Essays on Galileo and the History and Philosophy of Science: Volume 1 9781487572044

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ESSAYS ON GALILEO AND THE HISTORY AND PHILOSOPHY OF SCIENCE VOLUME I Stillman Drake Selected and introduced by N.M. Swerdlow and T.H. Levere

For forty years, beginning with the publication of the first modem English translation of the Dialogue Concerning the Two Chief World Systems, Stillman Drake was the most original and productive scholar of Galileo's scientific work. During those years, Drake published sixteen books on Galileo, including translations of almost all the major writings, and Galileo at Work, the most comprehensive study of Galileo's life and works ever written. Drake also published about I 30 papers, of which nearly I oo are on Galileo and the rest on related aspects of the history and philosophy of science. The three-volume collection Essays on Galileo and the History and Philosophy of Science includes 80 of those papers. Volume I contains a biographical sketch of Galileo and various essays covering the broad range of Galileo's scientific endeavors, including outlines of the humanistic and religious background of his era. Textual and bibliographical issues are investigated in essays dedicated to the analysis of Galileo's mass of notes, treatises, and numerous fragments, previously collected in folios, manuscripts, and unreliable copies. Drake's wide-ranging essays cover Galileo' s place in the philosophy of science, his relation to his forebears and impact on his successors, and his contribution to the study of astronomy. In addition, the papers take up ongoing controversies such as Galileo's stance on the affinity of science with the corpus of human knowledge. Volume I of Stillman Drake's Essays on Galileo and the History and Philosophy of Science serves as a comprehensive introduction to Galileo's life, science, and writings, and with its forthcoming companion volumes, will indeed be a fitting tribute to the memory of one of Canada's most accomplished scholars. is Professor, Department of Astronomy and Astrophysics, University of Chicago. T . H. LEVERE is Professor and Director, Institute for the History and Philosophy of Science and Technology, University of Toronto. N.M. SWERDLOW

Stillman Drake. Photo courtesy of Mrs Florence Drake.

Essays on Galileo and the History and Philosophy of Science VOLUME I Selected and introduced by N.M. Swerdlow and T.H. Levere

STILLMAN DRAKE

UNIVERSITY OF TORONTO PRESS Toronto Buffalo London

© University of Toronto Press Incorporated 1999 Toronto Buffalo London Printed in Canada Reprinted in 2018

ISBN

0-8020-0626-4 (cloth)

ISBN 978-0-8020-7585-7 (paper)

Printed on acid-free paper

Canadian Cataloguing in Publication Data Drake, Stillman Essays on Galileo and the history and philosophy of science ISBN

Includes bibliographical references and index. o-8020-o626-4 (v. I : bound) ISBN 978-0-8020-7585-7 (paper) 1.

Galilei, Galileo, 1564-1642. I. Swerdlow, N.M. (Noel M.). JI. Levere, Trevor H. (Trevor Harvey). JII. Title QB36.G2D667 1999

520'.92

Every effort has been made to obtain pennission to reproduce the illustrations that appear in this book. Any errors or omissions brought to our attention will be corrected in future printings. University of Toronto Press acknowledges the financial assistance to its publishing program of the Canada Council for the Arts and the Ontario Arts Council.

Contents

PREFACE

vii

ACKNOWLEDGMENTS INTRODUCTION

IX

Xi

PROLOGUE: DRAKE'S SPEECH ON RECEIVING THE INTERNATIONAL GALILEO PRIZE FOR HISTORY OF ITALIAN SCIENCE

Part I

xix

Galileo: Biographical and General

Galileo: A Biographical Sketch 5 The Scientific Personality of Galileo 20 3 I Galileo's Explorations in Science 34 4 / Galileo's Language: Mathematics and Poetry in a New Science 50 5 I Mathematics, Astronomy, and Physics in the Work of Galileo 63 6 I Measurement in Galileo's Science 89 7 / Exact Sciences, Primitive Instruments, and Galileo I o6 8 / The Accademia dei Lincei 1 26 9 I On the Conflicting Documents of Galileo's Trial 142 1o / Galileo and the Church 1 53 1 /

2 /

Part II 1 /

Galileo: Bibliographical and Textual Studies

167

Galilieo Gleanings XXI: On the Probable Order of Galileo's Notes on Motion 17 1

vi

Contents

Dating Unpublished Notes, Such As Galileo's on Motion 185 3 I Galileo Gleanings XXIY: The Evolution of De motu 201 4 / Galileo's Pre-Paduan Writings: Years, Sources, Motivations 215 5 I Galileo in English Literature of the Seventeenth Century 236 2 /

Part Ill

Galileo: Scientific Method and Philosophy of Science 253

1 / Galileo and the Career of Philosophy 257 2 / Ptolemy, Galileo, and Scientific Method 273 3 I Galileo's Procedures, and Metaphysics 293 4 / Theory and Practice in Early Modem Physics 306

Part IV

Galileo: Astronomy

32 1

Copemicanism in Bruno, Kepler, and Galileo 325 2 / Kepler and Galileo 340 3 I Galileo's Steps to Full Copemicanism, and Back 351 4 / Galileo's "Platonic" Cosmogony and Kepler's Prodromus 364 5 I Galileo's First Telescopic Observations 380 6 I Galileo, Kepler, and Phases of Venus 396 7 / Galileo and Satellite Prediction 410 8 I Galileo's Sighting of Neptune (with Charles T. Kowal) 430 9 I Galileo Gleanings III: A Kind Word for Sizzi 442 1o / A Neglected Galilean Letter 458 1 /

INDEX ILLUSTRATIONS

469

follow page 200

Preface

The idea for a collected edition of Stillman Drake's published papers originated at a memorial at the University of Toronto attended by his family, friends, and colleagues in November of I 993. The very next day the editors brought the proposal to the University of Toronto Press, which expressed great interest, and after five years the plan has become reality. In addition to his sixteen books on Galileo, Drake published about I 30 articles, distributed in many journals and collections over a period of more than forty years, of which nearly I oo are on Galileo and most of the rest on other, often related, aspects of the history of science. Precisely because of the concentration on Galileo, Drake's papers, taken as a single connected body of work, are of lasting importance, and do not duplicate, but supplement his books, many of which are translations of Galileo's works without the detailed analysis reserved for the papers. By the gathering together of the papers in this collection, the literature of Galileo and of the history of science is enriched by the concentration of more than twelve hundred pages of the work of one of the most productive and original scholars of our age. It is our hope that this collection will remain of permanent value, to those who have read the original publications as they appeared, to students who perhaps know Drake only through the Discoveries and Opinions of Galileo, surely the most widely read book on Galileo ever written, and finally to future generations, who we believe will value Drake's work as long as Galileo himself is studied, which will be a very long time. In all, we have included eighty papers containing about 80 per cent of the pages that Drake published as separate articles. Our selection has been made on the criteria of choosing papers of the greatest scientific and historical interest that can stand on their own. In the complete bibliography at the end of this collection, the included papers are marked with an asterisk. Whether "our friend," as Salviati called his teacher, would have approved of our selection is not alto-

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Preface

gether clear and perhaps even doubtful. We can imagine him saying, "Not that one; I corrected it later." And in fact Drake's own collection Galileo Studies (Michigan, 1970) contains revised versions of some of the papers included here. Nevertheless, it is our belief that the evolution of Drake's research on Galileo is itself of interest, and even if earlier papers contain one or another point corrected in later papers, the earlier papers also contain much that was not later corrected or repeated, and thus can still stand on their own. We began with a complete bibliography compiled by James Maclachlan for Nature, Experiment, and the Sciences, the Festschrift for Drake edited by Trevor H. Levere and William R. Shea (Kluwer, Dordrecht, 1990), supplemented by further lists Maclachlan prepared in which the papers were placed into categories, the basis of the sections into which this collection is divided. Within each section we have arranged the papers to go from the general to the specific and papers on specific subjects are ordered according to the chronology of Galileo's work, or the chronology of the history of science in section eight, or by what seemed a logical ordering of the subjects. Only where such distinctions have no meaning, or within a group of papers on the same subject, have we ordered the papers according to the chronology of their publication. According to our criteria, we have excluded nearly all shorter notes, many of which are contributions to discussions with other scholars on points that cannot necessarily be understood without all the other papers; reviews; eloges; several bibliographic papers listing sources or publishing short texts with or, usually, without translations; and a few duplicate publications and shorter versions of material in longer papers. With regret we have excluded the introduction to the reprint of Thomas Salusbury's Mathematical Collections and Translations, virtually a monograph of twenty-seven very large quarto pages that would run close to sixty pages when reset. Also excluded are ten articles from the Dictionary of Scientific Biography, including the article on Galileo, since the DSB is readily available in any university library; in any case a similar biographical article on Galileo is included in the first section. Although we realize that nothing could be more helpful, more essential, to a collection of this kind than a comprehensive index, particularly because the same subjects can be treated, not only in several papers in one section but in papers spread through two or three sections, the magnitude of the task has led us to the simpler solution of a name index and an index of principal topics. University of Toronto, N . M . SWERDLOW, University of Chicago December 1998

T . H. LEVERE,

Acknowledgments

Our especial thanks are due to Florence Drake and Daniel Drake, whose generous support and wholehearted cooperation have made possible the publication of these volumes. Next, and of great importance, has been extensive guidance and help from James Maclachlan. He is also the principal source for the bibliography, which is a revised version of one he compiled with the assistance of Andrew Ede. We are also grateful for support to the Institute for the History and Philosophy of Science and Technology, to the Senate Research Committee of Victoria University, and to Donald Femie and the Department of Astronomy at the University of Toronto. Richard Landon and Philip Oldfield of the Fisher Rare Book Library, University of Toronto, are custodians of the Drake collection there, and have been of great assistance in tracing and providing copies of Drake's papers. We are also grateful to Gary McIntyre and Lydia Scratch for preparation of the index, and to Judith Brander and Marianne Stevens for further help in preparing the text for the Press. Ron Schoeffel and Suzanne Rancourt at the University of Toronto Press were immediately enthusiastic when we first proposed this publication to them. They, Kristen Pederson, and Barbara Porter have ensured that these volumes are as handsomely produced as Stillman Drake would have wished. Permission to reprint articles and essays was granted by the following institutions, journals, individuals, and presses: American Association for the Advancement of Science American Journal of Physics Annali dell' lstituto e Museo di storia de/la scienza di Firenze Annals of Science

Atti dei conveRni lincei Catholic University of America Press The Council of the British Society for the History of Science Dalhousie University Press Limited Edinburgh University Press

x

Acknowledgments

Elsevier Science Ltd. ETC: A Review of General Semantics Garland Publishing Garzanti Giunti Gruppo Editoriale S.p.A Dr Ivor Grattan-Guinness Greenwood Publishing Group, Inc. Historia Mathematica History of Technology Isis Johns Hopkins University Press Journal for the History of A.stronomy Journal of the History of Ideas Kluwer Academic Publishers Eman McMullin

Nuncius The Physics Teacher Physis Quaderni d' ltalianistica Renaissance and Reformation The Renaissance Society of America Rivista di Studi /taliani Science Scientific American Studies in History and Philosophy of Science Undena Publications University of Washington Press Yale French Studies

Introduction

For more than forty years, the serious study of Galileo has been dominated by the work of Stillman Drake, whose name is virtually synonymous with the works of Galileo as they are read today. Drake became an academic, but he developed his scholarship and style outside the academy, to which he came late, but to which he was a prolific contributor. Including his translations, he wrote 16 books on Galileo, contributed to 15 others, and produced over 100 scholarly articles (of which around 80 per cent are reproduced here). Born in Berkeley, California, on 24 December 1910, he went to school and university there. He attended Marin Junior College from 1928 to 1930, and then studied at the University of California, Berkeley, for the next two years. He began his studies with chemistry, moved to philosophy, and graduated in 1932 with the degree of AB in philosophy. He was fond of saying that in his studies he had moved from the abstract (chemical atoms) to the concrete (the truths of mathematics and positive knowledge). While at Berkeley, he met Kenneth 0. May, who later became a historian of mathematics, and John W. Abrams, then an astrophysicist and later an expert in operations research and a historian of science and technology. Drake obtained a teaching certificate in mathematics in 1934. That was his formal education. In the depths of the Depression, he held a series of positions as a finance consultant, moved to the U.S. government as a specialist in bonds in 1941, and became a bond consultant after the war. Drake's professional curriculum vitae sums up the years 1934 to 1967 in three words: "Municipal Finance Consultant." He never saw any point in wasting words, and, in a different context, was prone to quote Wittgenstein approvingly: "Whereof one cannot speak, thereof one must be silent." Problems of language were among those that he and a group of friends discussed in an informal seminar that they started in 1938 for mutual edification

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Introduction

and self-education. William Wallace tells the story in his citation presenting Drake for the Sarton Medal of the History of Science Society in 1988: [Drake's] first contribution was to be a paper on comparative philology. Looking for materials, one Saturday afternoon in 1938, in a San Francisco bookstore, he came across an old book that sparked his interest - so much so that he parted with two hard-earned dollars (a lot in those days) to have it for himself. The book was Alexander Bryan Johnson's A Treatise on l.Anguage, published over a century earlier, in I 828. Comparatively unknown even to the present day, A.B. Johnson was a linguistic philosopher whose ideas bear comparison to those of Ludwig Wittgenstein. A philosopher Johnson certainly was, but not an academic philosopher, for he pursued instead a very successful career in banking. So impressed was Drake with that rare little book, and it was indeed rare, that he himself, working evenings and weekends, produced a limited hand-set edition of the book, 42 copies in all, that came off the press in 1940. That, you might say, was Stillman's first publication.' Significantly, it was in philosophy.

There are a number of foreshadow in gs of Drake's interests and achievements in that event. He was to become a noted bibliophile and book collector, with an interest in the history, the making, and the content of books (when he was the recipient of a volume of essays in his honour, the contents were of course important, but so was the physical object as an exemplar of craftsmanship); a scholar whose sensitivity to the meaning and use of words was central to his historiography as well as to the excellence of his translations; a disciplined and lifelong autodidact; and a convivial colleague, who invented a history of science dining and discussion club at the University of Toronto, modelled in part on the early seminar. After his reprinting of Johnson, and an article on Johnson and his works on language, Drake published his first note on Galileo, and his second privately printed book, A Book of Anglo-Saxon Verse, itself a decidedly rare volume. And then he started serious work on Galileo. With his characteristic instinct to begin at the top, in I 953 he published the first English translation since the seventeenth century of Galileo's Dialogue Concerning the Two Chief World Systems - Ptolemaic and Copernican, the first of a series of translations and studies that have probably brought more of Galileo's works to more readers than they had reached during the first three centuries after they were written. Graced with a foreword by Albert Einstein, in German and English, Drake's translation of the Dialogue has ever since stood next to the original Italian as the standard version throughout the world, for it captures the eloquence, clarity, and wit of Galileo himself. When Salviati dismisses some scholastic arguments against the motion of the earth quoted by Simplicio with, "But please, if there is anything more, let

Introduction

xiii

us hurry through this tedious stuff," and Sagredo remarks that if Simplicio can find nothing better he would prefer to take the air in a gondola, it is Galileo giving the back of his hand to academic pedantry; but it is also Drake, who had as little patience as Galileo himself with what he saw as academic pretense. In the following years, while still a finance consultant, Drake pursued his life-long, demanding, and brilliantly successful self-education, and produced another five books. Among these was his splendid introduction to Galileo, including translations of his shorter non-technical writings, entitled Discoveries and Opinions of Galileo, published in I 957, which has never since been out of print. The book contains translations of most of the Starry Messenger, the Letter to the Grand Duchess Christina, excerpts from the Letters on Sunspots, and the Assayer, along with other documents and letters in the introductions to each work . In I 960 he published a complete translation of the Assayer in the Controversy on the Comets of 1618 with C.D. O'Malley. These years, years when Drake's employment was in finance, and when Galileo became his avocation, were also the years when Drake became an astute collector of rare books in science. When he moved from California to Puerto Rico as a finance consultant, he sold his first collection, since the combination of heat and humidity would have been destructive to leather-bound volumes. But he soon began another collection, and came to own virtually all of Galileo's works, the works of other scientists, both Renaissance and more recent (including Heinrich Hertz and Einstein), and over two thousand books on Galileo. Those books are now in the Fisher Rare Book Library of the University of Toronto. Drake's library came with him in 1967, when he made two major changes in his life. First, he married Florence Selvin Casaroli, and second, he moved to Toronto, where, at his old friend John Abrams's invitation, he joined the University of Toronto 's newly formed Institute for the History and Philosophy of Science and Technology as a full professor. Kenneth May had also come to Toronto, and also encouraged Drake to join him there. This was Drake's first and only academic appointment, one which he regarded as an honour; it was also a real coup for the University of Toronto and its fledgling Institute. Drake taught there until his retirement in 1979, publishing steadily all the while. He became a Canadian citizen in 1986, and Toronto remained his home until his death on 6 October I 993. The Toronto years saw the bulk of what has to rank as Drake's greatest achievement, his restoration and reconstruction of Galileo as an experimenter in mechanics. The most demanding of Galileo 's works, containing his discoveries in mechanics and the resistance of bodies to fracture, and his most powerful attack on Aristotelian and scholastic natural philosophy, is the Discourses and

xiv

Introduction

Mathematical Demonstrations concerning Two New Sciences pertaining to Mechanics and Local Motion, which Drake translated and published in 1974. Drake had always been concerned with Galileo's mechanics, and had previously published with I.E. Drabkin translations of the early tracts On Motion and On Mechanics ( 1960) as well as translations of writings on mechanics by Tartaglia, Benedeui, and Guido Ubaldo (1969). But now, with the translation of the Two New Sciences and his study of Galileo's manuscripts, mechanics became central. It was above all this thorough knowledge of Galileo's work in mechanics that made possible Galileo at Work, His Scientific Biography, as Stillman put it, "Galileo in his working clothes, tending his scientific garden," surely the finest and most comprehensive study of Galileo ever wrillen, and invaluable as a source for every scholar of Galileo, particularly for its exploration of the forty-year background of research and discovery that led to the Two New Sciences. Within his work on Galileo's mechanics, Drake's most impressive scientific achievement concerned Galileo's laws for falling bodies. He for the first time arrived at a clear understanding of the profound difficulties Galileo faced in correctly describing continuously accelerated motion, with a new, critical emphasis upon the signal role played in Galileo 's work by Euclid Book V, which presents Eudoxus's theory of proportion. He showed that, although Galileo's mathematics did not countenance the formation of ratios between quantities of unlike kinds, such as distance and time, he nevertheless produced a selfconsistent system based on novel procedures for comparing continuously changing quantities with one another. Stillman's work here was one of the major creative accomplishments of the history of science, just as Galileo' s was for early modem science itself, requiring a profound and sympathetic understanding of now-unfamiliar mathematical techniques and methods of reasoning. Drake's conclusions were based on painstaking analysis of technically difficult and obscure manuscript notes on motion. Just as important as his interpretation of Galileo's numerical puzzles was his allention to paper, ink, watermarks, and changes in handwriting, all clues that enabled him to date and organize manuscripts that had escaped Galileo ' s previous editors. In the process, Drake refuted the orthodoxy established by Alexandre Koyre, who had argued that Galileo 's work had lillle to do with experiments. Thanks to Drake's work, such views are now utterly untenable. As a professor, Drake insisted, he had less time for scholarship than he had found as a finance consultant. After he retired from teaching and became Professor Emeritus, he became even more productive than before. One of us, not having seen him for a couple of months, asked him one March what he was up to. "Florence gave me a computer for Christmas," he said, "so I wrote a book."

Introduction

xv

His works in retirement included the most channing of his many books, Telescopes, Tides, and Tactics, in which he embedded a reading of the Starry Messenger, now complete, in an authentically Galilean dialogue between Salviati, Sagredo, and Galileo's old friend from the Veneto, Paolo Sarpi. Another dialogue, published in 1981, was Cause, Experiment and Science. A Galilean dialogue incorporating a new English translation of Galileo's "Discourse on things that rest upon water or move in it." While there was hardly anything in the sciences that did not interest Drake, the single most obvious feature of his published work is his dedication to Galileo. No one except Antonio Favaro, the editor of the National Edition of Galileo's works, whom Drake admired above all other historians of science, above all other scholars, contributed as much to the study of Galileo, and Favaro and Drake will surely remain the most important and productive of all Galilean scholars for a very long time, perhaps for all time. The reason for this dedication must have something to do with a similarity of temperament of Galileo and Drake, both enjoying above all figuring out how things work and figuring it out in his own way, for each could only do things in his own way and was little influenced by what others believed. There is an anecdote about Galileo during his old age at Arcetri that Drake tells at the beginning of Galileo at Work that is worth repeating here as it tells as much about Drake as about Galileo: Once some fathers came to see him, and he was working in his garden and observing how the buds came out. He said, "I am ashamed that you see me in this clown's habit; I'll go and dress myself as a philosopher." "Why don't you have this work done by someone else?" "No, no; I should lose the pleasure. If I thought it as much fun to have things done as it is to do them, I'd be glad to."

Like Galileo, Drake preferred doing things himself, carrying out his own investigations, making up his own mind, most important of all, thinking in his own way. And Drake's way of thinking was very much his own, if anything, like that of a skilled craftsman or engineer who knows just how to put things together, just what models to construct, to make things work as they should. Just as Galileo began his investigation in the Two New Sciences of the resistance of bodies of fracture with reflections on the enonnous size of supports and blocks that were there to be seen in the shipyard of the Venetian arsenal, so Drake himself analysed Galileo's notes on bodies descending inclined planes and pendulums by constructing real inclined planes and real pendulums to see how they worked with variation of conditions, such as the inclination of the plane and the arc of the pendulum, including the essential condition of scale. In

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Introduction

order to time the descent on the inclined plane, Drake used frets, minutely varying their placement to correspond to equal intervals of time, which, like Galileo, he could measure effectively by singing. Likewise, the placement of the inclined plane in relation to the edge of a table was varied to investigate the distance of horizontal projection and parabolic paths of projection. Not the pure mathematics of Platonism for Drake. Even for something as difficult to duplicate as Galileo's theory of the tides, he devised a hypothetical, but very material, model of a rotating grindstone with holes and channels cut into it. What all this shows is not just that Drake replicated some of Galileo's experiments, although that in itself is of great importance and refuted absolutely the opinion that Galileo did not carry out such experiments, but more that his way of thinking, like Galileo's, was practical, material, concerned with the sensible world rather than a world on paper, in which the ultimate test of any proposition is not whether it is abstractly reasonable - for neither science nor history is pure reason - but whether it really works in accounting for what is empirically known, whether that be through the analysis of original sources or replication of experiments and measurements. And just as experiments and measurements are not done once and for all, but again and again through a process of eliminating alternatives and successive approximation to the most accurate result, Drake never let a subject alone for long, but kept returning to it, correcting and refining his own interpretations and conclusions. He certainly had no hesitation about changing his mind. For a number of topics considered in Drake's books and papers, of which Galileo's experimental work on motion and mechanics is the most important, he was engaged for many years in a dialogue, sometimes with other scholars but far more often and far more importantly with himself, continuously reexamining questions in the light of additional documents and experiments or new insights into the meaning of a calculation or a list of numbers or a drawing in a document already subjected to seemingly exhaustive examination. It was Drake's view, as he mentioned more than once, that empirical science does not proceed so much by definitive demonstration and absolute proof, the domain of pure mathematics alone, as by preponderance of evidence, and he never ceased looking for the extra bit of evidence that could provide, not absolute certainty, but as close an approximation to it as possible among the difficulties and uncertainties of historical investigation dependent upon the often cryptic fragments, above all of Galileo's manuscript notes, that fortuitously survive to our own day. The papers in this volume on Galileo's mechanics will not be easy for the reader, as they were not easy for Drake, but the work of studying them through all their twists and turns and successive corrections will be well worth the effort in understanding how one of the great and original scholars of our

Introduction

xvii

age approached as closely as he could to scientific and, more difficult than that, historical truth. However, most of the papers in these volumes do not pose the difficulties of those on Galileo's notes on motion, for Drake was on the whole a writer of greater clarity, whether his subject was biographical, textual, technical, or even philosophical, upon which he exceeded in clarity any modem philosopher of science one could care to name. And he wrote not only with clarity, but with enthusiasm for the scientific research in the exposition and analysis of which he took such delight. One can never come away from Drake without believing that Galileo was the most ingenious, the most brilliant of scientists, but one will also find that his admiration extended far afield, not only to Kepler as would be expected, but to Eudoxus, Ptolemy, Bradwardine, Buridan, Oresme, Albert of Saxony, Tartaglia, Benedetti, Baliani, and Fabri, not to mention A.B. Johnson and J.B. Stallo, on all of whom he had a good deal to say, more often than not entirely original. And because Drake's way of thinking and working was so much his own - he was spared the impediment to originality of a graduate degree in the history or philosophy of science - it is not be wondered at that his work is sometimes controversial. Just as he did not hesitate to change his mind when the evidence warranted, for the same reason he did not hesitate to state his opinions directly. He made judgments about past science and about present scholarship, judgments grounded in his deep knowledge of Galileo's life and work, and particularly in mechanics, not only Galileo's, but from antiquity through the seventeenth century, and these judgments sometimes led to controversies with other scholars. Drake was a great admirer of excellence, and saw no reason not to recognize it in the past as well as the present, whatever historiographic fashions might seek to dictate. He devoted his energies to Galileo because he recognized his excellence, as a stylist, as an experimenter, as a debater, and as a committed protagonist of what he saw as the values of science. Galileo was for Drake the first modem scientist. Though it is no longer fashionable to think one past work better than another, Drake's great strength as a scholar derived precisely from his devotion to quality and to truth as he saw it, and to his refusal to cater to modem (not to say post-modem) tastes in such matters. One may quarrel with one or another analysis or reconstruction, all of them quintessentially Drake, even, perhaps especially, when he changed his mind. Nevertheless, Stillman Drake's Galileo will continue to engage, to instruct, and to inspire long after lesser creations have been forgotten . That Galileo was also a practical man who loved music and fine wine was an added attraction. Drake played the viola da gamba, had an especial relish for Renaissance music, enjoyed and knew his wines, and made a splendid mine-

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Introduction

strone soup. Hospitality at the Drakes was very much a hyphenated affair, Stillman-and-Florence, with music, intense and witty conversation, incursions from the beagle, and great wannth. Stillman's dedication of Galileo at Work was, " with ambiguity but without equivocation," to Florence. Drake's interests ranged beyond Galileo, Renaissance mechanics, music, and Italy. He had a gift for friendship, and his two sons, Mark and Daniel, were named for his best friends from his early manhood, Mark Eudey and Daniel Belmont. He was fascinated by the relations between language and science, an admirer of Wittgenstein and the less well-known Alexander Bryan Johnson. Sherlock Holmes was another passion for him. In a biographical note for the Scientific American, Stillman noted that he was an indentured Baker Street irregular, whose proudest claim was his logical reconstruction and solution of a Sherlock Holmes mystery, starting from only a single clue. Here, as in his approach to science, he knew the importance of evidence, persistence, and reason. He also appreciated craftsmanship and technology, and was the proud owner of a Studebaker Hawk that, in I 969, he generously offered to one of us to use to cross Canada. Drake was widely honoured for his work. He was twice a Guggenheim Fellow, received the Premio lntemazionale Galileo Galilei in Pisa, and was awarded the Sarton Medal, the U.S. History of Science Society's highest honour. He was a member of the International Academy of the History of Science (Paris), a Fellow of the American Academy of Arts and Sciences, and a Fellow of the Royal Society of Canada. He received honorary degrees from Berkeley, the University of Toronto, and, near the end of his life, most appropriately from the University of Padua, where Galileo had been Professor of Mathematics from I 592 to I 6 Io. NOTE I

Drake's first publication was in fact "Stack-Up, a Checkerboard Game," Games

Digest 2:3, 8-9.

Prologue Drake's speech on receiving the International Galileo Prize for History of Italian Science

By tradition, the recipient of the Premio Intemazionale Galileo Galilei delivers an address, brief but serious, bearing on the researches that awakened in him a particular interest in Italian culture. It is with pride, gratitude, and great joy that I receive the Premio, and I shall with pleasure follow that tradition; but first I wish to say that my interest in Italy and in Italians goes back to my youth, spent in California beside San Francisco Bay. The climate and the countryside differ little there and here in Tuscany, something which from the beginning attracted many Italian settlers. It was truly good fortune for us native Californians that the love of utility and of beauty, twin virtues so dear to Italians, became an integral part of our own culture. Our vineyards and wineries, the fisheries and fine From the Selection Committee's Report The work of Stillman Drake, Professor Emeritus in the History of Science at Toronto University, has always been, and is essentially still dedicated to the works and thought of Galileo Galilei, to the study of whose writings he has made a masterly and fundamental contribution in the English-speaking world, by editing, promoting and presenting a wide range of translations. Stillman Drake is a unique example among foreign scholars in the historiography of sciences, of almost exclusive dedication 10 the study of Italian science and to the fundamental, specific influence it had - through the work of Galileo - on the origins and development of modem science. Drake has not only translated Galileo's "Dialogo" and "Discorsi," in Dialogue Concerning the two Chief World Systems (1953, with a second edition in 1967) and Two New Sciences (1974); he has also translated many other important writings i.e. (in the order in which Galileo wrote them) Operations of the Geometric and Military Compass ( 1978), The St any Messenger, in Discoveries and Opinions of Galileo ( 1957), Discourse on Bodies in Water ( 1960), Lellers on Sunspots, Discoveries (cil.), JI Saggio/ore in the volume (in collaboration with C.D. O'Malley) Control'ersy on the Reprinted from Italian Cil'ilization and Non-Italian Scholars (Pisa: Giardini, 1986), 191-8, by permission.

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Prologue

restaurants of our coast, bespeak the love of the useful by those Italian pioneers, while San Francisco's sidewalk flower-stalls reflect their love for beauty. Thus it was that during my first visit to Italy I quickly felt myself at home. I arrived at Milan from London, where the language spoken is my own, more or less, but where I did not feel entirely welcome. Here, only the language written in books is mine; indeed, only in 17th-century books. But the cordial, kind, and courteous attitude that you Italians demonstrate towards us foreigners made me feel at home. Partly, one result of your habitually generous hospitality to strangers has been my still scant command of the spoken language, for which I ask your pardon. Now, my particular interests in Galileo goes back half a century, at thattime not so much for his science as for the vivid personality of the man. Only one of his books was then available in an English version, his Discourses on Two New Sciences. Interested in his science, I published in 1953 an English version of his famous Dialogue. Since then I have translated almost all Galileo's books for the benefit of readers of English. As you well know, Galileo has never lacked hostile critics who are not always attentive to exactly what he affirmed. I consider it a waste of time to reply to his detractors except by making easier the reading of Galileo's own books, in which he amply replied, once and for all time. In the field of music, to say nothing of painting or of sculpture, the historical importance of the Italian culture is recognized by everyone. In the field of science, by few indeed. That is not strange. With the passage of time, a musical or an artistic masterpiece appears more and more an astonishing and an admirable Comets of 16 I 8 ( I 960 ). This volume also contains the translation of Mario Guiducci 's Discourse on the Comets ( 1619). In a similar way, in Galileo against the Philosophers, edited by Drake, in which he collects Galileo's polemical writings against the philosophy of the Schools, he includes a translation ofCecco di Ronchi1ti's "Dialogo della stella nuova" (16o5). Interesting, also because they reflect Drake's original approach 10 Galileo's science, are the two collections, On Motions and on Mechanics ( 196) and Mechanics in XVI Century Italy ( 1969), the former of which includes minor writings by Galileo on the subject, and the laner of which contains writings typical of the cultural context which formed Galileo, translated by Drake and helpers. The originality and importance of Drake's studies on Galileo is however most evident in his many essays on the interpretation of Galileo's ideas and method; originally published in specialised journals, these have in part been collected in Galileo Studies (1970). Drake 's major work, Galileo at Work . His Scientific Biography (1978) should be mentioned al this point, since it is already a firm landmark in contemporary historiography of science. A more compact version of the ideas Drake sustains in this great work is 10 be found in his book Galileo, published by Oxford University Press in 1980. In connection with Galileo's methodology, he published Galileo's unpublished notes on motion in 1979-as Galileo's Notes on Motion- in the third Supplementodegli Annali del Museoe Is1i1u10 di Storia della scienza of Florence, a publication which gave rise to critical discussion among specialists over his interpretation of Galileo's symbolism.

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work of genius. A scientific masterpiece, to the contrary, appears to us more elementary with the passage of time; even primitive, obvious. I wish to cite a remark from the famed Dialogue of Galileo, who wrote: I admire much more the first inventor of the lyre - although one may believe that his instrument was very roughly made and even more roughly played - than a hundred other artists who, in later times, brought that profession to great refinement.

The Premio bears a name recognized everywhere, the name of a great pioneer among scientists. But I believe that Galileo's own science, as much here in Italy as abroad, has come by now to be generally considered entirely outmoded and hardly deserving of serious study. It does not appear so to me. Galileo was the "first inventor" of mathematical physics: I mean, of truly modem physics. But his was not "very roughly made." Already present were utility and beauty. Before the time of Galileo, physics lacked utility, being based on metaphysics without measurements. It also lacked that mathematical beauty introduced by Galileo with the law of falling bodies. It is useful to be able to calculate the positions of a body during fall, and it is beautiful to have to that end the elegant Galilean mathematical rule. Galileo's physics reminds me often of those twin virtues, dear to Italians, brought by them to my native place. But that is not all. The law of fall was not found without the aid of music, another integral part of Italian culture. This fact emerges from my researches in the National Central Library of Florence. There are some writings in Galileo's own hand there which were not published in the Edizione Nazionale of his works. One of them contains almost exact measurements of the successive positions of a ball that moved down a gently inclined plane, at the ends of eight equal times. Galileo used a musical rhythm for this. A few days later he discovered the

Such a disagreement does not however lessen the value of Drake's interpretation of Galileo, an interpretation which rests chiefly on the differences in Galileo's method compared both to the traditional philosophy of the Schools and lo the orientation towards a philosophy of nature (as seen in Descanes, for example, and Newton), which was 10 have considerable importance in the development of modem science. Drake emphasises the importance placed by Galileo on exact measurements and on the use of specially built instruments and procedures, a fact which is useful in order not lo lose sight of the specific nature of his scientific research, particularly today when historiography tends lo rightly accentuate the close connections between the New Science and certain philosophical concepts. For his research and his important contributions lo the understanding and the spreading of knowledge on Galileo's science, the Committee, by unanimous vole, confers the International Galileo Galilei Award on Stillman Drake.

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law of fall through work noted on a page relating to the pendulum. He had measured lengths to a few millimeters, and times to one-twentieth of a second. In astronomy also Galileo made measurement more precise. We usually regard his telescope as an instrument of discovery, and nothing more. But in 1612 Galileo added to it a type of optical micrometer, which he mentioned in his journal of observations of Jupiter's satellites. The next year, measuring angles in the sky to ten seconds of arc, he recorded a supposed fixed star near Jupiter that appeared to him to have changed its position. An astronomer in California, Dr. Charles Kowal , and I believe that this supposed fixed star was the planet Neptune, observed by Galileo two-and-a-half centuries before the famous discovery of Neptune as a planet in 1846. Galileo's notes were so precise that the astronomer is now searching for another planet, beyond Pluto, that may perturb the orbital motion of Neptune. Truly Galileo's friend Fra Fulgenzio Micanzio was right when he wrote to him: Your mind is like the shops of goldsmiths, where the outer doors are made so that not even the dust is lost, because it has gold mixed in.

The science Galileo wrote was truly new and was not, as the professors of philosophy and theologians maintained, in no way superior to Aristotelian natural philosophy. Their mistake persists today when historians identify Galilean science with a philosophy of nature, rooted in metaphysical principles, to which at that time was subordinated even observation itself. Galileo reversed that ancient order by subordinating metaphysical principles to careful and precise observation. In that way a new physics was born. Adopted by the Lincean Academy, by the Accademia del Cimento, and then by the Royal Society of London, the new conception of science introduced here in Tuscany was spread throughout Europe before the end of the 17th century. I notice with special pleasure that already on a similar occasion, the Premio was conferred in the area of history of science on an American, and also for his studies of 17th-century science. I can suggest a possible reason for such a coincidence. Every European nation took part in the great Scientific Revolution of that epoch. Each one boasts of its having contributed to it. Italy speaks of Galileo; Germany , of Johann Kepler; France, of Rene Descartes, and England of Sir Isaac Newton. In those days America did not exist as a nation, or as nations. Its colonists, too hard-pressed by the struggle for existence, could not take part in great cultural movements. We American and Canadians, as students of the history of science, lack any compatriot to favor as the true founder in modem science. Hence we can choose from the long list of illustrious candidates without

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fear of offending our fellow-citizens. The facts and objectivity lead us to put Italy in the first place, for its having separated science from metaphysics in order the better to study nature as she presents herself. It was precisely in the rich ambience of Italian cultural traditions that Galileo found the most direct road for that type of studies. The Galilean concept of precise measurements in the field of physics, following the footsteps of ancient astronomers instead of the opinions of philosophers (whether ancient or contemporary with him), created modem physics. In America, where useful science is preferred over speculative philosophy, Galileo is ever more recognized as the founder of exact science. This science is a worldwide heritage from Italian culture, no less than are the great Renaissance advances in music and in art. I hope that this may cease to be cast in doubt by foreigners when they confront Galileo himself, reading him in the languages most familiar to them. To make that possible has been my task for many years, as a service to truth and to my compatriots. The prize here conferred on me by highly esteemed judges, who have considered my work beneficial also to Italy, comes to me entirely unexpected and will remain for me the most cherished of all as long as I live. The Premio will serve always as a souvenir of the generosity of spirit shown to foreigners in Italy; I think of the Sala degli Stranieri at the University of Padua; of the monument at Bellosguardo to its past foreign residents, and of that splendid inscription of the fa~ade of the National Central Library of Florence, commemorating the assistance rendered by foreigners immediately after the flood some twenty years ago. Above all, in my heart, your generosity will keep alive my memory of Professoressa Maria Luisa Bonelli-Righini, without whose kindness I should never have been able to succeed in these Italian researches of mine.

PART I GALILEO: BIOGRAPHICAL AND GENERAL

There are many biographies of Galileo, and Drake wrote four. The largest is of course Galileo at Work ( 1978), a life and works with the emphasis very much on works. For the Past Masters series published by Oxford, he wrote Galileo ( 1980). Naturally, he wrote the article on Galileo for the Dictionary of Scientific Biography (1972), which is related to the first paper in this collection, "Galileo: A biographical sketch" ( 1 ), a life rather than a works, which fill the rest of this collection. Biography, however, is no longer the favored form of exposition in the history of science, which has moved more toward considerations of the relation of science and society and of the continuity of the history of ideas. While acknowledging the benefits of these approaches, in "The Scientific Personality of Galileo" (2) Drake considers aspects of Galileo's personal character that were essential to his scientific discoveries and thus to the history of science, in particular, his ability to reach generalizations on the basis of partial evidence, what might be called his scientific intuition, and his well-known willingness to fight for his convictions. Galileo's scientific intuition has an important role in the next paper, "Galileo's Explorations in Science" (3), which is a review of some of Galileo's most famous discoveries with particular attention to just how Galileo thought. "Galileo's Language: Mathematics and Poetry in a New Science" (4) is a discussion of the relation between descriptions of nature in language and nature itself in Galileo's writings. It is a paper on the relation of "words and things," and is concerned with the same issues that drew Drake to the work of A.B. Johnson (see Part IX, 1 and 2). "Mathematics, Astronomy, and Physics in the Work of Galileo" (5) is also concerned with Galileo's way of thinking, here in his application of mathematics to physics - Aristotelian physics and even the medieval treatment of motion were qualitative - and of physics to astronomy, with specific examples of his proof of the equilibrium of weights on inclined planes and the physical conclusions he drew about the heavens from his observations with the telescope. One of the ways in which physics is made mathematical is through measurement, and that is the subject of "Measurement in Galileo's Science" (6), in which examples are drawn from Galileo's measurements of motion on inclined planes, treated here in several papers in Part VI, and of the weight of the air discussed in the Two New Sciences, as well as Galileo 's measurements of the apparent diameters of planets and stars, showing that they were far smaller than previously believed. Measurement is taken up in far more detail in "Exact Sciences, Primitive Instruments, and Galileo" (7), which, in addition to a more extensive treatment of the preceding examples, considers Galileo's estimate of the separation of Jupiter from the fixed star that turned out to be Neptune (see Part IV, 8) and his measurements of horizontal projection (see Part VI, 3, 5, 15).

4

Galileo: Biographical and General

"The Accademia dei Lincei" (8) is again a historical and biographical paper, on the history of Federico Cesi's academy from its founding in 1603 to its dissolution following Cesi's death in 1630 - it was refounded in 1801 and has since become the leading learned society of Italy - with particular attention to Galileo's relations with Cesi and the Lincei following his election in 1611. The most famous event of Galileo's life is of course his appearance before the Holy Office in 1633 following the publication of the Dialogue. The principal accusation against Galileo was that at the residence of Cardinal Bellannine on 26 February 1616 he had been specifically warned not to hold, defend, or teach the Copernican theory in any way either in speech or writing, and that he had consented to this prohibition, which he had now violated by attempting to prove the Copernican theory in the Dialogue. The events of Galileo's interview with Bellannine have been much disputed, and "On the Conflicting Documents of Galileo's Trial" (9) is Drake's analysis of what might have happened and what role these events played in his inquisition. "Galileo and the Church" (IO) is an examination of the motivation of the original attack on Galileo and the condemnation of Copernicus in 1615-16, with the blame placed principally upon academic philosophers, and the effects of this on the publication of the Dialogue and Galileo's inquisition.

1 Galileo: A Biographical Sketch

It is presumed that those who are attracted to the present volume are already acquainted with the life and achievements of Galileo. Nevertheless, it may be useful to have at hand a sketch of his career in which some commonly repeated but erroneous or doubtful statements have been corrected, and to which some material that is not widely known has been added. An attempt has therefore been made to provide such an account of Galileo's life and character. Galileo was born at, or more probably near, Pisa on February 15, 1564 (according to the Julian calendar). His father, Vincenzio Galilei, was a Florentine by birth and a professional musician. His mother, Giulia Ammanati, was a woman of good intelligence and education, but selfish and difficult. Vincenzio was able to earn but a meager livelihood as a performer and teacher of music, though a number of his compositions were published. He was also the author of two respectable books dealing with music theory, and one spirited reply to his former teacher, the celebrated theorist Gioseffo Zarlino, who had sharply disagreed with some of Vincenzio's published opinions. With respect to Galileo's early background, it is worth mentioning that Vincenzio ridiculed reliance on authority alone, experimented with the monochord in order to interpret and reconstruct the ancient tonal systems, and displayed a good knowledge of and respect for mathematics. Galileo's early education was with the monks at Vallombroso, where it appears that he seriously considered entering upon the monastic life. His father, however, intervened and removed him from the monastery on the pretext that the boy's eyes required medical attention. In 1581 he was enrolled at the University of Pisa, in the school of medicine. His family having returned to FloReprinted from Galileo: Man of Science, ed E. McMullin (New York: Basic Books, 1967), 521--06, by permission of the editor.

6

Biographical and General

rence to live, Galileo resided at Pisa with the family of his mother's niece. At the university he gained the reputation of a rebel against the Galenist and Aristotelian authorities in medicine and philosophy. It was while he was a student at Pisa that Galileo observed the isochronism of the pendulum. Tradition has it that this came about through his observation that a heavy hanging lamp in the cathedral preserved the same period of swing as its arc diminished after having been drawn far back in order to be lighted. The fixture now in that place, known as "Galileo's lamp," was in fact not installed until 1587. Moreover the present lamp, though now electrified, was originally designed in such a manner that it would not have been withdrawn for lighting, since the subsequent swing back to center would have extinguished the flame. These facts contradict the name bestowed on the lamp by modem guides, but they scarcely support those writers who wish to classify the tradition as a myth - "as if," wrote Professor Antonio Favaro, " there was no lamp there previously; or as if its predecessor swung according to a different Jaw of physics." In any event, experiments with the pendulum formed an early and important part of Galileo 's insights into the Jaw of falling bodies, and later afforded him an invaluable means of improving the methods of timing for astronomical observations. Galileo's first formal training in mathematics came in 1583, not at the university but under the tutelage of Ostilio Ricci , a friend of his father's who was tutor to the pages of the Tuscan court. Ricci's mathematical interests were oriented toward practical applications, to judge by his surviving manuscripts; he was associated with the Academy of Design at Florence, and it is likely that Galileo 's preference for applied rather than pure mathematics had its origin in Ricci 's teaching. Galileo's father did not encourage his mathematical studies at first, probably because of the superior prestige and pay of the medical profession and because the most distinguished of Galileo's ancestors had been a physician. Ricci, however, interceded with Vincenzio on this point, and Galileo turned to mathematics in earnest, leaving the university without a degree in 1 584 after his failure to obtain a scholarship from the Grand Duke. He returned to Florence, where he continued his mathematical researches and composed his first scientific paper, la bilancetta, reconstructing the process by which Archimedes had detected the goldsmith's fraud in making the crown of Hiero and describing an ingenious and useful hydrostatic balance. He also developed some new theorems concerning the centers of gravity of certain solids about this time, concerning which he corresponded with the illustrious Jesuit mathematician Christopher Clavius at Rome, and with his friend and future patron, the Marquis Guidobaldo del Monte. He gave some lessons at Florence and at Siena, and then in 1587 he set out for Rome in the company of a scion of the wealthy Ricasoli family, with some idea of seeking his fortune in the Near East.

Galileo: A Biographical Sketch

7

Ricasoli, however, was afflicted with some mental disorder, and after the shortJived excursion he became the subject of protracted judicial proceedings to set aside his will and reclaim his impulsive gifts; Galileo's deposition in this lawsuit is still extant. In 1588, Galileo attempted unsuccessfully to gain the post of mathematician at the University of Bologna, with recommendations from those who had been impressed by his theorems on centers of gravity. The chair at Bologna was awarded to Giovanni Magini, who remained an antagonist of Galileo's, but in 1589 Galileo succeeded in getting the chair of mathematics at the University of Pisa on the recommendation of Guidobaldo. There he commenced the writing of a treatise, On motion, in opposition to Aristotle, which was clearly intended for publication but was not in fact published. Its central thesis is the destruction of Aristotle's two rules, that the speed of descent is proportional to weight and that it is inversely proportional to the density of the medium. Galileo attempted unsuccessfully to substitute for this a "hydrostatic" theory of fall , in which different speeds of descent would be accounted for in terms of a buoyancy principle. It is likely that he was led to this theory by his studies of specific gravity, though many of his conclusions resemble those published by Giovanni Battista Benedetti at Turin in 1585, and most scholars suppose him to have borrowed them without acknowledgment from that source. Several important results were obtained by Galileo, notably a fruitful demonstration of the conditions of equilibrium on inclined planes, but because of his failure to recognize at this time the importance of gravitational acceleration, he was unable to reconcile his conclusions about motion on such planes with the observed facts. His failure to complete and publish the treatise on motion suggests that he was dissatisfied with it on account of this conflict. Vincenzio Viviani, Galileo's "last pupil," who lived with him in his final years and doubtless had the story from his own lips, first described the celebrated (and much questioned) dropping of weights from the Leaning Tower during Galileo's professorship there. According to Viviani, weights of the same substance but different sizes were dropped, and came to earth simultaneously, thus contradicting Aristotle. He says further that the entire student body was present. The story has been challenged on several grounds, but principally because the descent is not strictly simultaneous in air, and because the university records show no trace of such an event, nor is it mentioned in contemporary letters. The controversy is aggravated by the habit of modem writers of referring to the event as an "experiment." In all probability it did occur, but it was certainly not an experiment; it was a demonstration. Galileo had already arrived at the conclusion that the descent should be simultaneous from his (incorrect) buoyancy theory of fall. The Aristotelians had a totally different view of the rel-

8

Biographical and General

alive speeds, and the demonstration was adequate to contradict that view, whether or not the impact of the weights was strictly simultaneous. But Galileo was by no means the first to contend that the different weights would fall together, nor was he the first to conduct a test of the conclusion, if indeed he did so. The proposition had been published by Benedetti in 1553, and the test had been made and published by the Flemish engineer Simon Slevin in 1586. Galileo, in later years, remarked that his attention had first been called to the fallacy of Aristotle by a hailstorm in his youth, in which very large and very small hailstones reached the ground together; had Aristotle been right, this would have necessitated either their origin at very different heights or their departure at times related to their sizes, either of which Galileo considered improbable . . At Pisa, Galileo was not only in conflict with many of the other professors, but he also gained the enmity of an important person, probably Giovanni de 'Medici, by point out the fallacy in an engineering proposal of his. Most likely this was a device for the use of floating cranes in the dredging of the Bay of Leghorn, based on the idea that the flatness of a surface adds buoyancy over and above that gained from the density of the material used. In any case, various disputes seem to have made him despair of advancement at Pisa, while his father's death increased his financial responsibilities, and in 1592 he resigned his post. Later in that year, again with the assistance of Guidobaldo, he was able to secure the chair of mathematics at the University of Padua, where he remained until 1610. At Padua the intellectual climate was vastly more to Galileo's taste than at Pisa. One of his close friends was Fra Paolo Sarpi, an astute student of mathematics and science until the theological troubles between Venice and Rome later came to monopolize his attention. Another was Giovanni Vincenzio Pinelli, whose home at Padua was the meeting place of distinguished scholars of all nations, and whose library was filled with treasures. A still more intimate friend was Giovanfrancesco Sagredo, a Venetian nobleman and talented amateur of science. Galileo maintained a large establishment at Padua, in which boarding students and their servants were housed, and in which a workshop was maintained for the manufacture of instruments. In addition to his assigned lectures, which included elementary astronomy and mathematics, Galileo gave private lessons in mechanics, military architecture, and other special instruction requested by his pupils. In 1593, Galileo composed an outline of his lectures on mechanics, which he revised from time to time, bringing it to its final form about 1600. Dealing with the inclined plane in this treatise, he stressed the fact that a body on a horizontal plane may be moved by any minimal force, contrary to the belief of Pappus. He had given a proof of this in his earlier treatise On motion, and it led him to his

Galileo: A Biographical Sketch

9

first idea of inertia, in opposition not only to Aristotle but to the medieval writers who had explained projectile motion in terms of an impressed force called "impetus." Galileo was the first to perceive that motion and rest were states of a body to which the body was indifferent. About the year 1602, he devised a thermoscope by warming the air in a glass bulb provided with a long thin neck, and then inverting it in water; the height of the water in the neck thereafter gave an indication of the temperature of the surrounding air. He had also noted the utility of the pendulum for time measurement, and adapted this to the purposes of medicine by devising a pulsilogium. This consisted of a board to which a pendulum was attached, in such a manner that the string could be stopped at any desired length by pressing the thumb against it. The swing of the bob was synchronized with the patient's pulse in this way, and markings on the board against which the thumb was pressed indicated whether the pulse was sluggish, normal, or feverish . Both these devices were taken up and improved by Sanctorio Sanctorius, another professor at Padua, who did much to make medicine more of a science. In 16o4, a conspicuous nova appeared which aroused much interest, partly from superstitious awe and partly because of the significant studies that had been made by Tycho Brahe of the nova of 1572. Galileo delivered three public lectures concerning this phenomenon, which aroused such interest that no hall at Padua would accommodate the audiences. The lectures are lost, but an idea of their content may be drawn from a satirical dialogue, published in the rustic dialect of Padua, in which Galileo is known to have had a hand. He poked fun at the Aristotelians as well as the astrologers, and probably used the nova to refute the idea that the heavens are unchangeable. A booklet on this nova was published by Baldessar Capra, a young student at Padua, who mentioned in it that the discovery was not made by Galileo but by him and his teacher, Simon Mayr, and reproached Galileo for not having duly credited them in his lectures. Galileo did not reply in print at the time, but in 1607 he took occasion to do so in connection with another matter. About 1597, Galileo had devised an instrument of great utility to engineers, probably on the basis of work by his patron Guidobaldo. It was a proportional compass, known today as a sector, containing various scales which enabled the user to solve a wide variety of problems dealing with map-making, construction of geometrically similar figures, computation of roots, and the calculation of densities. Galileo wrote a handbook for users of the instrument, which was manufactured for sale by a craftsman retained by Galileo, and in 1606 he had this booklet privately printed in Italian. On Mayr's instigation, Capra obtained one of the instruments and a copy of the book with the aid of his father, who was acquainted with Galileo. They then composed a Latin treatise on the construction and use of the instru-

1o

Biographical and General

ment, drawing heavily on Galileo's book. Capra claimed the invention for Mayr, and accused Galileo of having wrongfully appropriated it. Galileo brought the matter before the authorities, demonstrated his priority and the incompetence of Capra to explain many propositions in the book he had published, and had the publication suppressed and its ostensible author censured. Mayr, who was doubtless the true author, had returned to Germany, but his plagiarisms from Galileo were not yet finished . Galileo published an account of the proceedings in 1607, in a book called Defence against the calumnies and impostures of Baldessar Capra, in which he also replied to the criticisms that had been leveled against him in Capra's earlier book concerning the 1604 nova. By 1609, Galileo had arrived at many new and valuable propositions concerning mechanics and the strength of materials, and was about to publish them when a series of events focused his attention anew on astronomy. In the autumn of 1608, a Dutch spectacle-maker had applied for a patent on a device consisting of two lenses, which was capable of magnifying distant objects. From contemporary reports, this must have consisted of two convex lenses, since it inverted the image. Rumors of this interesting invention reached Italy soon afterward, Galileo's friend Fra Paolo Sarpi at Venice being one of the first to hear of it. Sarpi sought more information, and in the early part of July, 1609, its existence was confirmed by a former pupil of Galileo's, named Jacques Badovere (or Giovanni Badoer), in a letter sent probably to Sarpi. Galileo was visiting Venice at the time, and hastened back to Padua, where a visiting foreigner had already shown one of the instruments. Probably with the assistance of descriptions by friends who had seen it, he set to work at once to construct such an instrument himself. He first experimented with a convex objective and concave eyepiece fixed in a metal tube, and thus obtained an erect image. He quickly improved this instrument so that it would magnify about nine times, and returned to Venice late in August with a telescope which was vastly superior to any that had been previously reported. This he demonstrated to several senators and other Venetian dignitaries, showing that by means of it ships could be detected from the Tower of St. Mark long before they were visible to trained naked-eye observers. He then presented the device to the Venetian government, receiving in return an increase in salary and a lifetime appointment. But Galileo had not intended to commit himself to remain for life in the Venetian Republic. He had been negotiating for some time to obtain appointment by the Grand Duke of Florence, his friend and former pupil Cosimo II de'Medici, and lost no time paying a visit to Florence with one of his telescopes to renew his efforts along that line. Upon his return to Padua, Galileo worked hard to improve the telescope still further, and early in January, 1610, he was in possession of a thirty-power

Galileo: A Biographical Sketch

11

instrument which enabled him to make a number of startling astronomical discoveries. Apart from the mountainous character of the moon's surface and the detection of innumerable fixed stars never previously seen, he observed four satellites of Jupiter and commenced to plot their movements. In March, 1610, he published these discoveries in a book called Sidereus nuncius (Starry messenger), which caused a sensation throughout Europe. He christened the newly discovered satellites the "Medicean stars," and again visited Tuscany, this time with the hoped-for result, an appointment as Chief Mathematician and Philosopher to the Grand Duke, and Chief Mathematician of the University of Pisa without obligation to reside in that city. In the summer of 1610, he left Padua permanently for Florence. During his residence in Padua, Galileo had taken a Venetian mistress named Marina Gamba, by whom he had two daughters and a son. She remained in Padua with the infant son, Vincenzio, while Galileo's mother at Florence took temporary custody of the daughters. Galileo's relations with Marina Gamba remained amicable, and when Vincenzio was old enough for the trip, he also was sent to Florence. Galileo's mother, however, was a very difficult woman, and in order to solve his family problems, Galileo managed to have the two girls admitted to a convent near Arcetri, though they were not yet of full age for this move. The elder daughter took the name Maria Celeste, and was a source of much comfort to her father throughout her brief life. The younger daughter tended to be peevish and frail in health. Of the son, little is heard until many years later; it is frequently said that he was a problem to his father, but this appears to be largely a confusion with Galileo ' s nephew who bore the same name (Vincenzio Galilei) and who was sent to live in Italy while his father (Galileo ' s brother Michelangelo) remained at Munich. Michelangelo Galilei was a professional musician, like his father, but lacked the sense of responsibility characteristic of his more famous relatives. Instead of assisting in the financial problems of the family, or contributing to the dowries of his sisters, he left Galileo to meet these obligations and frequently asked for financial and other assistance himself. Shortly after his arrival at Florence, Galileo observed the phases of Venus (which had been too close to the sun for observation earlier in the year) and described the unusual shape of Saturn. Galileo ' s telescope did not resolve the rings, which he took to be two small stationary satellites close to the planet. These new discoveries he announced in cryptic form , as anagrams, pending their formal publication after full confirmation. Galileo ' s experience with Capra and Mayr seems to have converted him from an open-handed man , who prior to 1607 freely gave out his ideas and his writings, into an unduly suspicious man who thereafter guarded his discoveries jealously.

t2

Biographical and General

Johannes Kepler, to whom Galileo had transmitted the Sidereus nuncius and then made one of his telescopes available through the Tuscan Ambassador to the Emperor by whom Kepler was employed, fully confirmed Galileo's discoveries and beseeched him to reveal these new phenomena, which Galileo did in letters published by Kepler in his Dioptrice of 16 t t. Meanwhile considerable opposition to Galileo's claimed discoveries had developed. Many astronomers were unwilling to admit them, and even some who had had the opportunity to use Galileo's telescope were unable to see the things he had observed. Some books appeared attacking Galileo's claims, to which he did not reply in print. He preferred to journey to Rome and show his discoveries personally to the influential Jesuit astronomers with whom he was in correspondence. Illness detained him for some time, but he finally arrived at Rome in April, 161 I. There he was feted by important church dignitaries, won the support of the Jesuit astronomers, and was made a member of the Lincean Academy, the first true scientific society, organized in 1603 by Marquis (later Prince) Federico Cesi. While Galileo was establishing the highest reputation away from home, various adversaries of his at Florence did a good deal to undermine him there. Probably his original detractors were courtiers who did not want him to upset their influence on the young Grand Duke, and professors at Pisa who resented the special appointment given to him there. At any rate, there is evidence that his new post had already become uncomfortable by the summer of 161 1. Shortly after his return, in June, he took part in a philosophical disputation in which the nature of ice and the causes of bodies floating in water were discussed; Galileo took the Archimedean position in opposition to Aristotle. This led to open controversy, in which a certain Ludovico de lie Colombe boasted that he would defeat Galileo by experimental demonstrations. The debate was not actually held, and Galileo appears to have been asked by the Grand Duke to refrain from such oral debates and to confine his remarks to written treatises. Toward the end of September, the same subject was debated at the Grand Duke's own table, two cardinals being present; one of these, Maffeo Barberini, later to become Pope Urban VIII, took Galileo's side. Galileo then set down his entire position in writing, and it was published in 1612; the first edition being speedily exhausted, a second appeared in the same year. In his book, Bodies in water, Galileo set forth in Italian his scientific arguments, complete with descriptions of corroboratory experiments which might easily be performed by anyone. Galileo remarked in later years that ignorance had been his best teacher, as the ignorance of his opponents had led him to search for evident demonstrations which he would not otherwise have considered necessary. Late in 1612, a German Jesuit, Christopher Scheiner, wrote a series of letters

Galileo: A Biographical Sketch

13

to a distinguished amateur of science, Mark Weiser of Augsburg, describing sunspots and setting forth the erroneous theory that they were tiny planets revolving erratically about the sun. Weiser published these letters, concealing the author's name under the pseudonym Apelles, and sent them to Galileo for his comment. Galileo replied in three letters, published in I 6 I 3 under the auspices of the Lincean Academy . He stated that he had observed sunspots sometime before, and had shown them to friends while at Rome in I 6 1 I, but hesitated to come forth with a theory concerning them until he was sure of his ground. It was his opinion, however, that they were generated and dissolved on the very surface of the sun, which rotated on its axis in approximately a month. These views were stoutly opposed by the Aristotelians, who held the heavens to be perfect and not subject to generation and decay. Galileo, on the other hand, saw in the sunspots and the lunar mountains conclusive evidence for holding that heavenly bodies were of material similar to that of the earth, and moreover he declared himself unequivocally in his Letters on sunspots to favor the Copernican theory. Toward the end of 1613, Galileo's former pupil Benedetto Castelli, who had secured the chair of mathematics at the University of Pisa, was present at a discussion of Galileo's astronomical views at the table of the Grand Duke. In this discussion a professor of philosophy remarked that the earth could not be in motion, as this was contrary to the Bible. Castelli, who was a Benedictine monk, argued the point, and wrote to Galileo of the affair. Galileo replied with a long letter setting forth his opinion as to the relations of science and religion in such matters. This letter was circulated among the professors at Pisa. About a year later, a young Dominican named Tommaso Caccini denounced from the pulpit at Florence the views of Galileo and of scientists generally. An elderly Dominican, Nicolo Lorini, visited Pisa shortly afterward and expressed his regret at the intemperance of that sermon. Castelli obligingly showed him Galileo's letter, of which Lorini took a copy back to Florence. Having read it, he proceeded to notify the Roman Inquisition that the views of the Galileists should be reviewed as possibly heretical, forwarding a copy of the letter. When Galileo learned of this, he took steps to place a correct copy in the hands of church authorities who were friendly toward him, but inquiries conducted at Pisa on behalf of the Inquisition made him aware that a prohibition of the Copernican theory was more than a possibility. He proceeded to rework and improve the text of his letter to Castelli, addressing an extended version of it to the Grand Duchess Christina. Galileo's Bodies in water had been the subject of at least four published attacks, one by Colombe and three by university professors. Galileo had prepared extensive replies to their arguments, but in view of the battle that was

14

Biographical and General

brewing around him on other and more serious topics, he turned these over to Castelli, who published replies to Colombe and one professor in 161 5. This Risposta, without name of author but with an introduction signed by Castelli, was in fact almost entirely from Galileo's pen. During the summer of 1615, Galileo was seriously ill, but late in the year he journeyed once more to Rome, against the advice of his Roman friends and of the Tuscan Ambassador, in the hope of clearing his own name and also preventing action against the teaching of Copernicanism. In this he not only failed, but in all probability it was his public debating there which brought the matter to a head. A special commission appointed by Pope Paul V pronounced the twin affirmations of the stability of the sun and motion of the earth to be rash and contrary to Scripture. Galileo was enjoined by Cardinal Bellarmine, on express order of the Pope, to abstain from holding or defending these views any longer, and early in March 1616, a decree was issued against books which attempted to reconcile them with Scripture and suspending the De revolutionibus of Copernicus "pending correction." The Pope had ordered that if Galileo was recalcitrant to Bellarmine's injunction, then the Holy Office was to issue. a formal injunction forbidding him even to teach the condemned views orally or in writing, under penalty of imprisonment. It appears probable that this stronger language was in fact employed toward him by another official present at the interview, though its use was improper, since it does not seem that he had, in fact, been recalcitrant. 1 Rumors that Galileo had been forced to abjure circulated throughout Italy, and before he left Rome he applied to Bellarmine for documentary evidence that nothing of the sort had happened, which the Cardinal supplied in his own handwriting. Upon his return to Florence in mid-1616, Galileo entered a period of scientific inaction. He turned his attention primarily to the practical problem of the determination of longitudes at sea, which he tried to calculate on the basis of observations of the satellites of Jupiter. Negotiations with the Spanish government to conduct tests of his scheme and for its sale if successful were carried on, but came to naught. Meanwhile, he refrained from publishing anything further for a time. Toward the end of 1618, however, while he lay ill, three comets appeared in rapid succession, the last being unusually bright and of long duration. These comets were the subject of much discussion and of many pamphlets. The event offered Galileo a pretext for re-entering the field of astronomical debate without treading on forbidden grnund. He took the precaution of having his views on comets set forth by a pupil, Mario Guiducci, who was then Consul of the Florentine Academy, but he made it clear that he had little regard for the opinions expressed by an anonymous Jesuit writer at Rome, who followed the theories of Tycho Brahe. The Jesuit, Horatio Grassi, was much incensed and

Galileo: A Biographical Sketch

15

replied with a direct attack on Galileo himself, ignoring Guiducci, but concealing his own identity under a pen name. Galileo in tum replied in detail in 1623 with a great polemic, The assayer, in which he undermined the principal assumption of his opponent and illustrated, by vivid examples, the role played by scientific doubt in the acquisition of true knowledge. Galileo's Assayer is a book of interest and importance in several respects. In 1614, Simon Mayr had published in Germany a book called Mundus jovialis, in which he declared on the very title page that he had discovered the satellites of Jupiter in 1609, and in which he gave a long and rather implausible account of the circumstances. The date of his first claimed observation, computed according to the Julian calendar in use in Germany, was precisely that of Galileo's second published observation in the Sidereus nuncius of 16JO, as Galileo pointed out in the opening pages of The assayer. Galileo also mentioned a number of other incidents concerning his previous books, and among them he recounted the many writers who had claimed credit for the discovery of sunspots. Christopher Scheiner, who was unaware of any book on the subject other than Galileo's and his own, took great offense at this passage, with serious consequences in later years. It should also be mentioned that The assayer, which is of relatively small scientific importance and has not been widely read outside Italy, is usually portrayed as a book in which Galileo was wholly wrong and his Jesuit opponent right concerning the nature of comets. This view, which at one time I accepted on superficial evidence, is not tenable. Galileo's purpose in the book is not to set forth a theory of comets, but to show that his opponent's fundamental assumption might be completely erroneous, and that his entire argument would fall to the ground if comets were masses of lighted vapor rather than solid bodies. While this book was in the press, Galileo's old friend, Maffeo Cardinal Barberini, succeeded to the papal chair, with the result that many of his other friends received appointments to important Church posts. The assayer was dedicated to the new Pope and found great favor with him. In 1624, Galileo went once more to Rome. There he paid homage to Pope Urban VIII and sought permission to publish his long-promised book on the system of the world. In several long audiences, the new Pope granted him permission to discuss the rival theories "hypothetically" and impartially, but refused to revoke the earlier decree or to countenance "physical" arguments (as opposed to mathematical reasoning) in favor of Copernicus. Galileo returned to Florence and commenced work on a book which he believed was in compliance with these instructions. The Dialogue concerning the two chief world systems proceeded slowly, with many interruptions, but was finally completed in 1630. Galileo then returned to Rome with the manuscript, intending to have it licensed for publication there and have it printed by the Lincean Academy, as

16

Biographical and General

had been done with two of his previous books. It soon became apparent, however, that it would not be easy to secure the license, and Galileo had to return without it. There ensued many arguments and delays, during which Prince Cesi, the sole financial support of the Academy, died suddenly. Castelli, then at Rome, advised Galileo to have the book published at Florence instead, and after various negotiations the book was reviewed and approved by the Church authorities there. It was finally published at Florence in March, 1632, and was widely acclaimed. At Rome, however, Galileo's foes busied themselves to secure the Pope's displeasure with the book. Among these the leader was unquestionably Christopher Scheiner, who was now still further incensed against Galileo over a lengthy discussion on sunspots in the Dialogue, in which Galileo not only again asserted the priority of his observations, but gave a long and reasoned argument for the motion of the earth based upon the seasonal variations in sunspot paths. Scheiner was convinced that Galileo had learned of those variations from a book he had published in 1630, with the title Rosa ursina, though in fact Galileo's Dialogue was almost through the press before he ever saw a copy of Scheiner's book, in addition to which he could scarcely have introduced important new material after the securing of the imprimatur. At any rate, Scheiner and his friends were successful in getting Galileo into serious trouble, for a search of the Inquisition records disclosed an unsigned memorandum to the effect that Galileo had been ordered not to teach Copernicanism in any way, orally or in writing. When this was found, the Pope felt that he had been tricked into the granting of permission for Galileo to discuss this topic, and then into permitting the licensing of the book. Accordingly, he ordered Galileo to come to Rome to be tried by the Inquisition. Galileo, who was seriously ill and was nearly seventy years of age, asked for protection from the Grand Duke, but to no avail. In the spring of 1633, he faced trial at Rome. It was his contention that the book had been properly licensed and that in it he did not hold or defend the Copernican view, but merely discussed it impartially in conjunction with that of Ptolemy. When asked to recount the circumstances of Bellarmine's injunction of 1616, he produced the Cardinal's certificate that he had merely been apprised of the general decree, which had been published. Asked whether he had also been enjoined not to discuss Copernicanism in any way, he replied that he did not recollect any such order. The trial then dragged on for a long time. Galileo's authentic certificate from Bellarmine, the existence of which could not have been known to the inquisitioners, was a powerful document as against their own unsigned memorandum in the files. In the end, Galileo was induced to confess that he had gone too far in his book, but he did not admit any wrongdoing; rather, he said, the

Galileo: A Biographical Sketch

17

fault was one of the vanity every man has for his own arguments. Even this degree of confession was extracted from him only by extrajudicial dealings, and probably with the promise of a light penalty. When he then faced the judges and was sentenced to life imprisonment, the shock nearly killed him. The sentence was, however, speedily softened to allow him to return first to Siena, where he was in the custody of his old pupil and friend Ascanio Piccolomini, then Archbishop of Siena, and ultimately to Arcetri, near Florence, to his own villa. There he remained under the surveillance of officers of the Inquisition, but without fonnal imprisonment. One of the most distressing circumstances of his condemnation was that Galileo's works, published and unpublished, were forbidden. It will be recalled that before his astronomical observations with the newly devised telescope made him world-famous, Galileo had been about to publish a great work on mechanics and strength of materials. During his stay with the Archbishop of Siena, despite his great age, he turned again to this project of a quarter-century earlier, and proceeded to write in dialogue fonn, with the same interlocutors as those of the ill-fated book which had brought about his condemnation, a treatise on Two new sciences which is unquestionably the cornerstone of modem physics. A manuscript of this great work was taken out of Italy to France and was ultimately published, in 1638, by the Elzevirs at Leyden. No reprisals were carried out against Galileo, who pointed out in a preface to the book that arrangements for its publication had been made without his knowledge or consent by friends abroad, to whom it had been entrusted in confidence merely for its scientific interest. In the Two new sciences, Galileo gave to the world not only the true laws of accelerated motion and of falling bodies, but fundamental theorems concerning projectile motion and important applications of mathematics to a variety of other physical problems. In Galileo's last years he was afflicted with total blindness, which overtook him about the time of publication of his last book. He continued, however, in a vast scientific correspondence with the assistance of his son and of two young men, both to become scientifically illustrious in their own right, Vincenzio Viviani and Evangelista Torricelli. To his son he dictated a method of applying the pendulum to clocks. Early in I 642, being almost seventy-eight years of age, he died at Arcetri. The implacable hostility of Urban VIII, who had even made difficulties about his request to go into Florence for medical treatment at the time his sight was failing, prevented his honorable burial with a suitable monument to his greatness, "Jest any word of it reflect upon the Holy Office." He was interred in the Church of Santa Croce, at Florence, but nearly a century elapsed before his remains were moved to their present magnificent tomb, opposite that of Michelangelo near the entrance to the church.

18

Biographical and General

Galileo was of average stature, heavy-set, quick to anger and as quickly restored to good humor. His natural talents, his wit and his brilliant conversation won him an illustrious list of friends among dignitaries of the court, the Church and the universities, as well as among artists, musicians and craftsmen. At the same time he made a fonnidable number of bitter opponents by his biting sarcasm against those so unfortunate as to offer vulnerable arguments against his scientific views. Galileo had in his nature a curious mixture of prudent caution and uncompromising defiance. The former trait is apparent in his long hesitation to embrace unequivocally the Copernican theory, the latter in his fearless appearance at Rome in 1615-1616 when his own reputation as well as the fate of his scientific convictions was at stake, and when his bestinfonned advisers warned him against the probable consequences of an open fight. His reluctance to take a finn position on the Copernican theory long before 161 3, at least sixteen years after it had won his scientific preference, is often ascribed solely to his fear of public ridicule. That was certainly one of his reasons, as it had earlier been for Copernicus himself, but it was almost equally certainly not his sole motivation. The study of Galileo's entire scientific career indicates that he thoroughly understood, as indeed he preached, the overwhelming importance of reserving final judgment until mathematical certainty could be reached. It is likely that he was a long time in overcoming in his own mind all the formidable objections to the earth's motion as a physical fact even after he had arrived at a position generally favoring Copernicus as against Ptolemy and Brahe. It is noteworthy that most of his serious errors in scientific matters are to be found only in his unpublished manuscripts and not in his printed books. Had he been as much inclined to rush into print with his novel ideas as were most men of his time (and many of ours), his prodigious influence upon scholars of the first rank in his own day and for decades thereafter would doubtless have been greatly weakened. On the whole, it appears that problems and contradictions often held him back from publication and urged him to persevere in researches that were ultimately fruitful. Perhaps it is to this facet of his character that we owe the loss of several papers he is known to have composed (on mathematical indivisibles and continuity, for example, and on light and color) which would be of great interest to historians of science as well as to his own biographers. When he was a young man, he suffered an accident which probably led to his lifelong bouts with almost crippling arthritis or rheumatism. On a summer day , in search of relief from the heat, he and a number of companions took shelter in a cave where they lay down without clothing. The air of the cave was cool but noxious; several who fell asleep became very ill, and some of them died. Galileo was also afflicted in later life with a severe double hernia, for which he was

Galileo: A Biographical Sketch

19

obliged to wear an iron truss that made it excessively difficult and painful for him to travel any long distance. Galileo's talents were extremely varied. Apart from his scientific and literary abilities, he was a skilled musician, delighting especially in the lute, and so proficient in drawing that he seriously considered becoming a professional artist. Ludovico Cardi di Cigoli, his good friend, remarked that all his knowledge of perspective had been learned from Galileo; other artists consulted him, and many evidences of his familiarity with and liking for painting are to be found in his letters and essays. Of all his personal characteristics, however, the most striking is his extraordinary skill as an observer. Nothing seems to have escaped his attention, and the popular appeal of his books is attributable partly to the apt use of countless illustrations drawn from the experience, or potential experience, of anyone willing to repeat his observations. The appearance of distant clouds and mountains, of various lights at night, of rainbow colors in sunlit hair, of reflections in heated air; the sounds of nature and of music; the behavior of filings on a vibrating plate, and so on almost without end - when we read continual references to such phenomena, we are no longer astonished that Galileo, when he was confronted by countless fixed stars seen through his thirty-power telescope, immediately noted the linear arrangement of three near Jupiter, and on the following night knew that either they had moved or that Jupiter was going the wrong way, which led him to his most startling astronomical discovery. We are less astonished than we should otherwise·be by his noticing the isochronism of the pendulum and by his early recognition of its relation to the true laws of falling bodies, or by his utilization of the inclined plane to facilitate the observation of motions too fast in nature to permit precise measurement. It is probably to Galileo's inherent capacity to observe that modem science owes its inception; for despite his extraordinary capacity for reasoning, he turned away from excessive speculation about the causes of things in the tradition of philosophers. His desire was to see precisely what things happen and how they happen, rather than to explain why they happen so. NOTE 1

A full reconstruction of this famous and much debated interview will be found in Appendix I to my translation of L. Geymonat's Galileo Gali lei, New York, 1965 [and in the paper "On the Documents of Galileo's Trial" (see page 142), which is much the same. Eds .]

2

The Scientific Personality of Galileo

The meaning and value of the concept of "scientific personality," and its significance as applied to Galileo, may best be introduced by some remarks on the nature and present state of the history of science. The history of science is a relatively new discipline, and it has wisely been guided in its development by the progress of the old and well-established field of political history. Until the mid-nineteenth century, traditional histories centered on the exploits of great rulers, statesmen, and generals. The history of science at first emphasized likewise the achievements of such men as Galileo, Kepler, and Newton. Toward the middle of the last century, the portrayal of history as the product of the actions of famous men underwent a profound critique, as a result of which a notable change in emphasis took place in the writing of history. The findings of archaeologists, anthropologists, and sociologists assumed increasing importance, and the works of chroniclers and biographers ceased to dominate the field. A like change took place in the history of science. On the one hand, the relations of science and society were more fully explored and analyzed, while on the other hand the continuity of ideas important to the growth of modem science began to be traced back through the supposedly barren middle ages to the Arabs, the Greeks, and to much earlier civilizations. The older personal or biographical approach has now been almost abandoned in favor of two new theories of scientific historiography which I shall call the sociological and the ideological approaches. Each offers a kind of detenninism in place of the fonner tacit assumption that science was the product of an intermittent parade of geniuses who appeared fortuitously on the scene. The results, both in political history and in the history of science, have on the whole been beneficial. Many myths have been exploded, and the path has been Reprinted from Physis 11 ( 1969): I 81-94, by permission.

The Scientific Personality of Galileo

21

cleared to a more rational understanding of the events of the past. Yet it seems to me that historians of science have been rather more docile under the leadership of conventional historians than necessary. There is certainly an analogy between a great political or military leader and a leader in science, but it is only an analogy. The resemblances may be great, but so are the differences. Experience shows much more clearly that when a nation needs a leader, a suitable man of action will be found, than that when scientific insight is needed, social forces will produce an appropriate thinker. Social forces here seem to me to replace the gods in a conception that underlay the creation of myths in the earliest times; and little will be gained if now, in the course of overthrowing old myths, we uncritically accept as a principle of historical explanation something that may in tum give rise to new ones. Nevertheless, it is now fashionable to portray the origin of modem physical science not as dependent upon revolutionary ideas produced by the geniuses of Galileo and Newton, but as the outgrowth of hundreds of bits of knowledge pieced gradually together, with occasional spurts of progress related to general social changes. Thus Albert Einstein wrote, in his foreword to a translation of Galileo ' s Dialogue: "It may well be that ... the fetters of an obsolete intellectual tradition would not have held much longer, with or without Galileo .... Our age takes a more sceptical view of the role of the individual, ... for the extensive specialization ... of knowledge lets the individual appear 'replaceable' as it were, like a part of a mass-produced machine." 1 In describing science as it stands today, there is much to be said for that view. By and large, needed technical and theoretical advances seem to come forth as if extruded by a kind of social pressure, in a historically logical sequence. This makes it appear that the names of particular men associated with them are mere accidental sounds, having no real place in the history of science, where they are preserved only through tradition and courtesy. Now, it is true that there is no field of endeavor today in which is it more difficult for a man to leave the imprint of his personality on his work than the scientific field. One might say that it is in the very nature of science to exclude the subjective, and the personal along with it. So there is some justification for a theory of the history of science in which progress is made to appear impersonal and inevitable. But from this, it is all too easy to assume in retrospect that when the accumulation of knowledge in physics had grown large enough to warrant the creation of a separate field of study, almost anyone might have inaugurated it. I am distrustful of any theory which tends to make the origin of a field of science appear as inevitable as its subsequent progress. Perhaps my introduction here of the word "origin" begs the question, in the view of the ideological

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Biographical and General

school of historians. But no matter. My point is that if it were true even that modem scientists are like parts of a mass-produced machine, which may be doubted, that would be so only, or at least mainly, because of the standardization of scientific information and the ease of communication among modem scientists. Surely it is stretching things too far to assume analogous conditions in the epoch of Galileo. One may grant that the romanticizing of an individual may result in a distortion of historical facts, without losing sight of the perhaps equal danger that to depersonalize the figures of past scientists may diminish one's historical understanding. To me, at least, the history of modem physical science without the personality of Galileo is Hamlet without the Prince of Denmark. It is a tale told by a computer, purged indeed of sound and fury, but signifying little. Einstein's recognition of our contemporary historical emphasis on societies rather than individuals does not mean that he saw things the same way himself. Einstein described Galileo in the same foreword as: "A man who possessed the passionate will, the intelligence, and the courage to stand up as the representative of rational thinking against the host of those who, relying on the ignorance of the people and the indolence of teachers in priestly and scholarly garb, maintained and defended their positions of authority. His unusual literary gift enabled him to address the educated man of his age in such clear and convincing language as to overcome the anthropocentric and myth-ridden thinking of his contemporaries." 2 That succinct description points up some personal traits of Galileo's which appear to me to have played as important a role in the establishment of modem science as did his physical and astronomical discoveries. That is why I think that a proper understanding of the history of science, meaning by that those events of the past which have some evident connection with significant aspects of present-day science, needs to have at least three dimensions: first, an ideological dimension, that is, the study of fundamentally significant scientific ideas in their various historical forms and relationships; second, a sociological dimension, given by the study of the societies in which those ideas were put forth, whether they prospered or vanished at the time; and finally, a personal dimension, a study of the men who put them forth, especially those who ultimately established the place of those ideas in the body of science. No one questions the importance of the ideological and sociological dimensions of the history of science; certainly I do not. The personal dimension seems to most historians less significant in science than anywhere else. That may be true now, but personalities can throw light on the origins of modem science. The interest and importance of the scientific personality of Galileo was clearly indicated by the late Professor Leonardo Olschki in a paper published in

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1942, the tercentenary of Galileo's death. That paper opened up a large field for study; having borrowed its precise title, I propose here to develop somewhat the themes stated by Professor Olschki in the following words: "Galileo's intellectual independence was not merely a theoretical one ... but a ripening scientific conscience of an unmistakably personal character.... The explanation of fundamental human accomplishments as individual approaches, or as strokes of genius, may not satisfy the determinist tendencies of evolutionary historians; but there is no better way of doing justice to an outstanding personality, or of understanding his intellectual traits.'' 3 I shall add another justification: Galileo's personality was an essential ingredient in his scientific success, and therefore it cannot be neglected in a full comprehension of that scientific revolution in thought which distinguished the seventeenth century from those which had gone before. In saying this, I have in mind principally two quite separate aspects of Galileo's personality. One of them is undoubtedly familiar to everyone; that is his rather pugnacious disposition, as a result of which he engaged in numerous disputes which helped to overthrow tradition and vindicate his scientific position. The other, which I shall discuss first, is an aspect of Galileo's general temperament that parallels in a curious way the essential structure of modem physical science. Modem physical science, despite its admirable precision, is by no means a body of inalterable doctrine. Rather, it is a continually changing system of knowledge arrived at by a process of successive approximation; never entirely accurate, and never to be completed. Aristotelian physics, which prevailed up to the time of Galileo, was a body of inalterable doctrine and that is precisely what was wrong with it. Galileo was temperamentally opposed to the idea that any fixed doctrine would ever succeed in describing the real physical world which he saw changing about him. He used to say that Aristotle, if he were to come back to life, would be the first to recognize new knowledge and disavow the doctrinaire position of the Peripatetics. Were he but to look through the telescope, Galileo said, Aristotle would promptly withdraw the astronomical dogmas to which his disciples were stubbornly clinging. Galileo doubted that complete knowledge of anything could be achieved by human beings, and he declared that the more deeply one investigated any subject, the more one came to realize the extent of one's own ignorance. He illustrated this in his parable, in the Assayer, of a man who began by believing that he knew the cause of sound, and proceeded to investigate various sources of sound, as a result of which he eventually not only relinquished his original dogmatic confidence, but tolerantly allowed that there might be an infinity of sources still unknown to him. In speaking of physical science as a method of successive approximations, I mean generally that the progress of science may be characterized as the finding

24

Biographical and General

first of some rule that fits a great many data rather well; next, finding that there are other data, related to those, which it fits badly, or seems not lo fit al all. Those are in tum brought in by modifying the rule or replacing it by another, and the process goes on indefinitely. Now, in that kind of process, two quite different kinds of temperament have turned out lo be extremely useful. One is that of a man who delights in observing things, notes resemblances and relationships among them, and fonns generalizations without being unduly disturbed by apparent exceptions or anomalies. Such a personality is obviously valuable in the original discovery and fonnulation of laws that fit many phenomena tolerably well. The other general temperament useful to the progress of science is that of a man who frets and worries over any unexplained deviation from a rule, and who may even prefer no rule al all over one that does not always work with mathematical precision. Of course, both these attitudes are present to some extent in every scientist, but one or the other is likely to predominate. In their extreme fonns, the two conflicting temperaments are related in a way lo those which today characterize the theoretical physicist as opposed to the experimental physicist; and as we know, in extreme cases such men are likely not to speak highly of one another's work, though they both recognize grudgingly that they work on the same team. In Galileo's day there was no such profession as that of physicist, but the role of the theoretical physicist was played by the philosopher. By temperament and tradition, the philosopher liked to generalize and was not unduly perturbed by apparent anomalies; indeed, he welcomed them as things to explain, or al any rate to explain away. The role of the experimental physicist, to the extent that it was played at all , fell lo craftsmen, artisans, and mechanics. Philosophers and mechanics did not, then or now, work on the same learn , nor was there any apparent reason why they should. Consequently there was a highly developed branch of philosophy, called physics, which bore only a loose verbal relationship to reality ; and there was a highly developed technology, which was generally not even noticed by philosophers, let alone integrated with physics. Philosophers knew how physical objects ought to behave, and cared relatively little if they didn 'l always seem lo behave that way; craftsmen knew how objects behaved, and cared relatively little for theoretical explanations. Though both were deeply concerned, each in his own way, with precision, neither habitually associated that with mathematics. Galileo 's temperament was about as evenly balanced between the two extremes I have mentioned as it is possible lo conceive. He liked lo observe relations and generalize about them, though unexplained deviations from theory did bother him. He lived among professors, but he enjoyed discussing technical practices with artisans, and he liked to tinker. He saw mathematics as a com-

The Scientific Personality of Galileo

25

mon ground of the two demands for precision, and conceived of departures from mathematical regularity in tenns of a mercantile analogy which I should like to quote from the Dialogue: "What happens in the concrete," says Galileo, "happens the same way in the abstract. It would indeed be surprising if computations made in abstract numbers did not thereafter correspond to actual gold and silver coins and merchandise. Do you know what does happen, Simplicio? Just as the accountant who wants his calculations to deal with sugar, silk and wool must subtract the boxes, bales, and other packings, so the mathematical physicist, when he wants to recognize in the concrete the effects which he has proved in the abstract, must deduct the material hindrances; and if he is able to do that, I assure you that matters are in no less agreement than for arithmetical computations. The sources of error, then, lie not in abstractness or concreteness, not in geometry or physics, but in a calculator who does not know how to make a true accounting."4 It was thus that he maintained his belief in mathematical laws, without feeling that he should abstain from generalizing in the quest for perfection. His attitude toward theorizing is clear from his writing. He thought it highly creditable to Copernicus that the apparent absence of great changes in magnitude by the planet Venus did not induce the Polish astronomer to abandon his theory, from which such changes would be expected, but that rather he kept to the theory and left the apparent anomaly to be explained later - as it eventually was by Galileo's telescopic observation of the phases of Venus. Now it was certainly helpful, if not absolutely necessary, to the birth of modern physical science, for someone to fonnulate mathematical laws without waiting for their precise confinnation, but at the same time to refrain from merely speculating, as the philosophers had done in physics. Galileo's nice balance between the two extremes of temperament in this respect left its mark on his physics, and this was at first more a personal characteristic than an intellectual achievement. Such a balanced temperament was rare in his day, as shown by the contemporary examples of Marin Mersenne and Rene Descartes. Mersenne, who represents an over-balance of the critical temperament, was much distressed by the departure of his careful exper_i_m ents with falling bodies from the mathematical laws confidently announced by Galileo. Such a man as Mersenne, left to himself, would probably never discover the law of falling bodies; yet he quickly became a valuable part of the newly forming scientific team when that was done. Descartes, in whom a predilection for generalizing predominated strongly over a concern for precise observation, went astray in his fonnulation of physical laws, such as the laws of impact, and nevertheless helped to advance physics as a coherent mathematical structure. It is true that in his published works, Galileo often claimed for his scientific

26

Biographical and General

laws a precise accordance with experimental results that they did not have. Thus, with regard to the period of oscillation of a given pendulum, he asserted that the size of arc did not matter, whereas in fact it does; and with respect to the verification of the law relating space traversed to the square of elapsed time, he asserted that he had obtained precise correspondence in hundreds of trials on inclined planes, which is rather unlikely. Because of such exaggerations, it has been suggested that Galileo made few actual experiments or careful observations, and that his traditional place as founder of experimental physics is therefore undeserved. It is at least as likely, however, that he observed the discrepancies and attributed them to "material hindrances," considering them to be outweighed by the general coherence of his physics, as he had praised Copernicus for neglecting the apparent contradiction between observations of Venus and heliocentric astronomical theory. Moreover, many of Galileo's exaggerations in such matters may be regarded as literary devices, designed to excite the interest and wonder of his lay readers, rather than as attempts to conceal discrepancies from fellow scientists, whom he urged to make similar observations for themselves. That is, the exaggerations constituted the popularizing and not the sober content of his writings. And indeed, Galileo's preference for Italian over Latin even in scientific writing, his generous use of commonplace phenomena to illustrate for his readers the principles of physics, and generally his clear style in writing, may be counted as personal traits that had much to do with his intluence in propagating an interest in science. This leads us naturally back to the more familiar general aspect of Galileo 's personality which was an essential ingredient in his scientific success - that is, his willingness and ability to fight for his ideas. No doubt Galileo's most striking personal characteristic was his refusal to accept authority as a substitute for direct personal inquiry and observation. That refusal went counter to the whole social pattern of his time, and not only with respect to the Church. All political and most economic institutions of his day were authoritarian in structure. Even in the universities, the primary centers of intellectual life, the authority of ancient writers was sedulously preserved. Only a born fighter could hope to change in any field the well-established tradition of deference to authority in every field. Galileo's refusal to accept authority as a substitute for direct inquiry belonged specifically lo his scientific personality; it did not extend to a defiance of authority in other things. While he rejected dogma in physics, as symbolized by Aristotle, he did not combat it in politics or religion. On the contrary, he remained a good Catholic even through the ordeal of his trial by the Inquisition, and he was always a loyal subject of the Grand Duke of Tuscany, despite the fact that that worthy did not over-exert himself to protect Galileo's interests. A

The Scientific Personality of Galileo

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superficial evaluation of those facts might suggest that Galileo lacked the full courage of his convictions; that he sought the protection of some powerful authorities in order to fight against others. But that is very dubious. Galileo was not given to defiance on principle, and he saw the enormous difference between direct inquiry where it may significantly be made and its counterfeit in other fields. Here is a passage from the Dialogue in which he replied lo a defence of Aristotle's physics: "If what we are discussing were a point of law or of the humanities in which neither true nor false exists, one might trust in subtlety of mind and readiness of tongue and the comparative expertness of writers, expecting him who excelled in those qualities to make his arguments the most plausible; and one might judge him to be correct. But in the physical sciences, where conclusions are true and necessary and have nothing to do with human preferences, one must take care not to place oneself in the defence of error; for here, a thousand Demostheneses and a thousand Aristotles would be left in the lurch by any average man who happened lo hit on the truth for himself."5 Galileo urged his church not to exert its authority against freedom in scientific matters, but he never questioned its right or its power to do so, nor did he sympathize with the demands of Protestants for the right of free inquiry in matters of faith. His plea for a sharp distinction between scientific and theological questions may seem to us now a purely intellectual achievement, necessary for the establishment of science in the modem sense; but that is because we are not compelled lo view the question of the earth's motion, for example, as a dreadfully complicated question, with reason pulling in one direction and all our deeper feelings pulling in the other. Galileo's resolution of that problem was an expression of his personality even more than it was a product of his intelligence. It is an evidence of that "ripening scientific conscience" of which Professor Olschki spoke. That kind of conscience was new, and Galileo had to forge it in the smithy of his own soul under the heal of internal conflicts. We may take the demands of objective truth for granted, but we should not suppose them to have been always clearly perceived, at least so far as science is concerned. But Galileo's earliest conflicts with authority had nothing to do with religion. They were directed against the philosophers at the University of Pisa. Shortly after appointment there as professor of mathematics in 1 589, Galileo composed a formal treatise on motion. Its theme was that the physics of Aristotle was completely untenable, that physics must be established on the principles of mathematics, and that it must be in accordance with actual observation. Critiques of Aristotle were nothing new; in fact, they made up the bulk of the philosophical literature of the period. But Galileo's method of attack had an ele-

28

Biographical and General

ment of novelty. Where conventional philosophers, in whose province physics still lay, cited authorities for virtually every opinion they put forth, Galileo appealed directly to reason and observation. When he did cite an authority, as in presenting his early (but mistaken) theory of acceleration in falling bodies, he made it clear that he had first independently arrived at his theory, believing it to be original, and only later found it attributed by Alexander of Aphrodisias to Hipparchus. A conventional writer of the time would first have cited Alexander and Hipparchus, and only then have added his own new reasons in support of ancient authority. Had Galileo published his anti-Aristotelian theory of motion, it would certainly have gained him a reputation as early as 1 590; for in spite of its errors, it was original, and it was highly creditable by standards of the time. Yet, though Galileo polished the work, in the end he did not publish it; we know of it only because he preserved the various manuscript versions throughout his life, as I daresay most of us have preserved some youthful production of which we are privately proud, though we know it does not merit publication. Now considering the personal advantages that Galileo stood to gain from public notice at the age of twenty-six, in his first and poorly paid academic position, it is necessary to account in some way for his having withheld his treatise from the press. Here, I think, enters another conspicuous trait in Galileo's scientific personality; namely, prudence. I do not mean caution on the part of a young professor against offending his more powerful colleagues; that would indeed be an unGalilean trait. What I mean is scientific prudence, an attitude well summarized by Galileo in his book on sunspots of 1613, where he says: "I am quite content to be last and to come forth with a correct idea, rather than get ahead of other people and later be compelled to retract what might have been said sooner, indeed, but with less consideration." 6 Before his treatise on motion was fully completed, Galileo realized that even though his first ideas in physics were superior to those of Aristotle, they accorded in some respects no better with actual observation. He attributed some of the discrepancies to properties of matter - what he called "material hindrances" - friction, the yielding of surfaces, and the impossibility of achieving perfect flatness. But his predicted speeds of descent along inclined planes departed too far from observed events to be thus accounted for. Scientific prudence restrained him from publication of his results, and scientific curiosity kept him working at them until they were finally corrected and published, nearly half a century later. Galileo's scientific prudence is further illustrated by his delay in supporting openly the Copernican theory. He personally preferred that theory as early as 1597, but the first time he endosed it in print was in 1610, and then only mildly,

The Scientific Personality of Galileo

29

his positive endorsement being withheld until 161 3. Some writers have attributed his long delay to fear of criticism, a trait not elsewhere conspicuous in Galileo; others, to intellectual dishonesty, a charge which is too preposterous to be taken seriously. Such characterizations of Galileo's delay are no better founded than it would be to call Charles Darwin cowardly or dishonest for his having taken so long to publish his theory of evolution. The fact is that until I 6 Io, when Galileo had discovered the satellites of Jupiter, and 161 3, after he had seen the phases of Venus and carefully observed the motions of sunspots, he had no personal evidence on which to decide between the theories of Ptolemy and Copernicus, those theories being mathematically equivalent - as Galileo's foes still take a perverse joy in pointing out when they are criticizing him not for his long delay, but for his ultimate commitment. The significant point is that as soon as Galileo had what he considered to be ocular proof that Ptolemy was wrong, he spoke out openly for Copernicus. Here it should be mentioned that Galileo's rejection of authority as a substitute for direct inquiry or observation had its counterpart in his recognition of the decisive role of sensory evidence and his willingness to abide by the verdict of observation or experiment. It is important to note that Galileo was by habit an unusually keen observer, that he was perfectly aware that the senses themselves are not infallible, and that he rarely gave unequivocal support to a theory for which he did not have some direct sensory evidence of his own. Galileo came out openly for Copernicus as soon as he had what he considered to be ocular proof that Ptolemy was wrong. In recent years there have been scholarly discussions - I might better say "scholastic" discussions - on the question whether Galileo had any right, as a scientist, to conclude in favor of Copernicus on the basis of the evidence in his possession. Without going into the merits of the case, I think it is evident that intellectual boldness as well as intellectual prudence has a role in the progress of science. Either may be called for by the existing state of knowledge and the conditions favoring its advance. crucial point is not whether Galileo did or did not have ocular evidence decisively in favor of Copernicus; it is how he behaved when he considered that he did have such evidence. His words and actions in that and analogous instances are the means by which we may observe the "ripening scientific conscience" of which Professor Olschki spoke. A mature scientific conscience must exhibit both a positive and a negative aspect. On the positive side, it will drive a man to put forward, at whatever personal hazard, any scientific idea or discovery in his possession, and to oppose resolutely any forces that would act to suppress it. On the negative side it will inhibit a man from imposing on others with purported facts or observations, or with interpretations or theories known by him to be defective, even though he

The

30

Biographical and General

may have the power to persuade others to accept them. Now these intimate and personal drives can justly be appraised only by a careful study of a scientist's whole behavior; by everything he did and wrote, and by what his friends and enemies wrote about him. Galileo's ripening scientific conscience coincided in time with the beginnings of modern physical science; it was therefore put to unprecedented tests, and accordingly it offers a peculiarly interesting field for research. Ultimately it drove him to risk his own personal comfort and even his safety in a battle against overwhelming odds - which, as you know, he lost. And throughout his life, it restrained him from publishing conjectures that would have gained for him a fleeting prestige, not only when he was a young professor, as I have already indicated, but also in later life, when his established reputation would have enabled him to impose on less well-infonned men by means of specious arguments. Today, not only popular writers like Arthur Koestler, but some serious students as well, see in Galileo's propaganda for Copernicus certain arguments which they consider unsound, and some which they believe that he himself knew, or should have known, to be unsound. Two frequently-cited instances of this alleged blindness or duplicity are his argument for the earth's motion drawn from the seasonal variations in the paths of sunspots, and his theory of the causes of the tides. To examine these in detail here would lead me too far from matters directly related to Galileo's scientific personality. I have, however, examined both at length in published papers,? and it suffices here to say that I have found no evidence that Galileo's published views on those two subjects were in contradiction with any facts known to him, or that the convictions he expressed concerning them were in any way insincere or deceptive. And indeed, when one considers the caliber of his scientific friends and pupils, together with the extent of his influence over them - when one reads the many avowals of admiration and respect for him that are to be found in their letters and their publication·s - it is hard to believe that deception or insincerity on Galileo's part existed in his scientific teachings and escaped detection. On the other hand, Galileo was by no means above utilizing the prejudices of his opponents to neutralize their opposition. I find that quite amusing, and not at all the same thing morally as to impose on them with specious scientific arguments or assertions. For instance, in arguing for the circular motion of the earth, Galileo resorted in the opening pages of the Dialogue to the use of Aristotelian doctrines concerning circular motion in general. That performance is often interpreted as showing that Galileo had been unable to shake off entirely the old bonds of metaphysical tradition. I think it shows only that his scientific conscience was not so inflexible as to inhibit him from hoisting his opponents with their own petard.

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31

The maturing of Galileo's conscience had to contend with his personal ambition, for there is no doubt that Galileo was an ambitious man. An example often cited is his exploitation of the telescope as a means of improving his academic and financial position at Padua through his presentation of the instrument to the Venetian Senate. He then promptly used his advancement at Padua as a basis for negotiating a still better post at the Tuscan court, with the same salary and with freedom from all teaching duties. But, as Professor Olschki pointed out long ago, Galileo's resignation from the university after his first telescopic discoveries was the move of a man who could no longer conscientiously teach the old doctrines. Galileo's ambition was doubtless a factor in his writing of the early treatise on motion that has been mentioned previously. I believe that he wanted to remove physics from the jurisdiction of philosophers in the university and add it to his own department of mathematics. As a step in that direction, he undertook to overthrow the authority of Aristotle in physics. In that sense, one might say that any valuable new ideas arrived at during the composition of the treatise arose basically from Galileo's personal ambition and his temperamental distaste for Aristotle's dogmatic physics. Now, there was one such idea which turned out to be of enormous importance to the development of physics, and that was the first germ of the concept of inertia. The origin of that concept is universally treated by historians of every school as something that was totally independent of the personality of any man. To the ideological historians, it was the end-product of a Jong series of philosophical speculations about the motion of projectiles, beginning no later than the sixth century. To sociological historians, it may appear as an inevitable result of the invention of gunpowder and the military, economic and political consequences of artillery. I do not mean to deny that either or both of those views may be quite correct, so far as they are intended to explain the reception of the new idea; yet they are misleading to the extent that they purport to shed light on the actual manner in which the concept of inertia historically happened to come into being. At any rate, they shed less light on that interesting question than does the personal dimension I am concerned with. Medieval speculations on motion, far from accounting for the actual introduction of the inertial concept, only make it hard to see why the idea did not appear two or three centuries earlier, as a philosophical extension of earlier speculations about projectile motions. The idea took form in Galileo's mind, not among philosophers or society as a whole; and it met with opposition at first from representative philosophers familiar with earlier speculations. Aristotle's dictum that nothing violent could long persist lay at the basis of that opposition, and the same dictum can explain the failure of the inertial concept to appear so long as respect for authority dominated physical thought.

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Biographical and General

Galileo, spurred by personal ambition to overthrow Aristotle's authority in physics, sought to contradict his opinion that every motion was either natural or violent. To do this, he introduced the idea of "neutral" motions in his first unpublished treatise on motion. Only after years of reflection did he perceive that this idea was of particular use in the explanation of projectile motions. The implications of these facts for the history of science have been developed elsewhere.8 Here they are mentioned only to illustrate the importance of studying, wherever possible, the personalities of men who, like Galileo, contributed profoundly to the origins of new sciences. The origin of the inertial concept was as much a product of Galileo's ambition and his fight against authority in physics as it was of actual scientific research; that is, it was at least as personal as it was objective. Thus a scientist's personal motivations may not be irrelevant when we seek to understand the emergence of his fundamental contributions, even those which have now been linked logically to a long train of philosophical speculations about some topic to which they have a clear application, or are now shown convincingly to be the expression of some social need. Galileo was a controversial figure in his own day; he is still a controversial figure in ours. That in itself implies a vivid personality. Of its many facets, I have dealt with only a few which seem particularly significant in understanding his success in organizing, amplifying, and gaining adherents to the study of physical science. There were, of course, other traits of Galileo's personality that contributed to that same success. One was his gregarious nature, which allowed him to move among widely diverse groups - churchmen, courtiers, craftsmen, artists and men of the world - with the result that he could draw from many fields ideas and methods useful to science, and then explain his discoveries and opinions in language and examples familiar to any reader. I have already mentioned his preference for Italian over Latin, even in scientific writing; that aided in breaking the hold of tradition on physics and astronomy, and at the same time excited the interest of many people who would otherwise have been excluded from reading his works. Correlated with this was his amusing and witty, often sarcastic style, almost conversational in its ease of comprehension. His fondness for communication made him a voluminous correspondent and an active participant in scientific and literary academies, which greatly aided in the dissemination of scientific information. He was an outstanding teacher, as admitted even by his enemies, and that in itself implies a number of personality traits which played a part in Galileo's unquestionable ability to change the course of other men's thinking. Yet, as a teacher, he knew how difficult a task that was. In the Dialogue of 1632, after having spent a lifetime trying to destroy the authority of Aristotle in science, Galileo ruefully wrote that:

The Scientific Personality of Galileo

33

"There is no danger that a multitude of great, subtle and wise philosophers will allow themselves to be overcome by one or two of us who bluster a bit ... It is vanity to imagine that one can introduce a new philosophy by refuting some one author. It is necessary rather to teach the reform of the human mind, and to render it capable of distinguishing truth from falsehood, which only God can do." 9 NOTES I Galileo, Dialogue Concerning the Two Chief World Systems, tr. S. Drake (Berkeley, 2

3 4 5 6 7 8 9

1967), vii-viii. Ibid., vii. L. Olschki, "The Scientific Personality of Galileo," in Bulletin of the History of Medicine XII, 2 (July, 1942), 262 . Dialogue, 207-208 (Opere, VII, 234). Dialogue, 53-54 (Opere, VII, 78). S. Drake, Discoveries and Opinions of Galileo (New York, 1957), 90 (Opere, V, 95). S. Drake, "A Kind Word for Sizzi," in Isis, 49, 2 (June, 1958), 155-165; "Origin and Fate of Galileo's Theory of the Tides," in Physis III, 3 ( 1961 ), I 85-194. S. Drake, "Galileo and the Law of Inenia," in American Journal of Physics 32 ( 1964), 601-608; "The Concept of Inenia," in Saggi su Galileo (Florence, 1967). Dialogue, 57 (Opere, VII, 81-82).

3

Galileo's Explorations in Science 1

Explorations today apply the resources of science to obtain the most exact and useful information possible; we may call those "explorations by science." In this paper I shall describe some explorations long ago, through which science itself began to assume modem form . The explorer was Galileo, most of whose work consisted of what I call "explorations in science" contributing directly to astronomy and physics rather than to the application of science in other kinds of inquiry. Those in tum required him to make new explorations of science, when strong opposition to his discoveries and opinions made Galileo realize that the traditional view of science stood in the way of new explorations. During the seventeenth century the older abstract and philosophical approach to nature gained a new dimension of concreteness and utility, though only through a long struggle. Galileo's vision of new sciences was born in a society quite different from ours - a society in which admiration for the wisdom of the past was very great. He received the usual rewards and punishments that society metes out to such individuals, in his case so dramatically that the name of Galileo has come to stand as a symbol of discovery and of the battle for freedom of inquiry and expression. Whether or not historically accurate, the story of Galileo and the Leaning Tower of Pisa offers me a good place to begin, since it comes near the start of Galileo's career and it mirrors the society in which the Scientific Revolution took place. As a young professor of mathematics at the University of Pisa, Galileo was teaching his students something that contradicted the physics of Aristotle that they had learned from their professors of philosophy. Galileo told them that heavy bodies dropped from a height would fall at the same speeds regardReprinted from The Dalhousie Rel'iew 6 t ( 1981 ), 217-32, by permission of the publisher and the Estate of Stillman Drake.

Galileo's Explorations in Science

35

less of their weights, provided only that they were fairly heavy and were both of the same material. Aristotelian professors had told them that speeds in fall were proportional to weights; and if students then were like students now, they probably corrected Galileo. He replied by inviting them to bring along the philosophers and witness an actual test from the Leaning Tower. There they saw that a weight several times as heavy as another one of the same material did not reach the ground appreciably faster. Yet no professor appears to have changed his teaching. It was probably not a mere coincidence that Galileo's contract at Pisa was not renewed when it expired in 1592, and he moved to the University of Padua where he taught until 161 o. Late in life, writing notes, in the margin of a book by an opponent, Galileo mentioned a reason for which he had doubted Aristotle's rule when he himself was still a beginning student at Pisa. He remembered that in a hailstorm he had seen hailstones the size of a walnut striking the ground together with others smaller than a pea. If Aristotle had been right, the larger stones should have got far ahead of the others in so long a fall. We cannot blame Galileo's students, since they may not have seen hailstorms, which are even rarer at Pisa than in Halifax. But we can blame the professors who misinformed them, whether or not they had observed hailstorms. University science had always in the past depended not on observation but on pure logic. Hence if there was a logical weakness in Aristotle's rule of fall, professors of philosophy should have spotted it. Because something Galileo wrote while still at Pisa exposed such a logical defect, there was something wrong not just with Aristotle's rule of fall, but with the whole approach to science. It was only by accident that Galileo had observed and remembered what he did. But it was not just by accident that he conducted an exploration of science as taught to him. In a treatise on motion he wrote at Pisa, Galileo showed that Aristotle's rule could be refuted by logic alone. Two identical bricks would fall side by side; no doubt about that. If a piece of string was tied to them they still would. Shortening the string could not change that. Hence two bricks tied together end to end would fall at the same speed as either brick alone. Now throw away the string and glue the bricks together; no reason appears why this double brick of double weight should fall faster than two bricks tied together - or either one alone. In fall, one brick cannot weigh down on the other and push it faster. As Galileo remarked, that would be as impossible as it is to stab a man who is running away as fast as you are chasing him. What Galileo's reasoning proved was not how heavy bodies actually fall, but that by using logic alone Aristotle had reached one conclusion and Galileo reached the opposite. To know what actually happens - that is, lo have a useful science of physics - it is necessary at least once in a while to put matters to the

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Biographical and General

test of actual observation. The Leaning Tower story extends far beyond a single fact of physics. It pictures a certain society and two views about the nature and purpose of science in competition for the minds of students, and does this in a way that throws light on Galileo's career and on the entire Scientific Revolution of the seventeenth century. The question whether this episode took place exactly as Galileo's first biographer described it is irrelevant to that picture. What is relevant is the question why pure logic, application of which the philosophers regarded as truly scientific exploration of nature, had in four centuries failed to lead professors to Galileo's paradox. Even a similar test that had been published in Holland in 1586 failed to affect the teaching of Aristotle's rule as university physics. The Scientific Revolution began with such events and reached its climax half a century after Galileo's death in the work of Sir Isaac Newton, whose Mathematical Principles of Natural Philosophy was published in 1687 and established the basis of modem science. Twenty years earlier a group of Galileo's disciples published a book of scientific explorations in the name of a new scientific academy that adopted the motto provando e riprovando - testing, and testing again. This academy called itself the Cimento, meaning "ordeal" or even "torture," and the book was a collection of experimental investigations by which nature was put to the torture and forced to answer questions independently of philosophical opinion. The book was translated from Italian into English and Latin, was widely read throughout Europe, and had much to do with the founding and the policies of other early scientific academies. I do not mean to imply that logic and philosophical debate dropped out of science; far from it. But a truly new dimension was added to natural philosophy, as physics was then called, when deliberately designed experiments became an integral part of exploration in science. As Galileo put his point vividly in the famous Dialogue Concerning the Two Chief World Systems, philosophers had discussed a world on paper, whereas he and his friends were talking about the sensible world around them. When Galileo explored that world, he discovered not only errors in Aristotelian natural philosophy, but also previously unsuspected laws governing nature. As Shakespeare, who was born the same year as Galileo, had Hamlet say: "There are more things in heaven and earth than are dreamt of in your philosophy." It was no accident that thinkers as different as Shakespeare and Galileo, living far apart and writing for very different purposes, were both awake to the infinite variety of nature. In 1592, when Galileo moved to Padua and Shakespeare was revitalizing the English stage, a full century had gone by since Columbus had discovered the New World. It had been a century of exploration without rival in all past time. New plants, strange animals, even members of a

Galileo's Explorations in Science

37

race of men previously unknown in Europe had been brought back by navigators to show the truth of what must at first have seemed only tall tales invented by sailors. New things prepared the way for new ideas, though not quite sufficiently for the new sciences of Galileo, at least among those men who had always held authority in science. Had they been ready to listen; had professors of philosophy given support rather than opposition to Galileo 's discoveries and his view of science, theologians would not have intervened and Western culture might have been spared one of its greatest setbacks, of which some effects still linger today. I refer to the breaches that exist between religion, science, and philosophy itself. "More things in heaven and earth" was what Shakespeare wrote in 1604. It was discovery of new things in the heavens that brought Galileo fame in 161 o, only a year after his exploration of motions on the earth had yielded discoveries invaluable to Newton, who later credited Galileo for them. But Galileo did not publish those until near the end of his life, and since his explorations in the heavens were both more spectacular and more directly the source of opposition from philosophers, I shall speak of them first and leave Galileo's explorations in physics to the last. In March 1610 Galileo published at Venice a little book written in Latin, especially for the attention of astronomers and philosophers as he proclaimed on the title-page. He called it Sidereus Nuncius, or "The Starry Messenger," and in it he recounted discoveries made with the newly invented Dutch telescope which Galileo had improved to a power sufficient for astronomical use. For several months he enjoyed a virtual monopoly on telescopes that magnified twenty or more times, though instruments as strong as the ordinary fieldglass were not uncommon. Those had already made previously unseen stars visible, and Galileo's book included some in maps of familiar constellations. Because Aristotle had made it a basic principle of science that nothing new could ever appear in the heavens, even those observations stood as a challenge to the philosophers. Still worse was in store for them in Galileo's book, for it contained not just simple telescopic observations, but two new scientific conclusions against other principles of Aristotelian science. The first of these concerns the moon. According to Aristotle, all heavenly bodies were perfectly spherical. Galileo declared that the moon's surface was rougher than that of the earth, covered with deep craters and high mountains. That did not follow from simple telescopic observation, as did the existence of stars too small to be seen with the naked eye, but was deduced from the detailed effects of changing illumination of the moon by the sun. Rims of lunar craters were first lighted on the side away from the sun; the sunlight then spread, as Galileo watched, in the pattern familiar to dwellers in terrestrial val-

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Biographical and General

leys. Sometimes isolated points of light appeared suddenly beyond the illuminated part of the m~>0n, widening out and finally joining with that portion, just as earthly mountain peaks first catch the sunlight which then spreads downward . Now, to reason about heavenly bodies by analogy with the earth was objectionable to natural philosophers, who sharply distinguished celestial from terrestrial things. Galileo, on the contrary, regarded simple analogy as the best scientific approach - if not the only one possible. Noting the time required for complete illumination of one lunar mountain, he calculated its height as four miles, greater than any known to him on earth. So the moon, perfectly round in official science, was even rougher than the earth, not only relatively but absolutely. An argument brought against Galileo's illustrates the character of official science that was defended against new observation and deduction: Two philosophers, one in Italy and one in Germany, maintained that the moon's surface was perfectly smooth and consisted of transparent crystal. What Galileo saw, they said, lay inside this perfectly transparent shell, not on the surface. Galileo was asked by a friendly cardinal to comment. He replied that he would accept this crystal surface if his adversaries, with equal courtesy, would allow him to make mountains of it even higher than the one he had measured. How could they be sure that enormous irregularities did not exist, when they themselves assumed the moon's crystalline surface to be transparent? Their assertion, he said, was based on selecting one of many possibilities and then declaring that one to be true. The reason on which Aristotelians founded their conclusion was assumed perfection of the heavenly substance, and Galileo summed it up for them in his Dialogue thus: Being ingenerable, incorruptible, unalterable, invariant and eternal, celestial bodies must be absolutely perfect; and being perfect entails their having all kinds of perfection. Therefore their shape is perfect, which is to say that it is spherical; and absolutely so, not just approximately. 2

Galileo's own spokesman in the Dialogue had this to say: These doctors of philosophy never concede the moon to be less polished than a mirror; they would like it to be more so, if that can be imagined . ... If they were to grant me any unevenness, however slight, I would grasp for some other, a little greater; and since perfection consists in infinitesimals, a hair spoils it as badly as does a mountain. 3

The verbal and logical explorations that prevailed in science before Galileo

Galileo's Explorations in Science

39

departed from his visual and rationally deduced evidences, introduced with the telescope along with common terrestrial analogies. A second scientific exploration described in the Starry Messenger destroyed still another Aristotelian principle - that all heavenly bodies circle the earth as the unique center of celestial motions. Galileo's account shows how astronomical discovery is so embedded in the process of scientific exploration that it is hardly possible to set an exact moment for any discovery. Galileo wrote: On the seventh of January in this present year 1610, at the first hour after sunset when I was viewing the heavenly bodies with a telescope, Jupiter presented its body to me; and because I had prepared an excellent instrument I perceived - as I had not before, through weakness of my previous telescope - that beside the planet there were three starlets, very small indeed, but quite bright. Although I thought them to belong to the great host of fixed stars, they did arouse my curiosity somewhat by their appearing to lie exactly in a straight line parallel to the ecliptic [that is, along the zodiac or path of all the planets l, and by their being more splendid than other stars their size. 4

Since it is known that Galileo had seen three satellites of Jupiter, it is usually said that Jupiter's satellites were discovered on the night of 7 January 161 o. In the same way we say that America was discovered on 12 October 1492, though on that day Columbus still believed that he had arrived at lands already known to earlier explorers like Marco Polo. Galileo thought at first that he was observing three fixed stars, similar to hundreds he had seen through his telescope on other nights, these three being distinguished only by their lying along a certain straight line, as fixed stars close together rarely do, and by their being rather bright for their size. So Galileo did not express amazement, or even decide to follow up the observation, as he did later when he recognized a true scientific discovery. His narrative continued: I paid no attention to the distances between the starlets and Jupiter, for as I said, I believed them at the outset to be fixed stars. Now, returning to the same investigation on January eighth, led by I know not what, I found a very different arrangement. The three starlets were now all to the west of Jupiter, closer together, and at equal distances apart.5

The element of luck that enters into nearly every scientific discovery is seen from Galileo's remark that he did not know what led him to look again at Jupiter. The element of observational skill that always enters into scientific discovery, and the faith in one's memory that nearly always does, are shown by his certainty as to the previous position even though at the time he had not especially attended to it. For next he wrote:

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Biographical and General

At this point, though I still did not direct attention to the question how the starlets had gathered closer together, I did become concerned with the question how Jupiter could be eastward of all three stars when the night before it had been west of two of them. I wondered whether Jupiter was not moving eastward, contrary lo the calculations of astronomers, and by that motion had got ahead of the starlets. Hence I awaited the next night with great interest. But my hope was disappointed, as the sky was then everywhere covered by clouds. 6

Not only observational skill and memory, but also knowledge of planetary astronomy was needed at this step toward discovery. At that time Jupiter appeared from the earth to be moving westward among the fixed stars, as occasionally it does when the swifter-moving earth overtakes and passes it in their journeys around the sun. What Galileo saw did not seem to fit with that. The simplest solution might have been to suppose some error in the astronomical tables, since it would have been ridiculous to ascribe motion to what Galileo was assuming to be fixed stars. Another observation would confirm or contradict the tables, but of course that would require a clear sky. The next night was clear, and Galileo wrote: On the tenth of January ... there were only two starlets, the third, I supposed, being hidden behind Jupiter. As before, they were in a straight line with Jupiter and lay precisely along the zodiac. Noticing that, I knew that there was no way in which the change could be ascribed to Jupiter's motion alone. Yet I was certain that these were the same stars as before, no others in fact being visible for a long way along the line of the zodiac to either side of Jupiter. Thus my puzzlement was now transformed into amazement. Sure that the apparent changes of place belonged not to Jupiter but to the observed starlets, I resolved to pursue this investigation with greater care and attention.7

Galileo's amazement marked his realization that inescapable consequences of what he had seen could not be fitted with accepted science. Because he had considered every possibility as he went along, he was next forced to conclude that he was observing previously unknown planets, as all wandering stars were then called. That completed the destruction of Aristotle's principle forbidding new things in the heavens, already shaken by the existence of stars too small to be seen with the unaided eye. Moreover, it opened the way for rejection of still another ancient principle. On the night of 13 January Galileo first saw all four of the Jovian satellites which can be seen without powerful modem telescopes, no others having been found until I 890. On the fifteenth he concluded that their motions could be rationally explained only if they revolved around Jupiter as a center, contrary to the ancient notion that all celestial motions must have the

Galileo's Explorations in Science

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earth as their center. Thus a series of discoveries occurred during the course of this exploration before any final scientific conclusion was drawn. It is debatable which night should be called the date of discovery of Jupiter's principal satellites. On January seventh they were seen as fixed stars, and even the discovery on January tenth that the starlets must be moving did not reveal that they revolved around Jupiter. Galileo's astronomical explorations were far from ended in 1610, but these first few had been enough to draw fire from many astronomers as well as all natural philosophers. Ground of opposition ranged from Aristotle's authority in science to charges that Galileo had deliberately perpetrated some hoax . Others argued that because curved glass distorts vision, Galileo himself had been fooled by mere optical illusions. He did not reply in print, though two or three of his friends did, while Galileo confined his own remarks to letters. He offered a reward to any philosopher who produced a telescope that could show optical illusions around one bright point and not around others. To the great Gerrnan astronomer, Johann Kepler, who had supported him from the first, Galileo wrote that philosophers acted as if their wordy arguments were incantations that could conjure the new celestial objects out of the sky. With Galileo the days of wordy magic came to an end for science. The whole verbal basis of accepted science was faulty; as Galileo later wrote, the great book of nature stood always open, but could not be read without one's knowing the language of mathematics. Astronomy had been written in that language ever since Ptolemy devised a system for calculating from past observations any planetary position, past or future. Physics, however, still remained qualitative. No one had yet provided mathematical means for calculating the positions of a heavy body falling to the earth, even straight, let alone after being thrown. That was exactly what Galileo had been doing when the telescope diverted his attention to astronomy, so I shall now tum back to his early explorations in physics. At the time of the Leaning Tower episode not even Galileo, let alone Aristotle, had reasoned correctly about the fall of heavy bodies. Galileo had got closer to the truth, but he still had a long way to go. The real problem that had remained was to analyze accelerated motion, which in 1592 Galileo regarded as a mere temporary condition at the very beginning of fall, after which the body quickly attained a constant speed. Not until 1603 did he realize the need to take acceleration into account in his explorations of free fall . How he came to realize that need is made clear by examining his letters and working papers from 1602 to 1609. By 1602 Galileo had noticed that as a pendulum dies down with smaller and smaller swings, it still takes the same time for each swing, somehow adjusting its own speeds to the distances it has to travel. Using a pendulum eight or ten

42

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feet long, he explored this more closely and noticed that the bob goes on accelerating even when its path is almost horizontal. It followed that a ball rolling down an inclined plane would go on accelerating no matter how long the plane was. That contradicted Galileo's older idea that a steady speed is soon reached in free fall, which should always be faster than descent along an incline. Galileo was willing enough to abandon his former idea, but a new puzzle now arose. Before he began to consider acceleration seriously he had already reasoned out a remarkable theorem, which was that the same time is consumed in straight motion of a heavy body from any point on the rim of a vertical circle to its lowest point, regardless of the length and slope of the connecting line. Actual tests showed his theorem to be true. Galileo now realized that the whole motions were accelerated, but that he had derived his theorem without taking acceleration into account. That puzzled him so much that it led to his exploration of mathematical physics, his most important contribution to modem science. The fact was that Galileo's true theorem had been derived from false assumptions. People often overlook that true conclusions may follow logically from false premises, though no false conclusion can be logically reached from true premises. For example if we assume that polar bears are found in all very hot countries, and that Canada is a very hot country, it will follow that polar bears are found in Canada, as indeed they are. In arriving at his remarkable theorem, Galileo had assumed that acceleration could be ignored and that speed along an incline is steady at a rate depending only on the slope. When he later realized that acceleration cannot be ignored, he needed to find out exactly how the speeds increase during acceleration in natural descent. That is a difficult thing to find out, for several reasons. Actual fall of heavy bodies is very swift and therefore hard to observe. Nor can speeds be measured directly, and in fact "speed" had never been mathematically defined. To measure speed indirectly, Galileo had to measure distances, which was easy, and also times, which were then hard to measure with accuracy. After some useless guesses at a rule of increasing speeds, Galileo settled down to scientific exploration of his problem. First, to slow the motion down, he could roll a ball down a gentle slope and assume that the rule for increase of speed would remain the same as for straight fall, though the speeds would be quite different. He chose a slope of only sixty parts in two thousand, which is an angle less than two degrees. Along a grooved plane at this angle Galileo allowed a bronze ball to roll from rest through a distance of two metres, which takes about four seconds of time. To divide that into eight equal times, he used musical beats of a halfsecond. Finally, he measured the distances from rest to where the ball was at the end of each time. Because the times were equal, the speed during each time was proportional to the distance measured. These distances, and likewise the speeds,

Galileo 's Explorations in Science

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were found to go up proportionately to the odd numbers 1, 3, 5, 7 .. . and so on. Adding those numbers to get total distances from rest gave Galileo the square numbers 1, 4, 9, 16 ... and so on. In that way Galileo found the law of falling bodies, which states that distances from rest are as the squares of the elapsed times. The law of fall was found early in 1604, though Galileo did not publish it until years later. When he did, he did not explain how he had discovered it, but described instead the apparatus he had used to verify it for different slopes and different distances. The process of discovery remained unknown until about five years ago, when I found among Galileo 's working papers at Florence one on which he had written his original measurements together with notes and diagrams that made it possible to reconstruct his experiment. Previously there had been many debates among historians of science over the origin of the law of fall. Some believed Galileo to have found it by measurements, but others thought he had followed the ideas of medieval natural philosophers, while still others said he found the law by pure mathematics and never even tested it experimentally. That is still a very popular theory, despite the fact that for useful physics it is necessary at some point to connect every conclusion with the sensible world by careful measurements. The trouble with official science up to Galileo's time was, as he said, that it dealt only with a world on paper. Galileo created a new science of motion linked to the actual world. Only incredible good luck could account for that if he merely substitu1ed pure mathematics for Aristotle's traditional pure logic. Something more was necessary, and that something turns out to have been exact measurement. Measurements produce numbers that reveal mathematical laws. That is why physicists describe the apparatus and procedures of measurement that anyone can use in verifying the same results. Now, when Galileo finally published his new science of motion, he described apparatus and procedures that others could duplicate, rather than those I described for the original discovery. In his Two New Sciences of 1638 Galileo included a way of comparing small times by collecting and weighing water flowing through a small hole in a large bucket while a ball rolls through some exact distance measured in advance . In 1961 a historian of science built the apparatus described by Galileo, followed his procedures, and found that twice the accuracy claimed by Galileo could actually be attained. Of course we can now make measurements more accurate than Galileo could, but his method of exploration in science, producing results that can be duplicated by others, has not basically changed since he first devised it. That method replaced the verbalisms of Aristotelian natural philosophy that, as we saw in the Leaning Tower episode, had allowed different people to reach diametrically opposite conclusions.

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What I have said would be enough to establish Galileo as a pioneer explorer in, and of, science; but I am not yet through. What Galileo published in 1638, and guaranteed to be accurate within one-tenth of a second, fell far short of the precision he himself had attained in 1604. Modem analysis of his experiment shows that Galileo's accuracy in timing by half-second musical beats brought his original measurements of distances within a precision of one-sixtieth of a second. But of course he could not guarantee that kind of accuracy in tests by others, because individuals differ widely in their abilities to keep exact musical time. At beats of one-half second nearly anyone can detect a deviation of onetwentieth of a second, while trained musicians are sensitive to errors of onehundredth of a second. Galileo's father and brother were professional musicians, while he himself was a talented amateur on the lute. The precision of his own original experiment is thus understandable, though it may sound incredible because we are used to using precision instruments and forget the capabilities of our own senses. Some other things about Galileo's procedures are surprising. One that I have already mentioned is that, without a precedent to copy in science, when he published a procedure for verifying a mathematical law he took care to make it objective, so that anyone could follow it. He even specified the range of experimental error. Another is that Galileo avoided the use of measurements of single distances, times, or speeds. He used everything in the form of ratios, so that units of time or distance cancelled out, and anyone in England or France could test the law he discovered in Italy when there were no standard units of measurement. Likewise, by sticking to ratios, he did not have to specify such things as the size of hole in the bucket, because the ratio between volumes of water flowing through any hole while the ball rolls through distances in a given ratio will be the same no matter how much water flows, or how fast. His law of fall enabled Galileo to solve many problems ab~ut motions of heavy bodies, starting in 1604. In 1608 he applied the rule of speeds in acceleration to test an old idea of his, that speed remains uniform in horizontal motion without friction . To do this he gave his ball various speeds in known ratios, having it drop from a level table to the floor, and measuring its distances of horizontal advance during fall . A by-product of this exploration was Galileo's discovery that projectiles travel in parabolic paths. Together with his law of fall that led on to Newton's laws of inertia and gravitation, which remained the foundations of modem physics until Einstein modified them. To me it seems that an ear for music and a talent for devising experiments did more than philosophy in laying a basis for modem physics as early as 1608. In 161 o Galileo resigned his professorship at Padua and moved to Florence to become court mathematician to the Grand Duke of Tuscany. As he said in a let-

Galileo's Explorations in Science

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ter applying for that position, he wanted to be free from teaching to pursue his researches and to publish. Because his telescopic discoveries had contradicted official university science, he may also have wished to avoid conflicts with the professors of philosophy. But there was no escape; at Florence, in 161 1, Galileo became embroiled in a controversy with philosophers over the floating of solids placed in water. The book on hydrostatics he published in 161 2 was written in Italian, as were all his later books - not in Latin for the benefit of philosophers and astronomers. Galileo saw little hope of reforming university science, as is clear from a letter he wrote to a friend at Padua: I wrote my last book in the common language because I want everyone to read it. What inspires me to do this is my seeing how students in the universities, sent indiscriminately to become doctors or philosophers, apply themselves in many cases to professions when unsuited for them, while others who would be apt are occupied with family cares and other pursuits remote from the literary. Now, I want them to see that just as Nature has given them, as well as philosophers, eyes to see her works, so she has also given them brains to understand them. 8

It might seem unlikely that explorations in hydrostatics would interest the general public, but Galileo's results were so surprising, and so easy to check by carrying out simple experiments, that the book sold out quickly and a second, expanded edition was printed two months later. Four philosophers attacked it in print and then formed a league whose members opposed everything Galileo said from that time on. The reason was that Galileo questioned their whole conception of science, and especially the idea of finding causes, without which Aristotelian natural philosophy could not survive. Finding laws sufficed for Galileo's science. In 1613 Galileo published a book on sunspots, at the end of which he came out for the first time in print in support of Copernican astronomy and predicting its ultimate victory. That gave his foes a way to strike at him as if religion rather than philosophy had been called in question. Late in 1613 a philosophy professor at Pisa told Galileo's employers, in his absence, that belief in motion of the earth was contrary to the Bible. A Benedictine abbot happened to be present who had been a student of Galileo's at Padua and was now professor of mathematics at Pisa. Speaking as a theologian he defended Galileo, to whom he also reported what had happened. Galileo addressed to him a long letter on religion and science to make his own beliefs quite clear. In 1614 Galileo reached the age of fifty. He enjoyed the friendship of cardinals and other Church dignitaries, to say nothing of the very Catholic ruling family at Florence. No churchman had attacked Galileo or his science. Philoso-

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phers of the hostile league considered getting some priest to attack his views, but were rebuked at the home of the archbishop of Florence. Yet near the end of 1614 a young priest did denounce the Galileists from the pulpit of a principal church. Another priest copied Galileo ' s letter on religion and science and sent it to the· Roman Inquisition for investigation. Galileo 's position was that no conflict could exist between God's word in the Bible and God's works in Nature. The words of scripture had often been found to be metaphorical and to require interpretation by theologians. Scientific understanding of natural phenomena, on the other hand, required only sensible experience and necessary demonstrations. Those could better serve as a basis for biblical interpretation than the other way round. In judging scientific findings, Galileo wrote, the last thing to be consulted were scriptural passages. The Inquisition turned this letter over to a qualified theologian, who reported that it contained good Catholic doctrine, though some of its expressions might offend pious ears. The matter was dropped by the Inquisition. Galileo, however, feared that Copernican books would be prohibited unless responsible Church officials were fully infonned about new discoveries and the new direction of science. He asked pennission from the Grand Duke to visit Rome, where he could clear his own name and explain the new astronomy to theologians. The Tuscan ambassador at Rome cautioned the Grand Duke against letting Galileo come there and argue about the moon, because the pope was unfavourable to intellectuals. Nevertheless the Grand Duke sent Galileo to Rome and even lodged him with the ambassador, implying state approval of Galileo's mission. At Rome Galileo wrote out his theory of the tides, which he linked to simultaneous rotation and revolution of the earth. It was a scientific but mistaken theory, based on the kind of motions we feel when seated in those amusement park devices that spin us around at the end of a long beam that is simultaneously revolving. Such motions of the earth would disturb the waters in large seas, and Galileo reasoned that they accounted for tides. Despite Galileo's arguments the theologians empowered to qualify disputed propositions ruled that the Copernican motions were foolish and absurd in philosophy, and rash or even heretical in the Catholic faith . They did not consider metaphorical language in the Bible, but shifted their responsibility for interpreting scripture to the very philosophers who opposed Galileo. Copernican books were placed under regulation by an official edict early in 1616. Galileo had lost his battle, but he had said all along that he would abide by any official Church ruling, and he was as good as his word. For several years he wrote no more about Copernicanism . Instead he took up an exploration by science of a practical problem, the detennination of longitude on ships at sea. Galileo proposed that navigators use positions of Jupiter's satellites as a kind of

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celestial clock. He brought his tables of satellite motions to a high degree of reliability, but he failed to persuade admirals and sea-captains to accept his scientific solution of their practical problem. In 1618 three comets appeared and Galileo entered into a long controversy with Jesuit astronomers over such phenomena. This led in 1623 to Galileo's main book containing explorations of science, called The Assayer. Science could advance, he believed, only by giving up vain pretensions and settling down to practicable goals: To put aside hints and speak plainly, and dealing with science as a method of demonstration and reasoning that is capable of human pursuit, I hold that the more this partakes of perfection, the smaller the number of propositions will it promise to teach, and even fewer will it conclusively prove. Consequently the more perfect it becomes, the less attractive it will be, and the fewer its followers. On the other hand magnificent book titles and grandiose promises attract the natural curiosity of mankind and hold men forever involved in fallacies and chimeras, without ever offering them one single sample of that sharpness of true proof by which the taste may be awakened to know how insipid is the ordinary fare.9

Just as this book was being printed, an old friend and admirer of Galileo's became pope, and the book was dedicated to him. In 1624 Galileo went to Rome to pay homage to the new pope, who was an intellectual and wanted the support of others. He was aware that the 1616 edict was making that difficult to secure, especially in Germany where Copernicanism was flourishing. Galileo undertook to write, as a Catholic scientist, a book that would show that the Church edict did not hamper scientific explorations, but only forbade unauthorized biblical interpretations and imprudent statements that motion of the earth had been proved. Foreign misunderstanding of the edict would be encountered, the Church would benefit, and Italian primacy in science would continue. The pope liked the idea, and Galileo spent five years writing his book as a dialogue on the tides. But when its publication was licensed he was compelled to alter the title and with it the basic plan of organization. The consequences were disastrous; even the pope turned against Galileo, who was tried and condemned by the Inquisition. The book he wrote to rescue his church from consequences of an action he had warned it against has ever since been looked upon as an impudent defiance of that same church. That is not the usual interpretation of the events; it is my interpretation after long study of Galileo's career. I regret that time does not allow me to tell the whole complex story; that would require a lecture all by itself. Instead I have shown you Galileo as an explorer at a time when science as a mode of explora-

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tion of the universe was first assuming its modem fonn . What stood in its way was not just religious conservatism, but the vanity of a whole intellectual tradition that claimed to explain all of nature in one grand plan. In conclusion I shall read some remarks by an eminent modem scientist that encourage me greatly as a historian. In his bicentennial address to the American Academy of Arts and Sciences, Professor Victor Weisskopf said, in part: Since the beginning of culture man has been curious about the world in which he lives; he has continually sought explanations for his own existence and for the existence of the world - how it was created, how it developed and brought forth life and humankind, and how one day it will end. Early ideas on that subject were developed in a mythological, religious or philosophical framework. All these ideas have a common characteristic: they are directed to the totality of the phenomena; they want to account for everything that is. They intend to present the absolute truth by attempting to give immediate answers to the fundamental questions of existence such as Why is the world the way we find it? What is life? What is the beginning and the end of the universe? Several hundred years ago human curiosity took a different tum: instead of reaching for the whole truth, people began to examine definable and clearly separable phenomena. They asked not ... How was the world created? but How do the planets move in the sky? In other words, general questions were shunned in favour of limited ones to which it seemed easier to get direct and unambiguous answers. Then the great miracle happened. The restraint was rewarded as the answers to limited questions became more and more general. The renunciation of immediate contact with absolute truth, the detour through the diversity of experience, allowed the methods of science to become more and more penetrating and the insights to become more and more fundamental . The study of moving bodies led to celestial mechanics and an understanding of the universality of the gravitational law . ... Thus something like a scientific world view arose in the twentieth century, a synthesis of scientific insights gained over the past five hundred years. The world view of natural science differs ... from the religious, mythological and philosophical ones . ... What it perceives as "the scientific truth" is steadily revealed in partial steps, sometimes big ones, sometimes small ones and sometimes even steps backward. Some present knowledge will tum out to be mistaken. 10

It is this moderate world view that began with Galileo's explorations in science. As he wrote in his famous but ill-fated Dialogue: There is not a single effect in Nature, not even the least that exists, such that the most ingenious theorists can arrive at complete understanding of it. The vain presumption of understanding everything can have no other basis than never understanding anything.

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For anyone who had experienced just once the perfect understanding of one single thing, and who had truly tasted how knowledge is achieved, would recognize that of the infinity of other truths he understands nothing. 11 NOTES

1 This is essentially the text of a lecture given in the 1981 Killam Lecture series at Dalhousie University. 2 Galileo, Dialogue Concerning the Two Chief World Systems, tr. S. Drake (Berkeley, I 953), p. 84. 3 Dialogue, p. 80. 4 Galileo, The Starry Messenger, tr. S. Drake in Discoveries and Opinions of Galileo (New York, 1957), p. 51. 5 Starry Messenger, pp. 51-2. 6 Starry Messenger, p. 52. 7 Starry Messenger, p. 52. 8 Discoveries, p. 84. 9 Galileo, The Assayer in Discoveries, pp. 239-40. 10 Bulletin , The American Academy of Arts and Sciences, vol. xxxv, no. 2 (November, 1981 ), pp. 4-5. 11 Dialogue, p. IOI.

4

Galileo's Language: Mathematics and Poetry in a New Science

Names and attributes must be accommodated to the essences of things, and not essences to names; for things come first, and names afterward. Galileo ( 1613)

If the opinions of philosophers, and their words, have the power to call into existence the things they consider and name, why then I beg them the favor of their considering and naming "gold" a lot of old hardware I have about the house. Galileo (1623)

In his famous Dia/o~ue, written two decades after Galileo left his chair of mathematics at the University of Padua and took the post of chief mathematician and philosopher to the Grand Duke of Tuscany, he made his own spokesman declare that "Our discourses must relate to the sensible world, and not just to one on paper."' The demand would have been axiomatic to the practical Florentines at the Tuscan court. But to Galileo's former colleagues at the University it would have seemed in principle impossible of fulfillment, and in practice a revolutionary slogan threatening the very foundations of conventional philosophy. Now, the latter is precisely what Galileo intended it to be, and that fact has much to do with his insistence on the title of "philosopher" to the Grand Duke. What he meant by that word is pretty much what we mean today by the word

Reprinted from Yule Frmch Studi£'s 49 ( 1973), I 3-27, by permission.

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" physicist," a calling for which there was as yet no place in the universities. Accordingly he set up shop outside them, and proceeded to inculcate a rival discipline to theirs, founded on a new physics that dealt directly with the world of sensible phenomena. It is generally overlooked that the exposition of Galileo's new science was concerned in an essential way with language and its applications. He himself did not stress the point, but it is reflected in many passages such as the two that have been placed as mottoes at the head of this paper. The guiding idea is vividly illustrated in the Dialogue, where Galileo ridicules those who would deduce the nature of things from the writings of ancient philosophers and poets: I have a little book, much briefer than Aristotle or Ovid, in which the whole of science is contained, and with some little study one may form from it the most perfect ideas. It is the alphabet; and no doubt anyone who can join and order this or that vowel with these or those consonants can dig out of it the truest answers to every question, and can draw from it instruction in all the arts and sciences. Just so does a painter, from various simple colors placed separately on his palette, by gathering a little of this one with a bit of that and a trifle of the other, depict men, plants, buildings, birds, fishes - and in short represent every visible object - without any eyes or feathers or scales or leaves or stones being present on his palette. It is indeed necessary that none of the things represented, or any parts thereof, should be actually included among lhe colors, if one wants them capable of representing everything; for if among these there were, say, feathers, then those would not serve for depicting anything but birds, or feather-dusters." 2

This started as an obvious sarcasm directed against men who thought that by consulting the indexes to Aristotle's works, they could answer every question. But Galileo's metaphor went far beyond that. Quite possibly it constitutes the first clear recognition of the powers and limitations of language as a means of discoursing about the nature of things. The elements of the language used cannot be found in the things themselves. We shall see presently how this bears on Galileo's novel (and much misunderstood) view of the role of mathematics, and on his neglected but important view of the role of poetic metaphor, in science. For the present, let us note that he here asserted the possibility of discoursing in everyday language about problems that traditionally had always been dealt with by recourse to technical jargon. Galileo saw that what was really required in order to avoid turning the sensible world into a mere world on paper was not the artificial vocabulary of philosophers; rather, it was a certain kind of artistry in the use of the ordinary resources of language. It may be that others before Galileo had used similar analogies, or had otherwise attempted to make clear the role of language itself in dealing with the

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world of sense. But if so, I think they can have been neither many, nor influential. Francis Bacon warned about the same time of certain pitfalls inherent in the structure of language that had escaped the attention of philosophers. But that is hardly the same thing. To make the actual world come alive on paper takes more than the avoidance of logical and semantic errors. A man does not become a painter merely by avoiding distortions of natural colors and fonns; indeed, what often makes a painter great is his deliberate and skillful use of such devices. "To depict burnished annor, for example, one must alternate pure black and white, one beside the other, in parts of the annor where [in fact] the light falls evenly" (Dialogue, p. 79). Yet at the same time, craftsmanship is capable of abuse in philosophy as in painting: [Some philosophers] wish never to raise their eyes from those pages, as if this great book of the universe had been written to be read by nobody but Aristotle . ... These fellows ... put me in mind of certain capricious painters who occasionally limit themselves, for sport, to represent a human face or some other thing by throwing together [on canvas] some agricultural implements, or different fruits, or perhaps the flowers of a given season. Such bizarre performances, so long as they are put forth in jest, are both pretty and pleasant, and they reveal more resourcefulness in some artists than in others .... But if anyone ... should conclude in general that every other manner of representation was blameworthy ... he would be laughed to scorn by distinguished painters. (Discoveries, p. 1 27)

Galileo's avowed goal appeared unattainable in principle to many contemporaries because of the philosophical question, "How can words set down on paper deal with the sensible world that is quite independent of language?" Philosophers, lacking the artistry of poets (who manage that feat very well indeed), had long since abandoned the attempt to deal with the sensible world as such, leaving that part of physics to mere mechanics. In so doing, they had found a marvelous justification for their action. The sensible world is ephemeral, filled with illusion, and hardly worth the trouble of serious study. But behind it, they believed, there must lie pennanent things, transcending the sensible world in interest and importance, and perhaps transcending it in reality. It was to such things that philosophers directed their attention, and that is why Galileo's demand threatened the very basis of real scholarship. A typical dispute that occupied philosophers was waged between those who regarded mathematics alone as possessing eternal verities deserving of study for their own sake, and others who disparaged mathematics in favor of Aristotle's vocabulary and grammar as the key to lasting truth. These two persuasions are known as Platonism and Aristotelianism. If, with Josiah Willard Gibbs,3 we

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53

consider mathematics itself a language, then the traditional dispute centers on which of two languages holds the key to our universe: geometry, or Greek? In place of this ancient dilemma, Galileo introduced a new conception, though its element of novelty has generally escaped notice. This has happened because historians of science, like philosophers, are usually more interested in the dispute (which is indeed eternal) than in Galileo (who was certainly ephenneral). His celebrated metaphor was this: Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and to read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it: without these, one goes wandering about in a dark labyrinth. (Discoveries, pp. 237-38).

In their understandable zeal to classify Galileo as one of the traditional disputants, most commentators regard this passage as putting him squarely in the camp of the Platonists. It seems to them that he here identified the universe we live in with that of mathematics, as so many other powerful thinkers have done. But in this they entirely ignore the linguistic consideration that was the source and whole point of Galileo's metaphor. This may be seen from the context in which it appeared, where poetry and fiction were being contrasted with science. There are in fact three elements in Galileo's metaphor, and not just the two which concerned all previous (and most subsequent) philosophers. The three elements are: a certain book, what is written in it, and the language in which that is written there. Since the book is "the universe which stands continually open to our gaze," it can hardly be anything but the sensible world. Eternal mathematical truth does not stand open to our gaze, at least in the ordinary sense. We cannot gaze at partless points or breadthless lines. And Galileo was very keen on the ordinary senses of words, particularly such words as "gaze." What is written in that book (the sensible world) is proper philosophy. To the extent that other books bear that title but fail to deal with the sensible world, they concern only worlds on paper. This notion is clear in many other places in Galileo's writings. Finally, the language in which proper philosophy is written in the book (the sensible world) is the language of mathematics. This language is identified by Galileo neither with the sensible world nor with philosophy; still less is it treated as anything worthy of study for its own sake. Rather, Galileo speaks of the language of mathematics as the unique means to an understanding of some-

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thing else; and that something else is precisely the sensible world which Platonists disparaged as ephemeral and illusory, and undeserving of special study. Interest in the sensible world was anything but new, except perhaps to philosophers. But Galileo's linguistic metaphor was new, in that it presented mathematics as an instrument that would enable philosophy to discourse with accuracy about the sensible world. That was never Plato's conception. The desired end-product, however, need not be written in mathematical language at all, and certainly not exclusively. So far as Galileo was concerned, it was better written in Italian than in scholarly Latin. It was no accident that Galileo preferred a living language for the purposes of his new science; in the same way, his great Flemish contemporary, Simon Stevin, took Dutch to be the ideal language for science. The reason that Galileo once gave for his choice reflected a Renaissance penchant for popular education. (Another and more cogent reason will be given later.) When a Gennan adversary could not read his book on sunspots, Galileo asked a friend who was a fine Latinist to translate it, writing to him: I wrote it in the vernacular because I need to have anyone [here] able to read it; and for the same reason I also wrote my last little treatise [on hydrostatics] in Italian. The reason that moves me is my seeing how young men are sent indiscriminately to the university to be made into doctors, philosophers, and so on; and just as there are many who apply themselves to such professions but are most unsuited to them, so there are other men that would be apt, but who are taken up by family cares or other matters remote from letters. They have horse-sense, as Ruzzante would say, but because they cannot read things written in Latin, they persuade themselves that great new discoveries in logic and philosophy are published in awful books that remain way over their heads. Now, I want them to see that just as Nature gave to them, as well as to philosophers, eyes to see her works, so she has also given them brains capable of understanding those works. (Discoveries, p. 84)

Here, then, was a further linguistic characteristic (if not requirement) of Galileo's new science. The key was mathematics, but the goal was scientific discourse in easily intelligible tenns. Popular education seems to have been only a part of the reason for this. It is at least debatable whether even today it would be possible to write physics without any intennediation whatever of ordinary language. Certainly that was not possible in Galileo's time. The answer to the question, "How is it possible to discourse of the sensible world when that is separate from and independent of language?" is, roughly speaking, "By constant allusions that redirect attention from words to the things of experience." That answer is not likely ever to satisfy philosophers, but it was adopted in

Galileo's Language

55

practice by Galileo. And he realized that allusions to experience are far more effective, and much easier to manage, in the language of everyday life than in a specialized scholarly language. Galileo's books are filled with such allusions, often quite colloquial in style. His readers are thus constantly reminded of familiar experiences and observations; of little puzzles that occur to everyone but are usually pushed aside; and of palpable absurdities that no one would ever expect to encounter. The backspin of a bocce ball delivered overhand, the curious rebound of a tennis ball struck with the racket slantwise, and the mingled kiss-and-bite on the ear of a slight dissonance are as much a part of Galileo's science as are the parabolic trajectory and the regular beat of the pendulum. The way to put the sensible world on paper without thereby reducing it to a paper world was to keep the reader's mind on things of experience rather than on verbal technicalities. The poets are great masters of this art. They bring experience to life by a single word or a brief phrase, when the same experience would remain lifeless through a paragraph of objective description. Galileo borrowed their technique, and he ascribed his own clarity of style to his intimate familiarity with the poetry of Ariosto. It was probably this poetic artistry that suggested to him the analogy, previously cited, between the alphabet and the simple colors on a painter's palette. Poetry is acquired by continual reading of the poets; painting is acquired by continual painting and drawing; the art of proof, by reading books filled with demonstrations - and these are exclusively mathematical books, not books on logic. (Dialogue, p. 35)

Galileo's view of mathematics has already been touched on. His mistrust of logic will be mentioned again presently. In part, it mirrored his keen sensitivity for language and an attendant dislike for jargon. In this, he was indeed a follower of Plato, who "went to some pains to vary his terminology in what seems to be a deliberate attempt to resist the congealing of technical terms, and the implication of the Socratic-centered Platonic dialogue is still that two reasonably educated citizens can sit down and discuss these matters .... With Aristotle, the professionalism implicit in the founding of the Academy comes of age in language. "4 Aristotelian logic puts language in a straitjacket, expecting in this way to constrain it within any chosen universe of discourse - say that of the sensible world. But by its very insistence on precise definition, formal logic may sometimes remove words even further than necessary from the things of our experience. Freed from such restraint and used with artistry, ordinary words suffice to recall any common experience with remarkable efficiency and precision. Thus

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no logical description of the moon seen in daytime could be more effective in fixing its appearance than to say, with Galileo, that it resembles a little bleached cloud. Those words accurately present the moon of the sensible world under certain conditions. They fail utterly to present the mathematical moon of our astronomers, the physical moon of our scientists, or the Aristotelian moon that separates the elemental from the celestial regions. Galileo's phrase is one that poets might employ, though not for his purposes in invoking it. The phrase is poetic, but the purpose was scientific, as we shall see; and in his own words: "Nature does not delight in poetry .... Fables and fictions are in a way essential to poetry, which could not exist without them; while any sort of falsehood is so abhorrent to nature that it is as absent there as darkness is in light" (Discoveries, p. 238).s The use of a poetic device to portray anything in nature, when nature abhors fiction and poesy thrives on it, is logically unacceptable. On the other hand, the use of such a device not indeed to represent anything, but to call vividly to mind some actual experience, served a most useful purpose for Galileo. He saw in this the way to make sure that his discourse related to the sensible world, and not just to one on paper. How this was done will be seen below; since hardly any physicist after Galileo employed such devices, I think it worth givil)g this one example in full. It is not as trivial as it may seem, and the technique is far from unique among Galileo's published writings. Simplicio, who speaks for the philosophers, has just asserted that the gross and impure earth is unfitted to reflect sunlight as does the moon, a heavenly body and composed of the pure quintessential substance. The scientific question involved is Galileo's explanation of the moon's faint illumination near new moon, caused by reflection of sunlight from the earth. Ultimately coupled with this was the destruction of the Aristotelian dogma that the heavenly bodies are of a totally different substance from the elements surrounding us. This in tum relates to the principle of the uniformity of nature, on which all Galileo's new science (like the very existence of ordinary language itself) was made to depend. Thus the ensuing passage is an integral part of a vast program of reeducation intended to replace dogma with sensible evidence: SAL VIATI: Tell me; when the moon is nearly full, so that it can be seen by day and also in the middle of the night, does it appear more brilliant in the daytime, or at night? SIMPLICIO: Incomparably more at night. It seems to me that the moon resembles those pillars of cloud and of fire which guided the children of Israel; for in the presence of the sun it shows itself like a little cloud, but then at night it is most splendid. Thus I have sometimes observed the moon by day among small clouds, and it looked like a little bleached one; but in the night that followed it shone very splendidly.

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57

SALV.: So that if you had never happened to see the moon except by day, you would not have judged it brighter than one of those clouds? SIMP.: I do believe you are right. SAL V. : Now tell me, do you believe that the moon is really brighter at night than by day, or just that by some accident it looks that way? SIMP.: I believe that it shines intrinsically as much by day as by night, but that its light looks greater at night because we see it in the dark field of the sky. In daytime, because everything around it is very bright, by its small addition of light it appears much less bright. SALV.: Now tell me: have you ever seen the terrestrial globe lit up by the sun in the middle of the night? SIMP.: That seems to me to be a question that is not asked except in jest, or only of some person notorious for his lack of wit. SALV.: No, no; I take you for a very sensible man, and ask the question in earnest. So answer just the same, and then if it shall seem to you that I am talking nonsense, I shall be taken for the brainless one; for he is a greater fool who asks a silly question than he to whom the question is put. SIMP.: Then if you do not take me for a complete simpleton, pretend that I have answered you by saying that it is impossible for anyone who is on earth, as we are, to see by night that part of the earth where it is day; that is, the part struck by the sun. SALV.: So you have never chanced to see the earth illuminated except by day, while you see the moon shining in the sky on the darkest night as well. Now that, Simplicio, is the reason for your believing that the earth does not shine like the moon; for if you could see the earth illuminated while you were in a place as dark as night, it would look to you more splendid than the moon. And if you want to proceed properly with the comparison, the analogy must be drawn between the earth's light and that of the moon as seen in daytime - not the nocturnal moon, because there is no chance of our seeing the earth illuminated except by day. ls that satisfactory? SIMP.: So it must be. SALV.: Now you yourself have already admitted having seen the moon by day among little whitish clouds, and similar in appearance to one of them. This amounts to your granting at the outset that those little clouds, though made of elemental matter, are just as fit to receive light as is the moon. More so, if you will recall in memory having seen at times some very large clouds, white as snow. It cannot be doubted that if such a cloud could remain equally luminous on the darkest night, it would light up the surrounding regions more than a hundred moons. If we were sure, then, that the earth is as much lighted by the sun as is one of those clouds, no question would remain about its being no less brilliant than the moon. But all doubt on this point vanishes when we see the same clouds, in the absence of the sun, remaining as dark as the earth all night long; and what is more, there is not one of us who

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has not seen such a cloud, low and far off, and wondered whether it was a cloud or a mountain - a clear indication that mountains are no less luminous than those clouds. (Dialogue, pp. 87-89) I think it hardly possible to read the foregoing dialogue without recalling to mind actual experiences of one's own; that is, I believe it would take superhuman effort to read Galileo's argument while keeping one's attention focused solely and strictly on its words, forgetting how the things named actually look, and how we might expect things to look if we could see them under conditions that never do exist for us. You would look in vain for any counterpart of this kind of persuasion in ancient and medieval commentaries on Aristotle's Physica or De caelo, at least in those I have read. There you would indeed find compelling arguments, logically designed to convince you (with Simplicio) that gross earth is unfitted to shine like a heavenly body. In such arguments you are, it is true, invited to think of experiences, though not vivid ones: the experiences of grossness, of shining, and of the fitness of things. But it is not necessary that you do so, since the definitions suffice; and when we are reading dead languages, or technical tenns in living ones, there is little stimulus to recall our own experiences. Galileo would have been perfectly capable of writing the above argument in technical tenns, and even with the objectivity that we associate with scientific writing of today. Whether that would have made it better science is an interesting question, that in tum would raise questions about the purpose or goal of scientific writing. On the whole, the goal of modem science seems to me to resemble that of the Platonists and Aristotelians of Galileo's time a good deal more than it resembles Galileo's goal. It is therefore fitting that modem science tends to be written in technical tenns without the slightest tincture of poetic metaphor. It is of interest that Galileo rejected such a style, though it already prevailed around him. Had he adopted it, it is likely that he would have reached the top of the academic profession, would not have left the university to serve the Grand Duke, and would have died in universal esteem rather than as a condemned heretic. The style used in writing a scientific work in any era requires respect for precision. Galileo's predecessors sought logical precision; his successors sought mathematical precision. Galileo did not tum his back on either of these; instead, he recognized and added other ways of making things precise. One, as we have seen, was that of invoking experience vividly. Another was the application of horse-sense, for which Galileo had a respect unusual in academics of his time. Philosophers ... attribute the rumbling of thunder to the tearing apart of clouds, or to

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their knocking together. Actually, during the brilliance of the brightest flashes of lightning, not the slightest movement or change of shape is discerned in the clouds, and that is just when thunder is being created. I pass over in silence the fact that those same philosophers do not say that noise is produced by the striking of wool or hemp, but require the percussion of solid bodies to make sound. Yet at another time, when it suits their purpose, they assert that mists and clouds on striking together will render the loudest of all sounds. Tractable and benign indeed is such philosophy, so pleasantly and readily adapting itself to men's needs and wishes! (Discoveries, p. 269) Galileo's mistrust of logic may originally have grown out of its frequent abuse in such cases as the above; for only by misapplied logic could such a theory of thunder have originated. His preference for mathematics over logic may be attributable in part to the relative difficulty of similarly misapplying mathematics. Geometric shapes, or numbers obtained from measurement, are not the least bit tractable. Where mathematical expressions happen to apply to the sensible world, they do not readily adapt themselves to men's wishes. Often they do not apply at all, "But in this," Galileo wrote to a friend late in life, " I have been lucky; for the events of falling bodies do correspond punctually with the properties I had found" in the hypothetical treatment of accelerated motion. 6 It is evident from that remark that Galileo did not believe that everything mathematical has a counterpart in nature. No more did he believe that everything in nature must have some mathematical counterpart. That astounding revelation was reserved for his younger contemporary, Rene Descartes. In the Cartesian scheme of things, which quickly supplanted Galileo's, every phenomenon in the universe was in principle capable of explanation in terms of matter and motion, and hence mathematically - at the expense, of course, of reverting to the earlier custom of discoursing about worlds on paper. Galileo had said: There is not a single effect in nature, not even the least that exists, such that the most ingenious theorists can ever arrive at a complete understanding of it. The vain presumption of understanding everything can have no other basis than [that of] never having understood anything. For anyone who had experienced just once the perfect understanding of one single thing would recognize that of the infinity of other truths he understands nothing. (Dialogue, p. IOI) Galileo was, however, by no means pessimistic about the progress of science, so long as its objectives were kept within the bounds of men ' s powers: All things among which men wander remain equally unknown, and we pass by things both near and remote with very little or no real acquisition of knowledge. When I ask

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Biographical and General

what the substance of clouds may be, and am told it is a moist vapor, I shall wish to know in tum what vapor is. Peradventure I shall be told that it is water, which when attenuated by heat is resolved into vapor. Equally curious about what water is, I shall then seek to find this out, ultimately learning that it is this fluid body which runs in our rivers and which we constantly handle. But this final infonnation about water is no more intimate than what I knew about clouds in the first place; it is merely closer at hand and dependent on more of my senses. Similarly, I know no more about the true essences of earth and fire than I do about those of the moon or the sun .... But if what we wish to fix in our minds is the apprehending of some properties of things, then it seems to me that we need not despair of our ability to acquire this with respect to distant bodies as well as those close at hand - and perhaps in some cases even more precisely in the fonner than in the latter. Who does not understand the periods and movements of the planets better than those of the waters in our various oceans? Was not the spherical shape of the moon discovered long before that of the earth, and much more easily? Is it not still argued whether the earth rests motionless or goes wandering, whereas we definitely know the movements of many stars? (Discoveries, pp. 123-24) Galileo's new discoveries in the heavens had widely expanded the sensible world of which he wished to discourse, but he was in no great hurry to set forth any general theory about it. The first step was to take care that the words applied should obey the analogies of the sensible phenomena to which they were applied. In answer to a rival who argued that spots on the sun were impossible because all men agreed the sun to be lucid and pure, and who suggested instead that the appearances were stars, Galileo wrote: Men were in fact obliged to call the sun "most lucid and pure" as long as no shadows or impurities had been perceived in it. But now that it shows itself partly impure and spotty, why should we not call it spotted, and not pure? (Discoveries, p. 92) Nor are the sunspots stars. It is indeed true that I am quibbling over names, when I know that anyone may impose those to suit himself. So long as a man does not think that by names he can confer inherent and essential properties on things, it would make little difference whether he calls these "stars." Thus the novae of 1572 and 1604 were called "stars," and meteorologists call comets and meteors "stars," and for that matter, lovers and poets so refer to the eyes of their lady-loves: "When Astolfo's successor is seen By the glance of those two smiling stars."7 For like reasons, the sunspots may also be called stars; but ... stars are always of one shape and quite regular, while the spots are of various shapes and most irregular; the

Galileo' s Language

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fonner are consistent in size and shape, while the latter are always changing .... Now, I fail to see any reason for putting the spots with things that differ from them in a hundred ways. (Discoveries, pp. I 3-MN;.{ a .,o,...:

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