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  Lane Cooper was not a historian, nor a physicist. He was a professor of English. Hence, when he published his book showing that the story about the tower is not supported by evidence, many historians just dismissed it. For decades they belittled him and ignored his book. But Cooper used evidence to make his argument. It is encouraging that outsiders can contribute to a professional field such as history, especially by focusing on documentary facts rather than speculations. Legends about Galileo have propagated partly because people were willing to parrot the claims of specialists, believing authority, rather than evidence. Thus, the irony of this myth is that whereas it purports to criticize philosophers who blindly believed in the authority of Aristotle, in actuality it instead exhibits the gullibility of persons who repeat the tale, their readiness to believe on the basis of authority.

  The story of the Leaning Tower of Pisa captured people's imagination, I think, because it conveyed the dramatic illusion that in a single moment, one young man publicly dared to challenge an arbitrary tradition that had dominated for over a thousand years, and supposedly, his successful experiment abruptly and clearly revealed the truth. Allegedly, this simple, dramatic event constituted a turning point in the history of science; nature had spoken, delivering the death-blow to an arbitrary traditional belief. This epic mythical image was conveyed well in the early 1900s:

  As Galileo's statement was flouted by the body of professors, he determined to put it to a public test. So he invited the whole University to witness the experiment which he was about to perform from the leaning tower. On the morning of the day fixed, Galileo, in the presence of the assembled University and townsfolk, mounted to the top of the tower, carrying with him two balls, one weighing one hundred pounds and the other weighing one pound. Balancing the balls carefully on the edge of the parapet, he rolled them over together; they were seen to fall evenly, and the next instant, with a loud clang, they struck the ground together. The old tradition was false, and modern science, in the person of the young discoverer, had vindicated her position.24

  In the 1990s, experimental physicist Leon Lederman wrote a section of a book titled “The Truth of the Tower.” Lederman embraced the story, and described it as a media happening, the first great scientific publicity stunt: “Galileo knew in advance how it was going to come out. I can see him climbing the tower in total darkness at three in the morning and tossing a couple of lead balls down at his postdoc assistants.”25

  Sixty years prior to Lederman's narrative, Lane Cooper, perplexed by the widespread currency of the Leaning Tower story, commented on people's willingness to believe across the centuries:

  Again, there are many who as aforesaid believe the story about Galileo and the tower of Pisa, and have no better ground for accepting the story than hearsay. They have read or vaguely heard that it was so just as they believe that Aristotle said a certain thing about falling bodies of different weights, and that every one down to Galileo believed the same thing on the authority of Aristotle. As casual readers accept some modern authority for an opinion about the speed of bodies heavy and light in falling, so they accept upon authority, however vague, the tale about Galileo at Pisa.26

  2

  Galileo's Pythagorean Heresy

  EVEN without evidence, most people believe in Earth's motion. When asked why Earth moves, some college students reply: “because of the seasons” or “because astronauts see it from spaceships.” But seen from Earth, the spaceships seem to move instead, so who's right? And for thousands of years, it seemed that the seasons change just because the sun rises at different places on the horizon, taking different paths; so why not say that seasons are caused by the sun's motions? Centuries ago, teachers taught that the sun circles Earth, and it seemed obvious; now they teach the contrary, and it seems obvious. It's easy to accept basic scientific knowledge without knowing why scientists believe it, but that would make science seem like just another doctrine.

  Many myths are associated with the Copernican revolution. I'll now recount the dramatic struggles by which people changed their minds about Earth's motion, while also pointing out several myths. But mainly, I will trace the many connections to legends about Pythagoras and his followers. For centuries, writers have often associated the idea of Earth's motion with Pythagoras of Samos, a philosopher who lived in southern Italy in the sixth century BCE. But is there truth to such claims? Strangely, I find not a single historical account that systematically connects the diverse legends about Pythagoras and his followers to the Copernican revolution. Making that connection reveals a surprising dimension of Galileo's famous heresy.

  According to Aristotle, the philosopher with the aquiline nose, the so-called Pythagoreans believed that Earth moves in circles around the center of space: “they say that fire is at the center and that Earth is one of the stars, and that moving in a circle about the center it produces night and day.”1 But their arguments did not convince Aristotle, who had many good arguments to the contrary. For example, he proposed, if Earth moves across the heavens, then we should observe certain changes in the background of stars. Specifically, we should see apparent changes in the gaps between the stars. Consider a few objects in a row, as seen by someone running along. There's a line of sight to each object. The objects closest to the person will seem to be farther apart from one another, the two objects farthest away will seem to be closest together. But once the person has reached those farthest objects, the effect will be reversed.2

  Likewise, if Earth moves across the heavens, we would expect that the relative distances between the stars should change. Ancient astronomers could expect to see such effects, and more, if Earth were moving. But no such effects were observed. So Aristotle fairly argued that Earth does not move at all.

  Still, decades after Aristotle's death (in 322 BCE), the astronomer Aristarchus of Samos advocated that Earth travels in circles around a center, the sun. No treatise by Aristarchus (who died around 230 BCE) on this matter seems to have survived, but there are brief, indirect accounts. In particular, Archimedes mentioned the theories of Aristarchus in this address:

  You, King Gelon, know that ‘universe’ is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the ‘universe‘ just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun in the circumference of a circle, the Sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.3

  Archimedes rejected Aristarchus's theory, as did most mathematicians and astronomers. One problem was that it seemed to require a ridiculously immense universe. In order for there to be no visible shifting of the distances between the stars, such distances had to be almost unimaginably huge compared to the orbit of Earth around the sun. The last line of the quotation states that Aristarchus apparently claimed that the stars were virtually infinitely far away from Earth.

  By contrast, Pliny the Elder claimed by 77 CE that “the penetrating genius of Pythagoras” had inferred that the distance from the sun to the zodiac stars is merely three times the distance between Earth and the moon.4 If Pythagoras ever made such a claim, it was grossly incompatible with the later, allegedly Pythagorean, claim that Earth moves, because its motion would then cause apparent changes in the distances between the stars. In any case, Pliny ridiculed Pythagoras for “occasionally” drawing on music theory to describe the distances between Earth and the heavenly bodies as tones and half-tones, producing “a universal harmony” of seven
tones, “a refinement more entertaining than convincing.”5 I do not know what credibility Pliny had, but to undermine our reflex to respect and believe ancient authorities, it is useful to bear in mind any of the charming bits of nonsense that some readily proclaimed. For example, Pliny claimed that the saliva of a fasting human was the best safeguard against serpents and he praised the various magical and medicinal properties of spitting: on epileptics, on leprous sores, on insects in an ear, and upon your right shoe.6 Nonetheless, Pliny was a careful compiler of knowledge that he found in many books. The main problem is that he wrote more than five hundred years after Pythagoras died. The accuracy of Pliny's unspecified source on Pythagoras as an astronomer is called into question by the fact that the many prior scholarly commentators on astronomy, such as Aristotle, seem to have made no such claims about Pythagoras.

  Aristotle formulated the conception of the heavens that became widespread for centuries, and it was revised systematically around 150 CE by the Roman citizen Ptolemy, in Alexandria, Egypt. Earth was said to remain stationary at the center of the universe while the moon, the sun, the planets, and the stars all moved in circles around Earth.7 Everything below the moon was said to be in the terrestrial sphere, where things change and decay and violent motions, death, and rot take place. By contrast, the moon and everything above it was said to be perfect, unchanging, eternal.8 All heavenly motions seemed unforced and circular. Like rain and clouds, comets were assumed to happen not above the moon, but in Earth's atmosphere, since they too were fleeting, temporary phenomena.

  Every night the stars and planets cross the sky in a seemingly circular, westward path. But the planets lag slightly eastward, week after week, and when we track the positions of a planet such as Mars against the background of stars, we find that sometimes, instead of moving uniformly eastward in a circular path, Mars seems to slow down and pause, then go back. It loops backward and then again it continues eastward. This is called retrograde motion, and the ancient astronomers wanted to explain it.

  Apparently it was disturbing to think that heavenly things start and stop. In the first century BCE, the Greek writer Geminos noted:

  The Pythagoreans, who first approached such investigations, hypothesized that the movements of the Sun, Moon, and the 5 wandering stars are circular and uniform. For they did not accept, in things divine and eternal, such disorder as moving sometimes more quickly, sometimes more slowly, and sometimes standing still…. One would not accept such an anomaly of movement in the goings of an orderly and well-mannered man. This business of life is often the cause of slowness or of swiftness for men. But in the case of the incorruptible nature of the stars, it is not possible to adduce any cause of swiftness or slowness. For this reason, they put forward the question: how would the phenomena be accounted for by means of uniform and circular motions?9

  Later, Ptolemy also tried to explain retrograde motion. He argued that a planet such as Mars is carried along not in one circular motion alone but by two. Imagine that there is a great sphere that rotates around Earth and it traces a path as large as the orbit of Mars. And on this sphere there is a wheel, centered on a point on the sphere's surface, and Mars is attached to this wheel, as the wheel spins slowly around its center. Thus Mars traces a small loop on the sky as it moves carried by the sphere and wheel (epicycle).

  Additional geometric devices were also used to account for variations in the paths and speeds of the heavenly bodies. Centuries later, a legend developed: that whenever astronomers found that two circles did not suffice to account for the motion of a particular planet, they added more epicycles. By 1969 the Encyclopedia Britannica claimed that in Ptolemy's system, each planet required forty to sixty epicycles. Yet historian Owen Gingerich has shown that there's no evidence that anyone used more than one epicycle per planet.10 The story was a myth that grew, making it seem as though Ptolemy's scheme was ridiculously complicated and had collapsed under its encumbrances.11

  We tend to imagine that obsolete scientific theories were ridiculously complicated whereas contemporary theories are elegant and reasonable. Yet Ptolemy's geocentric account was extremely useful and successful. It was used for over 1,400 years. But there were growing problems. Based on Ptolemy's geometric system, astronomers devised numerical tables that helped to predict astronomical events, such as eclipses, alignment of planets, and equinoxes.12 By the 1500s, these tables didn't agree with the calendar that had been established by Julius Caesar (in 45 BCE). In the year 325 CE, for example, the spring equinox happened on 21 March, its official date according to the calendar—but over the centuries the spring equinox arrived progressively earlier, and by 1500 it fell instead on 11 March. This was a problem because the astronomical observations no longer matched the calendar. Yet people set the date of some important events, such as Easter, by reference to both. The Catholic Church was disturbed by the mismatch between the seasons and the calendar. And so, in 1514, Pope Leo X requested the help of astronomers.

  The Polish astronomer, Nicolaus Copernik, was one of the experts who provided advice on the problem. “Copernicus” was unsatisfied with the structure of Ptolemy's account and its limited precision. He disliked that some of Ptolemy's circular motions were not uniform relative to their centers. Therefore, Copernicus had studied ancient writings to find an alternative. In the works of Cicero and those attributed to Plutarch, he found reference to various Pythagoreans, including Philolaus, who claimed that Earth spins or moves.13 Thus Copernicus came to privately formulate a theory similar to that of Aristarchus, reasoning that it would be preferable to assume that Earth was not at the center of the universe, but that it moved like a planet, and that the planets orbited the sun. Remarkably, by centering the sun, it turns out that the orbital speeds of the planets, including Earth, fall in an ordered sequence: the speed of each planet varies according to its distance from the sun, the closer the planet is to the sun, the faster it moves. Copernicus realized that if indeed Earth circles the sun, then we would observe the apparent retrograde motions of the planets, since Earth sometimes overtakes them as it moves around the sun.

  The heavenly bodies circled the sun, the moon circled Earth. All moved in circular paths, as in Ptolemy's account. Earlier, Plato had claimed that God “made the universe a circle moving in a circle, one and solitary,” with its parts moving in circles.14 Copernicus argued that the planets move because “it is in the nature of perfect circles to rotate forever.” Also, he admitted epicycles into his system to account for deviations in the paths of the planets.15 Yet, his theory departed from tradition, in part, by breaking the barrier between the terrestrial and the celestial, by placing Earth in the heavens.

  Present methods of education lead us to see Copernicus's scheme as natural, simple, and reasonable. However, it had features that seemed utterly repulsive to Copernicus's contemporaries. For example, if Earth is a heavenly body, then why does it spin? None of the others seemed to spin. And if Earth is spinning, why aren't things flung off? Furthermore, if Earth is moving, why don't we feel it? Shouldn't physics and astronomy be based on our experiences? Also, if Earth were truly a planet, then would planets also be worlds like Earth? Would there be humans in other planets? Why would God create many worlds? Did Jesus Christ visit them too? Any such questions would be unsettling.

  Also, Copernicus's system was hardly geometrically simpler than Ptolemy's, partly because it too had epicycles. The small epicycles of Copernicus did not entail retrograde motions; instead, they served to account for irregularities in the changing velocities of each planet.

  Moreover, the motion of Earth entailed that there should be apparent changes in the separations between the stars throughout the year, but since no such changes were observed, Copernicus argued, like Aristarchus, that the distance between the planets and the stars was spectacularly immense. That means that the gap between Saturn and the stars should not be similar to the gap between two planets' orbit but much, much greater. That gap between Saturn and the stars should be at least around thir
ty thousand times greater than the distance between the sun and Saturn. Try to draw that. Why would there be such a huge and horrifyingly empty void between the planets and the stars? Why would God create such extraordinarily large emptiness? As later remarked by Blaise Pascal: “The eternal silence of these infinite spaces frightens me.”16

  Copernicus anticipated that his theory would be severely criticized, partly because the Catholic Church embraced the Aristotelian account. He also followed the reputed practice of the Pythagoreans to keep honest opinions private and reveal them only to friends.17 Therefore, he kept his work relatively secret for decades. Still, for Copernicus, the sun-centered system was elegant proof of God's plan and the divine order of things. In his manuscript On the Revolutions, he noted, “what better place could be found for this lamp in this exquisite temple than where it can simultaneously illuminate everything?”18 Yet his astronomical calculations led him also to acknowledge that the center of the sun is not located exactly at the center of the planetary orbits.