The Cave and the Light

by Arthur Herman

  Still, both Luther and Calvin display the power of Plato’s thymos in action. It is the enemy of moderation—but also of hypocrisy and complacency. For Luther, the goal for every member of a church built on faith alone was that he or she “contemplate this one thing alone, that he may serve and benefit others in all he does, considering nothing except the need and the advantage of his neighbor.”37 In the same way, Calvin’s Geneva, the original City on the Hill, drew thousands of grateful refugees to its gates. They weren’t repelled by Calvin’s rigid rules and religious services seven days a week; they were drawn to them. Indeed, for more than a century Geneva became the ideal model of a Christian commonwealth from the Scotland of John Knox to the Mayflower Compact.

  For in the mind of its creators and admirers, the Reformation was not about creating something new but about recovering something lost, the true Church of Christ. Like philology itself, it was about restoring forgotten meanings, obscured by centuries of error and corruption. Above all, it was a re-dedication to first principles laid down by Scripture and Saint Augustine: the ideal of the Church as a community united around a fervent faith and an adherence to God’s will as the true fount of spiritual freedom and wisdom. This freedom was the gift of God’s grace, Augustine had said, which so “diffuses love through [our] hearts that the soul, being healed, does good not from fear of punishment but for love of justice”—the goal for all men that Plato had wanted from the start.38

  * * *

  * “Lay” meaning clergy like priests and bishops who dealt with the laity; “regular” meaning monks, nuns, and friars in holy orders.

  † The most notorious early example is the so-called Wicked Bible, published by Robert Barker in London in 1631. In the Book of Exodus the typesetter made a fateful slip, so that the Seventh Commandment came out: “Thou shalt commit adultery.”

  ‡ See chapter 20.

  § See chapter 12.

  Medieval depiction of Aristotle’s cosmos, with Earth firmly in the center

  Nineteen

  SECRETS OF THE HEAVENS: PLATO, GALILEO, AND THE NEW SCIENCE

  It is the followers of Aristotle who have crowned him with authority, not he who usurped or appropriated it to himself.

  —Galileo Galilei, 1632

  Galileo’s publisher once wrote that a picture is worth a thousand precepts.1 Galileo’s revolutionary experiments on falling bodies began with a simple ball. In order to see Plato’s role in the birth of modern science, so will we.

  I see a soccer ball lying in the grass and pick it up. I rub my hands over its bumpy black-and-white-checkered surface. I breathe the smell of grass and plastic. This is what Plato called sensory awareness, eikasia in Greek: the lowest form of human knowledge.2

  I toss the ball into the air and kick it to a friend. She kicks it back, and soon we are running and passing it back and forth. A game begins to see who can keep the ball moving without stopping. We have entered the realm of pistis, the full recognition of objects and accepted beliefs and judgments about them, like “This must be a ball” and “This must be a game”—or, in a different context, “This must be money” and “This must be justice because the judge and jury say it is.”

  As I run along, I spot another ball, a golf ball, also sitting in the grass. I stop to examine it. It’s smaller than my soccer ball. It isn’t black and white like the soccer ball; it exists to be hit with a club instead of a foot. Still, the two balls have a lot in common, I realize, starting with their shape.

  The game breaks off as I comb the meadow, looking for other similar balls: baseballs, polo balls, beach balls. I go inside and start drawing diagrams of balls, both as spheres and then as circles. What do these spheres all have in common? Then I ask: What would the perfect sphere look like?

  I pull out a ruler and compass. I begin tracing circles and measuring their diameter and their circumference. I split them into sections, first on paper, then in my mind. I am in Plato’s realm of dianoia, the realm of geometry and number.3 I continue to draw and calculate and watch as the shapes dissolve into lines, points, triangles, and parabolas. Finally, only the numbers are left. I realize they express mathematical formulae that exist in perfect proportion to each other, with each ratio (1:2, 1:3) leading constantly to a higher and higher level of abstract order.

  Then I have it. This order and proportion is everywhere, eternal, and unchanging. A single unity governs all things. I cut my last links to the sensory material world and contemplate that unity of which my original soccer ball is only a distant, dim shadow.

  A voice at my shoulder tells me gently, “Now at last you are in the realm of the real and the intelligible.” I have achieved “the highest form of knowledge,” the voice tells me, “and the vision of the Good.” This is true knowledge, epistēmē: Plato’s realm of the Forms.

  The voice, of course, is that of Socrates from Book VI of Plato’s Republic.4 My adventure with the soccer ball is in fact a retelling of the Allegory of the Cave, describing a four-step ascent for truth that matches almost exactly the ascent of love in the Symposium. Plato’s allegory of man’s upward climb from the darkness of matter to the eternal light inspired the greatest minds of the ancient world, including Plotinus. It touched Christian thinkers like the Pseudo-Dionysius and Boethius and the greatest minds of the Renaissance from Ficino and Michelangelo to Erasmus. It also lurks in the deepest recesses of modern science.

  This may seem surprising. But the old idea that the rise of modern science involved a struggle between reason and religion is not merely wrong but misleading. It was really about the perpetual struggle between Plato and Aristotle. From the death of Nicolaus Copernicus in 1543 and Galileo’s famous trial in 1633, until 1687, when Newton’s Principia Mathematica first came off the press, Europe saw a steady transformation from a view of nature built around Aristotle to a new Platonized understanding that hit the Aristotelian schoolmen like a wrecking ball hitting a plate-glass window.

  Physics and astronomy were the first battlefields in this clash, and the most famous. The fight began in the late 1500s in northeast Italy, where a gifted young mathematician would risk everything to prove that religion and science were not at odds. On the contrary, in his Platonic scheme of things, they were two views of the same Big Picture, like Ficino’s divine and profane love.

  Science and religion, he averred, were in fact emanations of the same truth.

  Not many tourists go to the northeast Italian town of Padua today, except perhaps to see Giotto’s famous frescoes in the Arena Chapel. However, for more than one hundred years after Giotto put away his brushes and closed his paint pots, Renaissance Padua was Europe’s leading school of natural philosophy, or what today we call science.

  The fiercely empirical spirit of Roger Bacon’s Oxford and Ockhamist Paris had found a new home in the University of Padua. Like Bacon, Padua’s teachers stressed the original principle of Aristotle’s philosophy of nature: that knowledge is a process of discovery using the power of our senses. As one of Padua’s most celebrated teachers put it, “All [knowledge] progresses from the known to the unknown.”5 The Paduan Aristotelians taught students that the scientist should never be afraid to venture into unfamiliar territory. He may not only discover something new, he can add new support for tried-and-true scientific principles—which, as far as Padua was concerned, meant Aristotle’s principles.

  All this sounds very modern.6 So we aren’t surprised to learn that one of Padua’s distinguished alumni was Nicolaus Copernicus or that professors there were experimenting with rolling balls on inclined planes and swinging pendulums on horizontal crossbars. Nor are we amazed that the star of Padua’s school of medicine was Andreas Vasalius, who led the first classes on human dissection since the ancient Greeks; or that in 1592, the university decided to hire a twenty-eight-year-old mathematician from Pisa named Galileo Galilei.7

  Padua sounds like the perfect environment for a sharp, inquiring mind like Galileo’s. But he was deeply unhappy there.8 Why?

  T
here are rows and rows of books on Galileo. There is even a book about Galileo’s daughter. No one has yet written a bestseller about Galileo’s father, but Vincenzo Galilei may hold the real key to understanding his more famous son.

  Galilei worked as a court musician for the Medici in Florence in the 1560s and 1570s and published treatises on the theory of music. Glancing through the pages of his works, we see diagrams that remind us forcibly of diagrams of planetary movement in his son’s works.9 The reason is that Vincenzo Galilei was a mathematician as well as a musicologist. His goal was to return musical theory to its Pythagorean roots. The father, like the son, understood the power of number not as a way to count or measure, as Aristotelians did, but rather as Number, reason’s window into the hidden order of nature.

  Vincenzo must have demonstrated this to his son more than once, by picking up his lute and strumming a single note. Then he would put his son’s finger in the exact midpoint of the string and strike it again. The note would rise exactly an octave. Vincenzo would move his finger again, and the note rose proportionately to the next octave, and so on.*

  Pythagoras was the first to demonstrate that mathematical proportion was the essence of musical harmony. He also passed to his disciple Plato the notion that proportion was endowed with creative power. By cutting the string in half, we create two octaves where there was only one. In effect, we have doubled the string’s musical output.10

  So in music, so in life. Proportion in nature is not static but a dynamic progression, like the harmonies in music. Forms in music (like Bach partitas), as in nature and architecture, grow according to an orderly progression that is both pleasing to the senses and predictable to the mind. Mathematics reveals that growth through exact but abstract formal relations. “Things are Number,” Pythagoras is supposed to have said.11 From Euclid’s triangles and spheres to modern-day fractals, it’s a concept loaded with significance.

  We pick up our soccer ball again. This time we spin it on the end of our finger. The balancing point is the axis, the fixed unmoving line passing through its middle. Our senses tell us that the ball’s axis is imaginary. Yet the axis is there, exerting its power over the ball. When we give the ball a spin, it rotates on its axis just as every sphere rotates on its axis, whether on paper or in reality.12 In geometry, it is always the relationship between the parts, not the individual parts or balls, that matters.

  Now, Euclidean geometry is a world of pure forms, but not Platonic Forms. Geometry’s lines and points and circles, like the numbers in arithmetic, are still bound to empirical reality. This is why Plato gave it a ranking just below genuine knowledge, or epistēmē. But to other admirers, that is precisely its advantage. Plato himself could not resist making his five geometric solids the divine mind’s basic building blocks for constructing the world.† Their proportionate progression in size and complexity revealed to Plato the harmonious structure of the cosmos. Later, as we’ve seen, Christian Platonists argued they revealed the workings of the mind of God.

  Galileo was an eighteen-year-old medical student when he heard his first lecture on Euclid.13 He never looked back. As a math teacher, he began studying the mechanics of motion; it was as a mathematician that he developed a lifelong interest in ballistics and fortifications, first at his alma mater, the University of Pisa, and then at Siena. It was as a math teacher that he came to Padua in 1592. It was also for love of mathematics that he left Padua eighteen years later.

  Galileo had found that for all their belief in discovery and experiment, the Aristotelians at Padua held mathematics and geometry in very low regard. They looked at him the way a Princeton professor looks at a teacher of data processing at Dutchess County Community College: as a mere technician. To his disgust, Galileo’s salary was barely one-fifth that of an equivalent professor of philosophy.14 To the orthodox Aristotelian mind, mathematics was a useful but essentially abstract science, divorced from substantial reality.15 Above all, it was detached from what Aristotle had defined as the real goal of science, which was understanding the final causes of things, from horses and soccer balls to the creation of the polis and the movement of the planets. Finding the final cause meant examining substances to discover why they existed and what their ultimate purpose was. This was an investigation for which mathematics could provide no help. As Aristotle’s own critique of Pythagoras showed, it could end up being a positive distraction.16

  Galileo’s mind was moving in precisely the opposite direction. He was looking at ways in which mathematics could help to reveal preordained order in nature, open to empirical investigation. In the process, he was getting very different results from what the Aristotelians expected.

  When Galileo arrived at Padua in 1592, he had already completed his experiments on falling bodies, including the one that is still his most famous. By dropping balls off a tall building, Galileo had demonstrated that heavier objects fell not at a faster rate than lighter ones, as Aristotle stated in the Physics, but at exactly the same rate—a rate that could also be expressed as a constant number.‡

  It was the kind of work that should have won praise from the experiment-minded, discovery-loving Aristotelians of Padua. To his dismay, however, their reaction was a great yawn. So someone throws a couple of balls off the top of a building, they said, both of which seem to land at the same time. Who cares? In their minds, the experiment said nothing about the underlying truth of Aristotle’s physical theory, which had stood the test of time for centuries and been endorsed by greater minds than Galileo’s—including the distinguished professors at Padua.

  Galileo was furious. “Of all hatreds,” he wrote, “there is none greater than that of ignorance against knowledge.”17 He knew that his experiments had shown that Aristotle was wrong twice—not only about whether two balls of different weights would hit the ground at different speeds, but also about the reason why they don’t behave as Aristotle said they would. Aristotle had assumed that the motion of a falling body must have something to do with its substance or intrinsic qualities.18 Its rate of descent would depend, for instance, on whether it was heavy or light (like a feather versus a cannonball), or made of natural substances that drew it more quickly down toward its home in the earth, or contained substances like the air in a balloon that kept it drawn upward toward the celestial spheres.

  Galileo had shown, on the contrary, that the rate of descent of an object had nothing to do with its weight or what it was made of. Motion was a state, regardless of the object, and a uniform state for all objects. Aristotle had been wrong. And if he was wrong on small issues like falling bodies, then it was possible he was wrong on the bigger ones as well, like the movement of the heavenly bodies.

  We don’t know the exact date that Galileo first read Copernicus’s On the Revolutions of the Heavenly Spheres.19 We do know the proposition that the earth and other planets traveled around the sun rather than the other way around made a huge impression on him. It was made stronger in 1597, when he was given a copy of Johannes Kepler’s first book endorsing the Copernican model. Galileo wrote to Kepler, thanking him and “congratulating myself on the good fortune of having found such a man as a companion in the exploration of truth.” Galileo soon saw it was easier to explain phenomena like tides if you assumed the earth was not stationary, as Aristotle and Ptolemy had taught, but actually in motion.20

  What really focused Galileo’s attention on the heavens, however, was the sudden appearance of a supernova in the night sky in October 1604. Such a thing was not supposed to happen. According to Aristotle, no change should ever occur in the heavens. Everything existing in the celestial spheres, like the sky and the planets, was made from an immaculate and unalterable substance called the quintessence. The heavens were, as an Aristotelian philosopher says in one of Galileo’s later dialogues, “ingenerable, incorruptible, inalterable, invariant, eternal”—indeed, as perfect and definitive as Aristotle’s own works.21

  Galileo’s regard for Aristotle was already fading, thanks to his work on motion. The
appearance of the supernova only confirmed his suspicion that the more he saw of the workings of nature, the more slipshod Aristotle’s system seemed to be. He could recall the words of his father, Vincenzo, in a different context: “It appears to me that those who rely simply on the weight of authority to prove any assertion, without searching out the arguments to support it, act absurdly.”22 Now, Galileo decided, it was time to take the examination of nature to another level.

  One of Galileo’s close friends was Cardinal Paolo Sarpi, the official theologian of the Republic of Venice. One day in 1609, Sarpi told him that someone was trying to sell Venice a Dutch-made optical device that enabled men to see distant objects like ships at sea as if they were close up. It seemed a useful device for a seafaring nation like the Serene Republic. Sarpi wondered if Galileo thought that such a device might actually work and whether the Venetian Senate should buy it.

  With his mathematician’s understanding of optics, Galileo immediately realized that the device had to use two lenses, one in a concave shape and the other convex, in order to pass light and images from one to the other.23 So he told Sarpi, Don’t buy the thing yet. Give me a couple of weeks and I’ll see what I can come up with. By the beginning of August 1609, he had made his own device, which he called in Italian an ochiale and which we call a telescope.

  Galileo’s telescope was only about as powerful as a normal pair of binoculars. But that was enough to describe ships in detail as they entered Venice’s Grand Canal a full two hours before the sharpest-eyed sailor could spot them. It also allowed Galileo to turn his probing eye loose on the evening sky. The result was a series of astounding discoveries that tore the wheels off the entire Aristotelian and Ptolemaic system.