Galileo the Scientist - St. Thomas

Peter E. Hodgson

Galileo the Scientist

Introduction

The life and achievements of Galileo form a subject of enduringinterest. He is certainly one of the greatest scientists of all time andindeed has been called the founder of modern science. He showedthat natural phenomena obey mathematical laws and thus, Galileolaid the foundations of quantitative dynamics and used it to give thefirst accurate account of the motions of falling bodies and projectiles.He improved the telescope and used it to discover the moons ofJupiter, the mountains on the moon, the phases of Venus, and thespots on the sun. All this combined to throw doubt on Aristoteliancosmology and to support the heliocentric theory of Copernicus.More than any scientist, Galileo was responsible for initiating thetransition from the Aristotelian science of the Middle Ages to themathematical science of the following centuries.

Galileo lived at a critical moment in the development of science.According to the popular account, the ancient Greeks made the firststeps toward a scientific understanding of the world. The Greekwritings were inherited by the Muslim civilization and then

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transmitted to the new universities in the Middle Ages throughtranslations done mainly in Spain. Thereafter, an authoritarianChurch controlled the intellectual development of Western Europeand prevented any independent thought or scientific development.It was only during the Renaissance that the authority of the Churchwas challenged by men like Galileo who insisted on the greatervalue for science of experimentation and observation than relianceon ancient texts. This is dramatized by the story that Galileo droppedtwo balls of different masses from the Leaning Tower of Pisa andshowed that, contrary to Aristotle’s theory, they reached the groundsimultaneously. Thereafter, science developed as a free and inde-pendent search for truth.

The reality is, of course, different and highly instructive. Thefamiliar story, still heard today, that there was no science worthspeaking about in the long period from the time of the ancientGreeks to the flowering of genius in the Renaissance has long beendisproved by modern scholarship. Galileo himself was not only ahighly original scientist but remained a devout Catholic throughouthis life.1 He had a sound grasp of theology and saw clearly that thenew knowledge of the world gained by the scientific method was inno way inconsistent with the teaching of the Church, since bothcome from God. He also saw that some of the new knowledge raisedimportant problems of scriptural interpretation that could beresolved within the context of traditional Catholic theology. It is nowrecognized that Galileo’s views on the interpretation of Scripture arebasically correct, and he was particularly anxious to prevent thetragedy that actually happened—the condemnation by the Churchof a genuine scientific breakthrough. He was, however, overconfidentconcerning his scientific arguments, which were still at that timeinconclusive, 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 claimsuntil a definite proof was forthcoming. The main protagonists were

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all motivated to defend the truth, but they were strongly influencedby their intellectual backgrounds and possessed personal charactertraits that exacerbated their misunderstandings.

Before considering the achievements of Galileo, it is useful tosketch the understanding of the physical world that existed before histime.

The youthful Galileo was attracted to mathematics and avidlystudied the works of Archimedes. His interest in hydrostatics wasstimulated by Archimedes’ solution of the problem of King Hiero’scrown, which led to Galileo’s first publication, The Little Balance(1586). Nature, he realized, is written in the language of mathe-matics. Galileo was further stimulated by his experiments on therelation between musical tones and the length, weight, and tensionof strings. His work on the centers of gravity of solids led to hisappointment as the chair of mathematics at Pisa. His emphasis onmathematics shows the influence of Plato, who was widely influen-tial in the early Middle Ages due to the writings of Augustine. Platoheld that terrestrial phenomena are imperfect copies of abstractmathematical forms existing in the transcendent realm of ideas.Thus, mathematical relations are only approximately realized innature. It was Galileo’s greatest achievement to show how nature fol-lows mathematical laws, but he went beyond Plato in requiring exactcorrespondence, within the limits of experimental uncertainties.

It is important to distinguish between the professional Aris-totelians in the universities, who infuriated Galileo by insisting onthe literal text of Aristotle and refusing to listen to Galileo’s argu-ments, and the open-minded Jesuits at the Collegio Romano, whoso strongly influenced the young Galileo in his formative years.These Jesuits followed Aristotle in many respects and taught “asomewhat eclectic Thomism containing elements deriving fromScotist, Averroist and nominalist thought”2 that may be described asscholastic Aristotelianism. Therefore, although he bitterly attackedthe professional Aristotelians (particularly their views on mechanics

galileo the scientist


and cosmology), Galileo retained a basic adherence to Aristoteliannatural philosophy throughout his life.

Aristotle thought of nature as a process, an organism, and heldthat the main object of science is to see how it is related to man. Forhim, the aim of science was to obtain certain knowledge by under-standing the causes of natural phenomena. His cosmology was basedon direct commonsense experience, and this is why it has such astrong appeal, even today. Aristotle emphasized the primacy of thesenses, which takes precedence over any theory. Who can doubtthat the earth is solid and immoveable, with the sun, the stars, andplanets moving around it?

Astronomers studied the motions of the stars and the planets, andPtolemy was able to describe them quite accurately by compound-ing circular motions in the form of cycles and epicycles. This was apurely mathematical description, and it was not maintained that thecycles and epicycles corresponded to anything real. In contrast,Aristotle sought a more physical cosmology in terms of real entities.Johannes Kepler finally unified these two approaches in the early1600s.3

At the center of Aristotle’s cosmology is the immovable earth.Surrounding it are a number of concentric crystalline spheres bear-ing the moon and the inner planets Mercury and Venus, then thesun, and finally the outer planets Mars, Jupiter, and Saturn. Enclos-ing all is the sphere of the fixed stars, and outside this is nothing atall. There were differing views about the reality of the crystallinespheres: Aristotle believed there are fifty-five in all, made of a pure,unalterable, transparent, weightless, crystalline solid. The whole setof spheres rotates once a day, thus accounting for the diurnal motionof the sun and the stars. Seen against the background of the stars, thepaths of the planets sometimes show a retrograde or looped motion,and this was accounted for by fixing the planets to secondary sphereslinked to the main ones. In this way, the Aristotelian cosmology wasable to give an account of all observable celestial motions, includingthe prediction of eclipses.

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Guided by direct experience, Aristotle made a sharp distinctionbetween terrestrial and celestial matter: terrestrial matter is change-able whereas celestial matter is unchangeable. There are four typesof 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 perfectcurve, the circle. On the earth, natural motion is linear: the fallingof earth and water and the rising of air and fire. These motionsaccelerate as each body approaches its natural place. Unnaturalmotion, such as the flight of an arrow, requires the continuing actionof a mover. Aristotle’s physics was based on direct observation andaccounted 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 ofprojectile motion. He had no concept of force and denied the notionof inertia. Aristotle believed that because projectile motion is unnat-ural it requires the continued action of a mover, and this must be themedium. He therefore suggested that the thrower communicatesboth motion to the medium and the power to move.

Buridan, a fourteenth-century philosopher, rejected this theorybecause it cannot explain the continuing motion of a spinning wheeland also because it is common experience that the medium resiststhe motion of the projectile. Instead, Buridan proposed that thethrower gives the projectile impetus that carries it along after it hasleft the hand of the thrower. This is related to one of the argumentsagainst the motion of the earth. According to Aristotle, a projectilethrown vertically upward from a moving earth will fall behind andhit the ground west of its starting point, contrary to experience. Theimpetus theory, however, predicts that it retains an eastward impe-tus throughout its motion, and so returns to the same point asobserved.

Many philosophers believed that the ancient Greeks had achievedthe summit of knowledge; they knew essentially all that could beknown, and so the answer to any problem could be found by



scrutinizing ancient texts, particularly those of Aristotle. The dutyof a scholar was simply to understand, defend, and teach Aristotle’sideas. Within this mindset, the Aristotelians simply could not under-stand what Galileo was trying to do. To them, the world is a livingorganism that can be understood by experience and reason. Forthis, direct perception is all that was needed. They interpreted theworld in terms of a close-knit system of purposeful behavior, usingorganic categories and concepts like matter and form, act and poten-cy, essence and existence. Thus, the qualitative properties of thingssuffice to reveal their essences.

In sharp contrast, Galileo said that it is an illusion to think we canunderstand the essences of things; what we can and should do isdescribe their behavior as accurately as we can using mathematicsand then make experiments to test the validity of our ideas. Quan-titative relations are the real clues to the unique, orderly, immutablereality. By establishing them we can find out how things behave, butnot what they are. This seemed useless to the Aristotelians, who hada low view of mathematics; indeed, Aristotle “left to mechanics andother low artisans the investigation of the ratios and other secondaryfeatures of acceleration.”4 To the Aristotelians, number, weight, andmeasure have no philosophical significance; motion is interpreted interms of purpose, and for this, mathematics is irrelevant. They hadno interest in accurate descriptions of the motions of projectiles orin the mathematical description of levers and pulleys. Mathematics,they allowed, is an interesting game, but it tells us nothing about thereal world. Galileo, on the other hand, thought that the Aristotelians’elaborate structure of abstractions in fact led nowhere.

Because Galileo occupied a chair of mathematics, his duty was toexpound the works of Euclid and Archimedes. He could be muchfreer in his criticisms of Aristotle than if he had been a member ofthe philosophical establishment, whose main duty was to masterand teach the works of Aristotle.

It is important to distinguish between Aristotle’s general ideas

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concerning the scientific method, his natural philosophy, and theway it was applied to particular problems. Aristotelian physics wasan attempt to find the real structure of the world by discovering truefirst principles and using them with the evidence of sense experi-ence. Galileo shared Aristotle’s goal of discovering the truth aboutnature. Aristotle’s cosmology included many statements about theheavenly bodies and detailed theories of familiar physical processesthat have subsequently been found to be incorrect, but this does notnecessarily falsify the principles of his natural philosophy. AlthoughGalileo showed that many of Aristotle’s views are incorrect, Galileodid this within the framework of Aristotelian natural philosophy, andhe remained essentially an Aristotelian. In the end, Aristotle’sattempt was a heroic failure, largely because he underestimated thedifficulty of obtaining these principles, and also the value of precisemeasurement and detailed mathematical analysis.

Christian beliefs can be interpreted easily within the frameworkof Aristotelian cosmology. Hell is in the center of the earth, and vol-canoes provide evidence of its fires. Beyond the outermost sphere isthe abode of God and the saints. Knowing this, we can speak of thedescent into hell and the ascent into heaven. This imagery is lost inthe heliocentric system. If the earth is just one of the planets, thenis it not possible that people may be found on other planets? And ifso, how can they be redeemed by Christ? The Aristotelian universeaccommodated all that was known in a unified logical structure, andthis accounts for its great power over the human imagination. Tothrow doubt on any part of the Aristotelian universe would seem tothreaten the whole and upset the well-established order of theuniverse.

Central to the whole debate is the question of why we believe—what the criteria are that we apply to judge whether a scientifictheory is true. More fundamental, how do we justify the criteriaitself? 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



required to “save the appearances,” that is, to give predictions innumerical agreement with the experimental measurements. Last, ithad to be in accord with Scripture.

Galileo the Physicist

The Pendulum

Galileo’s earliest biographer, Viviani, claimed that in 1582, whenGalileo was still a medical student in Pisa, he observed the motionof a swinging lamp in a cathedral. Using his pulse to measure thetime of swing, he found it was independent of the amplitude of theswing, 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 asidebefore release. According to Viviani, this suggested to Galileo that apendulum could be used to measure the pulse rate. There is, how-ever, no other evidence for this story, as Galileo first mentioned theisochronous nature of the pendulum in a letter in 1602. He alsoshowed that the period of swing is independent of the material of thependulum and that the period is proportional to the square root ofthe length of the string. Galileo also compared the swing of the pen-dulum with the motion of a ball that runs down one inclined planeand up another one opposite to it. In another investigation, he foundthat the times of descent are equal for all chords from the highest orto the lowest points of a vertical circle.

The Dynamics of Free Fall 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 ofthe Jesuits at the Collegio Romano, whose lecture notes he usedextensively.5 They held, with Aristotle, that the aim of science is the

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understanding of natural phenomena in terms of evident principles,and Galileo continued to accept this throughout his life. However, hestrongly 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 afterabout forty pages of discussion Galileo exclaims:

Heavens! At this point I am weary and ashamed of having touse so many words to refute such childish arguments and suchinept attempts at subtleties as those which Aristotle cramsinto the whole of Book 4 of De Caelo, as he argues against theolder 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 profoundand more abstruse discoveries of geometry, but even of the most ele-mentary principles of this science.”7 A few pages later, discussinghow projectiles are moved, he writes, “Aristotle, as in practicallyeverything that he wrote about locomotion, wrote the opposite ofthe truth.”8

At that time, however, Galileo apparently thought that each of thecases he discussed was characterized by a constant velocity ratherthan a constant acceleration. He also accepted the false belief of thetime that if a light body and a heavy body are dropped together, thelight body will initially move more rapidly than the heavier, and sohe devoted several pages to ingenious arguments to explain whythis happens. If indeed there is experimental evidence for this effect,it probably occurs because a heavy body has to be held more tightlythan a light one, and so tends to be released a little later.

Galileo developed his views on motion throughout his life, and hismature conclusions are described in his Discoursi of 1638, which inmany respects is a precursor of Newtonian mechanics. The transitionfrom medieval to Newtonian mechanics is largely due to Galileo.



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 speed proportional to the difference between the den-sity of the moving object and that of the medium. As the effectivedensity is diminished by the medium, so is the natural uniformspeed. Nonnatural motions are due to an impressed force, and thisis responsible for the initial acceleration. These views constituted acoherent philosophy of motion, but Galileo could not find a singleexample of this uniform motion and so concluded that accelerationis 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 theacquired velocity is proportional to the time taken, he deduced thatthe distance covered is proportional to the square of the time taken.We can obtain this result more easily using Newton’s notation:

x = g, .x = gt, x = ½gt2.

Galileo soon found that it was difficult, if not impossible, for him tomeasure with sufficient accuracy the time taken for bodies to fall. Hetherefore hit on the ingenious idea of timing them as they rolleddown planes inclined at different angles. The times measured weremuch longer, and so could be measured more accurately. He couldmake measurements for a series of increasing angles and thenextrapolate to find the rate for free fall. The experiment is indeedquite practicable, as shown by Settle.9

Galileo also made further studies of motion that do not requiretime measurements. He let balls roll down an inclined plane, and atthe end of the plane they were deflected horizontally and thenallowed to fall freely until they hit a horizontal plane. The time-squared law implies that the path of free fall is a semiparabola, so thatby 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.

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One of the most familiar stories about Galileo, also due toViviani, is that he dropped two different weights from the top of theLeaning Tower of Pisa and that, to the dismay of the watching Aris-totelians, they hit the ground at the same time, disproving Aristotle’slaw. If ever he did the experiment, however, and if he succeeded inreleasing them at exactly the same moment, which is not as easy asit sounds, careful observation would have shown that, due to airresistance, the heavier body would have hit the ground slightly beforethe lighter body. This is still quite different from the proportionali-ty given by Aristotle.

Physicists (and Galileo was no exception) are sometimes proneto imagine that they have such a firm grasp of a particular phenom-enon that they can confidently say what is going to happen withoutmaking 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 givenfrom the history of science. Quantitative speculations, like that men-tioned above, are much more shaky.

The Velocity of Light

In his Dialogue Concerning Two New Sciences Galileo describes an exper-iment to determine the velocity of light. Two people, each with alantern, stand several miles apart. The first uncovers his lantern andimmediately after the light is seen by the second person, that personuncovers his own lantern. The first person measures the time thatelapses from the moment he uncovers his lantern to when he seesthe light of the second lantern. This time, divided by twice the dis-tance between the two people, gives the velocity of light. It wasfound, however, that the time was immeasurably small and so theexperiment failed. We now know that the velocity of light is sogreat 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



satellites of Jupiter. These were found to occur rather later thanexpected when Jupiter was far from the earth, compared with thetimes when Jupiter was near. This is due to the time taken by thelight to travel from Jupiter to the earth, and from this the velocityof light was determined.

Galileo also tried to develop a method of determining longitudeat sea by observing the satellites of Jupiter. Although this is possiblein principle, it was found to be impracticable because at that time itwas not possible to measure the time at sea with sufficient accuracy.Harrison achieved this feat later. The method has, however, proveduseful in surveying on land.

Galileo’s Scientific Method

When he was a young professor in Padua, Galileo was strongly influ-enced by the writings of the Jesuits teaching at the CollegioRomano, particularly Menu, Vella, Rugierius, and Vitelleschi, and hebased his lectures on their work. These Jesuits accepted Aristotle’sdefinition of science and treated logic and physical questions in arealist way, following Aquinas. This formed the solid basis ofGalileo’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 oftensurprisingly simple reality beneath. Thus, when he considered freelyfalling bodies, he wanted to establish the laws obeyed by all bodiesof whatever shape or material. He therefore considered fall in avacuum, but, as this cannot be realized in practice, he chose thebest approximation, namely, the fall in air of smooth, hard balls. Thephysicist is almost never able to make an experiment in an ideal sit-uation, so it is necessary to consider all the unwanted influences thatcould affect the final result and to allow for them. This often requiresa subsidiary experiment to study and quantify these influences. Thisevaluation of perturbing effects is a vital component of the art ofscientific investigation.

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Galileo also distinguished between primary and secondary qual-ities. He pointed out that all bodies have a shape and a size, that arein a particular place at a given time, that are moving or stationary andso on. These are primary or essential qualities and cannot be sepa-rated from the body. On the other hand, other, secondary qualitiessuch as color, taste, and smell, although grounded in the propertiesof the body, are in themselves sensations that exist only as they areperceived by the observer. The scientific research in which Galileowas interested is essentially concerned with studying the primaryqualities of bodies.

In his research, Galileo combined the insights of Aristotle andPlato and went beyond them. Like Aristotle, he insisted on the pri-mary importance of experience, of the knowledge that comes to usthrough the senses. This knowledge, however, cannot be taken at facevalue and must be tested by combining it with other experiences anduniting them all by a general principle or theory. This theory cannotbe deduced from the experiences; it is a creation of the humanmind. The theory should not only agree with the original experi-ences but also predict a range of other experiences that enable it tobe 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. Theoriesare tested by doing experiments, and the conditions are chosen so asto be as close as possible to the ideal situation. If the results disagreewith 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 uniformityand 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 indicatedby an existing theory. If this has a mathematical character it is nec-essary not only to observe but also to measure. The construction ofthe theory depends on the insight of the scientist and cannot be



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 respector another. Its consequences are likely to be extensive, and it is noteasy 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 adefect 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 awide range of experience, they may be said to give genuine, thoughstill limited, knowledge about the world. As confidence grows itbecome 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 thatrequire 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 Hecould claim with justice that he was a better Aristotelian than manyof the professed Aristotelians that criticized him. He, like Aristotle,observed nature and did not seek the answers to questions only inbooks. If Aristotle had been able to look through a telescope hewould have certainly modified his views. Likewise, Galileo was agood Platonist by his stress on the importance of mathematics, whichAristotle undervalued. However, Plato considered the materialworld to be an imperfect copy of the ideal world, whereas Galileobelieved 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 wasa pioneer with a vision of the future and had to develop his tools ashe tackled new problems. He was primarily interested in solvingproblems, not in explaining the methods he used to solve them,which he made up as he went along. Yet in so doing, he was inevitablythrowing doubt on the traditional Aristotelian natural philosophy,

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and this could have the most far-reaching and serious consequences.Structures of thought are linked far more tightly than is generallysupposed, so that it is not possible to modify one section withoutaffecting the others. This was clearly seen by many of Galileo’s oppo-nents and ensured their opposition, even if they were unable tomount effective criticism of his actual scientific work.

Galileo the Astronomer

The Invention of the Telescope

In 1609, Galileo heard that a Dutch optician, Lippershey, had foundthat if he put two lenses at either end of a tube and looked throughit, distant objects appeared much closer. Many of these telescopeswere made, but as their magnification was low and the images ratherblurred they were regarded more as interesting toys than as objectsof practical value. Galileo, however, immediately realized the impor-tance of this invention and how he could use it to further his careerby offering it to the Venetian state. He was alarmed to learn that aDutchman was already in Venice, hoping to sell his telescope to theDoge. He alerted his friend Sarpi, who succeeded in preventing theDutchman from obtaining an audience with the Doge and frantical-ly set to work to make a telescope for himself. He fitted two lensesat either end of a lead tube and indeed found that it magnified dis-tant objects. Later he said that he succeeded in making a telescopein a single day, but this seems improbable. It takes a long time togrind a lens, and it is unlikely that he already had commercial lens-es available or that they would be of sufficient quality. By a processof trial and error he made a series of telescopes of increasing mag-nification and technical excellence. As soon as he had made a goodtelescope he arranged with the help of Sarpi to have an audience withthe powerful Doge of Venice, who were impressed by its value to theVenetian navy. Astutely, Galileo presented his best telescope to theDoge as a gift and, not to be outdone, the Doge’s senate soon aftervoted to double Galileo’s salary, to reappoint him for life, and to give



him a large bonus. Subsequently he made many more telescopesand 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 anyothers, and he made sure that their merits were widely recognizedand that his career benefited.

The Discovery of the Moons of Jupiter

Galileo turned the telescopes to the heavens and was rewarded by aseries of outstanding discoveries. He looked at the planets andnoticed that there were one or two stars on either side of Jupiter,almost in a line. On subsequent nights he found that the stars hadmoved relative to Jupiter, and that there were now four stars. Herealized he was seeing four of the moons that orbit Jupiter just as themoon orbits the earth. By observing them for several weeks he wasable to determine their periods of rotation. He called them the“Medicean stars” in honor of Cosimo de Medici, and published anaccount of his discovery in a pamphlet called “Sidereus Nuncius,” or“Starry Messenger.” At first, his discovery was ridiculed, but mostpeople were soon convinced when they looked through one of histelescopes. He presented telescopes to several powerful princes,and they naturally asked their own astronomers to examine themand assess their merits. By this clever move, the astronomers wereforced 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 planet, similar toCopernicus’s suggestion that the planets orbit the sun. It did not, ofcourse, prove Copernicus’s theory, but showed that it was not nec-essary for everything to rotate about a single center and answeredthose who said that if the earth moves it will lose its moon.

This spectacular discovery made Galileo famous throughoutEurope, and he followed it by a whole series of new observations. He

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found hundreds more stars in the familiar constellations and showedthat the Milky Way is made up of thousands of individual stars. Heturned his telescope to the moon and observed the circular craterswe now know are due to the impact of meteorites. By observing thebehavior of the shadows of their edges as the moon waxed andwaned, he was able to show that they had a central depression sur-rounded by a high rim and estimated that they were about four mileshigh, a reasonably accurate value.

The discovery was important because Aristotle had said that theheavenly bodies were perfectly spherical, with no rough surfaces.The Aristotelians tried to explain Galileo’s observations by sayingthat the moon is surrounded by a smooth, transparent shell thatcovers all the craters. Galileo sarcastically replied that he wouldbelieve this if they would allow him to cover the moon with high andtransparent mountains.

These new results supported previous observations of changes inthe skies. In 1604 there appeared a new star that excited great pub-lic interest. Galileo gave three lectures on the phenomenon, admit-ting that he was not at all sure that it was really a star; for all he knewit might be due to the condensation of vapors in faraway space. Stud-ies of its parallax showed that it was much farther from the earththan the moon and so provided another example of imperfections inthe 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 thendemolishing 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 lectureon his discoveries, he was feted by them.



In 1611, Galileo observed the sunspots that provide anotherexample of imperfections in the celestial realm. He correctly sur-mised that they are clouds of vapor on the sun’s surface, and byobserving their motion deduced that the sun rotates with a period ofabout a month. Galileo did not discover the sunspots; the Chinese hadknown of them for centuries, and other European scientists had alsonoticed them. To maintain the incorruptibility of the heavens, theJesuit astronomer Scheiner suggested that sunspots are little planetsorbiting the sun. Galileo had little difficulty in demolishing Scheiner’stheory, but did so in a courteous way. Nevertheless, Scheiner wasoffended, and this was to cause Galileo much trouble later on.

To disprove Scheiner’s theory, Galileo observed that the sunspotsare approximately circular when they are near the center of thesun’s disk and progressively become more elliptical as they approachthe edge. This is just what would be expected if they are situated onthe surface of the sun; if they were spherical planets they would keepthe same circular shape as they moved around the sun. Although thisdoes not amount to a strict proof, Galileo was justified in using themotion of the sunspots as an argument in favor of the heliocentrictheory.

The Heliocentric Theory

Copernicus’s book De Revolutionibus, which put forward the helio-centric theory, remained Aristotelian in all except its central idea andis written so that, apart from some introductory sections, it can beunderstood only by professional astronomers. Initially, Copernicuswas concerned, like Ptolemy, to find the best way to calculate themotions of the planets and used the heliocentric hypothesis as a cal-culating device. As the work proceeded, he found that it accountednaturally 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. AsGalileo remarked in a letter to Monsignor Dini in 1615,

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From many years of observation and study, he was abundant-ly in possession of all the details observed in the stars, for it isimpossible to come to know the structure of the universewithout having learned them all very diligently and havingthem very readily available in mind; and so, by repeated stud-ies and very long labours, he accomplished what later earnedhim the admirations of all those who study him diligentlyenough to understand his discussions. Thus, to claim thatCopernicus did not consider the earth’s motion to be truecould be accepted perhaps only by those who have not readhim, in my opinion; for all six parts of his book are full of thedoctrines 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 ofthem began to use his methods, even if they continued to reject hisheliocentrism.

Subsequently, Tycho Brahe proposed a new cosmology, in whichall the planets revolve around the sun, which in turn revolves aroundthe earth. Providing the spheres of the fixed stars are sufficiently faraway, this is mathematically equivalent to the Copernican heliocen-tric system. It was adopted by many astronomers as a way of usingthe ideas of Copernicus while avoiding the apparent absurdities of amoving earth.

The heliocentric theory provided natural qualitative explanationsof several phenomena, such as the retrograde motions of the plan-ets, the phases of Venus, and the angular closeness to the sun of theinner planets Mercury and Venus. In the Ptolemaic system theseobservations were included by the special choice of the parametersof the ellipses. Although some astronomers, including Copernicus,became convinced of the correctness of the heliocentric theory, theyhad no conclusive arguments. It was easy to defuse the oppositionlikely to be encountered by the heliocentric theory by maintaining



that it was just a convenient mathematical scheme with no preten-sions to reality. The Lutheran theologian Osiander, who saw themanuscript of Copernicus through the press, inserted an anony-mous preface to this effect without Copernicus knowing.

Professional astronomers were well aware of the large numberof minor improvements that had been made in the Ptolemaic sys-tem over the previous centuries without significantly improvingthe fit to the unsatisfactory ancient data, and that proved quiteunable to fit the greatly improved data of Tycho Brahe, and theyincreasingly turned to the Copernican theory as the basis of theircalculations. Many of them still rejected the heliocentric theory asa real account of celestial motions and used the Copernican theorysimply as a method of calculation. The astronomers graduallyimproved the Copernican theory and found that it was much moretightly constrained than the Ptolemaic theory, so that it was not pos-sible to adjust the parameters of the planetary orbits independentlyof each other. And so, impelled by their practical concerns, the beliefof the professional astronomers gradually changed. By around 1616,the time of the Church’s first action against Galileo, the case forCopernicanism was respectable but still weak. By the time of hisrecantation in 1633, the tide had turned and geocentrism was almosta lost cause. According to Kuhn, “By the middle of the seventeenthcentury it is difficult to find an important astronomer who is notCopernican; by the end of the century it is impossible.” It took muchlonger for heliocentrism to be generally accepted; Milton, for exam-ple, in his great work treated the Ptolemaic and Copernican systemson equal footing.

It is important to recall that not one of the arguments for Coper-nicanism was conclusive. Galileo’s favorite argument from the tidesis fallacious. Bellarmine said that if the heliocentric theory wasproved correct (and by proof he meant certain knowledge throughcauses, following Aristotle), then it would be necessary to studycarefully how it could be reconciled with Scripture. However, the

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proofs that first convinced the astronomers were accessible only tothem; it is the cumulative effects of a large number of indications,individually inconclusive, that established the case and provided anexample of the unity of indirect reference akin to the illative sense ofNewman. This may also be described as the interpretation of signs,which can be done only by the prepared mind. When eventually thedefinitive proof of the heliocentric theory came two hundred yearslater with the measurement of stellar parallax by Bessel in 1838, thebattle was long over, and it is doubtful there was any great stir amongeither scientists or theologians.

If it had been a matter purely for astronomers, the Copernicanview 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 outof the domain of the professional astronomers and into the area ofpublic 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, themoons of Jupiter, and the phases of Venus. None of this proved theheliocentric theory, but by weakening the Aristotelian cosmology itmade it more worthy of consideration. Telescopes soon becamepopular, and Galileo had to make many more to satisfy demand. Atthe same time he announced his discoveries in well-written book-lets in the vernacular language. In contrast to the impenetrabletome of Copernicus, these were immediately accessible to non-professionals. Sure of his position, Galileo poured scorn on hisopponents and thus further inflamed the opposition. Heliocentrismbecame popular among those who opposed Aristotle for other rea-sons, even if they had little understanding of the astronomicalarguments.

Galileo maintained he was more faithful to Aristotle than theAristotelians. Aristotle believed in the importance of observation



and reason, and Galileo believed that if Aristotle had had theopportunity 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 thetruth about the physical world only by searching through musty oldtexts 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 woulddemolish all buildings and blow everything away. It is well known, itwas said, that an object dropped from the high mast of a ship fallsnearer to the stern because the ship moves while the object falls, andtherefore the effects due to any motion of the earth should be evenmore marked. Galileo responded by showing that this statement isfalse: the object lands at the foot of the mast because the object sharesthe forward motion of the ship all the time. He then pointed out thatif we are in a closed cabin in a steadily moving ship, we can play balland jump around just as we could if the ship were stationary. Wecould experience the up and down motion of the waves and anychanges in the ship’s forward speed, but these are all accelerations.This absence of effects due to a uniform velocity is known as the prin-ciple of Galilean relativity. The absence of such effects is no argumentagainst the translational motion of the earth.

It may be remarked that these arguments are strictly true onlyfor 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, thetop of the mast is moving slightly more rapidly than its foot due tothe earth’s rotation, and this implies that an object dropped fromthe top of the mast will hit the deck a small distance to the east ofthe 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

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accurate study was made by E. H. Hall at Harvard University in1902; he found a deviation of 1.50 millimeters (plus or minus 0.05millimeters) to the east for a drop of 23 meters, compared with acalculated value of 1.8 millimeters. Further confirmation of theearth’s rotation came from the detection of stellar parallax byCalandrelli in 1806.13

Another argument against the rotation of the earth is that objectswould fly off into space if the earth were rotating, as it is well knownthat objects can fly off a rotating wheel. Whether they actually do sodepends on the rotational velocity. In modern terminology, objectswill fly off a rotating body if the centrifugal force mv2/R due to therotation is greater than the force holding them on the rotator, thegravitational force mg in the case of the earth. So, the answer to thisobjection is that the earth does not rotate fast enough for objects tofly 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 isthe 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, theearth 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, andGalileo 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 termsof the configurations of the seas, but this was not convincing. He con-sidered the alternative explanations to be just fantasies, and hebrushed them aside.

Although Galileo was able to advance many cogent arguments forthe 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



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 ofthinking about the world. He rejected the traditional method ofseeking the answers to physical problems by studying the works ofmasters such as Aristotle and replaced it with quantitative measure-ment and analysis. Instead of philosophical discussions about thenature of motion, he measured as accurately as possible how long ittook for bodies to fall a certain distance and then tried to find amathematical relation between them. He was not the first to empha-size the importance of experiment; others, like Robert Grossetestein the thirteenth century, had laid the foundations of experimentalscience. 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 theoretical physics.

Galileo maintained that

philosophy is written in that great book which ever lies beforeour eyes, I mean the universe, but we cannot understand it ifwe do not first learn the language and grasp the symbols inwhich it is written. This book is written in the mathematicallanguage, and the symbols are triangles, circles and other geo-metrical figures, without whose help it is humanly impossibleto comprehend a single word of it, and without which onewanders in vain though a dark labyrinth.14

This is not correct to describe Galileo’s scientific method either asPlatonist or as hypothetico-deductive.15 He believed that nature issimple and that we can attain true knowledge of it. He did notaccept the view that a scientific theory preserves appearances,

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enabling us to calculate results that are more or less in accord withobservations and measurements but that tell us nothing about thereal nature of the world. Galileo was a realist, and he built on andcombined the methods of Archimedes and Aristotle to forge a newmethod. For this reason he is often regarded as the founder of mod-ern science.

Through his astronomical discoveries and his application ofmathematics to celestial phenomena, Galileo unified terrestrial andcelestial 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 ofphenomena has to be studied with its own concepts and laws, andeventually they may be united with other phenomena, as electricand magnetic phenomena were unified by Maxwell. The work isstill 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 aresometimes regarded as Galileo’s greatest discoveries, and hisachievement was to unify them in a way that led to the developmentof theoretical physics.

In addition to his work of unification, Galileo separated sciencefrom theology so that theology, and in particular the Bible, should notbe used as a source of scientific knowledge. Rather, what we find outby observation and experiment can sometimes assist the interpreta-tion of the Bible. Galileo is sometimes credited with the eliminationof metaphysics from science, but no scientific activity can ever be freefrom metaphysical assumptions. In particular, he had a strong beliefin the order and simplicity of nature and in its real existence, andthese and other beliefs presupposed by science are Christian beliefsthat played a determining role in the origin of modern science in theHigh Middle Ages. Likewise, Galileo distinguished the mathematicalapproach to physics from Aristotelian natural philosophy.

Although Galileo was largely responsible for the overthrow of



several conclusions of Aristotelian physics, he retained a generalcommitment to the principles of Aristotle’s approach to science, par-ticularly the need to attain a physical understanding of nature and touse the laws of logic. Galileo was a strong believer in the simplicityof nature and so continued to believe that the orbits of the planetsare circular. As a result, although he greatly admired the work ofKepler, he never showed much interest in Kepler’s three laws ofplanetary motion, which indeed provide strong support for theheliocentric theory. This belief in universal circular motion ledGalileo into great difficulties when he considered the explanation ofcomets. Neither did he spend time on the optical theories underly-ing the operation of the telescope, but constructed them by a processof trial and error.

Galileo’s second great achievement was the construction ofsignificantly improved telescopes and the astronomical discoveries hemade with their aid. These made him famous throughout Europeand changed his life. He soon became convinced that the helio-centric theory of Copernicus was correct and used his astronomicaldiscoveries to develop arguments in its favor. Individually, none ofthese arguments was conclusive, and at least one was incorrect, buttogether they were sufficient to convince the scientifically trainedmind.

If he had been content, like most scientists, to publish his resultsin weighty Latin tomes, Galileo might not have become embroiledin controversy. Instead, he vigorously publicized his work and wrotein the vernacular in a way that could be understood by the generalreader. This was necessary partly to obtain employment, but alsobecause 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 onscientific grounds, invoked the aid of theology, he countered with atreatise on the interpretation of Scripture. The theologians of theInquisition, angered by his incursion into their domain and con-cerned by the threat to the Church’s authority to be the sole, authen-

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tic interpreter of Scripture, persuaded the Inquisition to forceGalileo to abandon his support for Copernican astronomy. Theywere, for the most part, well motivated, and saw themselves asdefenders of a hallowed synthesis of natural and supernatural knowl-edge. They had, however, an inadequate understanding of Galileo’sscientific achievements, which made it absolutely essential for themto 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 knownthroughout Europe. His work on dynamics, in particular, culminat-ed in the achievements of Newton, who unified Galileo’s laws ofmotion and those of Kepler with his theory of gravitation. More gen-erally, Galileo inaugurated a new style of scientific thinking that wasto bear much fruit in the following centuries and identify him as oneof the founders of modern science.

Notes

1. Olaf Pedersen, “Galileo’s Religion,” in G. V. Coyne, M. Heller, and J. Zycinski, ed.The Galileo Affair: 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?” Annals of Science 52 (1995): 403.4. William R. Shea, Galileo’s Intellectual Revolution:Middle Period,1610–1632 (Sagamore

Beach, Mass.: Watson Publishing, 1977).5. William A. Wallace, Galileo and His Sources (Princeton: Princeton University Press,

1984).6. I. E. Drabkin, trans., “De Motu,” in Galileo Galilei 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.



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.

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