Ernst Mach as an Historian of Physics by

OTTO BLUH*

I Mach - Protects

During the last quarter century great advances have taken place in the study oE the history of science, leading to the conviction that it can exist as a discipline on its own, independent of the so-called philosophy of science. There is also a growing understanding that the history of science can make an important contribution to the education of the scientist, though we have not been fully successful1 in finding how best to achieve this aim. One of the first to appreciate the educational potentialities of the history of science was Ernst Mach. He clearly indicated the advanta- ges of the historical aspect of scientific studies, not for antiquarian rca- sons, but as an instrument for a critical evaluation of fundamental phys- ical concepts. Mach did not see himself as an historian, in spite of the fact that this name would be apt for a scholar engaged in many studies of a historicaI nature. To the older generation he is probabIy best known for his historical criticism,-to younger scientists and the public through the Mach number scale of aerodynamics-but the sum and substance of Mach's work is not exhausted by these two achievements. Mach was a modem Proteus, appearing in a variety of shapes, equally at home in physics and biology, in philosophy and psychology, in history and sociol- ogy. It would be impossible to write on Mach as an historian without at least touching on various other aspects of his work, and on his philosoph- ical standpoint.

Mach was born in 1838 and died in 1916, and the fiftieth anniversary of his death in 1966 was celebrated by symposia in Germany and in the Unites States'. Mach studied at Vienna, and received a degree in physics in 1860. Already as a lecturer in physics he took a great interest in what we now call biophysics, and his early research originated from the influences of the physiologists Briicke and Ludwig in Vienna, and

* 1900 Richard Jones Road, Nashville, Tennessee, U.S.A.

Centaurus 1968: vol. 13, nr. 1: pp. 62-84

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the psychologist-philosopher Fechner in Leipzig. The results of Mach’s psycho-physical investigations are described in his ‘Analysis of Sensa- tions’ (1885), on which much of Mach’s reputation as an experimental psychologist depends’. The so-called Mach bands, a type of optical illu- sion, have recently been made the object of modem investigations of the retinal processes by Ratliff; their acoustical, tactile and gustatory counterparts were investigated by BCkCsy and have shown Mach as an early founder of the concept of perceptual inhibition; that is, that light and other stimuli can annul each other, or in other words, that a local sensation is also dependent on the stimuli to which the surrounding is exposed3.

When Mach began to occupy the chair of physics at Prague Univer- sity in 1867, he and his students continued to work on psycho-physical problems, but this work gave way gradually to a greater emphasis on experimental physical research, for example, the ballistic experiments, on demonstration experiments and concern for educational questions. I have described Mach’s educational “Lehrjahre” and his didactic intercsts in an article in ‘Physics Today’,4 and only want to stress that Mach’s educational interests were not those of a dedicated schoolmaster, but, to use the words of his didactic mentor Herbart, were an “expression of his interest in the world and in humanity.” And it was as a result of his extensive teaching activity that Mach approached the historical considerations and began the composition of his books on mechanics? heat, and light along historical lines.

I1 The Historiography of the History of Science

Thc first prerequisite of gaining true evaluation of Mach‘s work in the history of physics seems to be an investigation into the scope and depth of the history of science in the second half of the nineteenth century. There is an astonishing lack of information on the history of the history- of-science in general. Historiography of science-history and its underly- ing concepts and ideas have only recently been made the subject of inves- tigations, e. g. by Kuhn5 and Agassi,6 but they do not provide any system- atic exposition of the development of the subject. George Sarton’ in an article “Is it possible to teach the History of Science?” gave in a few pa- ges an account of various writings on the history of science, but did not provide us with a complete picture.

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Mach, who was not an extrovert, never described the introduction he may have received to historical ways of thinking. Apparently he never had any formal training in universal history and certainly none in the history of science. However, as a student-as many a European student before and after him-a good part of his liberal education came from the club or the coffeehouse, if not the beer cellar. Mach’s daughter-in-law’ recently related that he met regularly with a group of young artists, mu- sicians and painters in a Viennese coffeehouse, as their spiritus rector, and we have it on the evidence of William James9 that in later years he was a brilliant conversationalist when he entertained James in the ‘Ca- sino’ at Prague. We may assume that much of his education in historical appreciation came from contact with fellow students and friends. Other sources of information were newspapers and magazines which were re- quisites of the old Viennese coffeehouse. Mach’s later writings show him, in fact, as a student of the belletristic school, as the true essayist who likes to step out of his role of scientific author with humanistic comments on personal experiences or moral opinions which give a particular flavor to all his writings.

Mach’s first scientific book was a physics textbook for students of medicine,1° a very original work, but one which shows no particular attention to historical detail. This book, with its novel basis toward the biological applications af physics, gives even less place to the history of the subject than was usual at the time, and probably reflects the attitude of the research oriented young scientist for whom historical questions had no great fascination.

A question arises: once Mach felt the need for systematic studies in the history of physics, what could be found in the literature of the subject field? There were various ‘histories’ available, many mentioned in Sar- ton’s bibliography of science history”. It can be expected that Mach read Goethe’s ‘Science of Color’ as well as his ‘Materials to the History of the Science of Color’,1z the latter a work full of biographical data and critical remarks. Goethe did not understand the importance of Newton’s experimentation and argued from the psychological rather than the phys- ical standpoint against Newton, which leads usually to the neglect of Goethe as a scientist. But the ‘Science of Color’ and the ‘Materials’ can rightly be considered the first intellectual histories of science. That Sar- ton in his bibliography of science-history neglected to mention Goethe’s work shows that in this relatively new field even a writer sympathetic to

Ernst Mach as an Historiun of Physics 65

the teaching of cultural history could not forget that Goethe was an ama- teur. Goethe himself foresaw this kind of narrowmindedness when he wrote the following passage which Mach may have read and taken to heart:

“Of the man who wants to give us the tradition of knowledge we can demand rightly that he should make us acquainted how the phenomena became known by-and-by, what has been imagined, what opinions and what thoughts formed. To describe all this co- herently is very difficult and to write a history is always a delicate matter; for, even with the most honorable purpose one is in danger of becoming dishonest. Yea, he who undertakes such a represen- tation does declare at the outset that he will illuminate certain things and obscure certain others13.”

It should be noted that Goethe’s research in the history of optics was probably ,the first which combined an historical account with a critical attitude. He also showed great appreciation, in the ‘Materials’, for historical development and there can be little doubt that Mach’s total position to the history of science as an instrument of criticism could have taken its starting point from the reading of Goethe.

I11 Whewell’s Influence

The most likely immediate influence on Mach could have come from William Whewell’s (1 794-1 866) ‘History of the Inductive Sciences, from the earliest to the present times;’I4 that is, 1837, the year of Queen Victoria’s accession. This work, according ,to Sarton, “maintained the dignity of a classic in English libraries and colleges during the whole of the Victorian age and even beyond15.” Mach refers to the book and also to the companion work ‘The Philosophy of the Inductive Scien- ces.’16 The first mentioned ‘History’ was translated into German by the Vienna astronomer Jospeh Johann von Littrow and Mach must have known this important work, especially since in his student days in Vien- na the son of J. J. Littrow, Karl Ludwig, was the professor of astrono- my.

Whewell’s interests ranged from mineralogy to moral philosophy, but he was foremost a classical scholar, and it was he who advised Faraday on the choice of Greek terminology in connection with his experiments

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on the conductivity of solutions; the terms electrolysis, electrolyte, ion, cation and anion, cathode, anode are Whewell’s inventions. His study of scientific history had been undertaken with an ideological motivation, namely to observe the Baconian method of induction at work, but at the same time to prove that the observed facts cannot be simply genera- lized and need to be organized by an intellectual process based on cer- tain axioms or necessary assumptions. He advocated the rationalism of Kant, and was attacked by his fellow-inductionist, John Stuart Mill for his “intuitionism.” Mach, whom we in general would expect to agree with Mill wrote, however, in the “Warmelehre” (Textbook on heat) in 1896:

“The English scientist Whewell maintained correctly that for the development of the natural sciences two factors have to act to- gether: Ideas and Observations. Ideas alone evaporate into sterile speculations, observations alone do not give organic knowledge. In fact, we see how much it depends on already existing ideas (Vor- stellungen) to adapt to new observations. Too great a flexibility with respect to each new fact does not allow the establishment of solid intellectual habits. Too rigid intellectual habits become a hindrance to free observations. Through a compromise between judgment (Urteif) and prejudice (Vorurteil), if one may say so, grows our understanding. Our whole psychological life, in partic- ular the scientific, consists of a continual adaptation of our imagina- tionL7. ”

Whewell’s understanding of the meaning of the axioms or ideas were only acceptable for Mach for practical-economical-reasons, and not as necessary categories of our thought. But he could firmly agree with Whewell’s motivation which the latter expressed in words of Bacon: ‘’. . . we are not laying the foundation of any sect or doctrine, but the profit and dignity of mankind18.”

IV Historicism

Whewell’s purpose in writing on the history of science was primarily a universal one, and in the vast compass of his work one cannot expect to find the most accurate inf~rmation’~. In political history one began only then to follow Ranke’s postulate of describing historical events “as they really happened,” that is, of making preliminary studies of original

Ernsf Mach as an Historian of Physics 67

documents, diplomatic reports, and ransacking whole archives. In the history of science the study of originals, of first drafts, or of correspon- dence was not yet recognized as an important scholarly pursuit. Only now, for example, can we get better acquainted with certain writings of New- ton. Mach, in his first larger work, the ‘Mechanics,’ obviously made an attempt to go to the sources and there is an Appendix with an impressive chronological list of original authors., from Archimedes to Heinrich Hertz, whom Mach used. However, Mach does not provide us with de- tailed references within the text and there is a lack of what is now ex- pected from a scientific and historical author with regard to bibliograph- ical accuracy.

We can only conjecture here that Mach’s awareness of the need for historical spade work, however incomplete in form, was awakened through a knowledge of the work at the ‘Institute of Historical Research’ in Vienna. This Institute, created in 1854, became prominent a few years later, during Mach’s student years, under Theodor von Sickel, who was also a professor at the Universityzo. He made great contributions toward precise standards of scholarship and elevated historiography to an exact field of knowledge, a humanistic “science.”

Another local influence on Mach’s historical thinking must have come to Mach from the arguments of Austrian economists against what they called “Historismus”, in English “historicism2* .” The term sugges- ted an inappropriate or unsuitable application of historical considera- tions. I t is not possible to describe the variety and confusion of opinions which gathered about this topic, but it should be of considerable impor- tance to the historian of science in view of its possible parallels. Mach may have heard about the new concept of “historicism” through the at- tack of the well-known Viennese economist Carl Menger who published a book ‘Errors of Historicism’22 in 1884, which was directed against the realistic-historical tendencies of German economical research. The year 1884 also saw the publication of Mach’s ’Mechanics,’ but it can be assumed that Mach had been familiar for some time with Menger’s ide- as, for he had already made a name for himself as a young man with the publications of ‘The Principles of Economics,’ in 187 1. Menger’s followers represented an analytical and abstract theory of economics which later, as the “Austrian School of Economics” became more suc- cessful than the Vienna School of neopositivism-there is an interesting similarity-in planting its doctrines in America.

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Mach was well acquainted with the Austrian political economist Ema- nuel Herrmann to whom he attributes the statement that “science also has a problem of thrift or economy,” and it stands to reason that Mach could have heard about Menger from Herrmann. Another good friend af Mach‘s was the engineer, economist and writer Josef Popper-Lyn- keusYz4 whose wide interests could also have helped to keep Mach informed. Even without knowing of Menger’s criticism of historicism, as an active scientist, Mach would hardly have accepted the thesis that the history of a scientific subject is equivalent to the science itself and that nothing but concern for the tradition of a science means full participa- tion in the life of that science. However, when Mach showed an interest in the historical development of physics, the debate on historicism in Vienna was a useful warning not to become overwhelmed by the record- ed facts, but to enter into the study of the past with a mind willing to weigh the evidence, just as he was used to do in his scientific research.

A more general anti-historical or a-historical movement which cannot have been without influence on any historically-minded writer was the publication of Nietzsche’s ‘Untimely reflection^'^^ in 1874. In this book the famous philosopher proclaimed his opposition to the “art of remembrance,” and asked for a break with the influences of the past which, as Goethe had already expressed it, had become a burden to every new generation. I t seems that this message also was not lost on Mach when he began to study critically the traditionally accepted concepts of Physics.

V History and Teuching

Mach’s so-called historical writings-Mechanics, Heat, Light-were re- sults of his teaching and were developed by what could be called a feed- back from his lecture-courses. In the preface to ‘Heat,”’ in 1896, he wrote that any instructor who lectures on generally accepted viewpoints may one day suddenly find that “his arguments no longer come from the heart and considering the matter further, he may find logical diffi- culties, which once recognized, become unbearable,”

In the preface to his ‘Mechanics’ (1884) Mach had already quite clearly declared that the book had an antimetaphysical purpose, and that its aim was one of enlightenment, to remove the cob-webs of erro- neous beliefs. Together with Nietzsche and Menger, Mach accepted

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from the start an undertone of anti-historicism, and thus none of his books were called “Histories.” The Mechanics book has the title ‘The development of mechanics, in historical and critical representation,’ and the word ‘development’ cannot only mean historical, but also logical development or just ‘exposition’. The English rendering of the title as ‘The Science of Mechanics’ takes this well into account. Mach’s two other main works carry the titles: ‘Principles of Heat’ and ‘Principles of Physical Optics’ and again only the subtitles refer to the historical aspects of the books. His books are not scissor-and-paste jobs. The more Mach penetrated into the study of the historical, the more he became convinced of the need for new interpretations and for abandoning a number of traditional concepts. Already in his brief, critical study of the concept of mass in 1867, Mach acted like a pioneer-the word used in the older meaning of a ‘digger’, one who probes at the fundaments, only to find that what had been considered essential cornerstones of phys- ics were unnecessary sub-structures, as it were, relics of a pre-scientific culture.

Mach’s first attempt to prove superfluous a long accepted mechani- cal concept arose from his teaching, when he tried to clarify the con- cept mass in what we now call an “operational way26.” Mach’s discus- sion of the mass-concept involved a criticism of Newton’s definition of mass as a quantity of matter, a problem with which we are still strug- gling in our classes today, and not always successfully. Mach probed the question at lenght in the ‘Mechanics,’ showing that equality of masses can be established when the masses, acting on each other, experience equal accelerations. Mach was not, as we often are, satisfied with an arbitrary definition that the mass-ratio is equal to the weight-ratio for equal gravitational acceleration.

Since his paper on mass did not gain recognition, Mach republished it as an appendix to a book on the history of the energy concept, in 187227. In this interesting little book he expressed already most of his scientific philosophy, namely that mechanics describes motions and does not explain them. Kirchhoff, in his ‘Lectures on Mechanics’, pub- lished in 1874, expressed the same idea, which since became wide- spread, so that every sophomore physics student prides himself in the knowledge ,that science must not ask why, but may only ask what. Mach went further by introducting his well-known principle of “scientific econ- omy,” which has also become a truismz8.

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This principle is regarded as one of Mach’s best known achievements and has met with as much misunderstanding as it has with reasoned ap- proval and mechanical repetition. Mach gave the credit for this thought, as mentioned before, to a remark by the economist Hermann, but he may also have come across the expression “economy of nature” in Goe- the’s ‘Materials for a Science of Mach also recognized that the understanding for economical thought processes came to him from wide experiences in thpv field of education.

In Prague, between 1867 and 1895, a span of 28 years, Mach lectur- ed regularly, semester by semester, giving a five-hour weekly lecture course, in the first few years called ‘Elements of Physics,’ and later ‘Ex- perimental At various times he offered a variety of special courses; on physical optics, the theory of heat, the theory of elasticity, and others. In all these courses he probably incorporated material of an historical and critical nature as he became more and more interested, and some of the special courses refer specifically to the ‘development’ (Entwicklung) of specific topics. It is interesting that for a few years- 1873 to 1876-Mach’s assistant and lecturer Dr. Vinzenz Dvoiak, gave one hour courses on ‘The optics of Huygens and Newton’, ‘The physics of Stevin and Galileo’ and ‘The development of mechanics in the age of Newton.’ We can assume that these courses were sponsored by Mach. Dvoiak worked with Mach on visual perception and time sensa- tion and his research is mentioned in the “Analysis of Sensations.” Mach does not anywhere refer to Dvoiak as his associate in the historical field; that he, however, maintained contact with his former pupil and confided in him we shall later see.

VI A Paradigmutic Period

The time in which Mach produced his historical writings was both auspicious and receptive to the undertaking. The period from 1870 to 1900 was a relatively quiet time in physics, a “paradigmatic” period, to use Kuhn’s term,31 in which most scientific statements were ac- cepted unhesitatingly and the solutions to problems sought according to sets of recognized formulas. This is of course an over-simplification, but in more than one sense the period 1870 to 1900 were halcyon days. It was also the time of various large compilations on the history of the

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sciences, and of the publication of many-volumed textbooks. Physics, with classical mechanics, thermodynamics and electromagnetics as major related blocks formed a semi-mechanical edifice and other branches of physics werc expected to be accomodated harmoniously into the main architecture. There were, of course, disturbing developments at this time, such as the introduction of statistical mechanics, but this could be considered as a temporary failure on account of the inability to observe events in submicroscopic dimensions. Electrodynamics was not quite understood, and new fields like spectroscopy could be ignored for some time as being on the fringes of physical research, if not a part of chemistry.

When Mach began his work in physics he felt attracted to the phys- iological and psychological sciences since classical physics, at least with respect to experimentation, had reached a stagnant state. The belief of many physicists that physics was a closed field is borne out by the story reported about Max Planck‘s experience as a student. When inquiring, in 1875, of his physics professor in Munich about the prospects of an academic career in physical research he was told that in physics all the important facts had been established, that this branch of scientific knowl- edge had terminated, and that it was hardly worth entering physics any- more3’. This exterminator of physics was Phillip von Jolly (1809-84), who, as professor in Heidelberg became famous for an incident, around 1840, with Robert Julius Mayer to whom he did not prove particularly helpful either33. From 1854 on he taught and worked in Munich.where he developed the sensitivity of weighings to a fine degree-to measure the next decimal-and among other experiments determined precisely the ‘density of the He was the paradigmatic character per sc3 and for this reason certainly the most unsuitable person to give advice to a young man like Planck.

As far as Mach was concerned, he may have been impatient with the status of physics in 1860, but he probably never adhered to the idea that physics in his own time had reached a final state. In the 2nd edition of the book on Energy (1 909), he writes in defense of history of science:

“Indeed, if from history one learned nothing more than the var- iability of views, it would be invaluable . . . Attempts to fix the fair moment by means of textbooks have always failed. Let us, then, early get used to the fact that science is unfinished, variable3s.”

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“Open-ended learning” is thus after all not quite such a new propo- sal as the modern educators of science would have us belicve! On the other hand, Mach would have been the first to admit that for the begin- ner in any science the setting of a definite scope is indispensable.

Mach evidently recognized a possible development of science not on- ly with respect to extension, but also as an internal mission which would re-evaluate the accepted results, probe the fundaments, and clean the structure from accretions and cob-webs. Mach did not sufficiently ap- preciate the fact that physics, in the nineties, began to experience a rapid transition, a “revolution,” perhaps because he had formed the opinion that scientific development is a slow, continuous process with no sudden jumps and abrupt breaks with the past36. After 1900 he no longer could or wished to deal with the new developments, partly because of illness and frustration, partly due to a strong belief in the ultimate truth of his scientific approach; that other periods of transition and other plateaux will be reached and that the next paradigmatic period would again be in need of critical attitudes with which to probe the new “fun- damentals,” as in fact we find in our present situation in physics, for example, the questions of uncertainty, time reversibility, and symmetry.

VII In Praise of Phenomenology

Of Mach’s three main books on mechanics, heat and light, the first two were written in the middle of Mach’s life. The ‘Optics’ was prepared later, and habent sun futa libelli, the manuscript was finished in 1912, but because of the war printing was delayed, and finally interrupted in 1916. The book was eventually published in 1923 by Ludwig Mach, a son and collaborator of Ernst Mach.

Since the books were the results of lecture courses, the historical and the educational are intermingled. In their time the books represented new approaches to physics teaching for advanced students and scientists -&-large. The first sentence in the preface to the 1st edition of the ‘Me- chanics’ makes it very clear that it is an unusual text, not a book for cramming: “The present work is not a textbook for memorizing the laws of mechanics.” This same tendency may be found in Mach’s two other books also.

I shall deal first with Mach’s book on heat because in this volume he expresses at some length his scientific attitude regarding the phenomeno-

Ernsi Mach as an Historian of Physics 73

logical and the mechanistic approach, and because we can then discuss important common points connected with both the ‘Mechanics’ and the ‘Optics.’

The book on ‘Heat’ was published in 189633. An English edition has never been published, but eleven chapters of a general character were translated into English in the American journal ‘The Open Court’ be- tween 1894 and 190334. These chapters comprise about one-third of the book on heat, but have only a limited relationship to the special problems of heat. In this way Mach intended to bring his ideas to the attention of the physicists who might not care to look for this material elsewhere. The titles of the general chapters show the wide range of Mach’s noetic in- terests, such as: ‘The contrast between mechanical and phenomenolog- ical physics’; ‘The development of science’; ‘The sense of the miracu- lous’; ‘Comparison as a Principle of Science’; ‘On Language’; ‘Trans- formation and Adaptation in Scientific Thinking’-the one from which I quoted before on Whewell; and ‘The economy of science.’ In one chap- ter he rejects causality as a strict principle of physics and replaces it with functionalism. But he modestly reminds us that “If physics achieves so much more with its methods than other sciences, we should consider that physics in a certain sense is presented with far simpler tasks.”

The technical parts of the book on heat-360 out of 470 pages-pro- vides us with an abundance of historical material which it would be im- possible to fully enumerate. There are chapters on thermometry, calori- metry, energy conservation, and the energy principles. Heat conduc- tion along the Fourier theory is developed at length since for Mach this was the “paradigm” of phenomenological considerations. Characteristic are paragraphs in which Mach compares the styles of different authors, e. g. a comparison of Thomson-Kelvin and Clausius. He writes:

“The papers on thermodynamics by Thomson and Clausius must be recognized as equal in importance. One can assume that the development of thermodynamics would have taken the same course, even if only one of the two main supporters of that science had taken part in its completion. With respect to the representation we notice a considerable difference between the two scientists. Thom- son’s work is . - . always a completely open one . . . the methods entirely transparent and the motivations which guide him are vis- ible to everybody. The exposition of Clausius always has a trait

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of . . . solemnity and reserve. One seldom knows whether Clausius is more eager to reveal or conceal something. Instead of the simple experiences which basically serve the calculations, they are erected on postulated axioms which assume the appearance of greater re- liability, without guaranteeing more than the experiences them- selvess8.”

The red thread running through all the work is the rejection of meta- physical concepts which Mach attributed to all submicroscopic visuali- zations for which no proof could be found. Mach was impressed with the successes of thermodynamics and he found the molecular theory to be just an off-spring of the old theory of mechanical atomism. He was not without appreciation of Boltzmann’s opposite attitude when he wrote:

“I have nothing to say against Boltzmann’s praise of the advantages for the physicists of the theory of atoms in preference to other the- ories. The researcher not only may, but should also use all means at his disposal which can help him. One would misunderstand me if one ascribed to me a partiality for a continuously occupied space. Light rays had long been investigated before their periodicity was discovered. Why should this not be found in the case of a spatial plenum? I only argue against constant adherence to arbitrary ad- di t ion~~~.’’

Mach’s basic anti-atomism was directed against the concept that atoms are entities having a few properties of the solid state, and in earlier writ- ings he had already suggested that they be visualized as vibrating systems23.

VIII Mechanics

Mach’s ‘Mechanics’ leaves much to be desired when seen as a history of the subject from the standpoint of the modern historian of science. For example, in recent years extensive studies have been made on me- chanical concepts in the Middle Ages, and indeed it has become fashion- able to save from.oblivion a number of Pre-Galilean scientists. It is true that in Antiquity and in the Middle Ages the knowledge of physics was greater than had been assumed, but Mach’s statement that “our fa- vorable opinions (on the science of antiquity) are again shaken by pas- sages containing such obvious errors which we cannot believe possible

Ernst Mach as an Historian of Physics 75

in an advanced scientific culture,” may still be valid4’. Mach, therefore, paid little attention to Greek mechanics, except to the Alexandrian pe- riod, Archimedes and Heron, some of which would have to be corrected today, ending the chapter on statics with Stevin, Pascal and Geryck.

The larger part of the ‘Mechanics’ is devoted to the principles of dy- namics which Mach recognized as a modern, 17th century science, al- though he was quite aware of certain of Galileo’s fore-runners. Mach al- so discusses Newton’s predecessors with respect to gravitational force, be- ginning with Copernicus. The most consequential part of Mach’s chapter on dynamics is on Newton’s views of Time, Space and Motion, in which he shows how superfluous the “absolute” concepts which Newton had postulated are. It appears, Mach wrote that:

“ . . . Newton has . . . acted contrary to his expressed intention only to investigate actual facts. No one is competent to predicate things about absolute space and absolute motion; . . . All our prin- ciples of mechanics are based on . . . experimental knowledge con- cerning the relative positions and motions of bodies . . . No one is warranted in extending these principles beyond the boundaries of experience. In fact, such an extension is meaningless, as no one possesses the requisite knowledge to make use of it42.”

Mach devotes some 50 pages in ‘Mechanics’ to issues of a general na- ture, e. g. theology, mysticism, etc. in which he discloses his Weltan- schauung. He vigorously fights for recognition of the fact that classical physics already has been seduced into imagination and speculation, and that modern physics of his time seemed to repeat this by wandering off into speculative mechanical and electrical atomistics. If one admits these entities and one’s predictions come out correctly, this does not confirm their existence, since one would have first to prove that no other expla- nation is possible.

It is well known that reading the parts of the ‘Mechanics’ which deal with Newton opened the eyes of Einstein, as Hume opened Kant’s eyes, or as Kant said “couched the cataract of his eyes.” Einstein acknowl- edge several times the stimulation he had received from ‘Mach’s princi- ple,’ that is, Mach’s discussion of the law of inertia. For the scientist in- terested in the history of gravitation and inertia, the work may still be of interest for it describes events in Mach’s own time and the chapter forms an important document about the immediate pre-Einsteinian world of mechanics.

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IX Optics

The situation is somewhat different with respect to Mach’s ‘Principles of Physical Optics,’ since to some degree this book remained a torso. Here also Mach wished to lay bare the origin and general concepts of optics and the historical thread of their development, “extricated from meta- physical ballast43.” The book is not organized along strictly chrono- logical lines, but has separate chapters on reflection, refraction, dis- persion, and polarisation. The optics book may strike the modem reader more for what it does not contain than what it offers, since for example, the ether theory and Maxwell’s theory are not found here, but were to be discussed in a proposed second volume. This second volume would also have included a chapter on relativity and on the history of the emis- sion theory of light and we may speculate whether this would have meant a discussion of the quantum of radiation.

is dated July 1913. Mach says that he yielded to pressure from his publisher and unwillingly gave permission for the printing, contrary to his usual practice. He was working on unspeci- fied “tedious experiments” with his son Ludwig and he intended to dis- cuss the relativity theory on the basis of new experimental findings on a later occasion.

The preface to

A modern biographer of Mach, K. D. Heller writes:

“For many years Ludwig attempted to continue the experiments which the preface to ‘Optics’ had announced for the second vol- ume and which should serve the purpose of disproving the theory of relativity. . . At the time of the second world war Ludwig’s experi- mentation had to be interrupted because of the erection of a high- voltage transmission line across the area where he performed his investigations. Driven to despair, he destroyed all the experimen- tal data, following a last wish of Ernst Mach, who wanted them de- stroyed if they would not lead to results. Thus we do not know any- thing more accurate about these investigationsu.”

The whole story has the ring of mystery around it. Ludwig tried to give a lame explanation about his father’s doubts on relativity in the pre- face which he wrote for the 9th edition of Mechanics in 1933. He does

Ernst Mach as an Historian of Physics 77

refer to certain experiments, but does not say anything about their con- tinuation. He also attempted to establish an unfortunate connection be- tween Mach and the Anti-Einsteinians lead by Lenard4’.

In order to understand Mach’s position on relativity, we have to fall back on an analysis of his remarks in the preface of ‘Optics’ ostensibly written in 1913. The contacts between Mach and Einstein have been investigated by Hemeck and more recently by H01ton~~. The relation- ship was never a very intimate one, to be sure, and it ran the stages from an admiring Einstein and a gratified Mach, to Mach accusing the ‘relati- vists’-Einstein is not mentioned by name-as being dogmatic, and Ein- stein, after he had read the preface in 1922, angrily declaring that Mach had been a “deplorable philosopher.” Holton has used part of the Ein- stein correspondence in order to show how Einstein moved away from a positivistic to a realistic standpoint, which he strongly defended in his later years in the well-known debates with Bohr. If the greatness of a philosopher depends on the constancy of his outlook, we will have to accord the palm to Mach rather than Einstein. Einstein, more voluble, evidently brought his philosophical views into harmony with his scientific interests rather than doing the opposite, and thus moved from a scien- tific pragmatism to a metaphysical realism. He abandoned the back- ground of his own early researches in statistics and quanta to become a believer in strict causality when this best served his thoughts on the cosmos and the unified-field theory. The whole story of Einstein’s intel- lectual development remained, of course, unknown to Mach and there could not have been any personal rancour toward Einstein when he wrote the preface. His concern was of a more general nature. This is reflec- ted in a letter of his old student Dvotak, who, as mentioned above, took his first steps in lecturing on the history of physics under Mach. In 1915, half-a-year before Mach’s death, Dvoiak wrote to Mach, recalling the good old days in Prague, and obviously reacting to a letter b y Mach: “You write about exaggerated speculation, mass suggestions and fashions in physics, and I believe that many of the best, present-day physicists would concur with you4’.”

We cannot doubt that the main argument against “relativity” must have come from a rejection af Minkowski’s “space-time continuum.” In the preface to ‘Optics’ Mach appreciates that “the study of relativity . . . has already been both fruitful and of permanent value to mathemat- ics,” and he apparently accepted with good grace the space-time con-

78 Otto Bliih

tinuum as a mathematical construct. But as a psychologist, the combina- tion of space and time in one concept and Minkowski’s grandiIoquent dec la ra t i~n ,~~ dismissing the individual concepts, making them fade a- way, could only appear to him as a “monstrosity.”

In all his writings Mach had stressed that science had to be empirical and that it was undesirable to give in to misguided curiosity for causal relationships and metaphysical speculations. When constructing models of sub-sensual dimensions, one must not consider them as ultimate real- ities. The only realities given to man-in his “human (i.e.biologica1) condition”-are his sensations or perceptions. Mach did not mean, as is often assumed, that we must accept our perceptions at face value. In fact, that is what the ‘Analysis of Sensations’ is about. He knew very well of the incessant communications between the brain and the senses. As the discoverer of the Mach bands he had not only observed the ele- mentary contrasts but had also attempted to explain them as a part of neural physiology.

For Mach the existence of a factual world behind the ‘elements’ of sensations was a matter of course, and needed no affirmation. He also knew that the idea of a cosmic order can act as a powerful stimulus and motivation to scientific work. Only he refused to discuss the world in any terms other than the existential realities, and his ordering process was more economico, and not more geometrico, that means, not based on axioms and principles as with Euclid, Spinoza, Newton, and the later Einstein.

Mach was quite aware also that different sciences would use the raw data differently and maintain methods of their own to describe their observations. Thus Mach wrote in the ‘Analysis’: “If we look more ac- curately, space and time represent, with respect to physiology, specific types of sensations, with respect to physics, however, functional de- pendencies of sensational elements49.” This standpoint excluded the ac- ceptance of a synthetic space-time reality; and equally monstrous for Mach would have been a union of space-time-mass in the guise of a spec- ulative metric as in general relativity. Today we can only wonder what standpoint Mach would have taken with respect to the extensive studies of increased perceptions through the use of drugs like mescalin and LSD, not to mention findings on extrasensory perception, or the psychedelic effects which claim to establish contact with an ‘integral’ level of experi- ence or with a metaphysical reality.

Ernst Mach as an Historian of Physics 79

X To make science safe for diversity

Mach’s analytic approach which confined science to the establishment of functional relationships on the grounds of a scientific economy, or a “conventionalism,” in PoincarC’s term, set itself a very modest, unso- phisticated task, a sort of minimum-philosophy, or as Mach said a “phi- losophy for domestic use” (H~usbacken)’~. He knew that there were other more grandiose philosophies, and in advocating his standpoint he was very much aware of current speculations and of their popular and social affects. He feared the return to an Hegelian position in which the real and the ideal are equated. He observed how the enlightenment had freed human thought from religious dogmatism, only to become a vic- tim of metaphysical dogmatism. At a time when “scientific thinking” had only just begun to enter political and social theories, Mach saw the opportunity for the introduction of an exemplary method through his concept of scientific economy, which he conceived as an oecumenical, science-wide method. Barred from the world of action, he tried to achieve this single-handedly, through his writings, without the support of a school, of “synod and council.”

His main concern was to prevent the metaphysical concept developed in one science imposing itself onto another science. When mechanical materialism was widely accepted as the super-science of the future Mach recognized clearly that science as a whole would need for its protection a modus vivendi rather than a dominant doctrine. Had he forseen the frightening potentialities of science for manipulating the body and soul of man, his concern would have carried even a greater urgency than it did 50 years ago.

To use a political parallel of which Mach, I think, would have whole- heartedly approved: in the words of the late President Kennedy, it has become an important task of our times “to make the world safe for di- versityS1.” What Mach through his methodology of the sciences wanted to achieve was just that: to make science safe for diversity, to make it safe for a scientific pluralism whose rapid expansion Mach un- derstood much better than any of the specialists of his day”. He saw that it was too late to attempt to make science safe only for physics, as it was too late, in 19 18 and in 1947, to make the international commu- nity safe for a single political doctrine. It was an anachronism when the Unity-of-Science movement of the Vienna School, which claimed to

80 Otto Bliih

follow Mach’s ideas, attempted after 1918 to lead the sciences into a new physicalism without regard to Mach’s original intention.

The recognition of the enormous diversity of scientific work and the variety of opinions came to Mach to a great extent from his historical studies. He did not emphasize in his books the work and opinions of “representative physicists”, as modern historians of science are inclined to do, yet his writings still leave us with the impression that historical generalizations are of secondary importance to the individual records which reflect the variety of the human intellect. Keeping the great po- tential of historical considerations in mind, Mach expected that studies in the history of science would make important contributions to the train- ing and the continuing education of the scientist. As his own teaching activity exemplifies, Mach did not expect such effects to be achieved from special history of physics courses, but from a constant attention to the diversity of historical and critical considerations in all physics courses. Such an historical involvement was for Mach part of wider edu- cational intentions. His permissive philosophy of life-which to many may appear today innocent and ineffective-makes it difficult to read his historical message clearly, But stating his views through a stronger, more forceful language, with the media at his disposal, would have meant for Mach acting against his own liberal principles.

REFERENCES AND NOTES

1. The Ernst Mach Institute, Freiburg i. Br., Germany, arranged a symposium, 11. and 12. March 1966. Another symposium was held at the meeting of the American Association for the Advancement of Science (Combined meeting of sections: ‘Physics’ and ‘History and Philosophy of Science’), at Washington, D. C. on 27. December 1966.

2. Ernst Mach, The Analysis of Sensations, and the Rrlafion of the Physical to the Psychical, 1st German edition 1885; English editions, 1897 and 1914. Dover Publications, with a new introduction by Thomas S. Szasz, 1959.

3. Cf. F. Ratliff, “Mach Bands in Physics, Physiology aid Psychology,” G. V. BCkCsy, “Lateral Inhabition Similar to Mach Bands in the Field of Hearing, Skin Sensation and Taste;” Symposium on Occasion of the 50th Anniversary of the Death of Ernst Mach, Erst-Mach-Znstitut, Freiburg i. Br., 1967, pp. 138 and 161 respec- tively.

4. Otto Bliih, “Emst Mach as a Teacher and Thinker,” Physics Today, Vol. 20, No. 6, p. 32, 1967.

Ernst Mach as an Historian of Physics 81

5. Thomas Kuhn, The Structure of Scientific Revolution, 1962. 6. Joseph Agassi, “Towards an Historiography of Science,” (History-Theory; Studies

in the Philosophy of Science, Suppl. 2, 1963). 7. George Sarton, Horus, A Guide to the History of Science, 1952, p. 44. 8. Anna Karma Mach, Address at Mach Symposium, Freiburg i. Br. cf. Ref. 3, p. 10. 9. Cf. The Letters of William James, edited by his son Henry James, Boston 1930,

p. 2111212. In the letter of 2. November 1882, James wrote that he rarely enjoyed a 48 hours better than in Prague where he met Ewald Hering, Carl Stumpf, Ernst Marty, and Mach, “genius of all trades.. . I spent four hours walking and supping with him at his club, an unforgettable conversation. I don’t think anyone gave me so strong an impression of pure intellectual genius.. . he has an absolute simplicity of manner and winningness of smile when his face lights up that is charming.”

10. Ernst Mach, Compendium der Physik fur Mediziner, 1863. 11. Cf. Ref. 7, for early histories of physics, pp. 157-163. Other historical sources

were articles in encyclopedias, obituaries, and biographical collections (pp. 78/79). 12. Johann W. v. Goethe, Zur Farbenlehre, 1810. The work has a didactic and a

polemic part, which contains the criticism of Newton’s Upticks. The (third) histor- ical part was published independently under the title Materialien zur Geschichte der Farbenlehre, 1810.

13. Coethes Werke, Wegner Verlag, Hamburg 1962, Vol. 13, p. 320. 14. William Whewell, History of the Inductive Sciences, 1837. IS. Ref. 7, p. 49. 16. William Whewell, The Philosophy of the Inductive Sciences, founded upon their

history, 1540; revised 1847. 17. Ernst Mach, Prinzipien der Wurmelchre, 1896; 4th edition 1922, p. 390. Mach

also mentions Whewell in his book Erkennrnis und Irrtum, 1905; 5th edition 1926, e.g. p. 138/139.

18. Ref. 14, p. 10. 19. A list of works on the history of science used by Whewell can be found on p. 9,

Footnote 1, in Ref. 14. 20. Cf. Arthur J. May, Vienna in fhe Age of Franz Josef, 1966, p. 61. 21. On “Historicism” cf. the article by M. Mandelbaum in The Enclopedia of Philos-

ophy (edit. P . Edwards), vol. 4, p. 22, 1967; also F. Meinecke, Die Entstehung des Historismus, 1936; K. Popper, The Poverty of Historicism, 1957.

22. Carl Menger, Die lrrtumer des Historismus in der deutschen Nationaliikonomie, 1884 (The Collected Works of Carl Menger, London School of Economics, Vol. 111, No. 19, 1935). Mach also refers to Menger in AnaIysis of Sensations, Ref. 2 (1914), p. 68.

23. Ernst Mach, History and Root of rhe Principle of the Conservation of Energy, 1872; English translation, 1911, p. 88.

24. Ref. 23, p. 16, Mach writes that only with Josef Popper couid he discuss his views “without raising a horrified opposition. Popper and I arrived at similar views on many points of physics independently, a fact I take pleasure in mentioning here.” A selection of Popper’s writings in English translation has been published by

6 CENTAUBUS. VOL. XIII

82 Otto Bliih

H. I. Wachtel, Security for AIL and Free Enterprise. A Summary of the Social Philosophy of Josef Popper-Lynkeus. 1955. See also: 0. Bliih, “The Value of Inspiration, a Study on Julius Robert Mayer and Josef Popper-Lynkeus,” Isis, vol. 43, Sept. 1952, p. 21 1.

25. Friedrich Nietzsche, Untimely Reflections, 1874. Collected Work (ed. 0. Levy), vol. 5, 1964. Mach refers to Nietzsche’s “insolent superman” in ‘Analysis of Sensations’, Ref. 2 (1914), p. 25, “who cannot, and I hope will not be tolerated by his fellow-men.’’ A discussion of Nietzsche in Mach’s letters is mentioned p. 69/10 in Ref. 44.

26. Carls Repertorium fur Physiknlische Technik, Vol. IV, p. 355, 1868. 27. Ref. 23. 28. It is often overlooked that the thrifty, puritanical, economy of Mach‘s days has

now been generally replaced by an economy of credit and affluence. Cf. Ref. 4, p. 40.

29. Cf. Goerlies Werke, Wegner Verlag, Hamburg, 1962, Vot. 14, p. 198. 30. A complete list of physics lecture courses a t the University of Prague during

Mach’s time was kindly prepared for me by Dr. Julius Kroczek, to whom I am very grateful.

31. Cf. Ref. 5. 32. Barbara L. Cline, The Questioners, 1965, p. 34. PIanck does not tell this story in

his autobiography, though he indicates that his teachers of physics in Munich were not inspiring. Cf. M. Planck, Scientific Autobiography and other Papers, 1949, p. 14. According t o F. Herneck, Bahnbrecher des Atomzeirafters, 1968, p. 153, Planck told the anecdote in a lecture at Munich in 1924.

33. Ernst Mach, Die Pritizipieti der Wiirmelchre, 4 Aufl. 1923, p. 2461247. 34. In the preface to ‘Mechanics’ (1883) Mach mentions Jolly as the author of a

“clear and lively booklet” (Schriftchen): Prinzipien der Mechnnik, 1852. In 1885 Mach received a call as Jolly’s successor primo et unico loco which he did not follow.

35. Cf. Ref. 23, p. 17. 36. Mach appears somewhat indifferent to the progress in physics after 1900, in

particular to such investigations as Brownian motion (Einstein; Smoluchowski, an Austrian; Perrin) and on the quantum of energy (Planck, Einstein). In a letter dated 9. August, 1909 Einstein asked Mach to read his paper on the Brownian motion “since here we have a motion which one believes one has to interpret as thermal motion.” (Reprinted by F. Herneck in Forschungen und Fortschritte, Vol. 37, p. 241, 1963.)

37. The Open Court. A weekly journal devoted to the religion of science, Vol. 8 (1894) to VoI. 17 (1903). See also Ernst Mach, Popular Scientific Lectures, Transl. by Th. J. McCormack, 1895, 1897, 1898, 1910.

38. Cf. Ref. 33, p. 300/301. 39. Cf. Ref. 33, p. 430. 40. Mach‘s various remarks on atomistics may appear to some as “double-talk”, since

in some passages he rejects the idea of transcendent atoms, in others appreciates atoms as useful for the description of certain facts, though his ideal is the phenom-

Ernst Mach as an Historian of Physics 83

41.

42. 43.

44.

45.

46.

47.

48.

enological description of thermadynamics. Cf. J. Petzold, “Mach und die Atomi- st&,” Naturwiss. Vol. 10, 2301231, 1922, in answer to an article by Hans Thirring, “Ziele und Methoden der Theoretischen Physik,” Naturwiss. Vol. 9, 1026, 1921. It should be noted, however, that the time of the Thirring-Petzold controversy was one 5 which much evidence for the “reality” of atoms could be advanced, whereas in Mach’s own time proof for the atomistic concept was scanty and-nota bene- atomism was still closely related to the picture of a hypothetical ether. E. N. Hie- bert reviewed “Mach‘s Early Views on Atomism” at the Washington Mach Symposium, Cf. Ref. 1 (Unpublished ms. 1967). Ernst Mach, The Science of Mechanics. A Critical and Historical Account of its Development, Transl. by J. McCormack. New Jntroduction by Karl Menger. From the Sixth edit. with revisions through the ninth (German) edition (1933). LaSalle, Ill. The Open Court Publ. Co. 1960, p. 3. Ibid., p. 280. Ernst Mach, The Principles of Optics. An historical and philosophical treatment. Transl. by J. S. Anderson and A. F. A. Young, 1953, p. VII. K. D. Heller, Ernst Mach, Wegbereiter der Modernen Physik, Wien - New York, Springer Verlag, 1964, p. 142/143. Ernst Mach, Die Mechanik in ihrer Entwicklung, 9. Aufl. Leipzig: F. A. Brock- haus, 1933, Preface by Ludwig Mach, pp. XVIII - XX. It is interesting to note that in this edition the preface to the 8th edition by J. Petzold has been omitted. In view of Ludwig’s attempt to gain support from Lenard, it is ironical that in 1935 Ludwig sought American assistance through Einstein for the foundation of an Ernst Mach Archive. (Cf. Morris R. Cohen in Life and Letters ed. Leonore C . Rosenfeld), N. Y. 1962, p. 376. Letter dated 9 December 1935 of Einstein to Cohen, and 2 January 1936 Cohen’s reply. F. Herneck, “Die Beziehungen zwischen Einstein und Mach, dokumentarisch dar- gestellt.” Wissenschaftl. Zeitschr. der Friedrich-Schiller Univcrsitiit Jena. Mathem. naturwiss. Reihe, Vol. 15, No. 1, 1966, pp. 1-14. Gerald Holton, “Ok est la rkalitt? Les rtsonses d’Einstein.” Science ef Synfh&e, 1967, pp. 97-140; also “Mach, Einstein, and the Search for Reality,” Daedalus, Spring 1968, p. 636, also “Influences on Einstein’s Early Work in Relativity Theory.” The American Scholar, Winter 1967-68, p. 59. On Einstein’s philosophical development cf. C . Lanczos, Albert Einstein and the Cosmic World Order, 1965. Letter of V. Dvoiak, who was professor of physics at Agram (Zagreb, Yugoslavia), dated 19. August 1915 (in Ernst Mach Institut, Freiburg i. Br.). H. Minkowski, “Raum und Zeit” (Lecture of 21. September 1908), Physikal Zeit- schr. Vol. 10, 1909, p. 104. The layman’s situation regarding the hybrid space-time concept is perhaps illustrated by the anecdote attributed to Heinrich Heine: I ‘ . . . when I was supposed to meet Rachel (the famous French tragedienne) friends dragged me many miles into the country where her family had a summer cottage. I arrived, one sits around the table, one meets papa Rachel, mama Rachel, sister RacheI, brother Rachel. “Where is Rachel?” I asked. “She went out,” I am told, “but voild here is her whole family”. And now I begin to laugh that everybody thinks I have lost my mind. But I was reminded of the story of the man who

.

84 Otto Bliih

goes to see a monster, advertised in the newspaper to be the off-spring of a carp and a rabbit. When he arrives and asks: “Where is the monster?” he gets the reply “We have sent is to the museum, but here is the carp and here is the rabbit; convince yourself.” (Gesprache mit Heine (ed. H . H. Houben), 1926, p. 610. See also p. 5881589.

49. Ref. 2, (1914). p. 348. 50. F. Herneck, “Unveroffentlichte Selbstbiographie von Ernst Mach.” Wissensch.

Zeitschr. der Humboldt Universitat Berlin, Mathem. naturwiss. Reihe, VI, 1956, p. 209.

5 1. John F. Kennedy, “Commencement Address a t American University,” Washington, D. C., 10. June, 1963.

52. Bohr’s complementarity can perhaps be considered as a special case of a Mach- principle of scientific diversity.