BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE

VOLUME XII

PHILOSOPHICAL PROBLEMS OF SPACE AND TIME

SYNTHESE LIBRARY

MONOGRAPHS ON EPISTEMOLOGY,

LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE,

SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE,

AND ON THE MATHEMATICAL METHODS OF

SOCIAL AND BEHAVIORAL SCIENCES

Editors:

DONALD DAVIDSON, Rockefeller University and Princeton Unit'ersity

J AA K K 0 HINTI K KA, Academy of Finland and Stanford Unirersily

GABRIEL NUCHELMANS, Unit'efsity of Leyden

WESLEY C. SALMON, Indiana University

BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE

VOLUME XII

EDITED BY ROBERT S. COHEN AND MARX W. WARTOFSKY

ADOLF GRUNBAUM Andrew Mellon Professor of Philosophy, University of Pittsburgh

PHILOSOPHICAL PROBLEMS

OF SPACE AND TIME

Second, enlarged edition

D. REIDEL PUBLISHING COMPANY

DORDRECHT-HOLLAND / BOSTON-U.S.A.

First printing: December 1973

Library of Congress Catalog Card Number 73-75763

ISBN-13: 978-90-277-0358-3 e-ISBN-13: 978-94-010-2622-2 001: 10.1007/978-94-0 I 0-2622-2

Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland

Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company, Inc.

306 Dartmouth Street, Boston, Mass. 02116, U.S.A.

All Rights Reserved Copyright © 1973 by D. Reidel Publishing Company, Dordrecht, Holland

Sotlcover reprint of the hardcover 1st edition 1973 No part of this book may be reproduced in any form, by print, photoprint, microfilm,

or any other means, without written permission from the publisher

To Thelma

TABLE OF CONTENTS

EDITORIAL INTRODUCTION

PREFACE TO THE FIRST EDITION

PREFACE TO THE SECOND, ENLARGED EDITION

ACKNOWLEDGMENTS

PART 1. PHILOSOPHICAL PROBLEMS OF THE METRIC OF SPACE AND TIME

Chapter 1. Spatial and Temporal Congruence in Physics: A Critical Comparison of the Conceptions of Newton, Riemann, Poincare, Eddington, Bridgman, Russell,

XIII

XV

XVII

XXI

and Whitehead 3 A. Newton B. Riemann C. Poincare D. Eddington E. Bridgman F. Russell G. Whitehead

Chapter 2. The Significance of Alternative Time Metrizations in Newtonian Mechanics and in the General Theory of

4 8

18 24 41 44 48

Relativity 66 A. Newtonian Mechanics 66 B. The General Theory of Relativity 77

Chapter 3. Critique of Reichenbach's and Carnap's Philosophy of Geometry 81 A. The Status of "Universal Forces" 81 B. The "Relativity of Geometry" 98

Chapter 4. Critique of Einstein's Philosophy of Geometry 106 A. An Appraisal of Duhem's Account of the Falsifi-

PHILOSOPHICAL PROBLEMS OF SPACE AND TIME VIII

ability of Isolated Empirical Hypotheses in Its Bearing on Einstein's Conception of the Inter-dependence of Geometry and Physics 106 I. The Trivial Validity of the 0-Thesis 111

II. The Untenability of the Non-Trivial D-Thesis 114 B. The Interdependence of Geometry and Physics in

Poincare's Conventionalism 115 C. Critical Evaluation of Einstein's Conception of the

Interdependence of Geometry and Physics: Physi­cal Geometry as a Counter-Example to the Non-Trivial 0-Thesis 131

Chapter 5. Empiricism and the Geometry of Visual Space 152 Chapter 6. The Resolution of Zeno's Metrical Paradox of Exten-

sion for the Mathematical Continua of Space and Time

PART II. PHILOSOPHICAL PROBLEMS OF THE TOPOLOGY OF TIME AND SPACE

Chapter 7. The Causal Theory of Time A. Closed Time

158

179 197

B. Open Time 203 Chapter 8. The Anisotropy of Time 209

A. Is There a Thermodynamic Basis for the Aniso-tropy of Time? 209 I. The Entropy Law of Classical Thermodynamics 219

II. The Statistical Analogue of the Entropy Law 236 B. Are There Non-Thermodynamic Foundations for

the Anisotropy of Time? 264 Chapter 9. The Asymmetry of Retrodictability and Predicta­

bility, the Compossibility of Explanation of the Past and Prediction of the Future, and Mechanism vs. Teleology 281 A. The Conditions of Retrodictability and Non-

Predictability 281 B. The Physical Basis for the Anisotropy of Psycho-

logical Time 289

IX Table of Contents

C. The Bearing of Retrodictability and Non-Predict­ability on the Compossibility of Explainability and Predictability 290

I. Evolutionary Theory 300 II. The Paresis Case 303

III. The Barometer Case 309 D. The Controversy Between Mechanism and Tele-

ology 311 Chapter 10. Is There a "Flow" of Time or Temporal "Becoming"? 314 Chapter 11. Empiricism and the Three-Dimensionality of Space 330

PART III. PHILOSOPHICAL ISSUES IN THE THEORY OF RELATIVITY

Chapter 12. Philosophical Foundations of the Special Theory of Relativity, and Their Bearing on Its History 341 A. Introduction 341 B. Einstein's Conception of Simultaneity, Its Preva-

lent Misrepresentations, and Its History 342 C. History of Einstein's Enunciation of the Limiting

Character of the Velocity of Light in vacuo 369 D. The Principle of the Constancy of the Speed of

Light, and the Falsity of the Aether-Theoretic Lorentz-Fitzgerald Contraction Hypothesis 386

E. The Experimental Confirmation of the Kinematics of the STR 397

F. The Philosophical Issue Between Einstein and His Aether-Theoretic Precursors, and Its Bearing on E. T. Whittaker's History of the STR 400

Chapter 13. Philosophical Appraisal of E. A. Milne's Alternative to Einstein's STR 410

Chapter 14. Has the General Theory of Relativity Repudiated Absolute Space? 418

Chapter 15. Philosophical Critique of Whitehead's Theory of Relativity 425

BIBLIOGRAPHY FOR THE FIRST EDITION 429

PHILOSOPHICAL PROBLEMS OF SPACE AND TIME x

PART IV. SUPPLEMENTARY STUDIES 1964-1973

1. Supplement to Part I

Chapter 16. Space, Time and Falsifiability (First Installment) 449 Abstract 449 Introduction 450 Criteria for Intrinsicness vs. Extrinsicness of Metrics and of Relations on Manifolds: Contents 457 1. Singly and Multiply Extended Manifolds 458 2. Intrinsicness vs. Extrinsicness of Metrics, Metrical

Equalities, and Congruences 468 3. What are the Logical Connections, if any, between

Alternative Metrizability, Intrinsic Metric Amor­phousness, and the Convention-Iadenness of Metr-ical Comparisons? 547

4. Intrinsicness and Extrinsicness of a Relation on a Manifold 563

Chapter 17. Can We Ascertain the Falsity of a Scientific Hypoth-esis? 569 1. Introduction 569 2. Purported Disproofs of Hypotheses in Biology and

Astronomy 572 3. Is it NEVER Possible to Falsify a Hypothesis

Irrevocably? 585 Chapter 18. Can an Infinitude of Operations Be Performed in a

Finite Time? 630

2. Supplement to Part II

Chapter 19. Is the Coarse-Grained Entropy of Classical Statistical Mechanics an Anthropomorphism? 646 1. Introduction 646 2. Entropy Change and Arbitrariness of the Partition-

ing of Phase Space 648 3. What is the Physical Significance of the Triple Role

of the Entropy for the Entropy Statistics in the Class U? 659

XI Table of Contents

4. Do the Roles of Human Decision and Ignorance Impugn the Physical Significance of the Entropy Statistics for the Class U? 663

3. Supplement to Part III

Chapter 20. Simultaneity by Slow Clock Transport in the Special Theory of Relativity 666 Introduction (co-authored with Wesley C. Salmon) 666 1. Summary 670 2. Examination of Ellis and Bowman's Account of

Nonstandard Signal Synchronizations 671 3. The Philosophical Status of Simultaneity by Slow

Clock Transport in the Special Theory of Rela-tivity 683

Chapter 21. The Bearing of Philosophy on the History of the Special Theory of Relativity 709 1. History and Pedagogy of the Light Principle 711 2. Contraction and Time-Dilation Hypotheses 715 3. Summary 726

Chppter 22. General Relativity, Geometrodynamics and Ontology 728 1. Introduction 728 2. The Philosophical Status of the Metric of Space-

Time in the General Theory of Reiativity 730 3. The Ontology of Empty Curved Metric Space in

the Geometrodynamics of Clifford and Wheeler 750 4. The Time-Orientability of Space-Time and the

'Arrow' of Time 788

APPENDIX 804

INDEX OF PERSONAL NAMES - Compiled by Mr. Theodore C. Falk 857

INDEX OF SUBJECTS - Compiled by Mr. Theodore C. Falk 865

EDITORIAL INTRODUCTION

It is ten years since Adolf Griinbaum published the first edition of this book. It was promptly recognized to be one of the few major works in the philosophy of the natural sciences of this generation. In part, this is so because Griinbaum has chosen a problem basic both to philosophy and to the natural sciences - the nature of space and time; and in part, this is so because he so admirably exemplifies that Aristotelian devotion to the intimate and mutual dependence of actual science and philosophical understanding. More than this, however, the quality of his work derives from his achievement in combining detail with scope. The problems of space and time have been among the most difficult in contemporary and classical thought, and Griinbaum has been responsible to the full depth and complexity of these difficulties. This revised and enlarged second edition is a work in progress, in the tradition of reflective analysis of modern science of such figures as Ehrenfest and Reichenbach.

In publishing this work among the Boston Studies in the Philosophy of Science, we hope to contribute to and encourage that broad tradition of natural philosophy which is marked by the close collaboration of philoso­phers and scientists. To this end, we have published the proceedings of our Colloquia, of meetings and conferences here and abroad, as well as the works of single authors. From the start, Adolf Griinbaum has been among the staunchest supporters of the Boston Colloquium for the Philosophy of Science. We are pleased to be able to include his significant treatise in our series.

ROBERT S. COHEN

MARX W. WARTOFSKY

PREFACE TO THE FIRST EDITION

My principal intellectual debt is to Hans Reichenbach's outstanding work Philosophie der Raum-Zeit-Lehre (Berlin, 1928) and to A. d'Abro's remarkable The Evolution of Scientific Thought from Newton to Einstein (New York, 1927).

In addition to those mentioned within the text, a number of colleagues and friends offered suggestions or criticisms which were of significant benefit to me in developing the ideas of this book. Among these, I should name especially the scientists Peter Havas, Allen Janis, Samuel Gulden, E. L. Hill, and Albert Wilansky as well as the following philosophers: Henry Mehlberg, Wilfrid Sellars, Abner Shimony, Grover Maxwell, Herbert Feigl, Hilary Putnam, Paul K. Feyerabend, Ernest Nagel, Nicholas Rescher, Sidney Morgenbesser, and Robert S. Cohen. Fruitful exchanges with some of these colleagues were made possible by the stimulating sessions of the Minnesota Center for Philosophy of Science to whose Director, Professor Herbert Feigl, I am very grateful for much encouragement.

I wish to thank Mrs. Helen Farrell of Bethlehem, Pennsylvania for typing an early draft of a portion of the manuscript, and Mrs. Elizabeth McMunn whose intelligence and conscientiousness were invaluable in the preparation of the final text for the printer. I am also indebted to Mr. Richard K. Martin for assistance in the preparation of the index and in the drawing of diagrams.

I have drawn on material which appeared in earlier versions in the following prior essays of mine: "Geometry, Chronometry and Em­piricism", Minnesota Studies in the Philosophy of Science (ed. H. Feigl and G. Maxwell), Vol. III, Minneapolis, 1962, pp. 405-526, and "Car­nap's Views on the Foundations of Geometry," in: P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap, Open Court Publishing Company, LaSalle, 1963, pp. 599-684. I wish to thank the editors and publishers of these essays for their kind permissions.

PREFACE TO THE SECOND, ENLARGED EDITION

Not Failure But Low Aim Is Crime

James R. Lowell, Autobiographical Stanza

A decade ago the first edition of this book was published by Alfred A. Knopf in New York (1963) and was also issued by Routledge and Kegan Paul in London (1964). A good many chapters of this edition were ex­tensively revised and/or enlarged for the Russian translation Filosofski Problemy Prostranstva I Vremini which appeared in the Soviet Union (1969) under the imprint of Progress Publishers, Moscow. The work had grown out of the tradition of Hans Reichenbach's philosophy of space, time and space-time as modified by ontological influences emanating from Riemann and Weyl.

Well before the first edition had gone out of print in 1971, I had become dissatisfied with it in at least two major ways, neither of which I had had the opportunity to remedy as part of the revisions that were incorporated in the Soviet edition. My two main dissatisfactions were due to the fol­lowing: (1) The valuable contributions by my Pittsburgh colleague G. J. Massey 1 and by my former student B. van Fraassen 2 to 'A Panel Discussion of Griinbaum's Philosophy of Science' (Philosophy of Science 36 [1969], pp. 331-399) had justly called for the provision of a more precise and more coherent account than heretofore of the Riemannian conception of an intrinsic as opposed to an extrinsic metric, a conception which I invoked foundationally in the ontology of physical geometry that I had espoused in the book, and (2) I came to think that the first edition's Chapter 14 'Has the General Theory of Relativity Repudiated Absolute Space?' was altogether insufficient to assure a balanced allocation of space in it between the special and general theories of relativity ('STR' and 'GTR' respectively). To remedy this imbalance, I have written a lengthy new chapter devoted to the GTR for the present edition {Chapter 22). Topics directly growing out of Einstein's theory of relativity ('TR')

1 G. J. Massey, 'Toward a Clarification of Grunbaum's Concept of Intrinsic Metric', Philosophy of Science 36 (1969), pp. 331-345. 2 B. van Fraassen, 'On Massey's Explication of Grunbaum's Conception of Metric', Philosophy of Science 36 (1969), pp. 346-353.

PHILOSOPHICAL PROBLEMS OF SPACE AND TIME XVIII

clearly merit detailed attention in a book on the philosophy of space and time, although the second edition of the present book, no less than the first, was written with the conviction that such a book should not be confined to topics from the TR.

After the first edition had gone out of print, its contents continued to elicit considerable critical as well as supportive commentary in the literature. 3 Hence I felt that it might be useful to incorporate the re­printed text of that edition within a substantially enlarged second edition. Thus, the present volume of twenty-two chapters plus Appendix adds further material which more than doubles the size of the first edition reproduced within its covers with the original Knopf pagination.

Chapters 16 and 22 respectively aim at now remedying the first edi­tion's stated two major defects. Besides, all of the additional materials by which the present book augments the Knopf edition correct and ex­tensively elaborate some of the main ideas set forth in the first edition and in later publications such as my "Reply to Hilary Putnam's 'An Examination of Grunbaum's Philosophy of Geometry'''. 4

As mentioned in the Acknowledgments below, the 15 chapters of the first edition as well as Chapters 16, 17, 18, and 20 were here reproduced by a photographic process. This mode of production precluded making even limited substantive corrections or addenda directly in their text. But it did prove technically feasible to correct all but three of the prior misprints which had come to the author's attention within that material. 5

In order to compensate for the impracticability of making even small

3 See, for example, the articles in the 1972 double issue (Nos. 1/2) of Synthese 24 on 'Space, Time and Geometry', edited by Patrick Suppes. For earlier detailed discussions, see Bas C. van Fraassen, An Introduction to the Philosophy of Time and Space, Random House, New York, 1970, passim, and J. J. C. Smart, Between Science and Philosophy, Random House, New York, 1968,passim.

4 A. Grunbaum, Geometry and Chronometry in Philosophical Perspective, University of Minnesota Press, Minneapolis, 1968, Chapter III, and "Reply to Hilary Putnam's 'An Examination of Grunbaum's Philosophy of Geometry' ", in Boston Studies in the Philosophy of Science (ed. by R. S. Cohen and M. W. Wartofsky), Vol. V, Reidel, Dordrecht, 1969, pp. 1-150. 5 The three residual misprints occur in the Bibliography of the first edition: On p. 432, Olivier Costa de Beauregard's last name should be 'Costa de Beauregard' and not merely 'de Beauregard'; on p. 438, the 4th entry under G. Ludwig ('Questions of Irreversibility and Ergodicity') should be listed as the 2nd entry under L. Rosenfeld on p. 441; the 'Po Tannery' entry on p. 444 belongs on p. 443.

XIX Preface to the Second, Enlarged Edition

changes within these chapters, I have devoted an Appendix at the end of the book to selected corrections and addenda. These are presented there in the form of chapter-by-chapter commentaries. Unfortunately, due to its scope alone, I was unable to react substantively to all of the critical and supportive discussion which the first edition, and my published elaborations of some facets of it during the intervening decade, have evoked. Therefore, in the Appendix I have endeavored to mitigate the incompleteness resulting from this kind of omission by also including a brief survey of some of the pertinent literature in the Commentaries, while relating the material to other relevant publications of mine as well.

Marginal notes in the text refer to the relevant section (§) of the Ap­pendix. These notes, together with Mr T. C. Falk's comprehensive in­dices of names and subjects, should facilitate connecting the corrections, addenda and citations of omissions to the pages of the volume where attention is devoted to the same topic or to related views of the same author. As noted on p. 449 of Chapter 16, some of the critical and sup­portive literature not dealt with here is due to be treated in a planned Part II of my Reply to the aforementioned 'A Panel Discussion ofGriinbaum's Philosophy of Science.' Part I of that Reply appears here as Chapter 16.

I am all too aware that, besides the kind of omission just mentioned, there are also more significant omissions of entire important topics whose treatment would be of interest to someone concerned with the full range of issues in space-time philosophy. Some such topics which are cognate to one or another of the chapters of this book are also briefly mentioned in the Appendix, along with some references to pertinent literature.

But I still adhere to my aforementioned initial conviction that essential­ly confining the book to topics directly arising from Einstein's STR and GTR would be too high a price to pay for the achievement of reasonably adequate coverage of the enormous philosophical import of the still burgeoning though troubled current TR. One, though only one, of my reasons for this conviction is set forth at the beginning of§4 of Chapter 22 by pointing to the lacunae in the TR which call for non-relativistic dis­cussions of time's arrow, for the employment of a non-relativistic ana­lytical mechanics of (electromagnetically) interacting particles, and for reliance on a non-relativistic quantum theory of atomic and molecular structure. I hope that the lengthy new Chapter 22 on the GTR in the present volume does redress the first edition's imbalance between the

PHILOSOPHICAL PROBLEMS OF SPACE AND TIME xx

amount of space devoted to it vis-a-vis the STR. But I should emphasize that the present edition makes no pretense to adequacy of coverage of the various major themes from contemporary TR. Yet, I hope that upon considering the topics from outside of the TR which I chose to treat instead, the reader may not deem this sacrifice of a certain amount of TR coverage an undue liability.

ACKNOWLEDG MENTS

I call attention to the various acknowledgments relating to the contents of particular chapters which are made within these chapters, and to those in the Preface to the first edition. Hence I shall here limit myself to ex­pressions of indebtedness which supplement those found elsewhere in the book.

The first 15 chapters are reproduced from the first edition, published by Alfred A. Knopf in New York in 1963.

Chapter 16 is reprinted from Philosophy of Science 37 (1970), pp. 469-588 and was published there as the first installment of my response to 'A Panel Discussion of Griinbaum's Philosophy of Science' by six authors, which had appeared in vol. 36 (1969), pp. 331-399.

Chapter 17 is based on a lecture which I gave at lohns Hopkins Uni­versity in May 1969 as part of the first series of the Alvin and Fanny Blaustein Thalheimer Lectures. It is reprinted from a volume containing this series: M. Mandelbaum (ed.), Observation and Theory in Science, The lohns Hopkins Press, Baltimore, 1971, pp. 69-129.

Chapter 18 is based on a Monday Lecture delivered at the University of Chicago in April 1968 and was first published by permission of the University of Chicago in British J. Philosophy of Science 20 (1969), pp.203-218.

Chapter 19 was written for a hopefully still forthcoming Festschriftfor Henry Margenau, edited by E. Laszlo and E. B. Sellon.

Chapter 20 first appeared in Philosophy of Science 36 (1969), pp. 1-43 as part of' A Panel Discussion of Simultaneity by Slow Clock Transport in the Special and General Theories of Relativity'. The chapter begins with a 4-page Introduction to this Panel Discussion, co-authored by Wesley Salmon and myself.

Chapter 21 is based on my vice-presidential address to the History and Philosophy of Science Section (L) of the American Association for the Advancement of Science, delivered during its December 1963 Cleveland meeting. It was first published in slightly different form in Science 143

PHILOSOPHICAL PROBLEMS OF SPACE AND TIME XXII

(1964), pp. 1406-1412, under the title 'The Bearing of Philosophy on the History of Science'.

Chapter 22 grew out of remarks I made as session chairman of the Geometrodynamics Symposium, held at the December 1972 Boston meeting of the American Philosophical Association, Eastern Division. It was written for this book, but some excerpts from it are to appear else­where at about the same time by prior arrangement with the Journal of Philosophy and with Patrick Suppes, Editor of Space, Time and Geometry, Reidel.

I wish to thank the various editors, journals, and publishers as well as Wesley Salmon for their kind permissions to use materials as specified.

Grateful acknowledgment is made for permission to quote from the following authors and/or publishers:

J. L Synge: Relativity: The Special Theory, North-Holland Publishing Company, 1956; quotations from pp. 14, 15, and 24.

L O'Raifeartaigh (ed.), General Relativity, © Oxford University Press 1972; quotations from pp. 64, 65, 68, 69, and 72 of the essay by J. Ehlers, A. E. Pirani and A. Schild, by permission of the Clarendon Press, Oxford.

Beginning with page by page comments on the orally delivered embry­onic form of Chapter 22, John Stachel generously gave me the immense benefit of his scholarship in relativity theory during personal discussions of a good many of the main issues treated in the final version of Chapter 22. I am cordially grateful to him. My warm thanks also go to the fol­lowing other colleagues and friends for their valuable assistance, either in person or by correspondence, with matters relevant to Chapter 22: Allen Janis, who was unstinting with his time, as always, when answering scientific questions and offering suggestions for improving earlier drafts; John Porter, who made himself available as a mathematical 'resource person' in various ways; Morris Kline, who gave me historical informa­tion regarding Riemann's influence on Clifford; Gerald Massey, who provided illumination on issues of logical presupposition and individua­tion; John Winnie, who is carrying forward some of the ideas set forth in § 3 (b); and J urgen Ehlers, whose influence is evident in the chapter and who supplied some references for the Commentary on it in the Appendix. Appreciation is also due to Clark Glymour for correspondence clari-

XXIII Acknowledgments

fying his views and for preprints of some of the papers by him which are discussed in the chapter; and to John Earman, who - as shown by my citations of him - was as generous with sending me preprints of his work as he was taciturn about where it was to be published.

Both the Appendix and some of the chapters have been affected, in ways too numerous to specify, by the intellectual impact and warm friendship which I have had the good fortune to receive from my dearly valued Pittsburgh colleagues in Philosophy, especially Alan Anderson, Nuel Belnap, Richard Gale, Laurens Laudan, Gerald Massey, Storrs McCall, Nicholas Rescher, Kenneth Schaffner, and Wilfrid Sellars. I am similarly indebted and grateful to my long-time friends Wesley Salmon and Robert Cohen, as well as to Helena Eilstein and my former doctoral students J. Alberto Coffa, Philip Quinn, and Bas van Fraassen. And I had helpful cor­respondence with William A. Newcomb on tachyons and retrocausation.

This second edition came into being as a volume of the Boston Studies through the kind cooperation of Gerard F. McCauley, Gerald T. Curtis, and Anton Reidel, and at the persistent initiative of Robert S. Cohen and Marx W. Wartofsky. It was Gerard McCauley who originally en­couraged me to write the first edition for publication by Knopf.

Struck by the patent inadequacies of the index in the first edition, Theodore C. Falk, who has professional competence in both philosophy and indexing, most obligingly offered to undertake the arduous labor of preparing the subject and name indices of the present edition.

Elizabeth R. McMunn bestowed the same care on the preparation of the material of this book for the press as she has on all other manuscripts of mine during the past dozen years.

I wish to thank all of these people as well as the staff of the Reidel Publishing Company very much for their protean assistance. And I am obliged to the National Science Foundation for the support of research which issued in a portion of this book over a period of time, as well as to the University of Pittsburgh for a sabbatical leave.

Last but not least, I must convey my gratitude to my distinguished Pittsburgh colleague Dr Jack D. Myers, University Professor of Medi­cine, who healingly wrought my almost phoenix-like recovery from a bout with insomnia and enabled me to resume work.

Pittsburgh, Pennsylvania July 1973