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Peter E. Hodgson

Galileo the

Introduction The life and achievements of form a subject of enduring interest. He is certainly one of the greatest of all and indeed has been called the founder of modern . He showed that natural phenomena obey mathematical laws and thus, Galileo laid the foundations of quantitative and used it to give the first accurate account of the of falling bodies and projectiles. He improved the and used it to discover the of , the mountains on the , the phases of , and the spots on the . All this combined to throw doubt on Aristotelian and to support the heliocentric theory of Copernicus. More than any scientist, Galileo was responsible for initiating the transition from the Aristotelian science of the Middle Ages to the mathematical science of the following centuries. Galileo lived at a critical in the development of science. According to the popular account, the ancient Greeks made the first steps toward a scientific understanding of . The Greek writings were inherited by the Muslim civilization and then logos 6:3 summer 2003 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 14

 logos transmitted to the new in the Middle Ages through translations done mainly in Spain. Thereafter, an authoritarian Church controlled the intellectual development of Western and prevented any independent thought or scientific development. It was only during the that the authority of the Church was challenged by men like Galileo who insisted on the greater value for science of experimentation and than reliance on ancient texts. This is dramatized by the story that Galileo dropped two balls of different from the Leaning Tower of and showed that, contrary to ’s theory,they reached the ground simultaneously. Thereafter, science developed as a free and inde- pendent search for truth. The reality is, of course, different and highly instructive. The familiar story, still heard today, that there was no science worth speaking about in the long period from the time of the ancient Greeks to the flowering of genius in the Renaissance has long been disproved by modern scholarship. Galileo himself was not only a highly original scientist but remained a devout Catholic throughout his life.1 He had a sound grasp of theology and saw clearly that the new knowledge of the world gained by the scientific method was in no way inconsistent with the teaching of the Church, since both come from God. He also saw that some of the new knowledge raised important problems of scriptural interpretation that could be resolved within the context of traditional Catholic theology.It is now recognized that Galileo’s views on the interpretation of Scripture are basically correct, and he was particularly anxious to prevent the tragedy that actually happened—the condemnation by the Church of a genuine scientific breakthrough. He was, however,overconfident concerning his scientific arguments, which were still at that time inconclusive, at least to nonscientists. In view of the delicate theo- logical questions raised by the heliocentric theory,it was not unrea- sonable for Church authorities to ask Galileo to moderate his claims until a definite proof was forthcoming. The main protagonists were 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 15

galileo the scientist  all motivated to defend the truth, but they were strongly influenced by their intellectual backgrounds and possessed personal character traits that exacerbated their misunderstandings. Before considering the achievements of Galileo, it is useful to sketch the understanding of the physical world that existed before his time. The youthful Galileo was attracted to and avidly studied the works of . His interest in was stimulated by Archimedes’ solution of the problem of King Hiero’s crown, which led to Galileo’s first publication, The Little Balance (1586). , he realized, is written in the language of mathe- matics. Galileo was further stimulated by his on the relation between musical tones and the length, , and tension of strings. His on the centers of of solids led to his appointment as the chair of mathematics at Pisa. His emphasis on mathematics shows the influence of , who was widely influen- tial in the early Middle Ages due to the writings of Augustine. Plato held that terrestrial phenomena are imperfect copies of abstract mathematical forms existing in the transcendent realm of ideas. Thus, mathematical relations are only approximately realized in nature. It was Galileo’s greatest achievement to show how nature fol- lows mathematical laws, but he went beyond Plato in requiring exact correspondence, within the limits of experimental uncertainties. It is important to distinguish between the professional Aris- totelians in the universities, who infuriated Galileo by insisting on the literal text of Aristotle and refusing to listen to Galileo’s argu- ments, and the open-minded Jesuits at the Collegio Romano, who so strongly influenced the young Galileo in his formative years. These Jesuits followed Aristotle in many respects and taught “a somewhat eclectic Thomism containing elements deriving from Scotist,Averroist and nominalist thought”2 that may be described as scholastic Aristotelianism. Therefore, although he bitterly attacked the professional Aristotelians (particularly their views on 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 16

 logos and cosmology), Galileo retained a basic adherence to Aristotelian throughout his life. Aristotle thought of nature as a process, an organism, and held that the main object of science is to see how it is related to man. For him, the aim of science was to obtain certain knowledge by under- standing the causes of natural phenomena. His cosmology was based on direct commonsense experience, and this is why it has such a strong appeal, even today. Aristotle emphasized the primacy of the senses, which takes precedence over any theory. Who can doubt that the earth is solid and immoveable, with the sun, the stars, and moving around it? studied the motions of the stars and the planets, and was able to describe them quite accurately by compound- ing circular motions in the form of cycles and epicycles. This was a purely mathematical description, and it was not maintained that the cycles and epicycles corresponded to anything real. In contrast, Aristotle sought a more in terms of real entities. finally unified these two approaches in the early .3 At the center of Aristotle’s cosmology is the immovable earth. Surrounding it are a of concentric crystalline spheres bear- ing the moon and the inner planets and Venus, then the sun, and finally the outer planets , Jupiter, and . Enclos- ing all is the sphere of the fixed stars, and outside this is at all. There were differing views about the reality of the crystalline spheres: Aristotle believed there are fifty-five in all, made of a pure, unalterable, transparent, weightless, crystalline solid. The whole set of spheres rotates once a day,thus accounting for the diurnal of the sun and the stars. Seen against the background of the stars, the paths of the planets sometimes show a retrograde or looped motion, and this was accounted for by fixing the planets to secondary spheres linked to the main ones. In this way,the Aristotelian cosmology was able to give an account of all observable celestial motions, including the prediction of eclipses. 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 17

galileo the scientist  Guided by direct experience, Aristotle made a sharp distinction between terrestrial and celestial matter: terrestrial matter is change- able whereas celestial matter is unchangeable. There are four types of terrestrial matter: earth, air,fire, and water,and each seeks its nat- ural place. Celestial matter is the quintessence (or fifth essence)— pure and unchangeable—and naturally moves on the most perfect curve, the circle. On the earth, natural motion is linear: the falling of earth and water and the rising of air and fire. These motions accelerate as each body approaches its natural place. Unnatural motion, such as the flight of an ,requires the continuing action of a mover. Aristotle’s physics was based on direct observation and accounted for many natural phenomena in a reasonable and coher- ent way.As a result, it was widely accepted for two thousand years. One of the weakest parts of Aristotle’s physics is his theory of . He had no concept of and denied the notion of .Aristotle believed that because projectile motion is unnat- ural it requires the continued action of a mover,and this must be the medium. He therefore suggested that the thrower communicates both motion to the medium and the to move. Buridan, a fourteenth-century philosopher, rejected this theory because it cannot explain the continuing motion of a spinning wheel and also because it is common experience that the medium resists the motion of the projectile. Instead, Buridan proposed that the thrower gives the projectile impetus that carries it along after it has left the hand of the thrower. This is related to one of the arguments against the motion of the earth. According to Aristotle, a projectile thrown vertically upward from a moving earth fall behind and hit the ground west of its starting point, contrary to experience. The impetus theory, however, predicts that it retains an eastward impe- tus throughout its motion, and so returns to the same point as observed. Many philosophers believed that the ancient Greeks had achieved the summit of knowledge; they knew essentially all that could be known, and so the answer to any problem could be found by 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 18

 logos scrutinizing ancient texts, particularly those of Aristotle. The duty of a scholar was simply to understand, defend, and teach Aristotle’s ideas.Within this mindset, the Aristotelians simply could not under- stand what Galileo was trying to do. To them, the world is a living organism that can be understood by experience and reason. For this, direct perception is all that was needed. They interpreted the world in terms of a close-knit system of purposeful behavior, using organic categories and concepts like matter and form, act and poten- cy, essence and existence. Thus, the qualitative properties of things suffice to reveal their essences. In sharp contrast, Galileo said that it is an illusion to think we can understand the essences of things; what we can and should do is describe their behavior as accurately as we can using mathematics and then make experiments to test the validity of our ideas. Quan- titative relations are the real clues to the unique, orderly,immutable reality. By establishing them we can find out how things behave, but not what they are. This seemed useless to the Aristotelians, who had a low view of mathematics; indeed, Aristotle “left to mechanics and other low artisans the investigation of the ratios and other secondary features of .”4 To the Aristotelians, number,weight, and measure have no philosophical significance; motion is interpreted in terms of purpose, and for this, mathematics is irrelevant. They had no interest in accurate descriptions of the motions of projectiles or in the mathematical description of levers and pulleys. Mathematics, they allowed, is an interesting game, but it tells us nothing about the real world. Galileo, on the other hand, thought that the Aristotelians’ elaborate structure of in led nowhere. Because Galileo occupied a chair of mathematics, his duty was to expound the works of Euclid and Archimedes. He could be much freer in his criticisms of Aristotle than if he had been a member of the philosophical establishment, whose main duty was to master and teach the works of Aristotle. It is important to distinguish between Aristotle’s general ideas 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 19

galileo the scientist  concerning the scientific method, his natural philosophy, and the way it was applied to particular problems. was an attempt to find the real structure of the world by discovering true first principles and using them with the evidence of sense experi- ence. Galileo shared Aristotle’s goal of discovering the truth about nature. Aristotle’s cosmology included many statements about the heavenly bodies and detailed theories of familiar physical processes that have subsequently been found to be incorrect, but this does not necessarily falsify the principles of his natural philosophy.Although Galileo showed that many of Aristotle’s views are incorrect, Galileo did this within the framework of Aristotelian natural philosophy,and he remained essentially an Aristotelian. In the end, Aristotle’s attempt was a heroic failure, largely because he underestimated the difficulty of obtaining these principles, and also the value of precise measurement and detailed mathematical . Christian beliefs can be interpreted easily within the framework of Aristotelian cosmology.Hell is in the center of the earth, and vol- canoes provide evidence of its fires. Beyond the outermost sphere is the abode of God and the saints. Knowing this, we can speak of the descent into hell and the ascent into heaven. This imagery is lost in the heliocentric system. If the earth is just one of the planets, then is it not possible that people may be found on other planets? And if so, how can they be redeemed by Christ? The Aristotelian accommodated all that was known in a unified logical structure, and this accounts for its great power over the human imagination. To throw doubt on any part of the Aristotelian universe would seem to threaten the whole and upset the well-established order of the universe. Central to the whole debate is the question of why we believe— what the criteria are that we apply to judge whether a scientific theory is true. More fundamental, how do we justify the criteria itself? In Galileo’s time, a theory was judged by the Aristotelian cri- terion: whether it gave an explanation in terms of causes. It was also 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 20

 logos required to “save the appearances,” that is, to give predictions in numerical agreement with the experimental measurements. Last, it had to be in accord with Scripture.

Galileo the The Galileo’s earliest biographer, Viviani, claimed that in 1582, when Galileo was still a medical student in Pisa, he observed the motion of a swinging lamp in a cathedral. Using his pulse to measure the time of swing, he found it was independent of the amplitude of the swing, providing that the amplitude is small. This is a rather sur- prising result, as it implies that it takes the same time for the pen- dulum to reach the nadir of its swing, however far it is drawn aside before release.According to Viviani, this suggested to Galileo that a pendulum could be used to measure the pulse rate. There is, how- ever, no other evidence for this story,as Galileo first mentioned the isochronous nature of the pendulum in a letter in 1602. He also showed that the period of swing is independent of the material of the pendulum and that the period is proportional to the of the length of the string.Galileo also compared the swing of the pen- dulum with the motion of a ball that runs down one and up another one opposite to it. In another investigation, he found that the of descent are equal for all chords from the highest or to the lowest points of a vertical circle.

The Dynamics of and Projectiles Galileo’s earliest work on mechanics was in his De Motu of 1592, which is devoted to a discussion of the fall of bodies in media of dif- ferent densities. In this work he was much influenced by the ideas of the Jesuits at the Collegio Romano, whose lecture notes he used extensively.5 They held, with Aristotle, that the aim of science is the 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 21

galileo the scientist  understanding of natural phenomena in terms of evident principles, and Galileo continued to accept this throughout his life. However,he strongly opposed the arid, textual Aristotelians found in universities, and it is against them that his polemics are directed. De Motu is large- ly a detailed analysis of the writings of Aristotle on motion, and after about forty pages of discussion Galileo exclaims:

Heavens! At this point I am weary and ashamed of having to use so many words to refute such childish arguments and such inept attempts at subtleties as those which Aristotle crams into the whole of Book 4 of De Caelo, as he argues against the older philosophers. For his arguments have no force, no learn- ing, no elegance or attractiveness, and anyone who has under- stood what was said above will recognise their fallacies.6

Later he remarks, “Aristotle was ignorant not only of the profound and more abstruse discoveries of geometry,but even of the most ele- mentary principles of this science.”7 A few pages later, discussing how projectiles are moved, he writes, “Aristotle, as in practically everything that he wrote about locomotion, wrote the opposite of the truth.”8 At that time, however,Galileo apparently thought that each of the cases he discussed was characterized by a constant rather than a constant acceleration. He also accepted the false belief of the time that if a body and a heavy body are dropped together, the light body will initially move more rapidly than the heavier, and so he devoted several pages to ingenious arguments to explain why this happens. If indeed there is experimental evidence for this effect, it probably occurs because a heavy body has to be held more tightly than a light one, and so tends to be released a little later. Galileo developed his views on motion throughout his life, and his mature conclusions are described in his Discoursi of 1638, which in many respects is a precursor of Newtonian mechanics. The transition from medieval to Newtonian mechanics is largely due to Galileo. 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 22

 logos Galileo’s views on motion went through several stages. At first, as described in De Motu, he believed that natural motion has a nat- ural uniform proportional to the difference between the den- sity of the moving object and that of the medium. As the effective density is diminished by the medium, so is the natural uniform speed. Nonnatural motions are due to an impressed force, and this is responsible for the initial acceleration. These views constituted a coherent , but Galileo could not find a single example of this uniform motion and so concluded that acceleration is a feature of all motion. He considered the possibility that veloci- ty is directly proportional to the distance but soon rejected this pos- sibility. Then, from the mean speed theorem, which implies that the acquired velocity is proportional to the time taken, he deduced that the distance covered is proportional to the square of the time taken. We can obtain this result more easily using ’s notation: . x¨ = g, x = gt, x = ½gt2.

Galileo soon found that it was difficult, if not impossible, for him to measure with sufficient accuracy the time taken for bodies to fall. He therefore hit on the ingenious idea of timing them as they rolled down planes inclined at different angles. The times measured were much longer, and so could be measured more accurately. He could make measurements for a series of increasing angles and then extrapolate to find the rate for free fall. The is indeed quite practicable, as shown by Settle.9 Galileo also made further studies of motion that do not require time measurements. He let balls roll down an inclined plane, and at the end of the plane they were deflected horizontally and then allowed to fall freely until they hit a horizontal plane. The time- squared law implies that the path of free fall is a semiparabola, so that by seeing how the length and angle of the inclined plane was relat- ed to the point of contact on the horizontal plane Galileo could ver- ify the correctness of the law. 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 23

galileo the scientist  One of the most familiar stories about Galileo, also due to Viviani, is that he dropped two different from the top of the and that, to the dismay of the watching Aris- totelians, they hit the ground at the same time, disproving Aristotle’s law. If ever he did the experiment, however, and if he succeeded in releasing them at exactly the same moment, which is not as easy as it sounds, careful observation would have shown that, due to air resistance, the heavier body would have hit the ground slightly before the lighter body. This is still quite different from the proportionali- ty given by Aristotle. (and Galileo was no exception) are sometimes prone to imagine that they have such a firm grasp of a particular phenom- enon that they can confidently say what is going to happen without making any experiments. Frequently their confidence is justified, especially when they are making qualitative predictions, but some- times they are wrong. Many instructive examples could be given from the . Quantitative speculations, like that men- tioned above, are much more shaky.

The Velocity of Light In his Concerning Two New Galileo describes an exper- iment to determine the velocity of light. Two people, each with a lantern, stand several miles apart. The first uncovers his lantern and immediately after the light is seen by the second person, that person uncovers his own lantern. The first person measures the time that elapses from the moment he uncovers his lantern to when he sees the light of the second lantern. This time, divided by twice the dis- tance between the two people, gives the velocity of light. It was found, however, that the time was immeasurably small and so the experiment failed. We now know that the velocity of light is so great that such experiments are bound to fail. An interesting sequel is that Romer made the first reliable mea- surement of the velocity of light by observing the eclipses of the 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 24

 logos satellites of Jupiter. These were found to occur rather later than expected when Jupiter was far from the earth, compared with the times when Jupiter was near. This is due to the time taken by the light to travel from Jupiter to the earth, and from this the velocity of light was determined. Galileo also tried to develop a method of determining at sea by observing the satellites of Jupiter.Although this is possible in principle, it was found to be impracticable because at that time it was not possible to measure the time at sea with sufficient accuracy. Harrison achieved this feat later. The method has, however, proved useful in on land.

Galileo’s Scientific Method When he was a young professor in , Galileo was strongly influ- enced by the writings of the Jesuits teaching at the Collegio Romano, particularly Menu, Vella,Rugierius, and Vitelleschi, and he based his lectures on their work. These Jesuits accepted Aristotle’s definition of science and treated and physical questions in a realist way, following Aquinas. This formed the solid basis of Galileo’s subsequent work.10 Galileo realized more clearly than anyone before him that the pri- mary task of the physicist is to understand the world as it is, to pen- etrate behind the apparent complexity of phenomena to the often surprisingly simple reality beneath. Thus, when he considered freely falling bodies, he wanted to establish the laws obeyed by all bodies of whatever shape or material. He therefore considered fall in a vacuum, but, as this cannot be realized in practice, he chose the best approximation, namely,the fall in air of smooth, hard balls. The physicist is almost never able to make an experiment in an ideal sit- uation, so it is necessary to consider all the unwanted influences that could affect the final result and to allow for them. This often requires a subsidiary experiment to study and quantify these influences. This evaluation of perturbing effects is a vital component of the art of scientific investigation. 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 25

galileo the scientist  Galileo also distinguished between primary and secondary qual- ities. He pointed out that all bodies have a shape and a size, that are in a particular place at a given time, that are moving or stationary and so on. These are primary or essential qualities and cannot be sepa- rated from the body. On the other hand, other, secondary qualities such as color, taste, and smell, although grounded in the properties of the body, are in themselves sensations that exist only as they are perceived by the observer. The scientific research in which Galileo was interested is essentially concerned with studying the primary qualities of bodies. In his research, Galileo combined the insights of Aristotle and Plato and went beyond them. Like Aristotle, he insisted on the pri- mary importance of experience, of the knowledge that comes to us through the senses. This knowledge, however,cannot be taken at face value and must be tested by combining it with other experiences and uniting them all by a general principle or theory. This theory cannot be deduced from the experiences; it is a creation of the human mind. The theory should not only agree with the original experi- ences but also predict a range of other experiences that enable it to be tested. To specify these new experiences we need not only Aris- totelian logic but also mathematics. The theory and the mathemat- ics refer to an ideal world and are thus Platonic in nature. Theories are tested by doing experiments, and the conditions are chosen so as to be as close as possible to the ideal situation. If the results disagree with the theory, then the theory must be modified so as to be con- sistent with the new experiences and then tested again. It is not nec- essary to make a large number of experiments; due to the uniformity and rationality of nature a few well-chosen experiments suffice. There are many practical difficulties in carrying out this pro- gram. What experiences do we start with? Usually this is indicated by an existing theory. If this has a mathematical character it is nec- essary not only to observe but also to measure. The construction of the theory depends on the insight of the scientist and cannot be 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 26

 logos specified by a set of rules; it may therefore be wrong in a funda- mental way or,more frequently,it may be inadequate in one respect or another. Its consequences are likely to be extensive, and it is not easy to choose the ones that make the sharpest test and yet are rel- atively easy to carry out. If there is a disagreement, is it due to a defect in the experiment or does it show a real defect in the theory? If the latter, then how should the theory be modified and so on? Many similar questions must be addressed. As the theories become more sophisticated and agree with a wide range of experience, they may be said to give genuine, though still limited, knowledge about the world. As confidence grows it become less necessary to make experimental tests, and this is cer- tainly true of the laws of motion. However, it always remains possi- ble that new experiences show inadequacies in the theory that require it to be modified. There are many examples of this in the his- tory of science. Galileo was neither a pure Aristotelian nor a pure Platonist.11 He could claim with justice that he was a better Aristotelian than many of the professed Aristotelians that criticized him. He, like Aristotle, observed nature and did not seek the answers to questions only in books. If Aristotle had been able to look through a telescope he would have certainly modified his views. Likewise, Galileo was a good Platonist by his on the importance of mathematics, which Aristotle undervalued. However, Plato considered the material world to be an imperfect copy of the ideal world, whereas Galileo believed in the possibility of an exact mathematical description. Galileo never formulated a fully articulated theory of the scien- tific method; indeed, this is still the subject of controversy. He was a pioneer with a vision of the future and had to develop his tools as he tackled new problems. He was primarily interested in solving problems, not in explaining the methods he used to solve them, which he made up as he went along.Yet in so doing, he was inevitably throwing doubt on the traditional Aristotelian natural philosophy, 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 27

galileo the scientist  and this could have the most far-reaching and serious consequences. Structures of thought are linked far more tightly than is generally supposed, so that it is not possible to modify one section without affecting the others. This was clearly seen by many of Galileo’s oppo- nents and ensured their opposition, even if they were unable to mount effective criticism of his actual scientific work.

Galileo the The of the Telescope In 1609, Galileo heard that a Dutch optician, Lippershey,had found that if he put two lenses at either end of a tube and looked through it, distant objects appeared much closer. Many of these were made, but as their magnification was low and the images rather blurred they were regarded more as interesting toys than as objects of practical value. Galileo, however,immediately realized the impor- tance of this invention and how he could use it to further his career by offering it to the Venetian state. He was alarmed to learn that a Dutchman was already in , hoping to sell his telescope to the Doge. He alerted his friend Sarpi, who succeeded in preventing the Dutchman from obtaining an audience with the Doge and frantical- ly set to work to make a telescope for himself. He fitted two lenses at either end of a lead tube and indeed found that it magnified dis- tant objects. Later he said that he succeeded in making a telescope in a single day, but this seems improbable. It takes a long time to grind a lens, and it is unlikely that he already had commercial lens- es available or that they would be of sufficient quality. By a process of trial and error he made a series of telescopes of increasing mag- nification and technical excellence. As soon as he had made a good telescope he arranged with the help of Sarpi to have an audience with the powerful Doge of Venice, who were impressed by its value to the Venetian navy. Astutely, Galileo presented his best telescope to the Doge as a gift and, not to be outdone, the Doge’s senate soon after voted to double Galileo’s salary,to reappoint him for life, and to give 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 28

 logos him a large bonus. Subsequently he made many more telescopes and presented them to many eminent friends and powerful princes. This story illustrates well Galileo’s ruthless opportunism and tech- nical genius. Certainly his best telescopes were far superior to any others, and he made sure that their merits were widely recognized and that his career benefited.

The Discovery of the Galileo turned the telescopes to the heavens and was rewarded by a series of outstanding discoveries. He looked at the planets and noticed that there were one or two stars on either side of Jupiter, almost in a line. On subsequent nights he found that the stars had moved relative to Jupiter, and that there were now four stars. He realized he was seeing four of the moons that Jupiter just as the moon the earth. By observing them for several weeks he was able to determine their periods of rotation. He called them the “Medicean stars” in honor of Cosimo de Medici, and published an account of his discovery in a pamphlet called “,” or “Starry Messenger.” At first, his discovery was ridiculed, but most people were soon convinced when they looked through one of his telescopes. He presented telescopes to several powerful princes, and they naturally asked their own astronomers to examine them and assess their merits. By this clever move, the astronomers were forced to examine his claims, whether they believed them or not, and indeed they soon endorsed them. Galileo was particularly excited by this discovery because it pro- vided an example of several moons orbiting a , similar to Copernicus’s suggestion that the planets orbit the sun. It did not, of course, prove Copernicus’s theory, but showed that it was not nec- essary for everything to rotate about a single center and answered those who said that if the earth moves it will lose its moon. This spectacular discovery made Galileo famous throughout Europe, and he followed it by a whole series of new . He 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 29

galileo the scientist  found hundreds more stars in the familiar constellations and showed that the is made up of thousands of individual stars. He turned his telescope to the moon and observed the circular craters we now know are due to the impact of meteorites. By observing the behavior of the shadows of their edges as the moon waxed and waned, he was able to show that they had a central depression sur- rounded by a high rim and estimated that they were about four miles high, a reasonably accurate value. The discovery was important because Aristotle had said that the heavenly bodies were perfectly spherical, with no rough surfaces. The Aristotelians tried to explain Galileo’s observations by saying that the moon is surrounded by a smooth, transparent shell that covers all the craters. Galileo sarcastically replied that he would believe this if they would allow him to cover the moon with high and transparent mountains. These new results supported previous observations of changes in the skies. In 1604 there appeared a new star that excited great pub- lic interest. Galileo gave three lectures on the , admit- ting that he was not at all sure that it was really a star; for all he knew it might be due to the condensation of vapors in faraway . Stud- ies of its showed that it was much farther from the earth than the moon and so provided another example of imperfections in the celestial realm. These new discoveries were highly uncongenial to the Aris- totelians, who redoubled their efforts to discredit Galileo’s work, maintaining that what he saw was due to imperfections in his tele- scopes. He defended himself vigorously,first developing the oppos- ing views and supporting them by real arguments, and then demolishing the whole structure with undisguised relish. His discoveries were soon accepted by other astronomers, par- ticularly by the Jesuits of the Collegio Romano, who became sup- portive of his work. When Galileo visited Rome in 1611 to lecture on his discoveries, he was feted by them. 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 30

 logos In 1611, Galileo observed the that provide another example of imperfections in the celestial realm. He correctly sur- mised that they are clouds of vapor on the sun’s surface, and by observing their motion deduced that the sun rotates with a period of about a month. Galileo did not discover the sunspots; the Chinese had known of them for centuries, and other European scientists had also noticed them. To maintain the incorruptibility of the heavens, the Jesuit astronomer Scheiner suggested that sunspots are little planets orbiting the sun. Galileo had little difficulty in demolishing Scheiner’s theory, but did so in a courteous way. Nevertheless, Scheiner was offended, and this was to cause Galileo much trouble later on. To disprove Scheiner’s theory,Galileo observed that the sunspots are approximately circular when they are near the center of the sun’s disk and progressively become more elliptical as they approach the edge. This is just what would be expected if they are situated on the surface of the sun; if they were spherical planets they would keep the same circular shape as they moved around the sun.Although this does not amount to a strict proof, Galileo was justified in using the motion of the sunspots as an argument in favor of the heliocentric theory.

The Heliocentric Theory Copernicus’s book De Revolutionibus, which put forward the helio- centric theory,remained Aristotelian in all except its central idea and is written so that, apart from some introductory sections, it can be understood only by professional astronomers. Initially, Copernicus was concerned, like Ptolemy, to find the best way to calculate the motions of the planets and used the heliocentric as a cal- culating device. As the work proceeded, he found that it accounted naturally for many observations that could be fitted by the geocen- tric model only by making specific assumptions in each case. Even- tually he came to believe that the Copernican theory is true. As Galileo remarked in a letter to Monsignor Dini in 1615, 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 31

galileo the scientist  From many years of observation and study, he was abundant- ly in possession of all the details observed in the stars, for it is impossible to come to know the structure of the universe without having learned them all very diligently and having them very readily available in mind; and so, by repeated stud- ies and very long labours, he accomplished what later earned him the admirations of all those who study him diligently enough to understand his discussions. Thus, to claim that Copernicus did not consider the earth’s motion to be true could be accepted perhaps only by those who have not read him, in my opinion; for all six parts of his book are full of the doctrines of the earth’s motion, and of explanations and con- firmations of it.12

Copernicus was highly regarded by professional astronomers, and they realized the many advantages of the new system. Many of them began to use his methods, even if they continued to reject his . Subsequently, proposed a new cosmology,in which all the planets revolve around the sun, which in turn revolves around the earth. Providing the spheres of the fixed stars are sufficiently far away, this is mathematically equivalent to the Copernican heliocen- tric system. It was adopted by many astronomers as a way of using the ideas of Copernicus while avoiding the apparent of a moving earth. The heliocentric theory provided natural qualitative explanations of several phenomena, such as the retrograde motions of the plan- ets, the , and the angular closeness to the sun of the inner planets Mercury and Venus. In the Ptolemaic system these observations were included by the special choice of the parameters of the ellipses. Although some astronomers, including Copernicus, became convinced of the correctness of the heliocentric theory,they had no conclusive arguments. It was easy to defuse the opposition likely to be encountered by the heliocentric theory by maintaining 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 32

 logos that it was just a convenient mathematical scheme with no preten- sions to reality. The Lutheran theologian Osiander, who saw the manuscript of Copernicus through the press, inserted an anony- mous preface to this effect without Copernicus knowing. Professional astronomers were well aware of the large number of minor improvements that had been made in the Ptolemaic sys- tem over the previous centuries without significantly improving the fit to the unsatisfactory ancient data, and that proved quite unable to fit the greatly improved data of Tycho Brahe, and they increasingly turned to the Copernican theory as the basis of their calculations. Many of them still rejected the heliocentric theory as a real account of celestial motions and used the Copernican theory simply as a method of calculation. The astronomers gradually improved the Copernican theory and found that it was much more tightly constrained than the Ptolemaic theory,so that it was not pos- sible to adjust the parameters of the planetary orbits independently of each other.And so, impelled by their practical concerns, the belief of the professional astronomers gradually changed. By around 1616, the time of the Church’s first action against Galileo, the case for Copernicanism was respectable but still weak. By the time of his recantation in 1633, the had turned and geocentrism was almost a lost cause. According to Kuhn, “By the middle of the seventeenth century it is difficult to find an important astronomer who is not Copernican; by the end of the century it is impossible.” It took much longer for heliocentrism to be generally accepted; Milton, for exam- ple, in his great work treated the Ptolemaic and Copernican systems on equal footing. It is important to recall that not one of the arguments for Coper- nicanism was conclusive. Galileo’s favorite argument from the is fallacious. Bellarmine said that if the heliocentric theory was proved correct (and by proof he meant certain knowledge through causes, following Aristotle), then it would be necessary to study carefully how it could be reconciled with Scripture. However, the 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 33

galileo the scientist  proofs that first convinced the astronomers were accessible only to them; it is the cumulative effects of a large number of indications, individually inconclusive, that established the case and provided an example of the unity of indirect reference akin to the illative sense of Newman. This may also be described as the interpretation of signs, which can be done only by the prepared mind. When eventually the definitive proof of the heliocentric theory came two hundred years later with the measurement of by Bessel in 1838, the battle was long over,and it is doubtful there was any great stir among either scientists or theologians. If it had been a matter purely for astronomers, the Copernican view would probably have gradually prevailed without drama. How- ever, the prestige of Aristotelian cosmology, and especially its inte- gration with Christian theology, made this impossible. Galileo’s discoveries brought the whole heliocentric debate out of the domain of the professional astronomers and into the area of public discourse. Using his telescopes, people could see the evi- dence for the celestial phenomena that were contrary to the Aris- totelian view,such as the mountains on the moon, the sunspots, the moons of Jupiter, and the phases of Venus. None of this proved the heliocentric theory,but by weakening the Aristotelian cosmology it made it more worthy of consideration. Telescopes soon became popular, and Galileo had to make many more to satisfy demand. At the same time he announced his discoveries in well-written book- lets in the language. In contrast to the impenetrable tome of Copernicus, these were immediately accessible to non- professionals. Sure of his position, Galileo poured scorn on his opponents and thus further inflamed the opposition. Heliocentrism became popular among those who opposed Aristotle for other rea- sons, even if they had little understanding of the astronomical arguments. Galileo maintained he was more faithful to Aristotle than the Aristotelians. Aristotle believed in the importance of observation 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 34

 logos and reason, and Galileo believed that if Aristotle had had the opportunity to look through a telescope, he would have been con- vinced by what he saw and would have revised his cosmology accord- ingly.Galileo had nothing but contempt for those who looked for the truth about the physical world only by searching through musty old texts instead of opening their eyes to the world around them. The commonsense belief in an immovable earth can be support- ed by rational arguments. If the earth is moving with the speed nec- essary to carry it around the sun, then surely the high winds would demolish all buildings and blow everything away. It is well known, it was said, that an object dropped from the high mast of a ship falls nearer to the stern because the ship moves while the object falls, and therefore the effects due to any motion of the earth should be even more marked. Galileo responded by showing that this statement is false: the object lands at the foot of the mast because the object shares the forward motion of the ship all the time. He then pointed out that if we are in a closed cabin in a steadily moving ship, we can play ball and jump around just as we could if the ship were stationary. We could experience the up and down motion of the waves and any changes in the ship’s forward speed, but these are all . This absence of effects due to a uniform velocity is known as the prin- ciple of relativity. The absence of such effects is no argument against the translational motion of the earth. It may be remarked that these arguments are strictly true only for rectilinear motion. On the earth, however, the situation is dif- ferent because the objects on the earth’s surface have circular tra- jectories, although the difference is small for short distances. So, the top of the mast is moving slightly more rapidly than its foot due to the earth’s rotation, and this implies that an object dropped from the top of the mast will hit the deck a small distance to the east of the base. The effect is small but not negligible and was first detect- ed by G. A. Guglielmini in Bologna in 1789 and confirmed by J. F. Benzenberg in 1802 and 1804, and by F. Reich in 1831. The most 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 35

galileo the scientist  accurate study was made by E. H. Hall at Harvard in 1902; he found a deviation of 1.50 millimeters (plus or minus 0.05 millimeters) to the east for a drop of 23 meters, compared with a calculated value of 1.8 millimeters. Further confirmation of the earth’s rotation came from the detection of stellar parallax by Calandrelli in 1806.13 Another argument against the rotation of the earth is that objects would fly off into space if the earth were rotating, as it is well known that objects can fly off a rotating wheel.Whether they actually do so depends on the rotational velocity. In modern terminology, objects will fly off a rotating body if the mv2/R due to the rotation is greater than the force holding them on the rotator, the gravitational force mg in the case of the earth. So, the answer to this objection is that the earth does not rotate fast enough for objects to fly off it. Because the period of rotation T equals 2πR/v, the cen- trifugal force is 4πmR/T2, where R is the radius of the earth, T is the period of the earth’s rotation and g the acceleration due to grav- ity. The ratio of these is gT2/4π2R, or approximately 287. Thus, the earth would have to rotate about seventeen times faster before bod- ies flew off. Galileo could have avoided all his troubles by saying that helio- centrism was just a calculational device that bore no relation to re- ality,and indeed he was strongly urged to do this. But scientists, and Galileo was no exception, know they are investigating an objective- ly existing world, and such subterfuge is unacceptable. The proof that Galileo considered the strongest was his explana- tion of the ocean tides. He proposed a physical explanation in terms of the configurations of the seas, but this was not convincing.He con- sidered the alternative explanations to be just fantasies, and he brushed them aside. Although Galileo was able to advance many cogent arguments for the motion of the earth, the one he emphasized most strongly is fal- lacious, and none of them amounted to a strict proof. He failed to 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 36

 logos meet the overrigorous conditions he had accepted to show that helio- centrism is not inconsistent with Scripture.

The Scientific Achievements of Galileo The main achievement of Galileo was to inaugurate a new way of thinking about the world. He rejected the traditional method of seeking the answers to physical problems by studying the works of masters such as Aristotle and replaced it with quantitative measure- ment and analysis. Instead of philosophical discussions about the nature of motion, he measured as accurately as possible how long it took for bodies to fall a certain distance and then tried to find a mathematical relation between them. He was not the first to empha- size the importance of experiment; others, like in the thirteenth century, had laid the foundations of experimental science. But Galileo was the first to stress the importance of estab- lishing mathematical relationships between the results of measure- ments. He was thus a pioneer in the mathematicization of nature, which ultimately led to the science of . Galileo maintained that

philosophy is written in that great book which ever lies before our eyes, I mean the universe, but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geo- metrical figures, without whose help it is humanly impossible to comprehend a single word of it, and without which one wanders in vain though a dark labyrinth.14

This is not correct to describe Galileo’s scientific method either as Platonist or as hypothetico-deductive.15 He believed that nature is simple and that we can attain true knowledge of it. He did not accept the view that a preserves appearances, 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 37

galileo the scientist  enabling us to calculate results that are more or less in accord with observations and measurements but that tell us nothing about the real nature of the world. Galileo was a realist, and he built on and combined the methods of Archimedes and Aristotle to forge a new method. For this reason he is often regarded as the founder of mod- ern science. Through his astronomical discoveries and his application of mathematics to celestial phenomena, Galileo unified terrestrial and celestial phenomena. He made everything subject to the same laws, and the laws are expressible in mathematical form. This unification, Galileo recognized, is not easily attainable. Initially, each realm of phenomena has to be studied with its own concepts and laws, and eventually they may be united with other phenomena, as electric and magnetic phenomena were unified by . The work is still in progress: gravitation and quantum mechanics still await uni- fication. Scholastic philosophers and other Renaissance mathemati- cians anticipated, in one way or another, many of what are sometimes regarded as Galileo’s greatest discoveries, and his achievement was to unify them in a way that led to the development of theoretical physics. In addition to his work of unification, Galileo separated science from theology so that theology,and in particular the Bible, should not be used as a source of scientific knowledge. Rather, what we find out by observation and experiment can sometimes assist the interpreta- tion of the Bible. Galileo is sometimes credited with the elimination of from science, but no scientific activity can ever be free from metaphysical assumptions. In particular, he had a strong belief in the order and simplicity of nature and in its real existence, and these and other beliefs presupposed by science are Christian beliefs that played a determining role in the origin of modern science in the High Middle Ages. Likewise, Galileo distinguished the mathematical approach to physics from Aristotelian natural philosophy. Although Galileo was largely responsible for the overthrow of 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 38

 logos several conclusions of Aristotelian physics, he retained a general commitment to the principles of Aristotle’s approach to science, par- ticularly the need to attain a physical understanding of nature and to use the laws of logic. Galileo was a strong believer in the simplicity of nature and so continued to believe that the orbits of the planets are circular. As a result, although he greatly admired the work of Kepler, he never showed much interest in Kepler’s three laws of planetary motion, which indeed provide strong support for the heliocentric theory. This belief in universal led Galileo into great difficulties when he considered the explanation of . Neither did he spend time on the optical theories underly- ing the operation of the telescope, but constructed them by a process of trial and error. Galileo’s second great achievement was the construction of significantly improved telescopes and the astronomical discoveries he made with their aid. These made him famous throughout Europe and changed his life. He soon became convinced that the helio- centric theory of Copernicus was correct and used his astronomical discoveries to develop arguments in its favor. Individually, none of these arguments was conclusive, and at least one was incorrect, but together they were sufficient to convince the scientifically trained mind. If he had been content, like most scientists, to publish his results in weighty tomes, Galileo might not have become embroiled in controversy.Instead, he vigorously publicized his work and wrote in the vernacular in a way that could be understood by the general reader. This was necessary partly to obtain employment, but also because he felt he had a duty to publish his new view of the world. When his jealous enemies, unable, so he claimed, to defeat him on scientific grounds, invoked the aid of theology, he countered with a on the interpretation of Scripture. The theologians of the Inquisition, angered by his incursion into their domain and con- cerned by the threat to the Church’s authority to be the sole, authen- 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 39

galileo the scientist  tic interpreter of Scripture, persuaded the Inquisition to force Galileo to abandon his support for Copernican . They were, for the most part, well motivated, and saw themselves as defenders of a hallowed synthesis of natural and supernatural knowl- edge. They had, however, an inadequate understanding of Galileo’s scientific achievements, which made it absolutely essential for them to rethink many of their cherished assumptions. The attempt to suppress Galileo’s support of Copernican astron- omy of course failed, and his writings became widely known throughout Europe. His work on dynamics, in particular, culminat- ed in the achievements of Newton, who unified Galileo’s laws of motion and those of Kepler with his theory of gravitation. More gen- erally,Galileo inaugurated a new style of scientific thinking that was to bear much fruit in the following centuries and identify him as one of the founders of modern science.

Notes

1. Olaf Pedersen, “Galileo’s Religion,” in G. V.Coyne, M. Heller, and J. Zycinski, ed. The : A Meeting of Faith and Science, Proceedings of the Cracow Confer- ence, May 1984; Specola Vaticana, 1985, 75. 2. William A. Wallace, “Galileo’s Trial and the Proof of the Earth’s Motion,” Catholic Dossier, 1,no.2 (July-August 1995): 7. 3. J. L. Russell, “What Was the Crime of Galileo?” 52 (1995): 403. 4. William R. Shea, Galileo’s Intellectual Revolution:Middle Period,1610–1632 (Sagamore Beach, .: Watson Publishing, 1977). 5. William A. Wallace, Galileo and His Sources (Princeton: Princeton University Press, 1984). 6. I. E. Drabkin, trans., “De Motu,” in on Motion and Mechanics, I. E. Drabkin, ed. (Madison: University of Wisconsin Press, 1960), 58. 7. Ibid., 70. 8. Ibid., 76. 9. Thomas B. Settle, Science (6 January 1961): 19. 10. Wallace, Galileo and His Sources, 198. 11. Thomas P.McTighe,“Galileo’s Platonism,” in Galileo:Man of Science, Ernan McMullin, ed. (New York: Basic Books, 1967), 365. 12. Maurice Finocchiaro, ed., The Galileo Affair (Chicago: University of Chicago Press, 1989), 60. 01-logos-hodgson-pp13-40 6/12/03 9:31 AM Page 40

 logos

13. William A. Wallace, “Galileo’s Trial and the Proof of the Earth’s Motion,” Catholic Dossier 1,no.2 (July-August 1995): 7. 14. Stillman Drake, trans., Discoveries and Opinions of Galileo (Chicago: Chicago Univer- sity Press, ), –. 15. William A. Wallace, Prelude to Galileo:Essays on Medieval and Sixteenth-Century Sources of Galileo’s Thought (Dordrecht, Holland: Reidel Publishing, 1981), 129 et seq.