeton University Press, 1984-1985), i:428. Every reference to Aristotle was taken from Past Masters internet resource <http://library.nlx.com> (Accessed via Harvard College Libraries, 22 April 2007).

640 Aristotle, Generation of animals, book 2, §742a16-742b17, in The complete works of Aristotle, i:1151.

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of instruments, not their materiality or lifelessness.641

For this reason Aristotle did not see a fundamental difference between the human

body and any other natural or artificial instrument. Epistemically speaking, anything that

generated an action leading toward an end was an organum. On the ontological side of

things, however, it was a different story. Here, substance mattered: “For if a piece of

wood is to be split with an axe, the axe must of necessity be hard; and, if hard, must of

necessity be made of bronze or iron. Now exactly in the same way the body, since it is an

instrument—for both the body as a whole and its several parts individually are for the

sake of something—if it is to do its work, must of necessity be of such and such a

character, and made of such and such materials.”642 In Aristotle’s system of nature, an

axe and a human organ were not composed of the same kind of material, though they

were both organa—made to accomplish a specific purpose. Aristotle, and the

Aristotelians after him, never pretended the human body was a machine. Whether the

hand was used as a mnemonic device, such as the so-called Guidonian hand to teach the

641 In his Politics, Aristotle described slaves and servants as property, which were also “instruments” for maintaining life: “Property is a part of the household, and the art of acquiring property is a part of the art of managing the household; for no man can live well, or indeed live at all, unless he is provided with necessaries. And as in the arts which have a definite sphere the workers must have their own proper instruments for the accomplishment of their work, so it is in the management of a household. Now instruments are of various sorts; some are living, others lifeless; in the rudder, the pilot of a ship has a lifeless, in the look-out man, a living instrument; for in the arts the servant is a kind of instrument. Thus, too, a possession is an instrument for maintaining life. And so, in the arrangement of the family, a slave is a living possession, and property a number of such instruments; and the servant is himself an instrument for instruments.” Aristotle, Politics, book 1, §1253b24-1254a17, in The complete works of Aristotle, ii:1989. For a sophisticated series of essays regarding the topic of material objects and intentionality, see Peter Kroes and Anthonie Meijers, “The dual nature of technical artifacts,” Studies in History and Philosophy of Science 37 (2006), 1-4 for the introduction to this whole issue dedicated to this question.

642 Aristotle, Parts of animals, book 1, §642a1-642a13, in The complete works of Aristotle, i:999. Regarding the human body as an instrument, Aristotle mentioned later in the same text: “As every instrument and every bodily member is for the sake of something, viz. some action, so the whole body must evidently be for the sake of some complex action. Thus the saw is made for sawing, for sawing is a function, and not sawing for the saw. Similarly, the body too must somehow or other be made for the soul, and each part of it for some subordinate function, to which it is adapted.” Ibid., 645b15-645b20, p. 1005.

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theory of music, or as a mathematical instrument, such as a nocturnal to tell the time at

night, it was essentially—ontologically—different from Ambroise Paré’s mechanical

hand. (See Figure 5.1.) Seventeenth-century mechanical natural philosophy eroded this

distinction.

FIGURE 5.1: THE HAND AS AN “INSTRUMENT” Above, the Guidonian hand in a manuscript from Mantua, last quarter of the fifteenth century (Oxford University MS Canon. Liturg. 216. f.168b recto) (Bodleian Library) Upper right, mathematical-instrument hand from Peter Apian, Instrument Buch, frontispice. Lower right, the mechanical hand by Ambroise Paré, Les Œuvres de M. Ambroise Paré conseiller, et premier chirurgien du roy (Paris, 1598), Chapter 22, “Des moyens & artifices d’adiouster ce qui defaut naturellement ou par accident.”

I argued in Chapter two that body and machines were socially and epistemically

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integrated into Descartes’s organon—the Cartesian method or logic of practice.

Furthermore, Descartes made absolutely no ontological distinction between a machine

and the human body. Here he went much further than Aristotle and most early modern

natural philosophers. As one of the chief figures of the new mechanical philosophy,

Descartes suggested that natural and artificial things alike were made of a collection of

basic parts. To understand fully the things under study, one had to investigate the size,

shape and motion of these basic parts. Descartes thus abstracted the concept of

mechanics, moving away from the physical machines per se. Sylvia Berryman has shown

that in later Antiquity, when someone suggested a “mechanistic” approach to nature, it

was more than an analogy: ancient Greek philosophers devised “mechanistic

conceptions” that attempted to use techniques from mechanical craftsmanship, and their

“mechanical” understanding of nature and organisms stemmed from the analysis of actual

devices. The exact same thing could be said of Renaissance engineering, when for

example Guidobaldo wrote that “mechanics can no longer be called mechanics when it is

abstracted and separated from machines.” Descartes’s mechanics, a contrario, was no

longer a science of machines; it had become, in Daniel Garber’s words, “a science of

things that operate through the physical configuration of their parts.” What was left was a

science of complex bodies whose condition was ascertained by the size, shape and

motion of their various parts.643

As developed in Chapter two, Descartes’s organum was an abstract concept, as

643 Daniel Garber, “Descartes, mechanics, and the mechanical philosophy,” Midwest Studies in Philosophy 26 (2002), 185-204, quote on p. 199. Sylvia Berryman, “Ancient automata and mechanical explanation,” Phronesis 48 (2003), 344-369. Idem, “Galen and the mechanical philosophy,” Apeiron: A Journal for Ancient Philosophy and Science 35 (2002), 235-253. For Guidobaldo’s quote, Garber, op. cit., p. 199. The best analysis of Descartes’s understanding of body and machine remains Dennis Des Chene, Spirits and clocks: Machine and organism in Descartes (Ithaca: Cornell University Press, 2001).

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was Bacon’s novum organum. They were both conceptualized for the sake of an end,

namely to think clearly and discover nature’s truths. The particularity of these two

organa was that they involved some heavy training, or a set of intellectual practices that

were not innate but had to be acquired through exercices. For Descartes, I used the

concept of habitus in trying to understand how one gets habituated to the method; for

Pascal, in Chapter three, I have drawn on the notion of coutume to explain how one could

make the arithmetical machine work properly. Whether material or not, an organum is

simply not something that works on its own. It needs a user, and the latter has to partake

in an intensive and specialized training to become proficient with the instrument.

Embedded in every organum, therefore, is an exclusive set of practices that ensured,

when correctly deployed, the desired result. Yet what exactly were these practices, and

how could they be characterized? As Don Bates explains, Aristotle’s own notion of

instrument was closely tied to the conceptual space of the human arts. To that effect,

Aristotle’s instrument often leaned in the direction of automaticity and regularity, both

integral part of the craftsman’s activities.644 As I will show in the following section, the

practices that can be associated to the notion of organum were still in the early modern

period influenced by the regularities of artisanal work. To explain what I understand by a

set of practices in using both a material and an abstract organum, I will rely on the

conception of a logic of practice behind the overall idea of what an instrument does—

recalling here the association already made between logic and organon.

644 Don Bates, “Machina ex deo: William Harvey and the meaning of instrument,” Journal of the History of Ideas 61 (2000), 577-593. Bates says something that is quite interesting when he proposes that Aristotelian instrumentalism “combines mechanism with teleology; it occupies a zone where mind and matter meet.” (p. 586) This reminds me of Galison’s “theory machine,” a concept he uses in trying to grasp what Einstein’s and Poincaré’s respective theory of relativity really were. Galison, Einstein’s clocks, Poincaré’s maps, esp. pp. 227-293.

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THE HABITUS ORGANICUS OR THE LOGIC OF PRACTICE IN NATURAL PHILOSOPHY

Since Antiquity, the notion of art was understood as the knowledge of making things (ars

est ratio faciendi). Things here should not only be grasped as material objects, but also as

productions of the mind (ars constat cognitione & effectione). Art, more precisely, was

acknowledged as a poietical or mechanical habitus (habitus ποιητικος seu μηχαυικος),

an organized and methodical disposition of body and mind to the production of things

and knowledge. Whether an art was defined as perfect or mediocre, it always entailed a

system of principles (or actions) leading to an end. For our purpose in this section, it is

the second definition of ars that is especially interesting. Related to the idea of an end, art

was said to be an habitus organicus, namely an instrumental habitus (like logic) that uses

the notion of organum and disposition of the body (or mind) to achieve a specific goal. In

trying to grasp what exactly was the logic of practice in natural philosophy, I investigate

the concept of habitus organicus.645

In music, an instrumentum organicum was a musical instrument which by virtue

of its construction was capable of being exactly tuned, and thus was endowed with a

perfect disposition to theoretical demonstration. The conception of organicus was

commonly associated to the Greek kataskeue organike, which was related to a

geometrical construction made with an instrument. The instrument here in question was a

compass or a straight-edge tool, considered more reliable than a stencil or the hand.646

645 Rodolphus Goclenius, Lexicon philosophicum (1613; facsimilé from New York: Georg Olms Verlag, 1980), s.v. ars.

646 Fritz Reckow (with Edward H. Roesner), Rudolf Flotzinger, and Norman E. Smith, “Organum,” Grove music online, ed. by L. Macy (Accessed 12 April 2007), <http://www.grovemusic.com>. On the concept of construction for kataskeue in Greek geometry, see

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(Bacon’s analogy of the compass for his novum organum, mentioned above, was not

fortuitous. Likewise for Descartes’s treatment of the same instrument in the Géométrie.)

Hence, behind organicus one found the abstract idea of mathematical exactness and

theoretical soundness in the construction of a mathematical proof—as well as of a

material object, a vocal polyphony, or even a thought. Regarding the latter, logic was

assuredly the paradigmatic habitus organicus—as defined in Goclenius’s Lexicon

philosophicum. Scipion Dupleix, following Aristotle, described logic and rhetoric as

instrumental arts (arts instrumentaires), art itself being by definition a habitus.647 In the

middle of the seventeenth century, in his book on the logica memorativa, Johann Just

Wynkelmann inserted an engraving depicting logic. According to an eighteenth-century

commentator, it shows Aristotle sitting in a profound meditation (from which we have to

assume that logic is a matter of the mind, not the body). In his right hand he holds a key

(to say that logic is not a science but the key to the sciences) and in his left hand a

hammer (which means that logic was an habitude instrumentale). This interpretation is

found in the Encyclopédie, and illustrates well the longevity of logic being described as a

habitus organicus.648 Since Antiquity, logic was understood as a special tool of the mind,

perhaps the best instrument to help distinguish the truth from the false.

In La Logigue, Dupleix explained that logic could be neither theory nor practice,

Reviel Netz, “Proclus’ division of the mathematical proposition into parts: How and why was it formulated,” The Classical Quarterly, New Series 49 (1999), 282-303, esp. p. 300.

647 Scipion Dupleix, La Logique ou art de discourir et raisonner (Paris: Fayard, 1984 [1607]), book I, chap. 11, p. 55.

648 Johann Just Wynkelmann, Logica memorativa; cujus beneficio compendium logicæ peripateticæ brevisimi temporis spacio memoriæ mandari potest (Halle Saxonum, 1659). I was unable to see a copy of this rather rare book. For the analysis, see entry on the “Art mnemonique” in Diderot’s and d’Alembert’s Encyclopédie.

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science nor art. It was not an art because it did not produce (faire) anything concrete once

the action was done. It was not a science (or a science theoretique) because logic did not

teach how to know nature through its causes.649 Could it be then one of Aristotle’s five

habits of the mind? Since it was neither science nor art, it only left sapience (wisdom),

intelligence and prudence. It could not be intelligence, because if science was to know

from causes, intelligence was the knowledge of the causes themselves. Wisdom being

above the latter two, logic could not be it either. Prudence, lastly, was a virtue not a

discipline, therefore unrelated to logic.650

Dupleix, however, found it absurd to reject from both the sciences and the arts an

“instrument” without which none of the latter activities could flourish. He tried hard,

therefore, to find a proper niche to place logic in both the sciences and the arts. Dupleix

reasoned (contrary to Aquinas and the scholastics) that if logic was understood as

instruisante, it could not be a science since it would only contain the naked precepts,

which by themselves are useless in finding the cause of things. Put into action (logique

usitée ou mise en usage), on the other hand, logic was a science because it linked those

same precepts with the natural things of physics or the supernatural things of

metaphysics. Science provided the substance and logic the manner and the form of

discourse.651 (Here Dupleix somewhat anticipated the authors of the Logique de Port-

Royal, who found it completely normal, despite their critics, to associate logic with

concrete examples taken from the sciences.652) Then again, logic was an art because, as

649 Dupleix, La Logique, book I, chap. 8, p. 49. 650 Dupleix, La Logique, book I, chap. 9, p. 51-52. 651 Dupleix, La Logique, book I, chap. 10, p. 53-54. 652 Antoine Arnaud and Pierre Nicole, La Logique de Port-Royal, ed. by Alfred Fouillée, new ed.

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mentioned above, it was considered an art instrumentaire, an instrument beneficial to all

subject matters. It was also an art because it was traditionally recognized as one of the

seven liberal arts. Finally, if an art was something deemed useful to human life, logic

certainly deserved to be named an art since what could be more indispensible to one’s life

than discerning the truth from the false in all circumstances?653

Goclenius’s definition of logic as an habitus organicus already stressed the fact

that logic was an art. In typifying logic as usitée ou mise en usage, rather than

instruisante, Dupleix (and later Arnaud and Nicole) emphasized as well the “scientific”

character of logic. What it did, actually, was to strengthen one facet of habitus in the

definition of logic as a habitus organicus. We have already seen that organicus meant

(Paris: Librairie Classique d’Eugène Belin, 1878 [1662]), 19-20: “De plus, comme ces exemples communs ne font pas assez comprendre que cet art puisse être appliqué à quelque chose d’utile, ils s’accoutument à renfermer la logique dans la logique, sans l’étendre plus loin, au lieu qu’elle n’est faite que pour servir d’instrument aux autres sciences; de sorte que, comme ils n’en ont jamais eu de vrai usage, ils ne la mettent aussi jamais en usage, et ils sont bien aises même de s’en décharger comme d’une connaissance basse et inutile. On a donc cru que le meilleur remède de cet inconvénient était de ne pas tant séparer qu’on fait d’ordinaire la logique des autres sciences auxquelles elle est destinée, et de la joindre tellement, par le moyen des exemples, à des connaissances solides, que l’on vît en même temps les règles et la pratique; afin que l’on apprît à juger de ces sciences par la logique, et que l’on retint la logique par le moyen de ces sciences.”

653 Dupleix, La Logique, book I, chap. 11, p. 55-56.

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FIGURE 5.2: GOCLENIUS’S DEFINITION OF HABITUS Goclenius’s schematic tree summarizing the overall concept of habitus. Goclenius, Lexicon philosophicum, s.v. habitus. theoretical soundness, and indeed the principles of logic led to rigorous judgment and

analysis. But first and foremost, logic was a habitus because it helped accomplish

operations that nature alone could not make easily or with consistency.654 Habitus,

following the standard definition, was associated to both the body and the mind. (See

Figure 5.2.) Habitus in corpore was usually related to the body’s health, or medicine.

Habitus in anima was linked to the passions (appetitive faculties), on the one hand, and to

the intellect, on the other. The latter, moreover, was divided into two parts: speculativus

for the sciences and operativus for the intellectual virtues (practicus, i.e. acting or things

done) and the art (poeticus, i.e. making or things made). Whether a science or an art (or

both), logic was clearly an habitus intellectus. A further division existed here, whether

one considered certain or uncertain knowledge (apprehensiones). (See Figure 5.3.) When

uncertain, the kind of knowledge one had to deal with was either an opinion, a conjecture

or a presumption. Regarding the things one could know for certain, the habitus intellectus

could be simplex or compositus. If simplex, it was either νοητικος, i.e. the simple and

naked things that were understood immediately (αμεσως) without the help of discourse

or demonstration, or διανοητικος, i.e. things that were understood through discourse and

reasoning.655 The former was associated to intelligentia, or the habitus intellectus from

654 Goclenius, Lexicon philosophicum, s.v. habitus: “Habitu primum sumitur Categorice pro Qualitatis prima specie, id est, pro qua litate, qua quis habilis est ad operationes, quas per naturam solam edere facile & constanter nequit.”

655 Goclenius, Lexicon philosophicum, s.v. habitus: “Habitus simplex νοητικος est qui intelligit res simplici nudaq[ue]; apprehensione, id est, sine medio seu discursu & demonstratione.” “Διανοητικος est, qui res intelligit cum discursu & ratiocinatione.”

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FIGURE 5.3: GOCLENIUS’S DEFINITION OF HABITUS INTELLECTUS Goclenius’s schematic tree summarizing the particular concept of habitus intellectus. Goclenius, Lexicon philosophicum, s.v. habitus. which first principles were believed to be true. The latter was associated to scientia when

the conclusion reached was unavoidable (necessarium) or to art and prudentia when there

was some chance or probability (contingens).656 Lastly, the habitus intellectus

compositus was the combination of intelligentia and scientia, or sapientia (wisdom), the

summum bonum of human understanding.657

656 Goclenius, Lexicon philosophicum, s.v. habitus: “Intelligentia est habitus intellectus, quo principia cognoscimus. Principia sunt primæ propositiones necessariæ & immotæ, seu axiomata αναποδεικτα, id est, quibus per se fidem habemus.” “Scientia est habitus intellectus apodicticus (qui comparatur per Demonstrationem) quo percipimus necessarias conclusiones è necessariis propositionibus.”

657 Goclenius, Lexicon philosophicum, s.v. habitus: “Habitus compositus ex Intelligentia

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The above definition and interpretation of habitus come almost directly from

scholasticism, especially Aquinas’s interpretation—which itself was much influenced by

Aristotle’s.658 We saw in Chapter two that Descartes criticized in his Regulæ ad

directionem ingenii this treatment of habitus within the realm of scientia. What he

disapproved of was the fact that the sciences had been connected to the uniqueness of

ars—that is to say, specific knowledge, to be acquired, demanded particular types of

instruments and habitus, which led to a variety of training. Aristotle plainly expressed

this condition when he wrote, for instance, that

science is an instrument of the intelligence (for it is useful to the intelligence just as flutes are useful to the flute-player), and many things in nature are instruments of the hands… Now it is natural that where the instruments are prior, the faculties should also come into being in us first (for it is by using the instruments that we acquire a disposition [habitus]); and the instrument of each faculty is related similarly to that faculty, and conversely, as the instruments are to one another, so are the faculties of which they are the instruments to one another.659

And as he said elsewhere, “for the exercice of any faculty or art a previous training and

habituation are required.”660 Hence every intellectual faculty or art necessitated its own

particular organum and habitus. Where Descartes saw a unity of scientia—an

Principiorum & scientia, dicitur sapientia.” 658 See especially Thomas Aquinas, The Summa theologica of St. Thomas Aquinas, 2nd ed. (1920),

internet resource <http://www.newadvent.org/summa/> (Accessed on 1 August 2007), prima secundæ partis, questions 49 to 58. Some very good analyses exists, like René Arnou, S.J., L’Homme a-t-il le pouvoir de connaître la vérité? Réponse de Saint Thomas: La connaissance par habitus (Rome: Presses de l’Université Grégorienne, 1970); Yuji Nagamachi, S.J., Selbstbezüglichkeit und Habitus. Die latente Idee der Geistmetaphysik bei Thomas von Aquin (St. Ottilien: EOS Verlag Erzabtei, 1997); Rolf Darge, Habitus per actus cognoscuntur. Die Erkenntnis des Habitus und die Funktion des moralischen Habitus im Aufbau des Handlung nach Thomas von Aquin (Bonn: Bouvier Verlag, 1996).

659 Aristotle, Problems*, book 30, §955b22-956a10, in The complete works of Aristotle, ii:1503. It is interesting to note here that the authors of the Logique de Port-Royal say something suggesting an analogous understanding when they write that “On se sert de la raison comme d’un instrument pour acquérir les sciences, et l’on devrait se servir, au contraire, des sciences comme d’un instrument pour perfectionner sa raison, la justesse de l’esprit étant infiniment plus considérable que toutes les connaissances spéculatives auxquelles on peut arriver par le moyen des sciences les plus véritables et les plus solides…” Arnaud and Nicole, La Logique de Port-Royal, 5-6.

660 Aristotle, Politics, book 8, §1337a20-1337a32, in The complete works of Aristotle, ii:2121.

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interconnectedness of knowledge commensurate with an universal wisdom—Aristotle

and the scholastics discerned elements of science from the uniqueness of the instruments

and dispositions needed in acquiring them.

This interpretation of habitus was fairly common in early modern Europe.

Habitus, furthermore, was not only about intellectual habits, but also about moral ones. It

was essential to figure out what made human beings good and excellent. According to

Aristotle,

There are three things which make men good and excellent; these are nature, habit, reason. In the first place, every one must be born a man and not some other animal; so, too, he must have a certain character, both of body and soul. But some qualities there is no use in having at birth, for they are altered by habit, and there are some gifts which by nature are made to be turned by habit to good or bad. Animals lead for the most part a life of nature, although in lesser particulars some are influenced by habit as well. Man has reason, in addition, and man only. For this reason nature, habit, reason must be in harmony with one another; for they do not always agree; men do many things against habit and nature, if reason persuades them that they ought. We have already determined what natures are likely to be most easily moulded by the hands of the legislator. All else is the work of education; we learn some things by habit and some by instruction.661

The things one learned by habit were of the moral kind; the things learned by instruction

were of the intellectual kind. Yet whether one dealt with the appetitive faculties

(passions, or moral) or the intellect (reason), goodness and excellence were found in

human virtues—which were themselves habitus in anima, owing to Aquinas’s line of

661 Aristotle, Politics, book 7, §1332a39-1332b12, in The complete works of Aristotle, ii:2114. He formulated a similar view in his Nichomachean ethics: “Excellence, then, being of two kinds, intellectual and moral, intellectual excellence in the main owes both its birth and its growth to teaching (for which reason it requires experience and time), while moral excellence comes about as a result of habit, whence also its name is one that is formed by a slight variation from the word for ‘habit’ [ethike from ethos]. From this it is also plain that none of the moral excellences arises in us by nature; for nothing that exists by nature can form a habit contrary to its nature. For instance the stone which by nature moves downwards cannot be habituated to move upwards, not even if one tries to train it by throwing it up ten thousand times; nor can fire be habituated to move downwards, nor can anything else that by nature behaves in one way be trained to behave in another. Neither by nature, then, nor contrary to nature do excellences arise in us; rather we are adapted by nature to receive them, and are made perfect by habit.” Idem, Nichomachean ethics, book 2, §1103a14-1103a25, in ibid., ii:1742.

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argument (virtutes humanæ habitus sunt).662 Aquinas explained that a “Virtue denotes a

certain perfection of a power” and that “a thing’s perfection is considered chiefly in

regard to its end. But the end of power is act. Wherefore power is said to be perfect,

according as it is determinate to its act.” Natural powers, for instance, were determinate

to their acts. Rational powers, however, which were proper to man, were not determinate

to a particular action. They might be disposed to several different ones. And since they

were determinate to acts by means of habitus, human virtues were habitus.663 Scipion

Dupleix fully agreed with Aquinas, most often than not using the phrase “intellectual

virtues” instead of “intellectual habits.”664

Although a virtue’s ultimate end was goodness and excellence in human beings,

Aquinas distinguished between two kinds of virtues, determined by which part of the

anima was examined. Habits of the speculative intellect were intrinsically different from

habits of the appetitive part of the soul. As he explained,

Since every virtue is ordained to some good, as stated above [quest. 55, art. 3], a habit, as we have already observed [quest. 56, art. 3], may be called a virtue for

662 Aquinas, The Summa theologica of St. Thomas Aquinas, quest. 55, art. 1. The original Latin comes from Aquinas, Opera omnia, 28 vols (facsimilé from New York: Musurgia Publishers, 1948- [1852-1873]), xi:189.

663 Aquinas, The Summa theologica of St. Thomas Aquinas, quest. 55, art. 1. For a thorough definition of virtue, see the Oxford English Dictionary Online, s.v. virtue.

664 Scipion Dupleix, L’Éthique, ou philosophie morale (Paris: Fayard, 1994 [1645]), book 3, chap. 1, 156, where he states “Or la vertu en general est une habitude, laquelle perfectionne celuy qui en est doüé, et rend ses actions droites et accomplies. Ainsi un homme sçavant est perfectionné par la science, qui est une vertu intellectuelle, laquelle luy fait distinguer la verité de la fausseté, et la certaine cognoissance de l’opinion douteuse, dont il est loüé et prisé.” Further in the book he writes: “Il faut donc tenir pour chose indubitable que les vertus intellectuelles sont en l’entendement comme en leur sujet, et que de là elles ont pris leur denominaison, combien que leurs objets ne soient pas immediatement receus ny perceus par l’entendement, ains par le moyen des sens et specialement de l’imagination ou fantasie. Elles sont aussi appellées rationnelles ou raisonnables, d’autant que la raison est inseparable de l’entendement auquel elles sont. De là nous colligeons quant et quant leur genre, qui est habitude, combien qu’en les considerant avec relation à leur objet elles puissent aussi estre appellées relations ou relatifs. Elles sont aussi vertus, d’autant qu’elles perfectionnent l’ame, et c’est le propre de la vertu de perfectionner son sujet. Mais estans vertus elles sont toujours habitudes et les habitudes sont qualitez.” (book 6, chap. 2, 357)

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two reasons: first, because it confers aptness in doing good [quia facit facultatem bene operandi]; secondly, because besides aptness, it confers the right use of it [quia cum facultate facit etiam usum bonum]. The latter condition, as above stated [quest. 55, art. 3], belongs to those habits alone which affect the appetitive part of the soul: since it is the soul's appetitive power that puts all the powers and habits to their respective uses. Since, then, the habits of the speculative intellect do not perfect the appetitive part, nor affect it in any way, but only the intellective part; they may indeed be called virtues in so far as they confer aptness for a good work, viz. the consideration of truth (since this is the good work of the intellect): yet they are not called virtues in the second way, as though they conferred the right use of a power or habit. For if a man possess a habit of speculative science, it does not follow that he is inclined to make use of it, but he is made able to consider the truth in those matters of which he has scientific knowledge: that he make use of the knowledge which he has, is due to the motion of his will. Consequently a virtue which perfects the will, as charity or justice, confers the right use of these speculative habits. And in this way too there can be merit in the acts of these habits, if they be done out of charity…665

The aptness in doing good did not only touch the speculative habits, however, but

also the operative ones, like art. Again, according to Aquinas,

Art is nothing else but ‘the right reason about certain works to be made.’ And yet the good of these things depends, not on man's appetitive faculty being affected in this or that way, but on the goodness of the work done. For a craftsman, as such, is commendable, not for the will with which he does a work, but for the quality of the work. Art, therefore, properly speaking, is an operative habit. And yet it has something in common with the speculative habits: since the quality of the object considered by the latter is a matter of concern to them also, but not how the human appetite may be affected towards that object. For as long as the geometrician demonstrates the truth, it matters not how his appetitive faculty may be affected, whether he be joyful or angry: even as neither does this matter in a craftsman, as we have observed. And so art has the nature of a virtue in the same way as the speculative habits, in so far, to wit, as neither art nor speculative habit makes a good work as regards the use of the habit, which is the property of a virtue that perfects the appetite, but only as regards the aptness to work well.666

Art and science, acknowledged as habitus in intellectu in Goclenius’s definition, were

665 Aquinas, The Summa theologica of St. Thomas Aquinas, quest. 57, art. 1. Latin from Aquinas, Opera omnia, xi:196.

666 Aquinas, The Summa theologica of St. Thomas Aquinas, quest. 57, art. 3.

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both considered virtues owing to their aptness in doing good—or to work well. Moral

actions (the appetitive faculties) had nothing to do with the accomplishment of

intellectual habits; they only concerned the right (moral) use of it. (A modern example

would be the development of the A-bomb versus whether or not it should be used.)

Making and acting, therefore, were different motions of the soul, animated by the overall

notion of an habitus in anima.667

Early modern interpretation of art and science thus shared a likeness too often

disregarded by modern scholars. It did not mean, however, that art and science were

thought equivalent. Dupleix described clearly the early modern need of a proper order in

intellectual virtues. We mentioned above that five such intellectual virtues existed:

science, intelligence, prudence, art and wisdom. Whether or not there were more than

five was often hotly debated. Dupleix, however, preferred to hold on to the conventional

five, considering other options like instruction, discipline, memory, ratiocination and

ingenium as instruments or distinct faculties of the soul.668 These five intellectual virtues

could be ordered in three different ways, which considerably changed the general

understanding and interpretation one might have of them. The order of dignity, for

instance, was the most excellent one because it favored a life of contemplation. Hence,

one found in succession wisdom, intelligence, science, prudence and finally art. The

methodical order was slightly different, because this one aimed at the systematic pursuit

of knowledge. Here intelligence came first, which then led to science and wisdom,

prudence and art closing the rank. Finally, the order of necessity was about action rather

667 Aristotle explained well this making versus acting distinction in his Nichomachean ethics. See, for instance, book 6, §1140a1-1140a23, in The complete works of Aristotle, ii:1799.

668 Dupleix, L’Éthique, book 6, chap. 1, 347-351.

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than contemplation, and was the most important to human life. Here, art and prudence

came before science, intelligence and wisdom. Indeed, how can human life sustain itself

without the art of agriculture, wine making, bread making, etc.?669

These three orders of intellectual virtues all had the same goal—excellence:

excellence of wisdom (truth in contemplation); excellence of science (the pursuit of

knowledge); excellence of art (in making material things). What does it say about the

logic of practice in early modern natural philosophy? The notion of habitus organicus

from which I started this section was labeled a synonym of ars; and for Goclenius the

paradigmatic example of an habitus organicus was logic, the instrument of reason. We

just saw, furthermore, that habitus was understood to be identical to the notion of virtue.

Art, as an instrumental habit, could be identified consequently to an instrumental virtue,

one—as we saw from Dupleix—that formed the basic foundation of the order of

necessity. Logic, similarly, was an instrumental virtue which, according to Dupleix again,

could even be considered a science. The concept of habitus organicus—or instrumental

virtue—can thus be employed to bring together art and science in an attempt to convey

the meaning of natural philosophical practice. And it was a virtuous logic of practice

because it showed how best to make things, whether they were in the mind or in the

material world.

Jim Bennett, though coming from a different angle than the one presented here,

used this same notion of instrumental virtue to account for the relationship between

instrument, operator and the mathematical sciences in sixteenth-century Europe. As

Bennett explains, “Instrumental virtue derives from the certainty of mathematical science,

669 Dupleix, L’Éthique, book 6, chap. 3, 359-362.

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but it can be properly and effectively deployed only through the expertise of a legitimate

operator, whose ‘virtue’ similarly depends on a grounding in mathematical science.”

Bennett uses virtue as a supplement to “certainty, doubt and error,” which were

connected to moral issues since these notions incorporated integrity and effectiveness of

action in instrument and operator alike. He thus argues that sixteenth-century geometry

was actually carrying both kinds of virtues as defined by Aquinas. Moral issues, Bennett

claims, “are relevant to both the instrument and the operator [of the mathematical

science], while [the mathematical] forms of knowledge do not stand independent of

action…” It thus appears that the dichotomy between things made and things done, or

between making and acting, collapsed in the mathematical practices of the Renaissance.

What Bennett concludes from his study of early modern geometry is the latter

“embodiment” in instrument and operator. Early modern geometry was, in other words,

founded on a science rendered applicable through virtuous instruments and through codes of practice mastered by the expert practitioner. Error in this context [was] not instrumental or operator error in the modern sense; error [was] failure of instrumental virtue or of operator morality.670

Virtue was not only found in the scientia of geometry, but also in the instrument and its

operator. Both acquired and displayed virtue, and in the end they were as dependent on

geometry’s virtue as the latter was on the instrument’s and operator’s virtues.671

We have shown in this section how the notion of habitus organicus could be

understood as a logic of practice for natural philosophy, a logic that encompassed both art

670 Jim Bennett, “Geometry in context in the sixteenth century: The view from the museum,” Early Science and Medicine 7 (2002), 214-230, quotes on pp. 229-230.

671 On virtue and self-cultivation in relation to mathematics and natural philosophy, see the excellent book by Matthew L. Jones, The good life in the Scientific Revolution: Descartes, Pascal, Leibniz, and the cultivation of virtue (Chicago: The University of Chicago Press, 2006).

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and science. This instrumental habit was connected to the habitus in anima, and thus the

organum in such a case could only relate to concepts such as Bacon’s induction or

Descartes’s method. The last thing remaining to be investigated is the second part of the

concept of habitus, the habitus in corpore. Using once more the notion of habit, or

habitus, I want to show in the next section how the material and tangible organum could

be associated to the habitus in corpore, which was not simply understood as the human

body’s health. If an instrument could embody the concept of virtue, we will explain next

how the body itself could incorporate the instrument through the medium of habit. Body,

mind and organum were, in short, closely related to one another.

HABITUS AND THE TECHNIQUES OF THE BODY

To appreciate the connection between body and organum, let us first return briefly to

music and the pneumatic organ. Like other types of instrument, the etymology of the pipe

organ is derived from the Greek organon and its subsequent Latin translation. In Greek

Antiquity, however, organon never referred to a pipe organ. The origins of organum as a

definition of a pipe organ came into being with St. Augustine and the Latin Church

Fathers. Only with the coming of the Christian era did one see a clear evolution from the

general connotation of organum to the more specific musical term.672

The meaning of organ as a musical instrument was so prevalent in Renaissance

Europe that Vincenzo Galilei felt the need to spell out the original sense of the term. An

organ, he wrote, was an instrument, whether natural or artificial, that could best achieve

672 Barbara Owen, Peter Williams, and Stephen Bicknell, “Organ,” Grove Music Online (Accessed 17 August 2006).

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its intended end:

Although we read the term ‘organ’ countless times in the ancient writers on the subject of musical instruments and other subjects, this arises from their understanding by the term whatever pleases them. Its meaning is ‘instrument’ and ‘rising to a height’ [ascendere in alto], which is the nature of every sound and voice. Ultimately, what remains is this particular name of that instrument which has the capacity to realize best the effect of its meaning.673

Galilei used the original Aristotelian definition of organum to argue against Zarlino’s

dichotomy between art and nature, discussed in Chapter one. Whether a body part, a tool

or a musical instrument, an organ was for Galilei an instrument made toward achieving

an end. Zarlino replied to Galilei in his Sopplimenti, asserting in contrast that the pipe

organ acquired the universal name of “organ” only because it had been invented by

imitation of nature, specifically the bodily organs that produced the human voice—the

only organum that could produce just intonations—, where the pipes stood for the throat,

the bellows for the lungs, the keyboard keys for the teeth, and the player for the

tongue.674 Zarlino’s analogy became a very common one in the seventeenth century,

mentioned by music aficionados as well as engineers like Salomon de Caus and scholars

such as Athanasius Kircher.675

673 Vincenzo Galilei, Dialogue on ancient and modern music, transl. by Claude V. Palisca (New Haven: Yale University Press, 2003), 361-362.

674 Gioseffo Zarlino, Sopplimenti musicali del rev. M. Gioseffo Zarlino da Chioggia… (Venice, 1588), book VIII, 288: “Per la qual cosa dico, che l’Organo proposto s’acquistò questo nome uniuersale & commune d’Organo proprio & particolare, per una certa eccellenza dalle parti naturali, che formano la Voce, che si chiamano Istrumenti naturali: percioche fù fabricato alla guisa del Corpo humano, corrispondendo le Canne alla Gola, I Mantici al polmone, I Tasti à I Denti, & colui che sona alla Lingua, & cosi l’altre parti di esso à quella che sono nell’Huomo.” Pierre Trichet mentions Zarlino’s viewpoint, adding a parallel between the function of the wind within the organ and the human soul within the body. Trichet, Traité des instruments de musique (vers 1640), ed. by François Lesure (Neuilly-sur-Seine: Société de musique d’autrefois, 1957), 25.

675 De Villiers to Mersenne, [mid-November 1633], in Correspondance du P. Marin Mersenne: religieux minime, ed. and annotated by Cornélis de Waard (with the collaboration of René Pintard), 17 vols. (Paris: G. Beauchesne, 1933-1988), iii: 547: “Et neantmoins de tous les instruments nul n’approche de si prez les organes de la voix de l’homme que l’orgue qui a, ce semble, les souflets pour poulmon, le porte-

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Descartes, who had read and mastered Zarlino,676 made famous this analogy

between the organ and the human body in his Treatise on man. But, contrary to what the

Italian humanist proclaimed, the human body here imitated the mechanical organization

of the pipe organ, not the opposite way around.677 Although such mechanical analogies

are traceable to Leonardo da Vinci, it was the seventeenth-century mechanists who

suggested a broad and far-reaching likeness between musical instruments and the human

body.678 Descartes established the general and standard interpretation when he

ascertained in the Principia philosophiæ that he saw no difference between machines

built by artisans and bodies created by nature, besides the fact that the latter’s mechanical

structure composed of pipes, springs and other instruments was so tiny, compared to

artisanal ones, it could not be detected by sense experience.679 It is often said in fact that

vent pour trachee artere, et pour le larinx, glotte, epiglotte et cavité depuis iceux jusq’au palais, le tuyau de l’orgue et ses partyes, en sorte mesme que de cette analogie, je conclurois l’orgue plus antienne que pas un autre instrument, n’ayant esté fait sur d’autre prototype que celuy des partyes dediees à la voix humaine.” Salomon de Caus, Les Raisons des forces movvantes Auec diuerses Machines tant vtilles que plaisantes Aus quelles sont adioints plusieurs deβeings de grotes et fontaines (Frankfurt, 1615), book 3, 4. Kircher, Musurgia universalis, sive Ars magna consoni et dissoni, 2 vols. (Rome, 1650; facsimile Hildesheim, Zürich, New York: Georg Olms Verlag, 2004), book 1, chap. XIII, i:24-25. A historical survey leading to the nineteenth century is found in Thomas L. Hankins and Robert J. Silverman, Instruments and the imagination (Princeton: Princeton University Press, 1995), chap. 8, “Vox mechanica: The history of speaking machines.”

676 Descartes, Abrégé de musique, transl. and ed. by Frédéric de Buzon (Paris: Presses universitaires de France, 1987), 7-8. There is only one reference in Descartes’s Compendium, and it is to Zarlino. See also Stephen Gaukroger, Descartes: An intellectual biography (Oxford: Clarendon Press, 1995), 74-80.

677 Descartes, Traité de l’homme, in Œuvres de Descartes, ed. by Charles Adam and Paul Tannery, 11 vols. (Paris: Librairie philosphique J. Vrin, 1996), xi:165-166 (hereafter cited as AT xi, 165-166).

678 Emanuel Winternitz, “Anatomy the teacher: On the impact of Leonardo’s anatomical research on his musical and other machines,” Proceedings of the American Philosophical Society 111 (1967), 234-247. See also Winternitz, Leonardo da Vinci as a musician (New Haven and London: Yale University Press, 1982). The best book on this topic regarding Descartes is Dennis Des Chene, Spirits and clocks: machine and organism in Descartes (Ithaca and London: Cornell University Press, 2001). The most general study regarding the relationship between body and music is Kassler, Inner music.

679 Descartes, Les Principes de la philosophie, AT ix, 321: “A quoy l’exemple de plusieurs corps, composez par l’artifice des hommes, m’a beaucoup seruy: car je ne reconnois aucune diference entre les machines que font les artisans & les diuers corps que la nature seule compose, sinon que les effets des

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Descartes came up with the idea of the human body as a machine by contemplating the

automated figures in the grottoes of the Royal gardens at Saint-Germain-en-Laye,

designed by the Francini brothers. Interestingly enough, looking at de Caus’s Raisons des

forces movvantes, for instance, one sees that most grotto automata were actually powered

by hydraulic organs. Perhaps more than anything else, I would argue, the collapse of art

and nature onto each other in Descartes’s thinking came from his mental picture of the

pipe organ.680

Marin Mersenne’s book on the voice in the Harmonie universelle also leaned

heavily on such an art-nature mechanistic interpretation. The ear, for example, was not

endowed with special invisible powers, but was just a mechanical instrument to catch

sounds: “I thus say the ear does not know sounds, and that it only serves as an instrument

& organ to guide [these sounds] towards the mind, which study their nature and

properties…”681 In describing the bodily organs producing sounds, Mersenne identified

them as the “instrumens & organes de la voix,” playing with the semantic and epistemic

meaning of these two words. He also explained that instruments were “the other parts of

harmony” since they put it into practice, “particularly if one includes the voice among the

instruments.” And to explain complex features of vocal sound production, Mersenne

machines ne dependent que de l’agencement de certains tuyaux, ou ressorts, ou autres instrumens, qui, deuant auoir quelque proportion auec les mains de ceux qui les font, sont tousjours si grands que leurs figures & mouuemens se peuuent voir, au lieu que les tuyaux ou ressorts qui causent les effets des corps naturels sont ordinairement trop petits pour estre apperceus de non sens.”

680 Hydraulic and engineering also greatly influenced William Harvey’s understanding of human physiology. Marjorie O’Rourke Boyle, “Harvey in the sluice: From hydraulic engineering to human physiology,” History and Technology 24 (2008), 1-22.

681 Mersenne, “De la voix, des parties qvi seruent à la former, de sa definition, de ses proprietez, & de l’oüye,” in Harmonie universelle, contenant la théorie et la pratique de la musique, 3 vols. (Paris: Centre national de la recherche scientifique, 1963), book I, prop. LII, ii:79: “Ie dis donc premierement que l’oreille ne connoist pas les sons, & qu’elle ne sert que d’instrument & d’organe pour les faire passer dans l’esprit qui en considere la nature & les proprietez…”

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often turned to analogies derived from mechanical components of a pipe organ.682

Music and musical instruments provided much more than a powerful mechanical

analogy between natural and artificial organa. Together, they actually exhibited one basic

feature of human bodies and mechanical automata alike: the ability to “learn” new

“tricks,” that is series of coordinated and rhythmic motions involving one or several

(bodily and mechanical) organs. According to Thomas Hobbes, for instance, we might

observe that

when one that has no skill in music first puts his hand to an instrument, he cannot after the first stroke carry his hand to the place where he would make the second stroke, without taking it back by a new endeavour, and, as it were beginning again, pass from the first to the second. Nor will he be able to go on to the third place without another new endeavour; but he will be forced to draw back his hand again, and so successively, by renewing his endeavour at every stroke; till at the last, by doing this often, and by compounding many interrupted motions or endeavours into one equal endeavour, he be able to make his hand go readily on from stroke to stroke in that order and way which was at the first designed.683

Fixing the levers, gears and wheels of an automaton, so it would perform a specially

designed task was as difficult as asking an organist to learn anew how to play the organ

on a 27-key per octave clavier—to borrow Mersenne’s example cited in Chapter one. Yet

it could certainly, if not easily, be done.

682 Mersenne, “De la voix, des parties qvi seruent à la former, de sa definition, de ses proprietez, & de l’oüye,” in Harmonie universelle, book 1, prop. XIII, ii:13: “La grande varieté des sons que l’homme fait procede de la diuersité des organes, & des instrumens de la voix, ou de la differente maniere dont ils se peuuent mouuoir pour battre l’air…” and prop. IV, 7: “Il n’y a rien qui puisse mieux seruir à l’explication de cette difficulté que l’anche des regales, que l’on appelle voix humaines; car à proportion que l’on ouure ceste anche en retirant le mouuement en haut, la voix deuient plus graue; & quand on le pousse plus bas pour fermer l’anche, elle deuient plus aiguë: De mesme quand la glotte s’ouure dauantage, elle fait la voix plus graue, & quand elle se ferme, elle la fait plus aiguë.” Mersenne, “Traité des instrvmens a chordes,” in Harmonie universelle, book 1, préface au lecteur, iii: n.p.). English translation in Mersenne, Harmonie universelle: The books on instruments, transl. by Roger E. Chapman (The Hague: M. Nijhoff, 1957), 13.

683 Thomas Hobbes, Elements of philosophy, part 3, chap. 22, 348, in Hobbes, The English works of Thomas Hobbes of Malmesbury, ed. by Sir William Molesworth, 11 vols. (London: J. Bohn, 1839-1845). Taken from Past Masters internet resource <http://library.nlx.com> (Accessed via Harvard College Libraries, 22 April 2007).

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What made such automatic actions possible was explained through the notion of

habit. Hobbes’s definition was typical of the time:

Habit … is a generation of motion, not of motion simply, but an easy conducting of the moved body in a certain and designed way. And seeing it is attained by the weakening of such endeavours as divert its motion, therefore such endeavours are to be weakened by little and little. But this cannot be done but by the long continuance of action, or by actions often repeated; and therefore custom begets that facility, which is commonly and rightly called habit; and it may be defined thus: HABIT is motion made more easy and ready by custom; that is to say, by perpetual endeavour, or by iterated endeavours in a way differing from that in which the motion proceeded from the beginning, and opposing such endeavours as resist…684

What Hobbes is describing here is evidently not limited to an habitus in corpore, namely

to bodily health and disposition as understood since Greek Antiquity.685 It was actually

related to bodily gestures, motions and actions, whether one was learning to play the

clavichord, crafting a new tool, or receiving pleasure from having sex.686 When Hobbes

684 Thomas Hobbes, Elements of philosophy, part 3, chap. 22, 348 (italics original). Hobbes continues: “Nor are habits to be observed in living creatures only, but also in bodies inanimate. For we find that when the lath of a cross-bow is strongly bent, and would if the impediment were removed return again with great force; if it remain a long time bent, it will get such a habit, that when it is loosed and left to its own freedom, it will not only not restore itself, but will require as much force for the bringing of it back to its first posture, as it did for the bending of it at the first.”

685 Aristotle, Problems*, book 28, §949a24-949b5, in The complete works of Aristotle, ii:1491. “Why is it that some men become ill when, after having been accustomed to live intemperately, they adopt a temperate mode of life? For example, Dionysius the tyrant, when during the siege he ceased drinking for a short time, immediately became consumptive, until he changed his manner of life and began to drink again. Is it because in every one habit is a matter of importance, since it soon becomes nature? Just, then, as a fish would fare ill if it continued long in the air or a man if he continued long in the water, so those who alter their manner of life suffer from the change, and a resumption of their accustomed mode of life is just as much their salvation as if they were returning to a natural condition. Furthermore, men waste away if they have been accustomed to large quantities of a particular diet; for if they do not receive their usual food, they are reduced to the condition in which they would be if they had no nourishment at all.” The first definition of habitude in French, taken from Antoine Furetière’s Dictionnaire universelle (Paris, 1690) is still about the human body: “C’est en Physique le temperamment, la complexion du corps humain.”

686 Aristotle, Problems*, book 4, §879a36-880a5, in The complete works of Aristotle, ii:1356. “[M]en take a pleasure in whatever they are accustomed to do and emit the semen accordingly. They therefore desire to do the acts by which pleasure and the emission of semen are produced, and habit becomes more and more a second nature. For this reason those who have been accustomed to submit to sexual intercourse about the age of puberty and not before, because recollection of the past presents itself to them during the act of copulation and with the recollection the idea of pleasure, desire to take a passive part owing to habit, as though it were natural to them to do so; frequent repetition, however, and habit become a

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says that habit was the result of “perpetual endeavour” or “iterated endeavours,” he

endowed habit with the notion of least effort. Endeavour had indeed a special meaning to

Hobbes. He defined it as a “Motion made in less Space and Time then can be given; that

is, less than can be determined or assigned by Exposition or Number; that is, Motion

made through the length of a Point.” Habit was thus more than the automation of

movements: it was a force. Through the repeated action of bodily organs, habit could

become like a natural force of nature—a second nature.687

Historian of science Pamela Smith, as we mentioned elsewhere, describes in her

well-illustrated book what she calls an “artisanal epistemology,” which involved on the

part of an artisan a “bodily engagement with matter,” a “bodily struggle” that often left

visible scars as well as generating a “certain knowledge of nature.” Artisans strove for

“an imitation of nature much more profound than the reflection of nature in a mirror;

beyond verisimilitude, the artisan sought a knowledge of materials and an ability to

produce.” Smith argues that such a cognition “led to a deep knowledge of nature, out of

which flowed an ability to manipulate materials resulting in the production of tangible

effects, or works of art.”688 Though she gives numerous and fascinating examples of the

type of works alchemists, goldsmiths, physicians and painters created, Smith is by and

large silent on how the “body of the artisan” was (naturally) associated to this new kind

of knowledge. What exactly did it mean to “struggle with matter”? What is hidden—

second nature.” 687 Hobbes, The elements of philosophy, the first section, concerning body, transl. by Sir Henry

Savile (London, 1656), 151. Quoted from Margaret J. Osler, “Whose ends? Teleology in early modern natural philosophy,” Osiris, 2nd series, 16 (2001), 151-168, on pp. 166-167.

688 Pamela H. Smith, The body of the artisan: Art and experience in the Scientific Revolution (Chicago: The University of Chicago Press, 2004), 98 and passim.

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some would say tacit—behind this statement? Scholars in various disciplines have dealt

with the training of the body as habits and how fundamental it was in generating original

knowledge about nature. In the following paragraphs, I offer a few examples taken from

phenomelogy, anthropology and ethnology that show the interest (urgency?) of reaching

out to other disciplines in trying to understand the significance of bodily practices to the

progress of early modern science.

The notion of habit offers an important insight into the knowledge-producing

disposition of “the body of the artisan.” One of the many things Maurice Merleau-Ponty

does in his study on the phenomenology of perception is to reestablish the authority of

the human body as a genuine source of knowledge. Merleau-Ponty discusses the notion

of schéma corporel—Paul Schilder’s Körperschema—which he uses to explain the total

awareness of the body’s movements (gestes) in the surrounding world. It is in fact only

through the action of the body in space that one grasps how the former occupies the

latter.689 Understanding the world is not simply an act of reason: it involves the whole

body. The body, Merleau-Ponty argues, is the vehicle of a being in the world. To have a

body is to be incorporated into a delineated milieu and to continuously engage with its

substance.690 A body is not in space, but inhabits space. There is a knowledge of this

space (lieu) that is unexplainable through a rational description or a silent geste.

689 Maurice Merleau-Ponty, Phénoménologie de la perception (Paris: Gallimard, 1945), 119 where the author writes: “c’est évidemment dans l’action que la spatialité du corps s’accomplit et l’analyse du mouvement propre doit nous permettre de la comprendre mieux. On voit mieux, en considérant le corps en mouvement, comment il habite l’espace (et d’ailleurs le temps) parce que le mouvement ne se contente pas de subir l’espace et le temps, il les assume activement, il les reprend dans leur signification originelle qui s’efface dans la banalité des situations acquises.”

690 Merleau-Ponty, Phénoménologie de la perception, 97: “Le corps est le véhicule de l’être au monde, et avoir un corps c’est pour un vivant se joindre à un milieu défini, se confondre avec certains projets et s’y engager continuellement.”

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Accordingly, it is not the objective body—the mental image of one’s own body into a

Cartesian space grid—but the phenomenological body that moves, the body mobilized by

the familiar objects, gestes and lieu in which it exists.691 The body’s motricity is the

original intention of consciousness: the latter is no longer an “I think” but rather an “I

can.” Motricity, therefore, is not a slave of consciousness. Because a body incorporates

its own world, it has no need of a rational representation. It is not subordinated to a

symbolical or objective function.692 Though a rational perception of space can eventually

liberate itself from the body’s motricity in space, one has first to inhabit that space before

objectivizing it. This non-objectivity of the inhabited space by a body in motion is what

Merleau-Ponty calls habit (habitude).

Habit is thus motion. To acquire a habit is to master a dynamics, incorporated into

the schéma corporel. The notion of habit laid out here is good for the body as well as for

an instrument attached to it. The blind walking stick, for instance, is no longer an object

for the visually impaired who wields it. The stick’s extremity has become a sensory point

improving the radius of touch of the blind. In a sense, it has become the blind’s eyes. The

perceived position of an object is not just given by the length of the stick itself, but rather

by the extent of the motion created by the arm and the stick as one. This habituation to

the stick means it has become a part of oneself and thus participates to the

voluminousness of the body.693 It has become an organum. The world of the blind is

691 Merleau-Ponty, Phénoménologie de la perception, 122-123. 692 Merleau-Ponty, Phénoménologie de la perception, 161-164. 693 Merleau-Ponty, Phénoménologie de la perception, 166-168: “S’habituer à un chapeau, à une

automobile ou à un bâton, c’est s’installer en eux, ou inversement, les faire participer à la voluminosité du corps propre. L’habitude exprime le pouvoir que nous avons de dilater notre être au monde, ou de changer d’existence en nous annexant de nouveaux instruments.” The example of the blind stick is taken from Paul Schilder. Merleau-Ponty also has a very nice example involving a pipe organ and an organist (pp. 169-170),

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thereby fully understood, fully “observed” by means of the stick’s motion. The habit is no

longer simply motion: it has become genuine perception. As Descartes claimed centuries

before, the blind stick has become a full-fledged appendix to the body, an instrumental

extension to the synthèse corporelle.694

Marcel Mauss stressed a decade before Merleau-Ponty that the “body is man’s

first and most natural instrument. Or more accurately … man’s first and most natural

technical object…”695 His description of the techniques of the body—the bodily

movements involved in child rearing, sleeping, running, swimming, jumping, dancing,

drinking, eating, washing and soaping, etc.—relied on habits that, according to Mauss,

“do not just vary with individuals and their imitations, they vary especially between

societies, educations, properties and fashions, prestiges.”696 The habits forming the

techniques of the body are utterly dependent on the physiology, psychology and

sociology of its practitioner. (Though all of these characteristics could almost be

summarized to one sphere of influence: education.) Mauss tried hard in this article to

taken from Jacques Chevalier. 694 Merleau-Ponty, Phénoménologie de la perception, 177-178: “A vrai dire, toute habitude est à la

fois motrice et perceptive parce qu’elle réside, comme nous l’avons dit, entre la perception explicite et le mouvement effectif, dans cette fonction fondamentale qui délimite à la fois notre champ de vision et notre champ d’action… L’analyse de l’habitude motrice comme extension de l’existence se prolonge donc en une analyse de l’habitude perceptive comme acquisition d’un monde.” Descartes, in the first discourse of the Dioptrique, has a similar argument apropos the blind stick. In trying to explain how we perceive colors (resulting from the reflection of light on matter) Descartes maintains that it is analogous to the blind touching different types of matter (trees, rocks, water, etc.). What is perceived by the blind, via its stick, is the different types of motion or resistance offered by various materials. The blind “sees” the material bodies surrounding him by the action of these bodies when they are sensed by the stick. It is in fact comparable to seeing with one’s eyes. Seeing results not only from the invisible action of the objects towards the eye, but from the eyes’s action tending towards the objects to be seen. The blind perceives his surroundings with its stick the same way normal seeing individual does it: through the action of an instrument, or organ. The stick and the human eye are simply analogous. Descartes, Dioptrique, in Œuvres de Descartes, ed. by Charles Adam and Paul Tannery, 11 vols (Paris: J. Vrin, 1996), vi:85-86.

695 Marcel Mauss, “Techniques of the body,” Economy and Society 2 (1973), 70-88, quote on p. 75.

696 Mauss, “Techniques of the body,” 73.

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The organum scientiæ and the Production of Natural Philosophical Knowledge

develop his conceptual scheme while disregarding the material culture. The fact remains,

however, that his article is filled with references to objects, or instruments—the examples

of the French spades during World War I or the Kabyle going downstairs with slippers

(babouches) come to mind. Body and object cannot be separated that easily.

That is Jean-Pierre Warnier’s take on Mauss. Starting from the techniques of the

body, Warnier emphasizes the “natural” integration of technological objects to the

schéma corporel. He does not claim, however, that technical objects are “incorporated”

to one’s body—the objects’ materiality always remains exterior to the human body. What

is incorporated instead is the dynamics of the object. An object’s embodiment (faire

corps avec l’objet) means that the body has memorized the exact and appropriate gestes,

which can then be repeated without any effort nor special attention.697 Had Mauss

understood this notion, his example of the Kabyle “man-with-slippers” would have

suggested to him that “‘the body’ he was interested in is not the anatomo-physiological

sum total of all the human organs, it is a dynamic synthesis of sensori-motricity in a

given materiality.”698 In the case of Pascal’s arithmetical machine discussed in Chapter

three, it was thus the dynamics of the machine that was embodied, not the material entity

itself. In fact, I argued that memory had shifted from the mind to the body. Once the

697 Jean-Pierre Warnier, Construire la culture matérielle. L’Homme qui pensait avec ses doigts (Paris: Presses Universitaires de France, 1999), 9-35. Warnier writes: “Je parlerai d’incorporation, non pas de l’objet, puisque l’objet reste extérieur au corps du sujet, mais de sa dynamique qui, elle, est intériorisée par la prise que le sujet exerce sur l’objet… L’incorporation de la dynamique de l’objet s’effectue par la mise au point de conduites motrices mémorisées par le corps et qui se manifestent par des stéréotypes moteurs. Ce sont des gestes ou des séries de gestes qui, à force de répétition, peuvent être effectués sans effort ni attention particulière, avec efficacité, dans la plus grande économie de moyens.” (p. 11) For a similar conceptual approach to material culture, see Marie-Pierre Julien and Jean-Pierre Warnier, eds., Approches de la culture matérielle. Corps à corps avec l’objet (Paris: L’Harmattan, 1999) and Bernard Conein, Nicolas Dodier and Laurent Thévenot, eds., Les Objets dans l’action. De la maison au laboratoire (Paris: Éditions de l’École des Hautes Études en Sciences Sociales, 1993).

698 Jean-Pierre Warnier, “A praxeological approach to subjectivation in a material world,” Journal of Material Culture 6 (2001), 5-24, quote on p. 7.

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The organum scientiæ and the Production of Natural Philosophical Knowledge

gestes involved in the handling of the pascaline were fully memorized by the body,

performing an arithmetical operation was no longer a feat of the mind, but rather one

entirely executed by the body. The machine itself did not embody mathematics, no more

than it was embodied by anything. Without motricity—gear motion and bodily gestes—

the pascaline was merely a dry and expensive piece of craftsmanship. Arithmetical

operations, in other words, were the result of a technical object finely-tuned and properly

manipulated by techniques of the body. Mathematics, in short, moved from the absolute

sphere of the mind to the down-to-earth materiality of human existence.699

For Hobbes, and most early mondern savants, habits were not about voluntary

actions—or free will. As mentioned earlier, Hobbes contended that habits were “attained

by the weakening of such endeavours as divert its motion.” Habits were all about

constraining these “endeavours” in order to compel the body in carrying on a specific

undertaking. Hobbes used music once more to explain the effect of habit. In the case of a

“man that playeth on an instrument with his hand”

it proveth only, that the habit maketh the motion of his hand more ready and quick; but it proveth not that it maketh it more voluntary, but rather less; because

699 The arithmetical machine represents furthermore an interesting example of Pierre Parlebas’s notion of “motor stereotypes.” In the context of sports, such motor habits are developed in a domesticated, entirely controlled environment (an indoor stadium) where weather uncertainties are removed. The materiality of the setting remains unchanged to ensure that the bodily drills are performed to perfection. In the case of the artisan manufacturing the arithmetical machine, or any other object, no such controlled environment existed. Matter was capricious and unpredictable. Mersenne’s organ pipe making table was as good as the deficient industry of men, “who cannot anticipate the great multitude of occurrences which accompany lead, tin, wood, and the other materials with which the pipes are made.” Artisans making organ pipes, mechanical gears and technical objects involving bodily techniques acquired instead what Parlebas’s called “motor algorithms,” namely specialized skills elaborated around a given materiality. In sports, say basketball, the motor habits are about dribbling, jumping, shooting and passing the ball, etc. These skills have to be constantly adjusted according to the unpredictable events occurring on a basketball court. In the world of craftsmanship, such tweaking could be easily compared to Smith’s bodily struggle with matter. The struggling, needless to say, does not come from a lack of skills, habitus, but rather from the ever changing state of materiality. Pierre Parlebas, Jeux, sports et sociétés. Lexique de praxéologie motrice (Paris: INSEP, 1999). For an analysis, see Warnier, “A praxeological approach to subjectivation in a material world,” 9.

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The organum scientiæ and the Production of Natural Philosophical Knowledge

the rest of the motions follow the first by an easiness acquired from long custom; in which motion the will doth not accompany all the strokes of the hand, but gives a beginning to them only in the first.700

The habitus in corpore, in other words, was not endowed with the power of creation ars

and scientia possessed in relation to the habitus in anima. With regard to the pascaline,

habitus in anima created the machine’s design; the bodily skills of the habitus in corpore

built it and set in motion. Yet both body and mind played a determinate role here.

Through Pascal’s machine—instrument, organum—we see the perfect coalescence of

early modern theoretical and practical knowledge.

I tried in this chapter, and throughout the dissertation, to call attention to the fact

that early modern habits of knowledge were as much about the savants’ minds as the

artisans’ abilities and the material culture of natural philosophy. Habit is the accurate

word here, because whether one dealt with ideas or matter they both involved special

repetitive training and skills to achieve their end. Whether it has to do with Descartes’s

sagacitas and perspicacitas or Mersenne’s organ pipe makers, body and mind have to

receive some sort of specialized training and education. These were surprisingly

equivalent, yet highly dissimilar. We have seen in this chapter how different was the

early modern habitus in anima from the habitus in corpore. While the former (ars,

scientia and sapientia) could be associated to intellectual virtues, the latter was all about

mechanical motion and bodily gestes. Whereas the former created knowledge, the latter

simply replicated deeds and material objects. They were habits nonetheless, which meant

they were all aiming at a specific end. Hence the epistemic value derived from the

700 Hobbes, Questions concerning liberty, necessity and chance. Clearly stated and debated between D. Brahmall Bishop of Derry, and Thomas Hobbes of Malmesbury (London, 1658), in Hobbes, The English works of Thomas Hobbes of Malmesbury, 354.

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The organum scientiæ and the Production of Natural Philosophical Knowledge

concept of organum. The instrument of knowledge, the organum scientiæ, was

represented as linking in the end both the mind and the body—the method as well as the

modus operandi. This, at least, is what I believe was demonstrated in this dissertation.

367

REFERENCES

PRIMARY LITERATURE

Académie des sciences, Procès-verbaux de l’Académie royale des sciences, Registre de mathématiques et de physique, 18 vols. (1667-1698). Amontons, Guillaume. Remarques et experiences phisiques sur la construction d’une clepsidre, sur les Barometres, Termometres, & Higrometres (Paris, 1690). Anonymous, Newes from Pauls: Containing A Relation of the angry Disputation betwixt the two Church-Quarrellers, Orange-Tawnie and Purple: Being A Contention about the Lawfulnesse or Unlawfulnesse of Organs and other Ceremonies (London, 1642). Apianus, Petrus. Instrvmentvm primi mobilis… (Nuremberg, 1534). Aquinas, Thomas. The Summa theologica of St. Thomas Aquinas, 2nd ed. (1920). Internet resource http://www.newadvent.org/summa/. ———. Opera omnia, 28 vols. (New York: Musurgia Publishers, 1948- [1852-1873]). Arnaud, Antoine and Pierre Nicole, La Logique de Port-Royal, ed. by Alfred Fouillée, new ed. (Paris: Librairie Classique d’Eugène Belin, 1878 [1662]). Aristotle. The Complete Works of Aristotle, ed. by Jonathan Barnes, 2 vols. (Princeton: Princeton University Press, 1984-1985) [Taken from Past Masters internet resource http://library.nlx.com.] Bacon, Francis. The New Organon, ed. by Lisa Jardine and Michael Silverthorne (Cambridge: Cambridge University Press, 2000). ———. Sylva Sylvarum: Or a Natural History, in Ten Centuries (London, 1683). ———. New Atlantis and the Great Instauration, ed. by Jerry Weinberger, rev. ed. (Wheeling, Ill.: Harlan Davidson, Inc., 1989). Baillet, Adrien. La Vie de Monsieur Des-Cartes, 2 vols. (Paris: Chez Daniel Horthemels, 1691). Battell, Ralph. The lawfulness and expediency of church-musick asserted in a sermon preached at St. Brides-Church… (London, 1694-95).

References

Bayle, François. Discours sur l’experience et la raison, dans lequel on montre la necessité de les joindre dans la physique, dans la medecine, & dans la chirurgie (Paris, 1675). Beeckman, Isaac. Journal tenu par Isaac Beeckman de 1604 à 1634, publié avec une introduction et des notes par Cornélis de Waard, 4 vols. (The Hague: M. Nijhoff, 1939-1953). Besson, Jacques. Theatrum instrumentorum machinarum (Orleans, 1569). Bion, Nicolas. Traité de la construction et des principaux usages des instrumens de mathematique. Avec les figures necessaires pour l’intelligence de ce traité… (Paris, 1709). Birch, Thomas. The history of the Royal society of London for improving of natural knowledge, from its first rise. In which the most considerable of those papers communicated to the society, which have hitherto not been published, are inserted in their proper order, as a supplement to the Philosophical Transactions, 4 vols. (London, 1756-57). Bodin, Jean. Les Six livres de la République (Paris: Fayard, 1986). Boethius, Anicius Manlius Severinus. Fundamentals of Music, transl. by Calvin M. Bower (New Haven: Yale University Press, 1989). Boileau, Etienne. Les Métiers et corporations de la ville de Paris, XIIIe siècle. Le Livre des métiers d’Etienne Boileau, publié par René de Lespinasse et François Bonnardot (Paris: Imprimerie nationale, 1879). Borel, Pierre. A Summary or Compendium, of the Life of the Most Famous Philosopher Renatus Descartes / Written Originally in Latin by Peter Borellus...; to which is also added an epitome of his life by Marcus Zurius Boxhornius... (London: Printed by E. Oakes, for George Palmer..., 1670). Briggs, Henry. Arithmetica logarithmica sive Logarithmorum chiliades triginta, pro numeris naturali serie crescentibus ab unitate ad 20,000: et a 90,000 ad 100,000 Quorum ope multa perficiuntur arithmetica problemata et geometrica. Hos numeros primus invenit clarissimus vir Iohannes Neperus baro Merchistonij: eos autem ex eiusdem sententia mutavit, eorumque ortum et vsum illustravit Henricus Briggius, in celeberrima Academia Oxoniensi geometriae professor Savilianus (London, 1624). Brookbank, Joseph. The well-tuned organ, or, An exercitation wherein this question is fully and largely discussed, whether or no instrumental and organickal musick be lawful in holy publick assemblies… (London, 1660).

369

References

Brouncker, Lord W. Renatus Descartes excellent compendium of musick: with necessary and judicious animadversions therupon (London, 1653). Brugmans, Henri-L. Le séjour de Christian Huygens à Paris et ses relations avec les milieux scientifiques français, suivi de son Journal de voyage à Paris et à Londres (Paris: Impressions Pierre André, 1935). Bullard, Beth, transl. and ed. Musica getutscht: A Treatise on Musical Instruments (1511) by Sebastian Virdung (Cambridge: Cambridge University Press, 1993). Buot, Jacques. Vsage de la rove de proportion, Sur laquelle on pratique promptement & facilement toutes les Reigles de l’Arithmetique & les Analogies de la Trigonometrie Geometrique & Astronomique. Oevvre tres-necessaire aux Marchands, Banquiers, Asseeurs des Tailles, Ingenieurs, Astronomes, &c. (Paris, 1647). Caus, Salomon de. Institutions harmoniques (Frankfurt, 1615). ———. Les Raisons des forces movvantes Auec diuerses Machines tant vtilles que plaisantes Aus quelles sont adioints plusieurs deβeings de grotes et fontaines (Frankfurt, 1615). Charron, Pierre. De la sagesse (Paris: Fayard, 1986). Cottingham, John, ed. Descartes’ Conversation with Burman (New York: Oxford University Press, 1976). Dansie, John. A Mathematicall manuel: Wherein Is handled Arithmeticke, planimetry, stereometry, and the embattelling of armies. Whereby any man that can but add and subtract, may learne to multiply and divide in two houres by rabdologie, without any trouble at all to the memorie. Whereunto is annexed the measuring of superficies, solids, the gageing of caske, with inuention of proportionall numbers, fitted to the subdiuisions of gageing rods; and the embattelling of armies according to the discipline now in vse. Written by Iohn Dansie student in the mathematiques (London, 1627). Denis, Jean. Traité de l’accord de l’espinette, new introduction by Alan Curtis (New York: Da Capo Press, 1969 [second ed. of 1650]). Descartes, René. Abrégé de musique, transl. and ed. by Frédéric de Buzon (Paris: Presses universitaires de France, 1987). ———. Règles utiles et claires pour la direction de l’esprit en la recherche de la vérité, ed. and transl. by Jean-Luc Marion (The Hague: Nijhoff, 1977). ———. Œuvres de Descartes, ed. by Charles Adam and Paul Tannery, 11 vols. (Paris: J. Vrin, 1996).

370

References

———. The Philosophical Writings of Descartes, transl. by John Cottingham, Robert Stoothoff, and Dugald Murdoch, 3 vols. (Cambridge: Cambridge University Press, 1984-1991). Dupleix, Scipion. La Logique ou art de discourir et raisonner (Paris: Fayard, 1984 [1607]). ———. L’Éthique, ou philosophie morale (Paris: Fayard, 1994 [1645]). Erasmus, Les Préfaces au Novum testamentum (1516), ed. by Yves Delègue, with the collaboration of J. P. Gillet (Geneva: Labor et Fides, 1990). Estienne, Robert. Dictionarium latinogallicum (1552). Floquet, A. Diaire ou journal du voyage du chancelier Séguier en Normandie après la sédition des nu-pieds (1639-1640) et documents relatifs à ce voyage et à la sédition (Rouen: Edouard Frère, 1842). Fontenelle, Bernard Le Bovier de. Histoire de l’Académie royale des sciences, 2 vols. (Paris, 1733). François, Jean, S.J. L’Arithmetique ov l’art de compter tovte sorte de nombres, Auec la Plume, & les Iettons (Renne, 1653). Furetière, Antoine. Dictionnaire universel (1690). Galilei, Galileo. Sidereus nuncius or The Sidereal Messenger, transl. by Albert van Helden (Chicago: The University of Chicago Press, 1989). Galilei, Vincenzo. Dialogue on Ancient and Modern Music, transl. by Claude V. Palisca (New Haven: Yale University Press, 2003). ———. Discorso di Vincentio Galilei, nobile Fiorentino intorno all’opere di messer Gioseffo Zarlino da Chioggia (Florence, 1589). Gallon, Jean-Gaffin, ed. Machines et inventions approuvées par l’Académie royale des sciences, depuis son établissement jusqu’à present; avec leur Description. Dessinées & publiées du consentement de l’Adadémie, par M. Gallon, 7 vols. (Paris, 1735-1777). Goclenius, Rodolphus. Lexicon philosophicum (New York: Georg Olms Verlag, 1980 [1613]). Grillet, René. Curiositez mathematiques (Paris, 1673).

371

References

Gunter, Edmund. Canon triangulorum, sive Tabulae sinuum et tangentium artificialium ad radium 10000.0000. & ad scrupula prima quadrantis. Per Edm: Gunter, professorem astronomiae in Collegio Greshamensi (London, 1620). ———. De sectore & radio. The description and vse of the sector in three bookes. The description and vse of the cross-staffe in other three bookes. For such as are studious of mathematicall practise (London, 1623). Henrion, Denis. Collection, ou recveil de divers traictez mathematiques. A sçavoir; d’Artithmetique, d’Algebre, de la solution de diuers Problemes & questions, tant Geometriques, qu’Astronomiques. Comme außi de plusieurs moyens pour mesurer toutes sortes de quantitez, soient lignes, superficies & corps. Item, de la Sphere du monde, auec l’vsage & pratique, tant de l’Astrolabe, du Quarré Geometrique, & des Globes, que du compas de proportion: Et encore de la construction des fortifications pratiquées aux pays bas (Paris, 1621). ———. Logocanon, ov regle proportionnelle svr Laquelle sont appliquées plusieurs lignes & figures, diuisées selon diuerses proportions & mesures, en faueur de ceux qui se delectent en la practique des diuines Mathematiques (Paris, 1626). ———. L’Vsage du mecometre. Qvi est vn instrvment Geometrique, auec lequel on peut tres-facilement mesurer toutes sortes de longueurs & distances visibles; prendre & rapporter au petit pied le plan ndes villes, Chasteaux & autres places; trasser tant sur le papier que sur la terre telles figures & fortifications qu’on voudra; faire toutes sortes de Cartes tant Geographiques que Chorographiques; & pratiquer toutes les autres operations d’Arithmetique & de Geometrie, qui se pratiquent auec le Compas de proportion, la Regle proportionnelle, le Graphometre & la Boussole (Paris, 1630). ———. L’Vsage dv compas de proportion, 4th ed. (Paris, 1631). Hettrick, William E., transl. and ed. The ‘Musica instrumentalis deudsch’ of Martin Agricola: A Treatise on Musical Instruments, 1529-1545 (Cambridge: Cambridge University Press, 1994). Hobbes, Thomas. Elements of Philosophy in The English Works of Thomas Hobbes of Malmesbury, ed. by Sir William Molesworth, 11 vols. (London: J. Bohn, 1839-1845). [Taken from Past Masters internet resource http://library.nlx.com.] Hubin, Machines nouvellement executees, et en partie inventees Par le sieur Hvbin, Emailleur du Roy. Premiere partie, ov se trouvent une Clepsydre, deux Zymosimetres, un Peze-liqueur, & un Themometre. Avec quelques Observations faites à Orleans, sur les qualitez de l’Air, & particulierement sur sa pesanteur (Paris, 1673). Huygens, Christiaan. Oeuvres complètes, 22 vols. (The Hague: M. Nijhoff, 1888-).

372

References

Huygens, Constantijn. Use and Nonuse of the Organ in the Churches of the United Netherlands, transl. and ed. by Ericka E. Smit-Vanrotte (Brooklyn, N.Y.: Institute of Mediaeval Music, 1964). Jean, Alexandre. Arithmetiqve au miroir. Par laquelle on peut (en quatre vaccations de demie heure chacune) pratiquer les plus belles regles d’icelle (n.p., 1637). Journal des sçavans (1665-1695). Kircher, Athanasius. Musurgia universalis, sive Ars magna consoni et dissoni, 2 vols. (Rome, 1650; facsimile Hildesheim, Zürich, New York: Georg Olms Verlag, 2004). ———. Correspondence. A project established by Michael John Gorman and Nick Wilding. Internet resource http://193.206.220.68/kircher/index.html#0. Lespinasse, René de., ed. Les Métiers et corporations de la ville de Paris, XIVe-XVIIIe siècles, 3 vols. (Paris: Imprimerie nationale, 1886-1897). Leupold, Jacob. Theatrum arithmetico-geometricum, das ist: Schau-Platz der Rechen- und Mess-Kunst, darinnen enthalten dieser beyden Wissenschaften nöthige Grund-Regeln und Handgriffe so wohl, als auch die unterschiedene Instrumente und Machinen, welche theils in der Ausübung auf den Papier theils auch im Felde besonderen Vortheil geben können, in sonderheit wird hierinnen erklaärt (Leipzig, 1727 [Hannover: Th. Schäfer, 1982]). Lister, Martin. A Journey to Paris in the Year 1698 (London, 1699). Loyseau, Charles. A Treatise of Orders and Plain Dignities, ed. and transl. by Howell A. Lloyd (Cambridge: Cambridge University Press, 1994 [1610]). Mayne, John. Socius mercatoris: or The merchant's companion: in three parts. The first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. The second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. The third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. By John Mayne, philo-accomptant. (London, 1674). Mei, Girolamo. Letters on Ancient and Modern Music to Vincenzo Galilei and Giovanni Bardi, annotated by Claude V. Palisca ([n. p.]: American Institute of Musicology, 1960). Mersenne, Marin. Traité de l’Harmonie universelle (Paris, 1627).

373

References

———. Les Prelvdes de l’Harmonie vniverselle, ov qvestions curievses Vtiles aux Predicateurs, aux Theologiens, aux Astrologues, aux Medecins & aux Philosophes (Paris: Chez Henry Gvenon, 1634). ———. Harmonie universelle, contenant la théorie et la pratique de la musique (Paris: Centre national de la recherche scientifique, 1963 [1636-1637]). ———. Harmonie universelle: The Books on Instruments, transl. by Roger E. Chapman (The Hague: M. Nijhoff, 1957). ———. La Vérité des sciences contre les sceptiques ou pyrrhoniens, éd. et annotation par Dominique Descotes (Paris: Champion, 2003). ———. Qvestions inovyes, ov recreation des sçavans (Paris, 1634; facsimile Stuttgart: F. Frommann, 1972). ———. Correspondance du P. Marin Mersenne: religieux minime, ed. and annotated by Cornélis de Waard (with the collaboration of René Pintard), 17 vols. (Paris: G. Beauchesne, 1933-1988). Miller, Clement A., transl. and ed. Hieronymus Cardanus (1501-1576): Writings on Music ([n. p.]: American Institute of Musicology, 1973). Monchrestien, Antoine de. Traicté de l’œconomie politique, ed. by François Billacois (Geneva: Droz, 1999). Monconys, Balthasar de. Journal des voyages de Monsieur Monconys, Conseiller du Roy en ses Conseils d’Estat & Privé, & Lieutenant Criminel au Siege Presidial de Lyon. Où les Sçavants trouveront un nombre infini de nouveautez, en Machines de Mathematique, Experiences Physiques, Raisonnemens de la belle Philosophie, curiositez de Chymie, & conversations des Illustres de ce Siecle... 3 vols. (Lyon, 1665-1666). Montaigne, Michel de. Les Essais (Paris: Le Livre de Poche, 2001 [1595]). Napier, John. Mirifici logarithmorum canonis descriptio, ejusque usus, in utraque trigonometria, ut etiam in omni logistica mathematica, amplissimi, facillimi, & expeditissimi explicatio. Authore ac inventore, Ioanne Nepero, Barone Merchistonii, &c. Scoto. (Edinburgh, 1614). ———. A description of the admirable table oe [sic] logarithmes with a declaration of the most plentiful, easy, and speedy vse thereof in both kindes of trigonometrie, as also in all mathematicall calculations / invented and published in Latin by that honorable L. Iohn Nepair ... ; and translated into English by the late learned and famous mathematician Edward Wright; with an addition of an instrumentall table to finde the part proportionall, inuented by the translator, and described in the end of the booke by Henry Brigs ... ; all perused and approued by the author, & published since the death of

374

References

the translator (London, 1616). ———. Rabdologiae, seu Numerationis per virgulas libri duo cum appendice de expeditissimo multiplicationis promptuario. Quibus accessit & arithmeticae localis liber vnus. Authore & inventore Ioanne Nepero, Barone Merchistonii, &c. Scoto (Edinburgh, 1617). ———. Rabdology, transl. by William F. Richardson (Cambridge, MA: MIT Press, 1990). Newte, John. Mr. Newte’s sermon concerning the lawfulness and use of organ in the Christian church (London, 1696). Nicéron, Jean-Pierre. Mémoires pour servir à l’histoire des hommes illustres dans la république des lettres, 44 vols. (Paris, 1727-1745). Nicot, Jean. Thresor de la langue française tant ancienne que moderne (1606). Orleans, Cherubin d’. La dioptriqve ocvlaire, ov la theorique, la positive, et la mechaniqve, de l’ocvlaire dioptriqve en tovtes ses especes (Paris: chez Thomas Jolly, au palais, et Simon Bernard, ruë S. Jacques, aux Armes de Hollande, 1671). Palisca, Claude V. G.B. Doni’s Lyra Barberina (Bologna: A.M.I.S., 1981). Palissy, Bernard. Oeuvres complètes, ed. by Marie-Madeleine Fragonard, 2 vols. (Mont-de-Marsan: Editions InterUniversitaires, 1996). Paré, Ambroise. Oeuvres complètes, revues et collationnées sur toutes les éditions..., 3 vols. (Paris and London: Chez J.-B. Baillière, 1840-1841). Paris, City of. Registres des délibérations du bureau de la ville de Paris, publiés par les soins du Service historique, 20 vols. (Paris: Imprimerie nationale, 1883-1984). Partridge, Seth. Rabdologia, or, The art of numbring by rods whereby the tedious operations of multiplication, and division, and of extraction of roots, both square and cubick, are avoided, being for the most part performed by addition and subtraction: with many examples for the practice of the same: first invented by the Lord Napier, Baron of Marchiston, and since explained, and made usefull for all sorts of men (London, 1648). Pascal, Blaise. Oeuvres complètes, ed. by Jean Mesnard, 4 vols. (Paris: Desclée de Brouwer, 1964-1992). ———. Pensées, ed. by Gérard Ferreyrolles (Paris: Le Livre de Poche, 2000).

375

References

Petit, Pierre. Dissertations academiques sur la nature du froid et du chaud. Avec un Discours sur la construction & l’usage d’un Cylindre Arithmetique, inventé par le mesme Autheur (Paris, 1653). [Picot, Jean-Baptiste]. Explication des modeles des machines et forces mouvantes, que l’on expose à Paris dans la ruë de la Harpe vis-à-vis Saint Cosme (Paris, 1683). Prætorius, Michael. Syntagma musicum II: De organographia, transl. and ed. by David Z. Crookes (Oxford: Clarendon Press, 1986). ———. Syntagma musicum: Textes relatifs à l’orgue, comprenant aussi la basse générale ou continue, transl. and ed. by Jacques Leguy (Chatenay Malabry: Éditions Ars Musicæ, 1999). Reading, John. A sermon delivered in the Cathedral Church of Canterbury, concerning church-musick… (London, 1663). Rohault, Jacques. Traité de physique, 2 vols. (Paris: De l’imprimerie de Denys Thierry, 1671). Recueil des edits, declarations, arrests, et reglemens concernant les arts et metiers de Paris & autres villes du royaume (Paris: Chez Charles Saugrain, 1701). Rossetti, Biagio. Libellus de rudimentis musices, ed. by Albert Seay, Critical Texts, no. 12 (Colorado Springs: Colorado College Music Press, 1981), 1-60. (Taken from the Thesavrvs mvsicarvm latinarvm, Center for the History of Music and Literature, University of Indiana. Internet resource http://www.music.indiana.edu/tml/14th/ZAMLAM_TEXT.html.) Morland, Samuel. A New and Most Useful Instrument for Adition and Subtraction of Pounds, Shillings, Pence, and Farthings (London, 1672). Schott, Gaspar. Organum mathematicum libris IX explicatum (Herbipoli [Würzburg], 1668). Schütz, Ludwig. Thomas-Lexikon: Sammlung, Übersetzung und Erklärung der in sämtlichen Werken des hl. Thomas von Aquin vorkommenden Kunstausdrücke und wissenschaftlichen Aussprüche. Internet resource http://www.corpusthomisticum.org/tl.html. Sorbiere, Samuel. Relations, lettres et discours de Mr de Sorbiere sur diverses matieres curieuses (Paris, 1660). ———. Lettres et discours de Mr de Sorbiere sur diverses matieres curieuses (Paris, 1660).

376

References

Towerson, Gabriel. A sermon concerning vocal and instrumental musick in the church as it was delivered in the parish church of St. Andrew Undershaft, upon the 31th of May, 1696, being Whit-Sunday, and the day wherein the organ there erected was first made use of (London, 1696). Trenchant, Jean. L’Arithmetique de Iean Trenchant, Departie en trois liures. Ensemble vn petit discours des Changes. Auec l’art de calculer aux Getons. Reueuë & augmentee en ceste derniere edition, tant de plusieurs regles & articles, par l’Autheur, que d’vne Table de poids de vingt deux Prouinces, correspondans l’vne à l’autre (Paris, 1618). Trichet, Pierre. Traité des instruments de musique (vers 1640), ed. by François Lesure (Neuilly-sur-Seine: Société de musique d’autrefois, 1957). Vlacq, Adriaen. Arithmetiqve logarithmetiqve ov la constrvction et vsage d’vne table contenant les Logarithmes de tous les Nombres depuis l’Vnité jusques à 100000. Et d’vne avtre table en laquelle sont comprins les Logarithmes des Sinus, Tangentes & Secantes, de tous les Degrez et Minutes du quart du Cercle, selon le Raid de 10,00000,0000 parties. Par le moyen desqvelles on resovlt tres-facilement les Problemes Arithmetiques & Geometriques. Ces nombres premierement sont inventez par Iean Neper Baron de Marchiston: Mais Henry Brigs Professeur de la Geometrie en l’Vniversité d’Oxford, les a changé, & leur Nature, Origines, & Vsage illustré selon l’intention du dit Neper (Gouda, 1628). Wingate, Edmund. Arithmetique made easie in tvvo bookes. The former, of naturall arithmetique: containing a perfect method for the true knowledge and practice of arithmetique, according to the ancient vulgar way, without dependance vpon any other author for the grounds thereof. The other of artificiall arithmetique, discovering how to resolve all questions of arithmetique by addition and subtraction. Together with an appendix, resolving likewise by addition and subtraction all questions, that concerne equation of time, interest of money, and valuation of purchases, leases, annuities, and the like (London, 1630). ———. Logarithmotechnia, or The construction, and use of the logarithmeticall tables by the help of which, multiplication is performed by addition, division by subtraction, the extraction of the square root by bipartition, and of the cube root by tripartition, &c. Finally, the golden rule, and the resolution of triangles, as well right lined, as sphericall by addition and subtraction. First published in the French tongue by Edmund Wingate, an English gentleman: and after translated into English by the same author (London, 1635). Zamorensis, Johannes Aegidius. Ars musica, in Scriptores ecclesiastici de musica sacra potissimum, 3 vols., ed. by Martin Gerbert (St. Blaise: Typis San-Blasianis, 1784; reprint ed., Hildesheim: Olms, 1963). [Taken from the Thesavrvs mvsicarvm latinarvm, Center for the History of Music and Literature, University of Indiana. Internet resource http://www.music.indiana.edu/tml/14th/ZAMLAM_TEXT.html.]

377

References

Zarlino, Gioseffo. Sopplimenti musicali del rev. M. Gioseffo Zarlino da Chioggia… (Venice, 1588). ———. Le Istitutioni harmoniche (Venice, 1561; facsimile of the second edition, Arnaldo Forni Editore, 1999).

SECONDARY LITERATURE

Ackermann, Robert J. Data, Instruments, and Theory: A Dialectical Approach to Understanding (Princeton: Princeton University Press, 1985). Adkins, Cecil. “Trumpet marine,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Alder, Ken, ed. “Focus: Thick Things,” Isis 98 (2007): 80-142. ———. “Making Things the Same: Representation, Tolerance, and the End of the Old Regime in France,” Social Studies of Science 28 (1998): 499-545. Alexander, Amir. Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (Stanford: Stanford University Press, 2002). Alpers, Svetlana. The Art of Describing: Dutch Art in the Seventeenth Century (Chicago: The University of Chicago Press, 1983). Amelang, James S. The Flight of Icarus: Artisan Autobiography in Early Modern Europe (Stanford: Stanford University Press, 1998). Angiolini, Franco and Daniel Roche, eds. Cultures et formations négociantes dans l’Europe moderne (Paris: Editions de l’Ecole des Hautes Etudes en Sciences Sociales, 1995). Ariotti, Piero E. “Aspects of the Conception and Development of the Pendulum in the 17th Century,” Archive for the History of Exact Sciences 8 (1971-2): 329-410. Armogathe, Jean-Robert. “Le Groupe de Mersenne et la vie académique parisienne,” XVIIe siècle 174 (1992): 131-139. Arnou, René, S.J., L’Homme a-t-il le pouvoir de connaître la vérité? Réponse de Saint Thomas: La connaissance par habitus (Rome: Presses de l’Université Grégorienne, 1970). Attali, Jacques. Blaise Pascal ou le génie français (Paris: Fayard, 2000).

378

References

Arnold, Keith. “Pascal’s Theory of Scientific Knowledge,” Journal of the History of Philosophy 27 (1989): 531-544. Aucante, Vincent. La Philosophie médicale de Descartes (Paris: Presses Universitaires de France, 2006). Aufrère, Sydney. La Momie et la tempête: Nicolas-Claude Fabri de Peiresc et la curiosité égyptienne en Provence au début du XVIIe siècle (Avignon: Editions A. Barthélemy, c1990). Austern, Linda Phyllis. “‘’Tis Nature’s voice’: Music, natural philosophy and the hidden world in seventeenth-century England,” in Music Theory and Natural Order from the Renaissance to the Early Twentieth Century, ed. by Suzannah Clark and Alexander Rehding (Cambridge: Cambridge University Press, 2001), pp. 30-67. Baines, Francis, Edmund A. Bowles and Robert A. Green, “Hurdy-Gurdy,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Baird, Davis. Thing Knowledge: A Philosophy of Scientific Instruments (Berkeley: University of California Press, 2004). Bakhtin, Mikhail. Rabelais and his World, transl. by Helene Iswolsky (Bloomington: Indiana University Press, 1984). Bannard, Yorke. “Music of the Commonwealth: A Corrected Chapter in Musical History,” Music & Letters 3 (1922): 394-401. Baron, Roger. Science et sagesse chez Hugues de Saint-Victor (Paris: Lethielleux, 1957). Bates, Don. “Machina Ex Deo: William Harvey and the Meaning of Instrument,” Journal of the History of Ideas 61 (2000): 577-593. Baxandall D. and Jane Pugh, Calculating Machines and Instruments (London: Science Museum, 1975 [1926]). Beaulieu, Armand. Mersenne: le grand minime (Bruxelles: Fondation Nicolas-Claude Fabri de Peiresc, 1995). Beaurepaire, Charles de. Dernier recueil de notes historiques et archéologiques concernant le département de la Seine-Inférieure et plus spécialement la ville de Rouen (Rouen: Imprimerie de Espérance Cagniard, 1892). Belfanti, Carlo Marco. “Guilds, Patents, and the Circulation of Technical Knowledge,” Technology & Culture 45 (2004): 569-589.

379

References

Belgioioso, Giulia. “Descartes e gli artigiani,” in La Biografia intellettuale di René Descartes attraverso la Correspondance, ed. by Jean-Robert Armogathe, Giulia Belgioioso, and Carlo Vinti (Naples: Vivarium, 1999), pp. 113-165. Bennett, James A. “The Mechanics’ Philosophy and the Mechanical Philosophy,” History of Science 24 (1986): 1-28. ———. The Divided Circle: A History of Instruments for Astronomy, Navigation and Surveying (Oxford: Phaidon and Christie’s, 1987). ———. “Practical Geometry and Operative Knowledge,” Configurations 6 (1998): 195-222. ———. “Geometry in Context in the Sixteenth Century: The View from the Museum,” Early Science and Medicine 7 (2002): 214-230. ———. “Shopping for Instruments in Paris and London,” in Merchants & Marvels: Commerce, Science and Art in Early Modern Europe, ed. by Pamela H. Smith and Paula Findlen (New York: Routledge, 2002), pp. 370-395. ———. “Knowing and Doing in the Sixteenth Century: What Were Instruments For?,” British Journal for the History of Science 36 (2003): 129-150. Bercé, Yves-Marie. Croquants et nu-pieds: Les soulèvements paysans en France du XVIe au XIXe siècle (Paris: Gallimard, 1991). Berger, Anna Maria Busse. “Agricola [Sore], Martin,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Berkel, Klaas van. Isaac Beeckman (1588-1637) en de mechanisering van het wereldbeeld (Amsterdam: Rodopi, 1983). ———. “Descartes’ Debt to Beeckman: Inspiration, Cooperation, Conflict,” in Descartes’ Natural Philosophy, ed. by Stephen Gaukroger, John Schuster, and John Sutton (London: Routledge, 2000), pp. 46-59. Berryman, Sylvia. “Galen and the Mechanical Philosophy,” Apeiron: A Journal for Ancient Philosophy and Science 35 (2002): 235-253. ———. “Ancient Automata and Mechanical Explanation,” Phronesis 48 (2003): 344-369. Biagioli, Mario. “The Social Status of Italian Mathematicians, 1450-1600,” History of Science 27 (1989): 41-95.

380

References

———. Galileo, Courtier: The Practice of Science in the Culture of Absolutism (Chicago: The University of Chicago Press, 1993). ———. “Etiquette, Interdependence, and Sociability in Seventeenth-Century Science,” Critical Inquiry 22 (1996): 193-238. ———. “Replication or Monopoly? The Economies of Invention and Discovery in Galileo's Observations of 1610,” Science in Context 13 (2000): 547-590. ———. “From Print to Patents: Living on Instruments in Early Modern Europe,” History of Science 44 (2006): 139-186. ———. Galileo’s Instrument of Credit: Telescopes, Images, Secrecy (Chicago: University of Chicago Press, 2006). Birembaut, Arthur. “L’exposition de modèles de machines à Paris en 1683,” Revue d’histoire des sciences 20 (1967): 141-158. Birn, Raymond. Le Journal des savants sous l’ancien régime (Paris: Klincksieck, 1965). Bjelic, Dusan I. Galileo’s Pendulum. Science, Sexuality, and the Body-Instrument Link (Albany: State University of New York Press, 2003). Blaise Pascal: mathématicien, physicien, ingénieur. 350e anniversaire de la conception de la machine arithmétique (Clermont-Ferrand: Bibliothèque Municipale et Interuniversitaire, 1993). Blake, Ralph M. “The Rôle of Experience in Descartes’ Theory of Method (I),” The Philosophical Review 38 (1929): 125-143. ———. “The Rôle of Experience in Descartes’ Theory of Method (II),” The Philosophical Review 38 (1929): 201-218. Blackwell, Richard J., ed. Christiaan Huygens’ Pendulum Clock or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks (Ames: The Iowa State University Press, 1986). Blanchard, Jean-Vincent. L’Optique du discours au XVIIe siècle. De la rhétorique des jésuites au style de la raison moderne (Descartes, Pascal) (Québec: Les Presses de l’Université Laval, 2005). Bonney, Richard. The Limits of Absolutism in Ancien Régime France (Aldershot, England; Brookfield, VT: Variorum, 1995). Borkenau, Franz. “The Sociology of the Mechanistic World-Picture,” Science in Context 1 (1988): 109-27.

381

References

Bos, Hendrik J. M., ed. Studies on Christiaan Huygens (Lisse: Swets & Zeitlinger, 1980). ———. “On the Representation of Curves in Descartes’ Géométrie,” Archives for the History of Exact Sciences 24 (1981): 295-338. Boschiero, Luciano. “Natural Philosophical Contention Inside the Accademia del Cimento: The Properties and Effects of Heat and Cold,” Annals of science 60 (2003): 329-349. Bottin, Jacques and Jochen Hook, “Structures et formes d’organisation du commerce à Rouen au début du 17e siècle: le cas de Michel van Damme,” in Le Négoce international, XIIIe-XXe siècle, ed. by François M. Crouzet (Paris: Economica, 1989), pp. 59-93. Bourdieu, Pierre. Le Sens pratique (Paris: Editions de Minuit, 1980). ———. Raisons pratiques: sur la théorie de l’action (Paris: Seuil, 1994). ———. Méditations pascaliennes (Paris: Seuil, 1997). Bowles, Edmund A. “Were Musical Instruments Used in the Liturgical Service During the Middle Ages?,” The Galpin Society Journal 10 (1957): 40-56. ———. “La hiérarchie des instruments de musique dans l’Europe féodale,” Revue de musicologie 42 (1958): 155-169. Bredekamp, Horst. Galilei der Künstler: der Mond, die Sonne, die Hand (Berlin: Akademie Verlag, 2007). Brentjes, Sonja. Peiresc’s Interests in the Middle East and Northern Africa in Respect to Geography and Cartography (Berlin: Max Planck Institute for the History of Science [preprint 269], 2004). Bresson, Agnès. “Le cabinet de Peiresc et de quelques autres.” Internet resource http://www.peiresc.org/Cabinet.html. Brian, Eric and Christiane Demeulenaere-Douyère. Histoire et mémoire de l’Académie royale des sciences: guide de recherches (London, Paris, New York: Tec & Doc, 1996). Briggs, Robin. “The Académie des sciences and the Pursuit of Utility,” Past and Present 131 (1991): 38-88. Brown, Bill. “Thing Theory,” Critical Inquiry 28 (2001): 1-22. Brown, Harcourt. Scientific Organizations in Seventeenth-Century France (1620-1680) (Baltimore: Williams & Wilkins, 1934).

382

References

Bruinsma, Henry A. “The Organ Controversy in the Netherlands Reformation to 1640,” Journal of the American Musicological Society 7 (1954): 205-212 Brunelle, Gayle K. The New World Merchants of Rouen, 1559-1630 (Kirksville, MI: Sixteenth Century Journal Publishers, Inc., 1991). Bryden, D. J. Napier’s Bones: A History and Instruction Manual (London: Harriet Wynter Ltd., 1992). ———. “Scientific Relics: John Napier’s Bones,” Bulletin of the Scientific Instrument Society 76 (March 2003): 6-9. Buchli, Victor, ed. The Material Culture Reader (Oxford and New York: Berg, 2002). Burnett, Charles “European Knowledge of Arabic Texts Referring to Music: Some New Material,” Early Music History 12 (1993): 1-17. Burnett, D. Graham. Descartes and the Hyperbolic Quest: Lens Making Machines and Their Significance in the Seventeenth Century (Philadelphia: American Philosophical Transactions, 2005). Buszin, Walter E. “Luther on Music,” The Musical Quarterly 32 (1946): 80-97. Cajori, Florian. A History of the Logarithmic Slide Rule and Allied Instruments and On the History of Gunter’s Scale and the Slide Rule During the Seventeenth Century (Mendham, NJ: Astragal Press, 1994). Camic, Charles. “The Matter of Habit,” The American Journal of Sociology 91 (1986): 1039-1087. Cardon, Dominique. La Draperie au Moyen Âge. Essor d’une grande industrie européenne (Paris: CNRS, 1999). Carraud, Vincent. Pascal et la philosophie (Paris: Presses Universitaires de France, 1992). Carreras Juan José and Bernardo García García, eds., The Royal Chapel in the Time of the Habsburgs: Music and Ceremony in Early Modern European Court, transl. by Yolanda Acker with English edition by Tess Knighton (Woodbridge, UK: Boydell Press, 2005). Carruthers, Mary. The Book of Memory: A Study of Memory in Medieval Culture (Cambridge: Cambridge University Press, 1990). Carter, Tim and John Butt, eds. The Cambridge History of Seventeenth-Century Music (Cambridge: Cambridge University Press, 2005).

383

References

Cavaillé, Jean-Pierre. “Descartes stratège de la destination,” XVIIe siècle 177 (1992): 551-559. ———. “‘Le plus éloquent philosophe des derniers temps’: les stratégies d’auteur de René Descartes,” Annales HSS (1994): 349-367. Cazaux, Christelle. La Musique à la cour de François Ier (Paris: École Nationale des Chartes, 2002). Cazeaux, Isabelle. French Music in the Fifteenth and Sixteenth Centuries (Oxford: Basil Blackwell, 1975). Certeau, Michel de. Art de faire, in L’Invention du quotidien, 2 vols. (Paris: Union générale d’éditions, 1980). Chareix, Fabien. “Experientia ac ratio: l’œuvre de Christiaan Huygens,” Revue d’histoire des sciences 56 (2003): 5-13. ———. La Vraye et saine philosophie de Christiaan Huygens (1629-1695) (Paris: Vrin, 2004). Charette, François. Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm al-Din al-Misri (Leiden: Brill, 2003). Christianson, John Robert. On Tycho’s Island: Tycho Brahe and his Assistants, 1570-1601 (Cambridge: Cambridge University Press, 2000). Chua, Daniel K. L. “Vincenzo Galilei, Modernity and the Division of Nature,” in Music Theory and Natural Order from the Renaissance to the Early Twentieth Century, ed. by Suzannah Clark and Alexander Rehding (Cambridge: Cambridge University Press, 2001). Clark, Elizabeth A. History, Theory, Text: Historians and the Linguistic Turn (Cambridge, MA: Harvard University Press, 2004). Clarke, Desmond M. Descartes’s Philosophy of Science (Manchester: Manchester University Press, c1982). Cohen, H. Floris. Quantifying Music: The Science of Music at the First Stage of the Scientific Revolution, 1580-1650 (Dordrecht: D. Reidel Publishing Company, 1984). ———. The Scientific Revolution: A Historiographical Inquiry (Chicago: The University of Chicago Press, 1993). Cohen, Sarah R. Art, Dance, and the Body in French Culture of Ancien Régime (Cambridge: Cambridge University Press, 2000).

384

References

Collins, Harry M. Changing Order: Replication and Induction in Scientific Practice (Chicago: The University of Chicago Press, 1992 [1985]). Conein, Bernard, Nicolas Dodier and Laurent Thévenot, eds. Les Objets dans l’action. De la maison au laboratoire (Paris: Éditions de l’École des Hautes Études en Sciences Sociales, 1993). Conner, Clifford D. A People’s History of Science: Miners, Midwives, and “Low Mechanicks” (New York: Nation Books, 2005). Cook, Harold J. Matters of Exchange: Commerce, Medicine, and Science in the Dutch Golden Age (New Haven: Yale University Press, 2007). Coquery, Natacha. L’Hôtel aristocratique. Le Marché du luxe à Paris au XVIIIe siècle (Paris: Editions de la Sorbonne, 1998). ———, ed. La Boutique et la ville. Commerces, commerçants, espaces et clientèles, XVIe-XXe siècle (Tours: Publication de l’Université François Rabelais, 2000). Corrette, Michel. La Belle vielleuse, introduction by Claude Flagel (Saint-Denis-le-Gast: J.F. Détrée, 1978). Court, Raymond. Sagesse de l’art (arts plastiques, musique, philosophie) (Paris: Méridiens Klincksieck, 1987). Crouzet, Denis. Les Guerriers de Dieu. La Violence au temps des troubles de religion (vers 1525-1610), 2 vols. (Seyssel: Champ Vallon, 1990). Daston, Lorraine. “Marvelous Facts and Miraculous Evidence in Early Modern Europe,” Critical Inquiry 18 (1991): 93-124. ——— and Katharine Park, Wonders and the Order of Nature (New York: Zone Books, 1998). ———, ed. Biographies of Scientific Objects (Chicago: The University of Chicago, 2000). ———, ed. Things that Talk: Object Lessons from Art and Science (New York: Zone Books, 2004). ——— and Peter Galison, Objectivity (New York: Zone Books, 2007). Daumas, Maurice. Les Instruments scientifiques aux XVIIe et XVIIIe siècles (Paris: Presses Universitaires de France, 1953). Davidson, Hugh M. Pascal and the Arts of the Mind (Cambridge: Cambridge University Press, 1993).

385

References

Davis, Natalie Zemon. “Mathematicians in the Sixteenth-Century French Academies: Some Further Evidence,” Renaissance News 11 (1958): 3-10. ———. “Sixteenth-Century French Arithmetics on the Business Life,” Journal of the History of Ideas 21 (1960): 18-48. Dear, Peter. Mersenne and the Learning of the Schools (Ithaca: Cornell University Press, 1988). ———. Discipline and Experience: the Mathematical Way in the Scientific Revolution (Chicago: The University of Chicago Press, 1995). ———. “A Mechanical Microcosm: Bodily Passions, Good Manners, and Cartesian Mechanism,” in Science Incarnate: Historical Embodiments of Natural Knowledge, ed. by Christopher Lawrence and Steven Shapin (Chicago: The University of Chicago Press, 1998), pp. 51-82. ———. Revolutionizing the Sciences: European Knowledge and Its Ambitions, 1500-1700 (Princeton: Princeton University Press, 2001). Des Chene, Dennis. Spirits and Clocks: Machine and Organism in Descartes (Ithaca: Cornell University Press, 2001). Descotes, Dominique. “Arithmétique et littérature: le “Potestatum numericarum summa,” Revue des Sciences Humaines 244 (1996): 53-79. Detienne, Marcel and Jean-Pierre Vernant. Les Ruses de l’intelligence. La mètis des Grecs (Paris: Flammarion, 1974). Develle, E. Les Horlogers blésois au XVIe et au XVIIe siècle (Blois: Emmanuel Rivière, Editeur, 1913). Devie, Dominique. Le Tempérament musical. Philosophie, histoire, théorie et pratique (Béziers: Société de musicologie de Languedoc, 1990). Deyon, Pierre. “Variations de la production textile aux XVIe et XVIIe siècles,” Annales: ESC 18 (1963): 921-55. Dijksterhuis, Fokko Jan. Lenses & Waves: Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century (Dordrecht: Kluwer Academic Publishers, 2004). Dournon, Geneviève. “Instrumentariums et classifications,” Revue de musicologie 79 (1993): 197-207.

386

References

Drake, Stillman. “Renaissance Music and Experimental Science,” Journal of the History of Ideas 31 (1970): 483-500. Duerr, Hans Peter. Nudité et pudeur: le mythe du processus de civilisation, transl. by Véronique Bodin and Jacqueline Pincemin (Paris: Maison des sciences de l’homme, 1998). Dufourcq, Norbert. Le Livre de l’orgue français, 1589-1789, 5 vols. (Paris: Editions A. & J. Picard, 1971-1982). Duncan, David Allen. The Tyranny of Opinions Undermined: Science, Pseudo-Science and Scepticism in the Musical Thought of Marin Mersenne (Ph.D. dissertation, Vanderbilt University, 1981). ———. “Persuading the Affections: Rhetorical Theory and Mersenne’s Advice to Harmonic Orators,” in French Musical Thought, 1600-1800, ed. by Georgia Cowart (Ann Arbor: U.M.I Research Press, 1989), pp. 148-175. Eagleton, Catherine and Boris Jardine, “Collections and Projections: Henry Sutton’s Paper Instruments,” Journal of the History of Collections 17 (2005): 1-13. Eamon, William. Science and the Secrets of Nature: Books of Secrets in Medieval and Early Modern Culture (Princeton: Princeton University Press, 1994). Eastwood, Bruce Stansfield. “Descartes on Refraction: Scientific versus Rhetorical Method,” Isis 75 (1984): 481-502. Edwardes, Ernest L. The Story of the Pendulum Clock (Altrincham: John Sherratt, 1977). Elias, Norbert. The Civilizing Process: Sociogenetic and Psychogenetic Investigations, rev. edn. (Oxford and Malden, MA.: Blackwell Publishers, 2000). Ellenberger, Michel. La Machine à calculer de Blaise Pascal (Paris: Nathan, 1993). Elzinga, Aant. “Huygens Theory of Research and Descartes’ Theory of Knowledge,” Zeitschrift für allgemeine Wissenschaftstheorie 2 (1971): 174-194; 3 (1972): 9-27. Endrei, Walter G. “The First Technical Exhibition,” Technology and Culture 9 (1968): 181-183. Epstein, Stephan R. “Craft Guilds, Apprenticeship, and Technological Change in Preindustrial Europe,” The Journal of Economic History 58 (1998): 684-713. ———. “Labour Mobility, Journeyman Organisations and Markets in Skilled Labour Europe, 14th-18th Centuries,” in Pratiques historiques de l’innovation, historicité de l’économie des savoirs (12e-19e siècles), ed. by L. Hilaire-Perez and A. Garçon (Paris,

387

References

2003). Escudier, Monique. Introduction à une étude musicale de la correspondance du Père Marin Mersenne de 1617 au 20 mars 1634, 2 vols. (Paris: Conservatoire national supérieur de musique, thèse présentée pour le Prix de Musicologie, 1972). Fabbri, Natacha. Cosmologia e armonia in Kepler e Mersenne: contrappunto a due voci sul tema dell’Harmonice mundi (Florence: L. S. Olschki, 2003). Fabbri, Paolo. “Norme et pratique du concert des voix et des instruments dans la liturgie catholique après le concile de Trente,” in Le Concert des voix et des instruments à la Renaissance, ed. by Jean-Michel Vaccaro (Paris: CNRS-Editions, 1995), pp. 97-103. Farr, James R. Hand of Honor: Artisans and Their World in Dijon, 1550-1650 (Ithaca: Cornell University Press, 1988). ———. “Cultural Analysis and Early Modern Artisans,” in The Artisan and the European Town, 1500-1900, ed. by Geoffrey Crossick (Aldershot: Scolar Press, 1997), pp. 56-74. Feingold, Mordechai. The Mathematicians’ Apprenticeship: Science, Universities, and Society in England, 1560-1640 (Cambridge: Cambridge University Press, 1984). Fenlon, Iain. “Isabella d’Este e i suoi contemporanei. Musica e mecenatismo presso le corti dell’Italia settentrionale,” in Bernardo Clesio e il suo tempo, ed. by Paolo Prodi (Rome: Bulzoni, 1986), pp. 607-637. Ferreyrolles, Gérard. Les Reines du monde. L’Imagination et la coutume chez Pascal (Paris: Honoré Champion Editeur, 1995). Field, Judith V. “What is Scientific about a Scientific Instrument?,” Nuncius 3 (1988): 3-26. Findlen, Paula. Possessing Nature: Museums, Collecting, and Scientific Culture in Early Modern Italy (Berkeley: University of California Press, 1994). Finney, Gretchen L. “‘Organical Musick’ and Ecstasy,” Journal of the History of Ideas 8 (1947): 273-292. Flagel, Claude. “La vielle parisienne sous Louis XV: un modèle pour deux siècles,” in Instrumentistes et luthiers parisiens, XVIIe-XIXe siècles, ed. by Florence Gétreau (Paris: Délégation à l’Action artistique de la ville de Paris, [1988]), pp. 117-134. Foisil, Madeleine. La Révolte des nu-pieds et les révoltes normandes de 1639 (Paris: Presses universitaires de France, 1970).

388

References

Forman, Paul. “Weimar Culture, Causality, and Quantum Theory, 1918-1927: Adaptation by German Physicists and Mathematicians to a Hostile Intellectual Environment,” Historical Studies in the Physical Sciences 3 (1971): 1-115. ———. “Behind Quantum Electronics: National Security as Basis for Physical Research in the United States, 1940-1960,” Historical Studies in the Physical Sciences 18 (1987): 149-229. ———. “The Primacy of Science in Modernity, of Technology in Postmodernity, and of Ideology in the History of Technology,” History and Technology 23 (2007): 1-152. Foucault, Michel. Les Mots et les choses: une archéologie des sciences humaines (Paris: Gallimard, 2001 [1966]). ———. L’Archéologie du savoir (Paris: Gallimard, 1969). ———. Surveiller et punir: naissance de la prison (Paris: Gallimard, 1975). Fouquet, Henri. Histoire civile, politique et commerciale de Rouen depuis les temps les plus reculés jusqu’à nos jours, 2 vols. (Rouen: Chez M. Métérie, libraire and Chez M. Augé, libraire, 1876). Franklin, Allan. The Neglect of Experiment (Cambridge: Cambridge University Press, 1986). Frémontier-Murphy, Camille. Les Instruments de mathématiques, XVIe-XVIIe siècle: cadrans solaires, astrolabes, globes, nécessaires de mathématiques, instruments d’arpentage, microscopes (Paris: Réunion des musées nationaux, 2002). Fumaroli, Marc. La Diplomatie de l’esprit, de Montaigne à La Fontaine (Paris: Gallimard, 1998). Gabbey, Alan. “The Mechanical Philosophy and Its Problem: Mechanical Explanations, Impenetrability, and Perpetual Motion,” in Change and Progress in Modern Science, ed. by Joseph C. Pitt (Dordrecht: D. Reidel, 1985), pp. 9-84. ———. “Huygens and Mechanics,” in Studies on Christian Huygens, ed. by H. J. M. Bos, M. J. S. Rudwick, Am M. Snelders, and R. P. W. Visser (Lisse: Swets & Zeitlinger, 1980), pp. 166-1999. Gal, Ofer. Meanest Foundations and Nobler Superstructures: Hooke, Newton and the “Compounding of the Celestiall Motions of the Planetts” (Dordrecht: Kluwer Academic Publishers, 2002). Galison, Peter. “History, Philosophy, and the Central Metaphor,” Science in Context 2 (1988): 197-212.

389

References

———. How Experiments End (Chicago: The University of Chicago Press, 1987). ———. Image and Logic: A Material Culture of Microphysics (Chicago: The University of Chicago Press, 1997). ———. Einstein’s Clocks, Poincaré’s Maps: Empire of Time (New York and London: Norton, 2003). ———. “Ten Problems in History and Philosophy of Science,” Isis 99 (2008): 111-124. Galluzzi, Paolo, ed. Scienziati a Corte. L'arte della sperimentazione nell'Accademia Galileiana del Cimento (1657-1667) (Livorno: Sillabe; Firenze: Istituto e Museo di Storia della Scienza, 2001). Garber, Daniel. Descartes’s Metaphysical Physics (Chicago: The University of Chicago Press, 1992). ———. Descartes Embodied: Reading Cartesian Philosophy Through Cartesian Science (Cambridge: Cambridge University Press, 2001). ———. “Descartes, Mechanics, and the Mechanical Philosophy,” Midwest Studies in Philosophy 26 (2002): 185-204. ———. “On the Frontlines of the Scientific Revolution: How Mersenne Learned to Love Galileo,” Perspectives on Science 12 (2004): 135-163. Garside, Charles Jr. “The Origins of Calvin’s Theology of Music: 1536-1543,” Transactions of the American Philosophical Society, New Series, 69 (1979): 1-36. Gaukroger, Stephen. Descartes: An Intellectual Biography (Oxford: Clarendon Press, 1995). ——— and John Schuster. “The Hydrodynamic Paradox and the Origins of Cartesian Dynamics,” Studies in the History and Philosophy of Science 23 (2002): 535-572. ———. Francis Bacon and the Transformation of Early Modern Philosophy (Cambridge: Cambridge University Press, 2001). Gauvin, Jean-François. “Artisans, Machines, and Descartes’s Organon,” History of Science 44 (2006): 187-216. Geertz, Clifford. Local Knowledge: Further Essays in Interpretive Anthropology (New York: Basic Books, 1983). Gewirtz, Alan. “Experience and the Non-Mathematical in the Cartesian Method,” Journal of the History of Ideas 2 (1941): 183-210.

390

References

Giancarlo, Nonnoi. “Galileo e Pascal, idee ed esperienze,” in Filosofia, scienza, storia: Studi in onore di Alberto Pala, ed. by Antonio Cadeddu (Milan: Franco Angeli, 1995). Gille, Bertrand. Les Mécaniciens grecs. La naissance de la technologie (Paris: Seuil, 1980). Gilson, Etienne. Index scolastico-cartésien (Paris, 1912). Ginzburg, Carlo. The Cheese and the Worms: The Cosmos of a Sixteenth-Century Miller, transl. by John and Anne Tedeschi (London and New York: Penguin, 1992). Gooding, David. Experiment and the Making of Meaning: Human Agency in Scientific Observation and Experiment (Dordrecht: Kluwer Academic Publishers, 1990). ———, Trevor Pinch, and Simon Schaffer, eds., The Uses of Experiment: Studies in the Natural Sciences (Cambridge: Cambridge University Press, 1989). Gordon-Seifert, Catherine. “From Impurity to Piety: Mid 17th-century French Devotional Airs and the Spiritual Conversion of Women,” The Journal of Musicology 22 (2005): 268-291. Gorman, Michael John and Nick Wilding, “Introduction,” in Kaspar Schott: La technica curiosa, ed. by Maurizio Sonnino, with a preface from Paolo Galluzzi (Roma: Edizioni dell'Elefante, 2000). Goubert, Pierre. Beauvais et le Beauvaisis de 1600 à 1730: contribution à l’histoire sociale de la France du XVIIe siècle (Paris: S. E. V. P. E. N, 1960). Gouk, Penelope. Music, Science, and Natural Magic in Seventeenth-Century England (New Haven: Yale University Press, 1999). Gozza, Paolo. “Introduction,” in Number to Sound: The Musical Way to the Scientific Revolution, ed. by idem (Dordrecht, Boston, and London: Kluwer Academic Publishers, 2000). Grafton, Anthony. Cardano’s Cosmos: The World and Work of a Renaissance Astrologer (Cambridge, MA: Harvard University Press, 1999). Green, Robert A. The Hurdy-Gurdy in Eighteenth-Century France (Bloomington and Indianapolis: Indiana University Press, 1995). Grmek, Mirko. “Mariotte et la physiologie de la vision,” in Mariotte savant et philosophe, ed. by Pierre Costabel (Paris: Vrin, 1986), pp. 155-185. Groothuis, Douglas. “Bacon and Pascal on Mastery over Nature,” Research in Philosophy and Technology 14 (1994): 191-203.

391

References

Hacking, Ian. Representing and Intervening: Introductory Topics in the Philosophy of Natural Science (Cambridge: Cambridge University Press, 1983). ———. Historical Ontology (Cambridge, MA.: Harvard University Press, 2002). Hackmann, Willem D. “Instrumentation in the Theory and Practice of Science: Scientific Instruments as Evidence and as an Aid to Discovery,” Annali dell’Istituto e Museo di storia della scienza di Firenze 10 (1985): 87-115. Harkness, Deborah E. The Jewel House: Elizabethan London and the Scientific Revolution (New Haven: Yale University Press, 2007). Hahn, Roger. The Anatomy of a Scientific Institution: The Paris Academy of Sciences, 1666-1803 (Berkeley: University of California Press, 1971). Halbwachs, Maurice. Les Cadres sociaux de la mémoire (Paris: La Haye, Mouton Editeur, 1975 [1925]). Halleux, Robert, et al., eds. Les publications de l’Académie royale des sciences de Paris (1666-1793), 2 vols. (Turnhout, Belgium: Brepols, 2001). Hamou, Philippe. La Mutation du visible. Essai sur la portée épistémologique des instruments d’optique au XVIIe siècle, 2 vols. (Villeneuve D’Ascq (Nord): Presses Universitaires du Septentrion, 1999). Hankins, Thomas L. and Robert J. Silverman, eds. Instruments and the Imagination (Princeton: Princeton University Press, 1999). Hannaway, Owen. “Laboratory Design and the Aim of Science: Andreas Libavius versus Tycho Brahe,” Isis 77 (1986): 585-610. Happel, Jean. “Orgues et organistes en Alsace au XVIe siècle. Le Rôle de l’orgue dans le culte protestant à Strasbourg,” Cahiers et Mémoires de l’orgue 15-16 (1976): 3-52. Hatfield, Gary. “Reason, Nature, and God in Descartes,” Science in Context 3 (1989): 175-201. Heilbron, John L. Electricity in the 17th and 18th Centuries: A Study in Early Modern Physics (Berkeley: University of California Press, 1979 [Dover, 1999]). Heilbron, John L. The Sun in the Church: Cathedrals as Solar Observatories (Cambridge, MA.: Harvard University Press, 1999). Helden, Albert van. “The Birth of the Modern Scientific Instrument, 1550-1700,” in The Uses of Science in the Age of Newton, ed. by J. G. Burke (Berkeley: University of California Press, 1983), pp. 49-84.

392

References

———. “Galileo and Scheiner on Sunspots: A Case Study in the Visual Language of Astronomy,” Proceedings of the American Philosophical Society 140 (1996): 358-396. ——— and Thomas L. Hankins, Instruments, Osiris 9 (1994): 1-250. Heller, Henry. Labour, Science and Technology in France, 1500-1620 (Cambridge: Cambridge University Press, 1996). Henry, John. “Animism and Empiricism: Copernicanism Physics and the Origins of William Gilbert’s Experimental Method,” Journal of the History of Ideas 62 (2001): 99-119. Herval, René. Histoire de Rouen, 2 vols. (Rouen: Maugard, 1947-49). Hilaire-Pérez, Liliane. L’Invention technique au siècle des Lumières (Paris: Albin Michel, 2000). Hilaire-Pérez, Liliane and Marie Thébaud-Sorger. “Les Techniques dans l’espace public: Publicité des inventions et littérature d’usage au XVIIIe siècle (France, Angleterre),” Revue de synthèse 127(2) (2006): 393-428. Hill, John Walter. Baroque Music: Music in Western Europe, 1580-1750 (New York: W.W. Norton & Company, 2005). Hill, Katherine. “‘Juglers or Schollers?’: Negotiating the Role of a Mathematical Practinioner,” British Journal for the History of Science 31 (1998): 253-274. Hirschfield, John Milton. The Académie royale des sciences, 1666-1683 (New York: Arno Press, 1981). Hodder, Ian, ed. The Meanings of Things: Material Culture and Symbolic Expression (London: Unwin Hyman, 1989). Holt, Mack P. The French Wars of Religion, 1562-1629 (Cambridge: Cambridge University Press, 1995). Hunter, Michael. Science and Society in Restoration England (Cambridge: Cambridge University Press, 1981). ——— and Simon Schaffer, eds. Robert Hooke: New Studies (Woodbridge, Suffolk: Boydell, 1989). Ihde, Don. Instrumental Realism: The Interface between Philosophy of Science and Philosophy of Technology (Bloomington: Indiana University Press, 1991).

393

References

Iliffe, Rob. “‘In the Warehouse’: Privacy, Property and Priority in the Early Royal Society,” History of Science 30 (1992): 29-68. ———. “Material Doubts: Hooke, Artisan Culture, and the Exchange of Information in 1670s London,” British Journal for the History of Science 28 (1995): 285-318. ———. “Foreign Bodies,” Canadian Journal of History 52 (1998): 467-490. ———. “Foreign Bodies II,” Canadian Journal of History 53 (1999): 23-50. Irwin, Joyce L. Neither Voice nor Heart Alone: German Lutheran Theology of Music in the Age of the Baroque (New York: Peter Lang, 1993). Isherwood, Robert M. Music in the Service of the King: France in the Seventeenth Century (Ithaca: Cornell University Press, 1973). Israel, Giorgio. “Des Regulæ à la Géométrie,” Revue d’histoire des sciences 51 (1998): 183-236. Jacomy, Bruno, ed. De la machine à calculer de Pascal à l’ordinateur: 350 ans d’informatique (Paris: Musée national des techniques, CNAM, 1990). Jackson, Myles W. “Music and Science During the Scientific Revolution,” Perspectives on Science 9 (2001): 106-115. Jacson, Myles W. Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany (Cambridge, MA: MIT Press, 2006). James, Frank ed. The Development of the Laboratory: Essays on the Place of Experiment in Industrial Civilization (London: Macmillan, 1989). Jansen, P. “Les Carrosses à cinq sols et Christiaan Huygens,” Revue d’histoire des sciences 4 (1951): 171-172. ———. “Une tractation commerciale au XVIIe siècle,” Revue d’histoire des sciences 4 (1951): 173-176. Jardine, Lisa. The Curious Life of Robert Hooke: The Man Who Measured London (London: Harper Collins, 2003). Jeannin, Pierre. “Les Manuels de pratique commerciale imprimés pour les marchands français (XVIe-XVIIIe siècle),” in Le Négoce international, XIIIe-XXe siècle, ed. by François M. Crouzet (Paris: Economica, 1989), pp. 35-58. Jones, Matthew L. “Descartes’ Geometry as Spiritual Exercises,” Critical Inquiry 28 (2001): 40-71.

394

References

———. “Writing and Sentiments: Blaise Pascal, the Vacuum, and the Pensées,” Studies in History and Philosophy of Science 32 (2001): 139-181. ———. The Good Life in the Scientific Revolution: Descartes, Pascal, Leibniz, and the Cultivation of Virtue (Chicago: The University of Chicago Press, 2006). ———. The Matter of Calculation: Early Modern Calculating Machines, Statecraft and Thinking about Thinking (forthcoming). Johnston, Stephen. “Mathematical Practitioners and Instruments in Elizabethan England,” Annals of Science 48 (1991): 319-344. ———. “An English Mathematical Aide-Memoire of the 17th century.” Internet resource http://www.mhs.ox.ac.uk/staff/saj/aide-memoire. Judd, Cristle Collins. Reading Renaissance Music Theory: Hearing with the Eyes (Cambridge: Cambridge University Press, 2000). Julien, Marie-Pierre and Jean-Pierre Warnier, eds. Approches de la culture matérielle. Corps à corps avec l’objet (Paris: L’Harmattan, 1999). Jurgens, Madeleine. Documents du Minutier central concernant l’histoire de la musique (1600-1650), 2 vols. (Paris: S.E.V.P.E.N., 1967; La Documentation Française, 1974). Kaiser, David. Drawing Theories Apart: The Dispersion of Feynman Diagrams in Postwar Physics (Chicago: University of Chicago Press, 2005). Kalkman, Wouter. “Constantijn Huygens en de Haagse orgelstrijd,” Tijschrift der Vereeniging voor Noord-Nederlands Muziekgeschiedenis 31 (1981): 167-177. Kasser, Michel. “Picard et le renouvellement de l’art du nivellement à la fin du XVIIe siècle,” in Jean Picard et les débuts de l’astronomie de précision au XVIIe siècle, ed. by Guy Picolet (Paris: Editions du CNRS, 1987), pp. 255-263. Kassler, Jamie C. Inner Music: Hobbes, Hooke and North on Internal Character (London: Athlone, 1995). Keating, Peter and Albert Cambrosio. Biomedical Platforms: Realigning the Normal and the Pathological in Late-Twentieth-Century Medicine (Cambridge, MA.: MIT Press, 2003). Keller, Alex. “A Manuscript Version of Jacques Besson’s Book of Machines, with His Unpublished Principles of Mechanics,” in On the Pre-Modern Technology and Science: Studies in Honour of Lynn White, Jr., ed. by B. S. Hall and D. C. West (Malibu: Undena Publications, 1976), pp. 75-95.

395

References

Khalfa, Jean. “Pascal’s Theory of Knowledge,” in The Cambridge Companion to Pascal, ed. by Nicholas Hammond (Cambridge: Cambridge University Press, 2003), pp. 122-143. King, David A. In Synchrony with the Heavens: Studies in Astronomical Timekeeping and Instrumentation in Medieval Islamic Civilization, 2 vols. (Leiden: Brill, 2004-05). King, Henry C. Geared to the Stars: The Evolution of Planetariums, Orreries, and Astronomical Clocks (Toronto: University of Toronto Press, 1978). Kingery, W. David, ed. Learning from Things: Method and Theory in Material Culture Studies (Washington, D.C.: Smithsonian Institution Press, 1996). Klein, Ursula. “Paper Tools in Experimental Cultures,” Studies in History and Philosophy of Science 32 (2001): 265-302. ———. Experiments, Models, Paper Tools: Cultures of Organic Chemistry in the 19th Century (Stanford: Stanford University Press, 2003). Knorr-Cetina, Karin. Epistemic Cultures: How the Sciences Make Knowledge (Cambridge, MA: Harvard University Press, 1999). Kohler, Robert E. Lords of the Fly: Drosophila Genetics and the Experimental Life (Chicago: The University of Chicago Press, 1994). Korrick, Leslie. “Instrumental Music in the Early 16th-Century Mass: New evidence,” Early Music 18 (1990): 359-370. Kottick, Edward L. “Building a 15th-century Lute,” The Galpin Society Journal 26 (1973): 72-83. Kroes, Peter and Anthonie Meijers, “The Dual Nature of Technical Artifacts,” Studies in History and Philosophy of Science 37 (2006): 1-4. Kronick, David A. A History of Scientific & Technical Periodicals: The Origins and Development of the Scientific and Technical Press, 1665-1790, 2nd ed. (Metuchen, N.J.: The Scarecrow Press, Inc., 1976). Landes, David S. Revolution in Time: Clocks and the Making of the Modern World (Cambridge, MA. and London: The Belknap Press of Harvard University Press, 1983). Launay, Denise. La Musique religieuse en France du Concile de Trente à 1804 (Paris: Publications de la Société française de musicologie; Editions Klincksieck, 1993). Latour, Bruno and Steve Woolgar. Laboratory Life: The Construction of Scientific Facts (Beverly Hills: Sage Publications, 1979).

396

References

———. Science in Action: How to Follow Scientists and Engineers Through Society (Cambridge, MA.: Harvard University Press, 1987). ———. The Pasteurization of France, transl. by Alan Sheridan and John Law (Cambridge, MA.: Harvard University Press, 1988). Lawrence, Christopher and Steven Shapin. Science Incarnate: Historical Embodiments of Natural Knowledge (Chicago: The University of Chicago Press, 1998). Lazar, Horia. “L’Habitude de penser: de la machine arithmétique à l’‘abêtissement’,” Chronique: Institut catholique de Toulouse (1995): 57-70. Le Cerf, G., ed. (with the collaboration of E. R. Labande). Les Traités d’Henri-Arnaut de Zwolle et de divers anonymes (ms B.N. Latin 7295) (Paris, 1932). Le Gall, André. Pascal (Paris: Flammarion, 2000). Lefèvre, Wolfgang, Jürgen Renn, and Urs Schoepflin, eds. The Power of Images in Practical Mechanics, 1400-1600 (Basel: Birkhäuser, 2003). ———. Picturing Machines, 1400-1700 (Cambridge, MA.: MIT Press, 2004). Lenoble, Robert. Essai sur la notion d’expérience (Paris: J. Vrin, 1943). ———. Mersenne, ou la naissance du mécanisme (Paris: J. Vrin, 1943). Lesure, François. “La facture instrumentale à Paris au seizième siècle,” The Galpin Society Journal 7 (1954): 11-52. ———. “Pierre Trichet’s Traité des instruments de musique: supplément,” The Galpin Society Journal 15 (1962): 70-81. Levasseur, Emile. Histoire des classes ouvrières et de l’industrie en France avant 1789, 2 vols. (Paris: A. Rousseau, 1900-1901). Lévi-Strauss, Claude. Anthropologie structurale (Paris: Plon, 1958). Levy Kenneth and John A. Emerson. “Plainchant,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Libin, Laurence. “Organology,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Licoppe, Christian. La Formation de la pratique scientifique: le discours de l'expérience en France et en Angleterre, 1630-1820 (Paris: La Découverte, 1996).

397

References

Lindley, Mark. “Mersenne on Keyboard Tuning,” Journal of Music Theory 24 (1980): 166-203. ———. “Temperaments,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Long, Pamela. “Power, Patronage, and the Authorship of Ars: From Mechanical Know-How to Mechanical Knowledge in the Last Scribal Age,” Isis 88 (1997): 1-41. ———. Openness, Secrecy, Authorship: Technical Arts and the Culture of Knowledge from Antiquity to the Renaissance (Baltimore: The Johns Hopkins University Press, 2001). Loriferne, Hubert. “L’influence de Picard dans les travaux d’alimentation en eau du château de Versailles sous Louis XIV,” in Jean Picard et les débuts de l’astronomie de précision au XVIIe siècle, ed. by Guy Picolet (Paris: Editions du CNRS, 1987), pp. 275-311. Lundwall, Eric. Les Carrosses à cinq sols. Pascal entrepreneur (Paris: Science Infuse, 2000). Lynch, Michael. Art and Artifact in Laboratory Science: A Study of Shop Work and Shop Talk in a Research Laboratory (London: Routledge, 1984). MacCulloch, Diarmaid. The Reformation (New York: Viking, 2003). Mahoney, Michael S. “Huygens and the Pendulum: From Device to Mathematical Relation,” in Emily Grosholz, Herbert Breger, eds., The Growth of Mathematical Knowledge (Dordrecht: Kluwer, 2000), pp. 17-39. ———. “Reading a Machine.” Internet resource http://www.princeton.edu/~hos/h398/readmach/modeltwin.html ———. “Drawing Mechanics,” in Picturing Machines, 1400-1700, ed. by Wolfgang Lefèvre (Cambridge, MA.: The MIT Press, 2004), pp. 281-306. Maine de Biran, Pierre. Influence de l’habitude sur la faculté de penser, in Oeuvres complètes, ed. by Pierre Tisserand, 14 vols. (Geneva: Slatkine, 1982 [1920-1949]), vol. 2. Marguin, Jean. Histoire des instruments et machines à calculer. Trois siècles de mécanique pensante, 1642-1942 (Paris: Hermann, 1994). Massip, Catherine. “Facteurs d’instruments et maîtres à danser parisiens au XVIIe siècle,” in Instrumentistes et luthiers parisiens, XVIIe-XIXe siècles, ed. by Florence Gétreau (Paris: Délégation à l’Action artistique de la ville de Paris, [1988]), pp. 17-34.

398

References

Mayer Brown, Howard and Richard Freedman, “Vers mesurés, vers mesurés à l’antique,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Mayr, Otto. Authority, Liberty & Automatic Machinery in Early Modern Europe (Baltimore: Johns Hopkins University Press, 1986). Major, J. Russell. From Renaissance Monarchy to Absolute Monarchy: French Kings, Nobles, & Estates (Baltimore: Johns Hopkins University Press, 1994). Marcel-Dubois, Claudie. Les Instruments de musique de l’Inde ancienne (Paris: Presses Universitaires de France, 1941). Marconell, Maria Helena. Christiaan Huygens: A Foreign Inventor in the Court of Louis XIV. His Role as a Forerunner of Mechanical Engineering (Ph.D. dissertation, Open University, 1999). Marion, Jean-Luc. Sur l’ontologie grise de Descartes. Science cartésienne et savoir aristotélicien dans les Regulæ, 2nd edn (Paris: Vrin, 1981). ———. “Cartesian Metaphysics and the Role of the Simple Natures,” in The Cambridge Companion to Descartes, ed. by John Cottingham (Cambridge: Cambridge University Press, 1992), pp. 115-139. Mauss, Marcel. “Body Techniques,” in Sociology and Psychology: Essays, ed. by Ben Brewster (London: Routledge, 1979), pp. 97-135. Maury, Jean-Pierre. A l’origine de la recherche scientifique: Mersenne (Paris: Vuibert, 2003). McCarthy, John C. “Pascal on Certainty and Utility,” in John C. McCarthy, ed., Modern Enlightenment and the Rule of Reason (Washington, D.C.: Catholic University of America Press, 1998). McClaughlin, Trevor. “Un exemple d’utilisation du Minutier central de Paris: La bibliothèque et les instruments scientifiques du physicien Jacques Rohault selon son inventaire après décès,” Revue d’histoire des sciences 29 (1976): 3-20. ———. “Was There an Empirical Movement in Mid-Seventeenth Century France? Experiments in Jacques Rohault’s Traité de physique,” Revue d’histoire des sciences 49 (1996): 459-481. McKinnon, James W. “The Meaning of the Patristic Polemic Against Musical Instruments,” Current Musicology 1 (1965): 69-82. ———. “Musical Instruments in Medieval Psalm Commentaries and Psalters,” Journal of the American Musicological Society 21 (1968): 3-20.

399

References

Mehl, Edouard. Descartes en Allemagne, 1619-1620 (Strasbourg: Presses Universitaires de Strasbourg, 2001). Melchior-Bonnet, Sabine. Histoire du miroir (Paris: Imago, 1994). Meli, Domenico Bertoloni. “The Role of Numerical Tables in Galileo and Mersenne,” Perspectives on Science 12 (2004): 164-190. ———. Thinking with Objects: The Transformation of Mechanics in the Seventeenth Century (Baltimore: The Johns Hopkins University Press, 2006). Merleau-Ponty, Maurice. Phénoménologie de la perception (Paris: Gallimard, 1945). Merton, Robert K. Science, Technology and Society in Seventeenth-Century England (Bruges, Belgium: Saint Catherine Press, 1938). Mesnard, Jean. Pascal et les Roannez, 2 vols. (Paris: Desclée de Brouwer, 1965). Meurillon, Christian. “La Machine arithmétique à la genèse des ordres pascaliens,” Revues des sciences humaines 186-187 (1982-83): 147-158. Middleton, W. E. Knowles. The History of the Barometer (Baltimore: The Johns Hopkins University Press, 1964 [1994]). ———. “A Footnote to the History of the Barometer: An Unpublished Note by Robert Hooke, F.R.S.,” Notes and Records of the Royal Society of London 20 (1965): 145-151. ———. A History of the Thermometer and Its Use in Meteorology (Baltimore: The Johns Hopkins University Press, 1966). ———. The Experimenters: A Study of the Accademia del Cimento (Baltimore: The Johns Hopkins University Press, 1971). Miller, Clement A. “Erasmus on Music,” The Musical Quarterly 52 (1966): 332-349. Miller, Daniel, ed. Material Cultures: Why Some Things Matter (Chicago: The University of Chicago Press, 1998). Miniati, Mara. “Les cistæ mathematicæ et l’organisation des connaissances au XVIIe siècle,” in Studies in the History of Scientific Instruments, ed. by Christine Blondel et al. (London: Rogers Turner Books Ltd, 1989), pp. 43-51. Moran, Bruce T. “Knowing How and Knowing That: Artisans, Bodies, and Natural Knowledge in the Scientific Revolution,” Studies in the History and Philosophy of Science 36 (2005): 577-585.

400

References

Moreno, Jairo. Musical Representations, Subjects, and Objects: The Construction of Musical Thought in Zarlino, Descartes, Rameau, and Weber (Bloomington: Indiana University Press, 2004). Morgan, Betty Trebelle. Histoire du Journal des sçavans depuis 1665 jusqu’en 1701 (Paris, 1929). Mourlevat, Guy. Les Machines arithmétiques de Blaise Pascal (Clermont-Ferrand: Académie des Sciences, Belle-Lettres et Arts, 1988). Moyer, Ann E. Musica scientia: Musical Scholarship in the Italian Renaissance (Ithaca: Cornell University Press, 1992). Muchembled, Robert. Culture populaire et culture des élites dans la France moderne (XVe-XVIIIe siècle), 2nd edn. (Paris: Flammarion, 1991). Nagase, Haruo. “Rhétorique de la machine arithmétique: signification de son invention dans la pensée de Pascal,” Etudes de langue et de littérature françaises 72 (1998): 17-30. Naux, Charles. Histoire des logarithmes de Neper à Euler, 2 vols. (Paris: Librairie scientifique et technique A. Blanchard, 1966-1971). Neal, Katherine. “The Rhetoric of Utility: Avoiding Occult Associations for Mathematics Through Profitability and Pleasure,” History of Science 37 (1999): 151-178. Netz, Reviel. “Proclus’ Division of the Mathematical Proposition Into Parts: How and Why Was It Formulated,” The Classical Quarterly, New Series 49 (1999): 282-303. Ong, Walter J. Ramus, Method, and the Decay of Dialogue: From the Art of Discourse to the Art of Reason (Cambridge, MA: Harvard University Press, 1983 [c1958]). Orden, Kate van. Music, Discipline and Arms in Early Modern France (Chicago: The University of Chicago Press, 2005). Ornstein, Martha. The Rôle of Scientific Societies in the Seventeenth Century (London: Archon Books, 1963 [1913]). O’Rourke Boyle, Marjorie. “Harvey in the Sluice: From Hydraulic Engineering to Human Physiology,” History and Technology 24 (2008): 1-22. Osler, Margaret J. “Whose Ends? Teleology in Early Modern Natural Philosophy,” Osiris, 2nd series, 16 (2001): 151-168. Ouin-Lacroix, Ch. Histoire des anciennes corporations d’arts et métiers et des conféries religieuses de la capitale de la Normandie (Rouen: Lecointe Frères, 1850).

401

References

Owen, Barbara, Peter Williams, and Stephen Bicknell, “Organ,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Palisca, Claude V. “Scientific Empiricism in Musical Thought,” in Seventeenth-Century Science and the Arts, ed. by H. H. Rhys (Princeton: Princeton University Press, 1961), pp. 91-137. ———. Humanism in Italian Renaissance Musical Thought (New Haven: Yale University Press, 1985). ———. The Florentine camerata: Documentary Studies and Translations (New Haven and London: Yale University Press, 1989). ———. “Was Galileo’s Father an Experimental Scientist?,” in Music and Science in the Age of Galileo, ed. by Victor Coelho (Dordrecht: Kluwer Academic Publishers, 1992), pp. 143-151. ———. “Mersenne pro Galilei contra Zarlino,” Nuova civiltà della macchine 16 (1998): 74-80. ———. “Vincenzo Galilei, scienziato sperimentale, mentore del figlio Galileo,” Nuncius 15 (2000): 497-514. ———. “Music and Scientific Discovery,” in idem, Music and Ideas in the Sixteenth and Seventeenth Centuries (Urbana: University of Illinois Press, 2006), pp. 131-160. Pérez-Ramos, Antonio. Francis Bacon’s Idea of Science and the Maker’s Knowledge Tradition (Oxford: Clarendon Press, 1988). Perry, Curtis, ed. Material Culture and Cultural Materialisms in the Middle Ages and Renaissance (Turnhout, Belgium: Brepols, 2001). Pickering, Andrew. The Mangle of Practice: Time, Agency, and Science (Chicago: The University of Chicago Press, 1995). Pickstone, John V. “Working Knowledges Before and After Circa 1800: Practices and Disciplines in the History of Science, Technology, and Medicine,” Isis 98 (2007): 489-516. ———. Ways of Knowing: A New History of Science, Technology and Medicine (Chicago: The University of Chicago Press, 2000). Picolet, G., ed. Jean Picard et les débuts de l'astronomie de précision au XVIIe siècle (Paris: Editions du Centre national de la recherche scientifique, 1987).

402

References

Poitras, Geoffrey. The Early History of Financial Economics, 1478-1776: From Commercial Arithmetic to Life Annuities and Joint Stocks (Cheltenham, UK and Northampton, MA.: Edward Elgar, 2000). Polanyi, Michael. Personal Knowledge: Towards a Post-Critical Philosophy (London: Routledge and Kegan Paul, 1958). Pouzet, Régine. Chronique des Pascal: Les affaires du monde, d’Etienne Pascal à Marguerite Périer, 1588-1733 (Paris: Champion, 2001). Pratt, Vernon. Thinking Machines: The Evolution of Artificial Intelligence (Oxford: Basil Blackwell, 1987). Prizer, William F. “Isabella d’Este and Lorenzo da Paria, ‘Master Instrument-Maker’,” Early Music History 2 (1982): 87-127. Pumfrey, Stephen. “Ideas Above His Station: A Social Study of Hooke’s Curatorship of Experiments,” History of Science 29 (1991): 1-44. Radder, Hans ed. The Philosophy of Scientific Experimentation (Pittsburg: University of Pittsburg Press, 2003). Ravaisson, Felix. De l’habitude [and] Métaphysique et morale (Paris: Presses universitaires de France, 1999 [1838]). Reckow, Fritz (with Edward H. Roesner), Rudolf Flotzinger, and Norman E. Smith, “Organum,” Grove Music Online, ed. by L. Macy http://www.grovemusic.com. Rheinberger, Hans-Jörg. “Experimental Systems: Historiality, Narration, and Deconstruction,” Science in Context 7 (1994): 65-81. ———. Toward a History of Epistemic Things: Synthesizing Proteins in the Test Tube (Stanford: Stanford University Press, 1997). Ribe, Neil M. “Cartesian Optics and the Mastery of Nature,” Isis 88 (1997): 42-61. Ricœur, Paul. La Mémoire, l’histoire, l’oubli (Paris: Seuil, 2000). Riggins, Stephen Harold, ed. The Socialness of Things: Essays on the Socio-Semiotics of Objects (Berlin and New York: Mouton de Gruyter, 1994). Righini Bonelli, Maria Luisa and Albert van Helden. Divini and Campani: A Forgotten Chapter in the History of the Accademia del Cimento (Florence: Supplemento agli Annali dell'Istituto e Museo di Storia della Scienza, 1981). Ripin, Edwin M. “The Early Clavichord,” The Musical Quarterly 53 (1967): 518-538.

403

References

———. “A Reevaluation of Virdung’s ‘Musica getutscht,’” Journal of the American Musicological Society 29 (1976): 189-223. Roberts, Lissa, Simon Schaffer, and Peter Dear, eds., The Mindful Hand: Inquiry and Invention from the Late Renaissance to Early Industrialisation (Amsterdam: Koninklijke Nederlandse Akademie van Wetenschappen, 2007). Roche, Daniel. Histoires des choses banales. Naissances de la consommation, XVIIe-XIXe siècle (Paris: Fayard, 1997). ———. Humeurs vagabondes. De la circulation des hommes et de l’utilité des voyages (Paris: Fayard, 2003). Rodis-Lewis, Geneviève. “Descartes’ life and the development of his philosophy,” in The Cambridge Companion to Descartes, ed. by John Cottingham (Cambridge: Cambridge University Press, 1992), pp. 21-57. Rokseth, Yvonne. La Musique d’orgue au XVe siècle et au début du XVIe (Paris: Librairie E. Droz, 1930; reprint ed., Hildesheim: Olms, 1996). Rooyen, A. J. Servaas van. “Huygens contra Calckman en vice-versa,” Tijschrift der Vereeniging voor Noord-Nederlands Muziekgeschiedenis 9 (1912): 170-173. Rossi, Paolo. Francis Bacon: From Magic to Science, transl. by Sacha Rabinovitch (London: Routledge and Kegan Paul, 1968). ———. Philosophy, Technology, and the Arts in the Early Modern Era, trans. by Savaltor Attanasio (New York: Harper & Row, 1970). ———. Logic and the Art of Memory: The Quest for a Universal Language, transl. by Stephen Clucas (Chicago: The University of Chicago Press, 2000). Rossum, Gerhard Dohrn-van. The History of the Hour: Clocks and Modern Temporal Orders, transl. by Thomas Dunlap (Chicago: The University of Chicago Press, 1996). Routh, Francis. Early English Organ Music from the Middle Ages to 1837 (London: Barrie & Jenkins, 1973). Ruggiu, F. J. “Tel père, quel fils? La reproduction professionnelle dans la marchandise et l’artisanat parisiens au cours des années 1650 et 1660,” Histoire, Economie et Société 4 (1998): 561-582. Rupp, Gordon. “Andrew Karlstadt and Reformation Puritanism,” The Journal of Theological Studies 10 (1959): 308-326.

404

References

Sabra, A. I. Theories of Light from Descartes to Newton (Cambridge: Cambridge University Press, 1981). Sakellariadis, Spyros. “Descartes’s Use of Empirical Data to Test Hypotheses,” Isis 73 (1982): 68-76. Sarasohn, Lisa T. “Nicolas-Claude Fabri de Peiresc and the Patronage of the New Science in the Seventeenth Century,” Isis 84 (1993): 70-90. Schackelford, Jole. “Tycho Brahe, Laboratory Design, and the Aim of Science: Reading Plans in Context,” Isis 84 (1993): 211-230. Schaffer, Simon, Trevor Pinch, and David Gooding, eds. The Uses of Experiment: Studies in the Natural Sciences (Cambridge: Cambridge University Press, 1989). ———. “Experimenters’ Techniques, Dyers’s Hands, and the Electric Planetarium,” Isis 88 (1997): 456-483. Schama, Simon. Landscape and Memory (New York: Vintage Books, 1996). ———. The Embarrassment of Riches: An Interpretation of Dutch Culture in the Golden Age (New York: Vintage, 1997). Schmitt, Charles B. “Experience and Experiment: A Comparison of Zarabella’s View with Galileo’s De Motu,” Studies in the Renaissance 16 (1969): 80-138. Schouls, Peter A. Descartes and the Possibility of Science (Ithaca: Cornell University Press, 2000). Schrynemakers, Arthur H. “Descartes and the Weight-Driven Chain-Clock,” Isis 60 (1969): 233-236. Schuster, John A. Descartes and the Scientific Revolution, 1618-1634: An Interpretation, 2 vols. (Ph.D. Dissertation, Princeton University, 1977). ———. “Descartes’ mathesis universalis, 1619-1628,” in Descartes, Philosophy, Mathematics and Physics, ed. by Stephen Gaukroger (Sussex: Harvester Press; Totowa, N.J.: Barnes & Noble Books, 1980), pp. 41-96. Seck, Friedrich, ed. Wilhelm Schickard Briefwechsel, 2 vols. (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 2002). Serfati, Michel. “Les Compas cartésiens,” Archives de Philosophie 56 (1993): 197-230. Shea, William R. The Magic of Numbers and Motion: The Scientific Career of René Descartes (Canton, MA.: Science History Publications, U.S.A., 1991).

405

References

———. Designing Experiments & Games of Chance: The Unconventional Science of Blaise Pascal (Canton, MA.: Science History Publications, U.S.A., 2003). Shapin, Steven and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton: Princeton University Press, 1985). ———. A Social History of Truth: Civility and Science in Seventeenth-Century England, (Chicago: The University of Chicago Press, 1994). ———. The Scientific Revolution (Chicago: The University of Chicago Press, 1996). Sherr, Richard. “Questions Concerning Instrumental Ensemble Music in Sacred Contexts in the Early Sixteenth Century,” in Le Concert des voix et des instruments à la Renaissance, ed. by Jean-Michel Vaccaro (Paris: CNRS-Editions, 1995), pp. 145-156. Shiner, Larry. The Invention of Art: A Cultural History (Chicago: University of Chicago Press, 2001). Sibum, Otto. “Reworking the Mechanical Value of Heat: Instruments of Precision and Gestures of Accuracy in Early Victorian England,” Studies in History and Philosophy of Science 26 (1995): 73-106. Silbiger, Alexander. “Fantasy and Craft: The Solo Instrumentalist,” in The Cambridge History of Seventeenth-Century Music, ed. by Tim Carter and John Butt (Cambridge: Cambridge University Press, 2005), pp. 426-478. Simms, D. L. “Archimedes and the Burning Mirrors of Syracuse,” Technology and Culture 18 (1977): 1-24. Smith, Pamela H. The Business of Alchemy: Science and Culture in the Holy Roman Empire (Princeton: Princeton University Press, 1994). ———. “Artists as Scientists: Nature and Realism in Early Modern Europe,” Endeavor 24 (2000): 13-21. ———. The Body of the Artisan: Art and Experience in the Scientific Revolution (Chicago: The University of Chicago Press, 2004). ——— and Benjamin Schmidt, eds., Making Knowledge in Early Modern Europe: Practices, Objects, and Texts, 1400-1800 (Chicago: The University of Chicago Press, 2007). Smith, Woodruff D. Consumption and the Making of Respectability, 1600-1800 (New York: Routledge, 2002). Solmsen, Friedrich. “Nature as Craftsman in Greek Thought,” Journal of the History of Ideas 24 (1963): 473-496.

406

References

Speiser, David. “Le Horologium oscillatorium de Huygens et les Principia,” Revue philosophique de Louvain 86 (1988): 485-504. Star, Pieter van der. Christiaan Huygens (1629-1695), Genius of Practical and Theoretical Physics (Hilversum: Radio Nederland Wereldomroep, 1963). Stoffele, Bram. Christiaan Huygens—A Family Affair. Fashioning a Family in Early Modern Court Culture (Master’s thesis, Utrecht University, 2006). Stroup, Alice. “Christiaan Huygens and the Development of the Air Pump,” Janus 68 (1981): 129-158. ———. A Company of Scientists: Botany, Patronage, and Community at the Seventeenth-Century Parisian Royal Academy of Sciences (Berkeley: University of California Press, 1990). ———. “Science, politique et conscience aux débuts de l’Académie royale des sciences,” Revue de Synthèse 114 (1993): 423-453. Sturdy, David J. Science and Social Status: The Members of the Académie des sciences, 1666-1750 (Woodbridge, Suffolk, UK; Rochester, NY, USA: Boydell Press, 1995). Tari, Lujza. “Women, Musical Instruments and Instrumental Music,” Studia Musicologica Academiæ Scientiarum Hungaricæ 40 (1999): 95-143. Taylor, E. G. R. The Mathematical Practitioners of Tudor & Stuart England (Cambridge: Cambridge Univerity Press, 1954). Terrier, Max. “L’Invention des ressorts de voiture,” Revue d’histoire des sciences 39 (1986): 17-30. Tilley, Christopher. Reading Material Culture: Structuralism, Hermeneutics and Post-Structuralism (Oxford and Cambridge, MA: Basil Blackwell, 1990). ———. Metaphor and Material Culture (Oxford: Blackwell, 1999). Truant, Cynthia. The Rites of Labor: Brotherhoods of Compagnonnage in Old and New Regime France (Ithaca: Cornell University Press, 1994). Turner, Anthony J. “Mathematical Instruments and the Education of Gentlemen,” Annals of Science 30 (1973): 51-88. ———. “William Oughtred, Richard Delamain and the Horizontal Instrument in Seventeenth-Century England,” Annali dell’Istituto e Museo di storia della scienza di Firenze 6/2 (1981): 99-125.

407

References

———. Early Scientific Instruments: Europe, 1400-1800 (London: Published for Sotheby's Publications by Philip Wilson Publishers; New York, NY: Distributed in the U.S.A. by Sotheby's Publications, Harper & Row, 1987). ———. “‘Utile pour les calculs’: The Logarithmic Scale Rule in France and England During the Seventeenth Century,” Archives internationales d’histoire des sciences 38 (1988): 252-270. ———. “From Mathematical Practice to the History of Science,” Journal of the History of Collections 7 (1995): 135-150. ———. “Mathematical Instrument-Making in Early Modern Paris,” in Luxury Trades and Consumerism in Ancien Régime France. Studies in the History of the Skilled Workforce, ed. by Robert Fox and Anthony J. Turner (Aldershot: Ashgate, 1998), pp. 63-96. Vaccaro, Jean-Michel. La Musique de luth en France au XVIe siècle (Paris: Éditions du Centre National de la Recherche Scientifique, 1981). ———, ed. Le Concert des voix et des instruments à la Renaissance (Paris: CNRS-Editions, 1995). Valleriani, Matteo. Galileo Engineer (Ph.D. Dissertation, Max Planck Institute for the History of Science, 2007). Vendrix, Philippe. “La dichotomie vocal/instrumental dans la théorie musicale aux confins de la Renaissance et du Baroque,” in Le Concert des voix et des instruments à la Renaissance, ed. by Jean-Michel Vaccaro (Paris: CNRS-Editions, 1995), pp. 71-81. Vilain, Christiane. La Mécanique de Christiaan Huygens: la relativité du mouvement au XVIIe siècle (Paris: Blanchard, 1996). Vittu, Jean-Pierre. Le Journal des savants et la République des lettres, 1665-1714 (thèse de Doctorat d'État ès Lettres, Paris I-Sorbonne, to appear in the éditions Honoré Champion). Voelkel, James R. The Composition of Kepler’s Astronomia Nova (Princeton: Princeton University Press, 2001). Wainwright, Jonathan and Peter Holman, eds. From Renaissance to Baroque: Change in Instruments and Instrumental Music in the Seventeenth Century (Aldershot: Ashgate, 2005). Walker, Daniel P. “Musical Humanism in the 16th and Early 17th Centuries,” Music Review (1941).

408

References

———. Studies in Musical Science in the Late Renaissance (London: The Warburg Institute; Leiden: E.J. Brill, 1978). ———. Music, Spirit, and Language in the Renaissance, ed. by Penelope Gouk (London: Variorum Reprints, 1985). Wardhaugh, Benjamin. Mathematical and Mechanical Studies of Music in Late Seventeenth-Century England (D. Phil., University of Oxford, 2006). Warner, Deborah J. “What is a Scientific Instrument, When Did it Become One, and Why?,” British Journal for the History of Science 23 (1990): 83-93. Warnier, Jean-Pierre. Construire la culture matérielle: l’homme qui pensait avec ses doigts (Paris: PUF, 1999). ———. “A Praxeological Approach to Subjectivation in a Material World,” Journal of Material Culture 6 (2001): 5-24. Watson, E. C. “The Early Days of the Académie des sciences as Portrayed in the Engravings of Sébastien Le Clerc,” Osiris 7 (1939): 556-587. Weber, Jean-Paul. La Constitution du texte des Regulæ (Paris: Société d’édition d'enseignement supérieur, 1964). Werrett, Simon. “Wonders Never Cease: Descartes’s Météores and the Rainbow Fountain,” British Journal for the History of Science 34 (2001): 129-147. Westfall, Richard S. “Science and Technology During the Scientific Revolution: An Empirical Approach,” in Renaissance and Revolution: Humanists, Scholars, Craftsmen and Natural Philosophers in Early Modern Europe, ed. by J. V. Field and Frank A. J. L. James (Cambridge: Cambridge University Press, 1993), pp. 63-72. Westman, Robert S. “The Astronomer’s Role in the Sixteenth Century: A preliminary study,” History of Science 18 (1980): 105-147. Wilkin, Rebecca M. “Figuring the Dead Descartes: Claude Clerselier’s Homme de René Descartes (1664),” Representations 83 (2003): 38-66. Williams, Helen and Peter. “Milton and Music; or the Pandaemonic Organ,” The Musical Times 107 (1966): 760-763. Williams, Peter. “The Meaning of organum: Some Case Studies,” Plainsong and Medieval Music 10 (2001): 103-120. Wilson, Catherine. The Invisible World: Early Modern Philosophy and the Invention of the Microscope (Princeton: Princeton University Press, 1995).

409

References

Winkler, Mary G. and Albert Van Helden. “Representing the Heavens: Galileo and Visual Astronomy,” Isis 83 (1992): 195-217. Winternitz, Emanuel. Musical Instruments and Their Symbolism in Western Art (New Haven: Yale University Press, 1979). ———. “Anatomy the Teacher: On the Impact of Leonardo’s Anatomical Research on his Musical and Other Machines,” Proceedings of the American Philosophical Society 111 (1967): 234-247. ———. Leonardo da Vinci as a Musician (New Haven: Yale University Press, 1982). Wise, M. Norton. “Mediating Machines,” Science in Context 2 (1988): 77-113. ———. “Mediations: Enlightenment Balancing Acts, or the Technologies of Rationalism,” in World Changes: Thomas Kuhn and the Nature of Science, ed. by Paul Horwich (Cambridge, MA.: MIT Press, 1993), pp. 207-256. Wolf, C. Histoire de l’Observatoire de Paris, de sa fondation à 1793 (Paris: Gauthier-Villars, 1902). Wymeersch, Brigitte van. Descartes et l’évolution de l’esthétique musicale (Sprimont: Mardaga, 1999). Yates, Frances. The French Academies of the Sixteenth Century (London: Warburg Institute, 1947; reprinted in London: Routledge, 1988). ———. The Art of Memory (London: Pimlico, 1992 [1966]). Yoder, Joella G. Unrolling Time: Christiaan Huygens and the Mathematization of Nature (Cambridge: Cambridge University Press, 1988). Zilsel, Edgar. “The Origins of William Gilbert’s Scientific Method,” in The Social Origins of Modern Science, ed. by Diederick Raven, Wolfgang Krohn, and Robert S. Cohen (Dordrecht: Kluwer Academic Publishers, 2000), pp. 71-95. Zittel, Claus. “Mirabilis scientiæ fundamenta: Die Philosophie des jungen Descartes (1619-1628),” in Seelenmaschinen: Gattungstraditionen, Funktionen und Leistungsgrenzen der Mnemoteckniken vom späten Mittealter bis zum Beginn der Moderne ed. by Jörg J. Berns and Wolfgang Neuber (Wien: Böhlau, 2000), pp. 309-362.

410