The Cave and the Light

by Arthur Herman

  Galileo discovered that the moon was not a perfect unblemished geometric sphere, as Aristotle’s cosmology demanded. It was rutted with craters and studded with mountains. He then turned his attention to Venus. He found that it was illuminated in a series of phases like the moon, suggesting that Venus must revolve around the sun as a fixed source of light.

  He also found a series of smaller objects: the moons circling Jupiter. Aristotle’s arguments about why there were only seven planets, one sun, and one moon in the sky, and why there could be no more and no fewer, were suddenly nonsense. The perfect system of the Aristotelian cosmos was anything but, and the way the Aristotelian mind had tried to understand the workings of nature turned out to be a mirage.

  That’s the way it looked to Galileo. In 1610, he quickly assembled his discoveries in a little book he titled the Starry Messenger and dedicated to the Grand Duke of Tuscany, Cosimo de’ Medici. The problem was that no one believed him. From the start, Aristotelians dismissed what Galileo had seen through his telescope as an optical illusion. When Johannes Kepler saw the same things through his telescope, they said it was still an optical illusion. Even when Galileo gave them his telescope and offered to let them see the moon’s craters for themselves, they refused to look. Aristotle had said that all celestial bodies were perfect. This meant they couldn’t have any flaws. Therefore the moon’s craters didn’t exist, any more than the moons of Jupiter (or, as Galileo soon discovered, the moons of Saturn).

  “They have shut their eyes to the light of truth. Faced by arguments like this,” Galileo told Kepler, “I don’t know whether to laugh or cry.”24 Still, Galileo refused to see that their objections had a strong empirical basis. The Aristotelians, who included professors of philosophy as well as several churchmen, were not idiots. They understood the principle of magnification. But how, they asked not unreasonably, could Galileo be magnifying objects that couldn’t be seen with the unaided eye in the first place? It defied common sense. The academic establishment was furious with Galileo not because he was inquiring into things better left to theology, but because they thought he was a fraud.25

  Indeed, this was the dirty little secret about the Copernican theory. None of it could be confirmed with direct evidence. Copernicus had come up with the notion that the earth must be going around the sun along with the other planets without making any new astronomical observations. He had simply found the idea in a book on the ancient Greek mathematician Aristarchus.§ Again, the chief reason Copernicus did not publish his theory during his lifetime was not that he feared the disapproval of the Church—he was worried it was so contrary to our everyday experience, it would be laughed off the stage.26 Nothing any astronomer had ever seen, not even Tycho Brahe’s meticulous observations from his island observatory outside Copenhagen, confirmed any aspect of it. Brahe himself felt perfectly comfortable sticking to the old geocentric theory.

  All Copernicus’s theory had done was make the calculations of movements of the heavenly bodies easier. In fact, as Johannes Kepler demonstrated when he published his mathematical study of the elliptical orbits of the earth and other planets, it made them easier to the point of harmonious elegance.27

  This was all the average Platonist needed to hear. He didn’t care about “saving the appearances,” as Aristotelians did—that is, making sure that everything we see and perceive has some explanation in our general theory. The Platonist knows appearances can deceive, because matter changes. Soccer balls come and go; they get run over or get stolen. However, the geometry describing their behavior, whether spinning on their axis or at rest, lasts forever. And what it says stands true not just for soccer balls, but for every sphere, real or imaginary, including the earth.

  It was the math that mattered. And when the math yields a pattern of harmonious proportion, whether it’s the golden section of the Greeks or the Sierpinski gasket and Mandelbrot set of modern fractal geometry, the Platonist knows, as Archimedes did many centuries before, that he is standing at the threshold of the truth.28

  Thomas Taylor, the eighteenth-century mathematician and first person to translate the complete works of Plato into English, phrased it best: “Geometry enables its votary, like a bridge, to pass over the obscurity of material nature, as over some dark seas to the luminous regions of perfect reality.”29

  The Renaissance figure who grasped this point long before Galileo was Leonardo da Vinci. His voluminous notebooks reveal his peculiar fascination with observation and invention. This is his Aristotelian side. But his famous etching of Vitruvian Man reveals his more mystical, Platonic side. Leonardo was steeped in the Pythagorean formulae of harmonious proportion. He understood the creative power of the golden section. He provided the illustrations of Plato’s five geometric solids for mathematician Fra Luca Pacioli’s Divine Proportion in 1509, the first ever done using a three-dimensional perspective.30

  The Vitruvian Man sprang from the same passion. Leonardo borrowed the Roman architect Vitruvius’s belief that the parts of the human body all exist in exact proportion to one another, in order to construct a visual allegory of man’s place in the cosmos.

  Leonardo’s man stands at the center of not one but two geometric figures, the square and the circle. Far from trying to combine the two, in other words “squaring the circle,” Leonardo was content to show that the ratios derived from the golden section place the human being at the center of both geometric figures, depending on our perspective.31 As with Ficino, Leonardo’s man bridges the gap between infinity and matter, between divinity and mortality. But this time, it is mathematics and the science of proportion, not love, that enable us to see it and grasp our mediating role. No wonder Leonardo wrote in his Treatise on Painting, “Let no one ignorant of mathematics enter here”—almost exactly Plato’s motto over the gate of the Academy.

  Sixteenth-century astronomer and scientist Giordano Bruno was Galileo’s older contemporary and chose to carry this fusion of Platonic theology and mathematics to the next level. His writings offered a direct parallel between geometry and Plato’s theory of divine love and suggested that the revelations of the one would inspire the same mystical frenzy and creative vision of the other.

  They evidently did for Bruno, who saw in mathematics a power others never imagined. For Bruno, the “dark seas” of material nature were not dead or inert. They teemed with spirits and demons, all waiting to be brought to life. These would then reveal nature’s secrets to their mathematician master, just as Bruno was convinced they once had to the ancient Egyptians and the Pythagoreans.32

  This conviction led Bruno to black magic and alchemy. His later works contain multiple geometric diagrams that are supposed to summon demons the way a finger on a button boots up a hard drive.33 It is also why Bruno never doubted the truth of Copernicus’s proposition that the earth moved. For Bruno, the earth was a living being.

  The story of Bruno’s dark, unstable genius and his Pythagorean magical math ends badly.‖ The Roman Inquisition sent him to be burned at the stake in 1600. They did so unwillingly. “You are more reluctant to pronounce this sentence,” Bruno sneered at his inquisitors, “than I am to receive it.” However, it was an object lesson for Galileo in how not to challenge traditional intellectual authority, especially concerning a Copernican theory that Bruno had upheld and which an Aristotle-dominated Catholic Church had denounced as contrary to orthodox faith.

  In 1610, however, Galileo had little reason to worry. He was friends with the most powerful man in papal Rome, Cardinal Robert Bellarmine. The Jesuit order had tested his telescope and declared the mountains on the moon were genuine. By 1611, he even had the pope himself, Paul V, actively supporting his work and applauding his genius.

  Of course, privately Galileo thought the condemnation of Copernicus was wrong. “The Bible tells us how to go to Heaven,” he once quipped, “not how the heavens go.” All the same, he made it clear he would not get dragged into a dispute over the Church’s power to decide what was true in matters of fact (like the
shape of the solar system) as opposed to matters of faith.34

  Even after certain published remarks earned him an admonition in 1616 to say no more about the Copernican theory, he accepted the ruling without demur. He also continued his research without letup. In his mind, this was no battle between religion and science. This was a battle between what he called “two chief world systems,” one based on the traditional Aristotelian view of nature and the other new one confirmed by both the power of observation and Platonic mathematics.

  Here Galileo also wanted to avoid the error of his colleague Johannes Kepler (1571–1630). For all his brilliant work, Kepler had insisted on making the five Platonic solids the basis for his model of the solar system, rendering it useless for further empirical research. It was a bizarre example of carrying the faith in the perfection of mathematics too far.35 By contrast, Galileo understood that even a divinely ordered cosmos could not be perfect. There were craters on the moon and spots on the sun. Kepler himself had shown that the planetary orbits were not perfect circles as Aristotle and even Copernicus had assumed, but ellipses.

  “There is no event in Nature,” Galileo wrote, “such that it will be completely understood by theorists.”36 God’s perfection was to be found in the numbers, not in the shapes or objects. Yet without real objects, the math can become an exercise in pure speculation or even hallucination, as Giordano Bruno’s life revealed.

  Galileo’s science managed to fuse the Platonist’s faith in mathematics with the Aristotelian faith in experience as the basis of discovery. All his work on mechanics, optics, and astronomy was deeply rooted in experiment and empirical research. When experience proved ambiguous or unreliable, however, Galileo realized then that mathematics must take over.

  The universe, Galileo wrote, “is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single world of it.” Without mathematics, he concluded, “one wanders about in a dark labyrinth”—or what Plato might have called a cave.37

  This was Galileo’s most important contribution to the future of science. Galileo knew that if he could measure it mathematically, then it must exist even if he could not see it. This was whether one was talking about his own concept of velocity or, later, Newton’s concept of gravity. His “mathematization of Nature” allowed scientists for the first time to anticipate discoveries and work out scientific theories, including Einstein’s relativity three centuries later, long before the means of testing them existed.

  Galileo had replaced a universe tied down to final causes that were inherent in things themselves with a universe infinitely open to possibility and change. This is still our universe, as when we speculate about the possibility of life on Mars or some distant planet. However, Galileo himself never doubted God’s part in it, any more than Leonardo or Ficino did. As he put it in a fine Neoplatonic formulation, “Holy Scripture and Nature are both emanations from the divine Word.” Like other Platonists, Galileo didn’t have to see God to believe in Him. He only had to feel His perfection in His creation and stand aside in awe.

  Others were not willing to accept the new paradigm.38 They waged war on Galileo both in print and behind his back. What they couldn’t do to Martin Luther, namely put him on trial in Rome, they were desperate to do to Galileo—and for many of the same reasons.

  Lutheranism and Calvinism had pulled up the theological certainties built around Aristotle by the roots. Galileo was doing the same to Aristotle’s physical sciences. Aristotle’s defenders, churchmen and professors alike, saw themselves as trustees of a centuries-old orthodoxy. When Galileo dismissed them as ignorant blockheads and wrote, “If Aristotle had been such a man as they imagine, he would have been of intractable mind, obstinate spirit, and barbarous soul,” they were bound to hit back with everything they had.39

  It took them nearly fifteen years to get him in the end. They also had to overcome the biggest obstacle of all: the new pope, Urban VIII, who as Cardinal Maffeo Barberini had been Galileo’s closest friend and one of his most enthusiastic supporters. It was Urban’s election in 1623 that prompted Galileo to begin work on his magnum opus, not an erudite scientific treatise in Latin but a lively Platonic-style dialogue in everyday Italian, called Dialogue Concerning the Two Chief World Systems. It would finally prove to every reader why the Copernican heliocentric view was right and the old Aristotelian view wrong: all with—he hoped—the approval of the pope himself.

  In the spring of 1632, the work was finally finished. Galileo was approaching seventy. He was in poor health, one of his beloved daughters had died, and he was experiencing problems with his eyesight that would eventually leave him all but blind. The Dialogue, however, was a smash hit.

  Like Plato and his own father, Galileo preferred the dialogue form as a way to debate first principles, in this case scientific principles. The Dialogue takes place between a partisan of Copernicus and a partisan of Aristotle. Galileo also throws in a neutral observer who acts as the judge as to which has the better argument. However, Galileo gives the game away when he names Aristotle’s advocate Simplicio (or Simpleton), and the odds are running against Aristotle from the first page.a

  Over four fictional days of discussion and five hundred pages of text and diagrams, it is Aristotle versus Galileo head-on, as Simplicio’s objections to Copernicus are demolished one by one. The men discuss celestial substances in light of the imperfections of the moon’s craters and mountains; planetary motion and sunspots; and then finally, on the fourth day, ocean tides and how large recurrent shifts of the seas and oceans would be impossible if the earth were actually perfectly still.

  More than any previous work, Galileo’s Dialogue showed that if Copernicus wasn’t right on every detail of the working of the solar system, Aristotle and Ptolemy were both very clearly wrong. The first printing sold out almost at once. Clerics and laymen alike sang its praises. One reader, the Dominican friar and militant Platonist visionary Tommaso Campanella, pronounced it the beginning of a new era.

  However, not everyone bought the Dialogue for the same reasons. One of Galileo’s friends, a papal official, was in a Roman bookshop when a Jesuit father came bursting in through the door. He wanted a copy of Galileo’s latest book, he told the bookseller.

  We’re sold out, the man informed him. Trembling with rage, the Jesuit insisted. “I’ll pay you ten scudi if you can get me a copy at once.” The bookseller shrugged, and the cleric left in a fury.

  Galileo’s friend watched him go and turned to his companion. “The Jesuits,” he said, “will persecute this book with the utmost bitterness.” He was right.40

  In the early morning hours of October 1, 1632, there was a knock at the door of Galileo’s house in Florence. A sleepy servant swung open the door to reveal a man in black robes and a hooded cowl.

  Galileo recognized him at once. He was the inquisitor of Florence. He had a summons for Galileo, he said, to present himself to the Holy Office in Rome within thirty days.

  Galileo collapsed to the floor. His servants had to carry him to his bed. He knew that the summons meant that his enemies had finally turned his old friend the pope against him.

  They had shown Urban VIII their copies of the Dialogue, with its clear support for Copernicus’s heliocentric theory. He had waved away their suspicions. Then they had pulled out their ace in the hole. It was a copy of a papal memorandum from 1616 that summarized an injunction from then pope Paul V, explicitly ordering Galileo never to discuss Copernicus or his theories again.41 Urban VIII was aghast. Galileo had never told him about the order. It seemed to him that Galileo had lied and deceived him and also defied the authority of the Holy See. What Cardinal Maffeo Barberini might have overlooked in an old friend, Pope Urban VIII could not. He immediately ordered Galileo to Rome.

  Galileo argued for a delay, pleading “my great age, my many physical infirmities … the hazards of the journey.” Couldn’t the trial take place in Florence?
Galileo probably knew the Florentine inquisitor would be on his side: the man had read the Dialogue and said he found nothing wrong with it.

  The pope, however, was adamant. “He must come,” he told Galileo’s friends, “he can come by very easy stages, in a litter, with every comfort, but he really must be tried in person.” Urban added, “May God forgive him for having been so deluded as to involve himself in these difficulties,” because the pope never would.42

  Galileo reached Rome in early November. He was still frightened, but he was (as the Florentine ambassador, who gave him lodging, noted) calm and collected. No one knew it, but Galileo had an ace of his own. He only needed the right moment to play it.

  The trial of Galileo, the most famous in Inquisition history, did not begin until April 1633. Not a word was said about scientific theories. The charge of heresy rested entirely on the accusation that Galileo had disobeyed a papal order. The inquisitors presented their evidence against him, including copies of the Dialogue and the 1616 memorandum mentioning the papal injunction.

  Then Galileo cleared his throat and began. He told the inquisitors he had no recollection of any such injunction. But there was more.

  “In the month of February 1616,” Galileo said, “Cardinal Bellarmine told me that since the opinion of Copernicus absolutely contradicted Holy Scripture, it could not be held or defended.” However, he added, the cardinal conceded that “it might be taken hypothetically and made use of,” as, for example, in research and writings such as his Dialogue Concerning the Two Chief World Systems.43

  The inquisitors shifted uneasily in their seats. Could this be true? Bellarmine had been dead for nearly twelve years. Galileo then produced an affidavit Bellarmine had signed and sent him, stating that Galileo in no way had to abjure or do any penance for his previous support of Copernicus. The document acknowledged that he had been informed of the pope’s declaration that a doctrine declaring the earth moved around the sun could not be held or defended. But there was no mention of any papal injunction against Galileo and no mention of future punishment if he failed to comply.