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  Allegedly Pythagoras used numbers to divine the future.81 A Christian satirist ridiculed Pythagoras for claiming that souls are made of “number in motion.”82 One of the most famous professed followers of Pythagoras, Apollonius of Tyana, a reputed prognosticator and exorcist, had been repeatedly denounced as practicing demonic magic to imitate Christ's miracles.83 In the late 1500s, the Vatican launched an attack on the occult arts. At the time, various books on magic discussed the powers of Pythagoras.84 Fortune-tellers used the so-called “Wheel of Pythagoras” for divination.85 They also used “Pythagorean” numerology that related the letters of the alphabet to the planets, the days of the week, and the signs of the zodiac.86

  These extensive, esoteric connotations could scarcely be avoided by simplistically referring to Pythagoras as a geometer. Even the word mathematician, so proudly used by Galileo and Kepler, still involved implications of astrology, occult numerology, and divination. Saint Augustine had cautioned: “The good Christian should beware of mathematicians and anyone who practices unholy divination, most especially if they speak truly, lest the soul be ensnared by consorting with demons.”87

  Hence, for centuries, some Catholic theologians construed the Pythagorean outlook as overtly anti-Christian. In 1616, the Inquisition “completely prohibited and condemned” Father Foscarini's scriptural defense of the “New Pythagorean System of the World,” a rejection more forceful and damning than the injunctions against Copernicus and Galileo. Likewise, in 1622, a book on Pythagorean symbols was banned by the Index of the Inquisition for religious reasons.88 Thus it is understandable that some Jesuits denounced Galileo's book as more vile and harmful than the writings of the heretical reformers. At least the Protestants did not defend a pagan system of the world.89

  Contrary to the certificate that Galileo had received from Cardinal Bellarmino, the Inquisition now claimed that Galileo had been granted no implicit permission to teach and discuss the Copernican theory. They professed a document to that effect, though it lacked the signature of Bellarmino, who had died in the meantime. Then, in the trial depositions, Galileo lied: he pretended that in his Dialogue he was “refuting” the theory of Copernicus, showing that it was “invalid and inconclusive,” with only the “purest intention.”90 Officials of the Inquisition then showed, to the contrary, that his book vigorously defended and taught the theory that he actually seemed to believe. The Inquisition ruled that Galileo indeed had trespassed against the Church.

  The Holy Roman Inquisition then declared Galileo guilty of heresy—punishable with torture, prison, or death. They forced him to kneel and recant his claims. He then spoke: “with a sincere heart and unfeigned faith I abjure, curse and detest the above-mentioned errors and heresies [the Copernican account], and in general each and every other error, heresy, and sect contrary to the Holy Church.”91

  Yet according to legend, as he finally stood up Galileo also muttered “Still it moves.” But there is no historical evidence supporting that, which would have been an utterly brash and dangerous act. Apparently, the story of Galileo's defiant words first appeared in print in 1757, in English, by a native of Turin, Giuseppe Baretti, who wrote: “The moment he was set at liberty, he looked up at the sky and down to the ground, and, stamping with his foot, in a contemplative mood, said Eppur si move.”92 There is no evidence of this, but a painting from the 1640s portrays an old Galileo in a dark dungeon holding a nail with which he has scratched a few figures on the wall, Earth circling the sun, and the words: E pur si muove.93

  The cardinals condemned Galileo to lifelong imprisonment. They also banned his book. He was not imprisoned in a dungeon, although that myth, like the painting above, has prevailed.94 He was allowed to serve his sentence by staying confined to his house in Florence, watched by guards. In the summer of 1633, Melchior Inchofer, a Jesuit theologian who had testified against Galileo published a book justifying the Catholic opposition to the heliocentric theory, “to rally everyone as soldiers of religion.” Among various objections, Inchofer complained that “since the Pythagoreans have gradually come to oppose the faith, it must be shown that the truth is found in the Scriptures, and as our major authors knew, is opposed to them.” He required that “the Copernican theory and its related Pythagorean philosophy should not be taught at all.” The Commissary General of the Roman Curia promptly approved the book for publication, noting, “This theologian has given a Christian refutation of these Pythagoreans. And he shows rightly that mathematics and the human sciences should be subordinated to the rule of Sacred Scripture.”95

  The traditional story about Galileo says that in ancient times, Pythagoras argued that Earth and the planets orbit the sun; his theory was later adopted and refined by Copernicus, and it led Galileo to clash with the Catholic Church. This story is defective because half of it is fictitious. Instead, we can replace it with the following: Galileo attributed the heliocentric theory to Pythagoras, but this association entailed pagan connotations that could hardly help its acceptance among Catholics. This sentence does not summarize the main aspects of the Galileo affair, but it is the sort of thing we can fairly say if we wish to remark on its connection to a Pythagorean context.

  Three and a half centuries later, the Catholic Church admitted that theologians had made some errors in the trial of Galileo.96

  In any case, we have seen that in the phases of Venus, for example, Galileo found convincing evidence against the accounts of Aristotle and Ptolemy. Given that, plus all his other findings and arguments, had he actually proven the truth of the Copernican scheme? Not at all. Tycho Brahe's account explained the phases of Venus equally well. Galileo's strategy in his Dialogue had been essentially to ignore Brahe's account. Yet Jesuit astronomers were well aware of it, and they knew that it served well enough to accommodate Galileo's findings. By the 1620s, the Jesuit astronomers had adopted Brahe's system. While despising the “Pythagorean” scheme, these Catholics had adopted a worldview contrived by—a Lutheran.

  As for the moons of Jupiter, Ptolemy had not predicted them, but neither had Copernicus. They could be added onto any account, though ruining the Aristotelian claim that there is only one center of motion in the universe. Moreover, some of Galileo's favorite mathematical and physical arguments that purportedly showed Earth's motion were wrong. In particular, his Dialogue argued as though the most compelling proof of Earth's motion were the oceans' tides. Galileo reasoned that if Earth were perfectly still, the waters would also be still, and that, like any vessel carrying water, its motion affects the water. He knew that Kepler argued that the changing tides were correlated to the motion of the moon. But Galileo denied it. Kepler was right, yet Galileo dismissed those arguments as if Kepler were childishly speculating about occult astrological influences of the heavenly bodies on terrestrial phenomena. Thus Galileo's main “evidence,” supposedly showing Earth's motion, was wrong.

  Hence, astronomers and the Catholic Church were not irrational in criticizing Galileo, for he advocated more than was certain at the time. Again, if Earth spins constantly to the east, then why is it that when things are thrown up into the sky they do not deviate from a straight downward path? Galileo had no good answer. We now know that, actually, things do deviate as they fall, only very slightly so. This effect was demonstrated beautifully in Paris in 1851 by Jean Bernard Léon Foucault. He showed that as a pendulum swings repeatedly, its direction changes gradually throughout the day, just as if Earth indeed spins to the east. An example is that if you were in a moving car, and you tossed something straight forward toward the windshield, just as the driver turned the steering wheel to the left, you would see that the object you tossed would not hit the spot where you aimed it, but would tend instead to the right. Likewise, as a pendulum swings, its direction seems to change very slightly, which we attribute to Earth's spin. Lacking such results, Galileo had no clear proof of Earth's motion, just many interesting findings and analogies, along with some bad ones. Just as Aristotle and Ptolemy were wrong about many things, so were
Copernicus and Galileo. The sun is not immobile, it is not at the center of the universe. Contrary to their expectations, the sun is a star. The stars are not immobile, either; they are not embedded in a sphere. And importantly, the orbits of the planets are not circular.

  Returning to the start, Aristotle had explained that if Earth moves we should be able to detect some shifts in the relative positions of the stars. Like Brahe, Galileo saw no such shift. Such effects do exist, but Galileo's telescopes were far too weak to detect them. Thanks to the use of improved instruments, Friedrich Bessel, a school-dropout largely self-trained in astronomy and math, successfully detected and measured stellar parallax in 1838.97 Aristotle was right! If Earth really moves, the stars should seem to shift—and they do.

  3

  Newton's Apple and the Tree of Knowledge

  LET'S dispel another widespread myth: that Newton was born in the same year Galileo died. This mistake continues to appear in recent literature, such as in this example: “He died in 1642, within a few days of Isaac Newton's birth.”1 Writers often claim that both events happened in 1642, which, by the way, would fit nicely with the Pythagorean idea of the transmigration of souls. I have even found some writers who claimed that Newton “was born on the very day on which Galileo died.”2 As other writers know, the mistake stems from using the Gregorian calendar to date the death of Galileo while using the old Julian calendar to date the birth of Newton. Actually, there transpired almost a year's difference. In the Gregorian calendar, Galileo died on 8 January 1642 and Newton was born on 4 January 1643. In the old Julian calendar, Galileo died on 29 December 1641 whereas Newton was born on Christmas Day, 25 December 1642.

  It's actually necessary to write the exact dates, as otherwise, we meet additional confusions. For example, bestselling physicist Stephen W. Hawking wrote the following: “Galileo died on 8 January 1642, exactly three hundred years before the day I was born. Isaac Newton was born on Christmas Day of that year in the English industrial town of Woolsthorpe, Lincolnshire. He would later become Lucasian Professor of Mathematics at Cambridge University, the chair I now hold.”3 This wonderful passage has several mythic dimensions. The coincidences of space and time seem to imply a connection between Galileo, Newton, and Hawking. But Hawking was confused about Newton's birth; using the Gregorian calendar it was not on Christmas Day and it was not the same year as when Galileo died. Woolsthorpe was not an “industrial town,” it's a small village. Note also the use of the phrase “He would later become,” as if Newton was destined at birth to become great. Other writers echo the mistake about dates, and some even do it on purpose. One textbook, using the same dates given by Hawking, adds this footnote: “Because England had not yet reformed its calendar, 25 December 1642, in England was 4 January 1643, in Europe. It is only a small deception to use the English date.”4 Instead of just fixing the factual mistake, the editors preferred to keep it.

  Anyhow, let's talk about the apple. For more than two centuries, hundreds of commentators have written thousands of words about the story of Newton's apple. But most of these are based on very little evidence. Even good biographers who cite evidence tend to just allude to documents, rather than quote them, and they ignore or omit various sources. Since there exists no comprehensive account of the historical evidence and its early interpretations, I will now give one.5

  By comprehensive, I do not mean exhaustive, I merely mean that I've assembled more evidence on the matter than is available in any other source. To do so, I have abstained from any of the many psychological, speculative, and literary themes that many writers develop when referring to this topic. While I find many of those commentaries to be engaging and insightful, I will focus on a plain accounting of documentary evidence. I hope that the following material helps to facilitate the systematic study of myths in science and how they grow.

  In 1662, the nineteen-year-old Isaac was experiencing intense religious concerns. To confess his sins in a private, hidden way, he wrote them in a brief, cryptic code. He listed sins that, across the years, he had occasionally committed against God. First on Newton's list was “Using the word ‘God’ openly”; he also included, “Not loving Thee for Thy self,” “Not desiring Thy ordinances,” “Fearing man above Thee,” and “Caring for worldly things more than God.”6 Newton also listed various acts that he should not have done on God's day: twisting a cord, making a mousetrap, making pies, idle chatting, squirting water, swimming, and, second on his list: “Eating an apple at Thy house.” He also included graver sins: lying, stealing, robbing his mother's box of plums and sugar, putting a pin in someone's hat to prick him, punching his sister, “Striking many” people, wishing death to some, and threatening to set his stepfather and mother on fire: “Threatening my father and mother Smith to burne them and the house over them.”

  The fiery threat dates from more than ten years earlier. His actual father had died shortly before his birth, and the boy despised his mother's second husband: the Reverend Barnabas Smith, who, anyhow, died before the boy's eleventh birthday. The fiery threat was the thirteenth sin on his list; eating an apple in Church was, again, second.

  In the summer of 1665, at twenty-two years of age, Isaac kept away from his college, Trinity at Cambridge, to escape from the spreading crisis: the bubonic plague that was killing thousands of people throughout England. He subsequently spent about two years in relative isolation. While living at his family farm in Woolsthorpe at Lincolnshire, he spent time thinking and working on problems in physics and mathematics.

  One of the most famous stories in the history of science is that Newton was inspired to think about universal gravitation by seeing an apple fall in his garden at Woolsthorpe in 1666. Some writers, for various reasons, accept this story. Other writers dismiss it as mere legend. Yet there is evidence that Newton himself told it. In a manuscript, Newton's friend William Stukeley reported that on 15 April 1726, he dined with the then-very-old Newton and that:

  after dinner, the weather being warm, we went into the garden, & drank tea under the shade of some appletrees; only he & my self. amidst other discourse, he told me, he was just in the same situation, as when formerly, the notion of gravitation came into his mind. “why should that apple always descend perpendicularly to the ground,” thought he to himself; occasioned by the fall of an apple, as he sat in a contemplative mood. “why should it not go sideways, or upwards? but constantly to the earth's center? assuredly, the reason is, that the earth draws it. there must be a drawing power in matter. & the sum of the drawing power in the matter of the earth must be in the earth's center, not in any side of the earth. therefore dos this apple fall perpendicularly or toward the center. if matter thus draws mater; it must be in proportion of its quantity. therefore the apple draws the earth, as well as the earth draws the apple.” that there is a power like that we here call gravity, wch extends its self thro' the universe.7

  Newton died in 1727, aged eighty-four. That same year, Robert Greene reported in print, in Latin, that his friend Martin Folkes (vice president of the Royal Society when Newton was president) had told him that Newton's idea of universal gravity was inspired by an apple: “which famous proposition, all things considered, originates, as disclosed to our knowledge, from an apple; that which I learned from a most ingenious & most learned man, and also the finest, and friendliest to me, Martin Folkes Esquire, truly meritorious Fellow of the Royal Society.”8 Similarly, a memo drafted by Newton's friend John Conduitt in 1727 or 1728 reported, “& in the year 1665 when he retired to his own estate on account of the Plague he first thought of his system of gravity which he hit upon by observing an apple fall from a tree—.”9 In another draft of the same, Conduitt wrote “he discovered his system of gravity / he took the first hint of it from seeing an apple fall from a tree.”10 And in yet another manuscript, Conduitt wrote (crossing out some words, as noted, and inserting others, noted here between slashes):

  In the year 1666 he retired again from Cambridge on acct of the plague to his mother at Boothby
in Lincolnshire & whilst he was musing in a garden it came into his thought that the same power of gravity (wch brought made an apple fall from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought—Why not as high as the Moon said he to himself & if so that must influence her motion must be influenced by it & perhaps retain her in her orbit,…11

  One more writer recorded the story at this early time. And in a way, it is the most epic, dramatic version. When Newton died, Voltaire was visiting England. He spent time with a group of individuals who were more or less close to the famous old physicist, including his niece. And Voltaire promptly reported what he heard about Newton. Like Greene, he first published it 1727, writing in English. Voltaire was praising the great skills of the poet John Milton when he inserted one sentence about Newton. Voltaire wrote that Milton, in his youth, was traveling in Italy and saw a dreadful play. It was a comedy about “the Fall of Man; the Actors, God, the Devils, the Angels, Adam, Eve, the Serpent, Death, and the seven mortal Sins.”12 Voltaire recounted that the play began with an extravagant chorus of angels discoursing about the rainbow, planets, time, and winds, all making music, rising in a “Profusion of Impertinence.” He wrote that Milton then saw through the absurdity of that show, and sensed the great, hidden Majesty of the subject, which years later, led to his epic poem, Paradise Lost. Right then, Voltaire mentioned Newton and the apple, as he discussed Milton's response to the extravagant play: