The Cave and the Light

by Arthur Herman

  The accusations were brought not by the Athenian government, but by three private citizens. Socrates tried to deflect their charges, including atheism and impiety, with his usual caustic sense of humor. He even suggested that his “punishment” should be receiving a pension from the city of Athens for services rendered: “for I spend all my time going about trying to persuade you, young and old, to make your first concern not your bodies or your possessions but the highest welfare of your souls” and teaching them that goodness is the true wealth both for the individual and for the state.27

  The jury members were not amused. They chose to condemn to death the man who for decades had harassed and harried them with his inconvenient questions.

  As the condemned man, Socrates spoke last. He remained quietly defiant. He warned the jury that his ultimate responsibility was not to them, but to his conscience, or what he called his “inner voice”: his own soul. For his soul’s sake, he would not stoop to servility in serving the Thirty Tyrants. Now he would not stoop to indignity by pleading for his life. “But I suggest, gentlemen, that the difficulty is not so much to escape death; the real difficulty is to avoid doing wrong, which is far more fleet of foot”—as their own verdict evidently proved.

  As for death, Socrates told the jurors (in words that were probably as close as Plato came to giving an exact transcript of his master’s words), “nothing can harm a good man either in life or after death; and his fortunes are not a matter of indifference to the gods.” If Socrates was right, death would even be a blessing. “I [go] to die, and you live,” he said as a farewell, “but which of us has the happier prospect is unknown to anyone but God.”28

  A month later he was dead.

  * * *

  * Thales’s pupil Anaximander, for example, seems to have considered the balance among the four elements as a matter of proportion and cosmic justice. It may be the first time proportion and justice were linked in Greek thought.

  † For example, the statement, “One of my black swans is white” is a clear contradiction in terms and obviously false, even if we’ve never met any of your swans.

  Three

  THE MIND OF GOD

  God is always doing geometry.

  —Saying attributed to Plato

  Socrates insisted that it was better to suffer wrong than inflict it, and his last days proved it. It’s why Cicero dubbed Socrates “the wisest and most upright of men” and why centuries later, Mahatma Gandhi took him as a personal role model and called him “a soldier for Truth.” Socrates’s quest to lead his fellow citizens to a higher vision of themselves and their society, while living that example himself, even when it cost him his life, raised him to the level of the heroic, where he has stayed more or less ever since.1

  Plato, his heartbroken disciple, took things a step further. The fact that Athens had sentenced Socrates to death was more than an unjust act. It was final proof that human institutions were flawed by their nature, even those ostensibly concerned with democracy and justice, because they are all based on opinion and illusion. The fate of Socrates proved to Plato that true knowledge lay permanently beyond the reach of the masses. Indeed, as he implied in the Myth of the Cave, they are instinctively hostile toward its devotees. Truth on Plato’s terms is destined to be a quarry reserved for a tiny minority, those trained in the rigors of dialectic and who are ready to make the same arduous climb out of the cave that Socrates made, in order to discover how to lead a virtuous life and show others how to do the same. For the purposes of this philosophical safari, he created his famed Academy in Athens, and composed his dialogues to serve as basic texts for his students. Through their dramatic settings and vivid characters, Plato turned Socrates’s insights into a complete theory of ethics (as in the Philebus), of love and friendship (the Symposium), of language (the Phaedrus), and of politics (the Gorgias and Republic).

  As one would expect from an Athenian, Plato returns to politics again and again. Even late in life when his own thinking had moved on to questions like the origin of the universe, he still found time to write about the practical side of running a fair and wise government in his Laws. The Gorgias, Republic, Statesman, and Laws: All reveal Plato’s political thinking in different stages. The one common thread is Plato’s desire to avoid the kind of disastrous democratic politics he had seen wreck Athens and kill his teacher. Politics on Plato’s terms always involves the search for a foundation more elevated and certain than custom or public opinion or majority rule, because all of them reflect, to a greater or lesser degree, the realm of ignorance and error. It would be one of the major sources of conflict with his student Aristotle.*

  Yet none of this—not even Plato’s politics—would be possible, or even imaginable, without Plato’s God.

  Socrates talked a lot about God and the gods. He even told his jurors that “God orders me to fulfill the philosopher’s mission of searching into myself and other men,” and he seems to have believed that his inner voice that kept urging him to ask questions and seek knowledge was indeed the voice of God.2 Ironically, one of the charges against Socrates was atheism. It was so evidently false that Socrates brushed aside the accusation. But the fact remains that Socrates’s God was clearly very different from the ones ordinary Athenians were used to: Zeus, Apollo, and the other deities of the classical pantheon with their superhuman powers and more than human appetites and foibles. It was even different from the impersonal divine forces explored by secret societies like the Orphic and Pythian mystery cults.3

  The God that Socrates presented to his disciples stood above and beyond the familiar myths and rituals. Socrates’s God shares the same transcendent immortality as the soul and lies beyond all material space and time. He dwells naturally in the same afterlife as the Forms: indeed, Socrates’s entire doctrine of recollection depends upon it.

  In some of the later dialogues, Plato has Socrates give us a pretty clear picture of this afterlife.† At the end of the Republic, for example, he outlines how the just and the unjust receive their rewards and punishments after death, in which every wrong we have committed against others requires a tenfold punishment, and “those who are responsible for many deaths, for betraying a state or army, or have cast others into slavery” must pay ten times for each offense.4

  Socrates describes souls on the march through a mighty chasm past judges and guardian spirits, who snatch away the guilty, skin them alive, and impale them on thorns along the roadside, prior to being cast into Tartarus, or hell. The souls of the just, by contrast, move across a meadow to a realm of splendor where they are assigned new bodies by lot, all under the dome of the sky supported on a “shaft of light stretching from above straight through heaven and earth, like a pillar [and] resembling a rainbow, only brighter and clearer.”5

  It is striking how much Plato’s vision resembles later Christian accounts of heaven and hell; nor is it entirely coincidental. But serious questions remain about this afterlife, and the soul’s place in it, that Socrates never answers. Plato’s Socrates never takes time to flesh out the relationships between God and the soul, the afterlife and the Forms—and never explains how these Forms actually shape the material reality of appearances in this world.

  Toward the end of his life, however, Plato himself did. And the answer he arrived at was so astonishing, so complex, and yet so persuasive that it formed the bedrock of Western religious and scientific thinking for the next thousand years. Without it, Christianity as we know it might not exist. Neither would modern physics or astronomy.

  Plato’s startling vision appears in the most enigmatic of his writings and one of his last: the Timaeus. It must have been written when he was seventy.6 Compared with earlier dialogues, it is a strange, almost impenetrable work. The Timaeus is made even more mysterious because it opens with a long description of a lost civilization and a lost continent, which Plato called Atlantis. It’s kindled the imagination of thinkers and writers—even moviemakers—ever since.‡ But Atlantis plays little part in the main thrust o
f the dialogue.

  Like most of Plato’s other late writings, the Timaeus pushes the figure of Socrates into the background. We have to assume that Plato is no longer giving an account of his teacher’s doctrines, but reveals his own thoughts. In this case, Plato chooses a wandering scholar named Timaeus to act as his spokesman. Timaeus, as it happens, is from Italy—a crucial clue to understanding the radical new direction Plato’s thought was about to take.

  What Timaeus offers his listeners, and the reader, is nothing less than a complete account of the creation of the universe. It is a vision of creation (the Greek word is genesis) dominated by a rational God, acting as Supreme Creator. In the process, Plato demonstrates that the ideal Forms, the models of perfection out of which God has fashioned the visible world, are actually numbers. To do this, Plato turns to the most enigmatic of Socrates’s predecessors, and the one whom Plato would make into the most influential of the pre-Socratics: the mystical mathematician Pythagoras.

  By Plato’s time, the name Pythagoras was already shrouded in legend. There is no doubt he had been an actual person, and although details of his life are skimpy, he was probably alive c. 530 BCE.§ Apart from a few snippets preserved by other writers, absolutely nothing survives of his writings—assuming he wrote anything at all. However, we do know that while living in the Greek colonies of southern Italy, Pythagoras established a secret brotherhood of fellow mathematicians, who preserved his famous theorem (the one that the slave boy in the Meno discovers, with Socrates’s help, that the square of the hypotenuse of any right-angle triangle is equal to the square of the opposite two sides), and his experiments in music theory. (Pythagoras was the first to discover the mathematically proportioned intervals of the harmonic scale.) But above all, Pythagoras was convinced that number was the secret language of nature.7

  Where did Pythagoras get this idea?

  Possibly from the Babylonians, who were the masters of mathematics in the early ancient world. Perhaps also from the Egyptians, who pretty much invented geometry to survey and resurvey landholdings after periodic floodings of the Nile.8 Pythagoras’s contribution was to take their geometry (literally “earth measure”) in a new, more abstract direction. He wanted to show that geometry was not just a way to measure things like land or build monuments like the Pyramids, but a way to understand the fabric of reality. “Figures as archetypes, not figures for profit,” he is supposed to have said. The Pythagorean program was to prove that math and geometry are the starting points of Being itself, and that “all things are numbers.”9

  Pythagoras started with the number one—literally a pebble in the sand. One (the Monad) forms the starting point for all numbers and geometry, while two pebbles (the Dyad) generate the line and spatial extension—literally the base line of all subsequent forms.10 Putting one and two together gives us three. The Triad serves as the three points of the triangle, Pythagoras’s first geometric surface and (thanks to Pythagoras’s theorem) the basis of the square and every other geometric figure.

  Then Pythagoras added an imaginary fourth pebble standing above the other three. This creates the pyramid, or geometry’s first solid form, as the relations between the numbers and their ratios move into the realm of three-dimensional actuality.11 The number four also served for what later Pythagoreans called the Tetrad, the sign of harmonious completion. Just as four intervals form the musical scale, so there are four seasons in the year and so on.12

  In the digital age, Pythagoras’s belief in a number-generated reality might seem less far-fetched than it used to.13 Plato certainly didn’t find it far-fetched. By his time, a mathematician named Archytas was reviving the Pythagorean teachings at a school in Tarentum (modern-day Taranto), on the inside heel of the boot of south Italy. We know Plato went to Italy at about the same time and made contacts with members of Archytas’s circle and learned of their belief that nature, like man himself, is governed by a permanent geometric and mathematical order.

  Pythagoras taught Plato that number was the language of nature.

  It is also tempting to argue that what Plato found in Pythagoras was the kind of anchor that had been missing in his life with the death of Socrates.‖ In the world he knew, the values of the traditional Greek polis and city-state, and the moral and social consensus on which they rested, were falling apart. Everywhere Plato looked, he saw nothing but chaos and disorder.14

  In Pythagoras, by contrast, he found a reassuring vision of the opposite: a mathematically harmonious cosmic order. After his Pythagorean encounter, Plato became obsessed with unlocking the final secrets of a sacred geometry that would bind human beings to the cosmos and the starry heavens—a cosmic order graspable by the workings of Socrates’s a priori reason.15

  Any informed reader opening the pages of the Timaeus has to admit that Pythagoras had a decisive impact on Plato, so decisive that one ancient writer accused him of outright plagiarism.16 Be that as it may, the Timaeus is the crucial Platonic dialogue, preserved through the centuries. It firmly embedded mathematics and geometry in the Western understanding of reality and allowed Plato to solve the questions about the soul and God that Socrates had raised but never fully answered.

  In the dialogue, Timaeus (who is an obvious stand-in for Plato’s friend Archytas) gives an account not simply of how creation takes place, but, just as important, why. Timaeus admits that giving “a consistent and accurate account” of God’s purposes through reason alone is impossible. Still, he says, our understanding must be rooted in the fact that, being the supreme source of all goodness and perfection, God would want all things to be as like Himself as possible and therefore as perfect as possible. Thus, “finding the visible universe in a state not of rest but inharmonious and disorderly motion, [He] reduced it to order from disorder, as He judged that order was in every way better” than disorder.17

  To do this, God decided to use as His model “the highest and most completely perfect of intelligible beings,” namely Himself. If the world “were manufactured according to [that model’s] pattern,” then the universe would be not only the most perfect creation possible, a union of body and soul, but also unique—indeed, our universe is and will continue to be His only creation.18

  It is the relation between number and figure, Timaeus affirms, that allows God to do this: “In the first place it is clear to everyone that fire, earth, water, and air are bodies, and all bodies are solids. All solids again are bounded by surfaces, and all rectilinear surfaces are composed of triangles.”19 The two basic forms of triangles, right angle and equilateral, form for God (and Plato) the basic architecture of matter, from squares to the first solid figure, the pyramid—which is also the form of fire. The cube (made up of four squares or eight triangles) forms earth; the eight-sided octahedron (eight squares) defines air; the next elaboration of square and triangle, the twenty-sided icosahedron, is the basic building block of water.

  The most complex of all is the dodecahedron, a multisided solid that defines the sphere. It alone is made not from triangles, but from the pentagon—which also happens to be Pythagoras’s own figure for the irrational numbers like the square root of 2 or the square root of 3, from which a mathematician can generate the so-called Golden Section, traditionally the most harmonious physical scale for everything from architecture to pictorial landscapes.a From Plato’s perspective in the Timaeus, the sphere is the most perfect shape of all, with which God “embroidered the heavens” and the earth itself.20

  Out of these five geometric solids, which mathematicians still refer to as the Platonic solids, God goes on to generate the cosmos, which in turn is fitted within the copy of Himself He has already made, the World Soul. The Timaeus gives us an extraordinary picture of God literally cutting strips of “soul stuff” in proportion with the intervals of the musical scale (4:4:2:1) and then laying them crosswise, into a +. Then God bends each strip into a circle, so that He ends up with two circles at right angles to each other, which eventually encompass the entire sky.21

  “And he m
ade these circles revolve in contrary senses relative to each other,” Timaeus says; some according to the same invariable motion—which is the motion of the fixed stars—and others according to variable but harmoniously proportioned motions—the motion of the planets and the sun. Within this great spherical arena, the God of the Timaeus “proceeded to fashion the whole corporeal world within it, fitting it center to center.” Then He created the human soul and its three parts—reason, emotion, and appetite—in order to fit them into the human body.22

  And so it goes. It is without doubt the most grandiose vision of ordered creation the ancient world had ever seen or ever would see. The material world acts as a kind of receptacle into which a plan of divine perfection is steadily poured. At each step, we see how everything fits into the cosmos as a totality, extending from the “music” of the heavens (so called because the planets are spaced in the Timaeus according to musical harmonies) to the specifications of the human body, right down to every living and nonliving thing. As Plato puts it, where “we can trace divine goodness [that is, perfection] we can trace divine purpose”; and where we see material creation, we see the conscious, ordering mind of God.23

  What God has put into the world, a preordained mathematical order, we can trace back to God through that same order. Like Leonardo da Vinci’s famous drawing of the man standing in the square and circle, divine geometric proportion turns out to be written into every feature of our lives and is only waiting to be revealed like a crucial message inscribed in invisible ink. Thanks to Pythagoras’s mystical math, Socrates’s cave suddenly comes alive in the divine order and meaning.