RAPHAEL'S SCHOOL OF ATHENS
By Silenos Socrates

In 1510, upon hearing of the abilities of the young Raphael, Julius II ordered him from Florence. Once in Rome, Raphael was ordered by the pope to destroy the paintings on the walls of his council chambers in the Vatican Palace: to plaster over the frescoes by Piero della Francesca, Signorelli, Perugino, Raphael's friend Sodoma and the rest, and to cover the walls of the rooms now known as the Stanze of Raphael with subjects of his own choice.

While Michelangelo was next door painting on the Sistine Chapel ceiling his version of the Christian world, Raphael was painting on the walls of the Vatican Palace his vision of the world of Humanist thought. It is true that the soaring vaults of Raphael's temple also recall the vaults of a real-world ruin: the Baths of Caracalla, which Raphael doubtless visited and studied while in Rome. But Raphael called his picture "The School of Athens." And by this he meant, not any school that actually existed there, such as Plato's Academy, but an ideal community of intellects from the entire classical world. To house this ideal vision, Raphael created this airy, spacious hall that recalls the "temples raised by philosophy" written of by the Roman poet Lucretius.

Within the clear, uncluttered space of this imaginary setting Raphael displays, like classical statues or clear and distinct ideas, idealized portraits of his contemporaries to represent the major figures of classical wisdom and science.

In the center, their heads framed by the furthest arch through which they have just entered, Plato and Aristotle are discussing the respective merits of Idealism vs. Realism. In his left hand red-robed Plato holds his book TIMAEUS, one of the few books by Plato that had so far been recovered by the Renaissance, while explaining how the universe was created by the demiurge (interpreted by the Renaissance as a divine architect) from perfect mathematical models, forms and the regular geometric solids, the "Platonic solids," as they called them. With his right hand Plato gestures upwards, indicating that the eternal verities and forms, such as the ideals of Beauty, Goodness and Truth, are not in or of this world of space, time and matter, but lie beyond, in a timeless, spaceless realm of pure Ideas.

Dissenting from his teacher's extreme idealism, his blue-robed student Aristotle points with his right hand straight ahead out into the solid world of material reality, into the world of physical science and practical reason. In his left hand Aristotle holds his ETHICS.
These two Athenian philosophers are placed to left and right of an invisible central axis that divides them, and of a central vanishing point that disappears, in the distance between their heads, at a point at Infinity: in other words, in the mind of God.

Corresponding to this point in the visual distance is a similar point in the viewer's eye and mind. This is the apex of a visual pyramid or cone of vision whose base is the surface of the wall before him, on which the painting stands like a mirror: from that surface as a base another visual cone or pyramid recedes into the distance in the picture, focussing at the central vanishing point. In that pictorial pyramid or cone, its most prominent contour lines or "rays" are those which follow the ceiling lines or cornices where the half-barrel vaults overhead meet the walls. These two strong diagonals, along with those leading back from the floor pattern, lead the eye irresistibly to the central vanishing point where they all converge.

Notice how the series of concentric circles from the vaults, beginning with the outermost semi-circle of the Stanze arch in front, culminates in the inner circle around the heads of Plato and Aristotle. The circle is an ancient symbol of perfection: therefore these circles, and especially the inmost one, represent the mind of God, which encompasses the minds of both philosophers. This is a neo-Platonic and somewhat mystical idea of God which was circulating in Italy in Raphael's day. Moreover, Raphael and his friends were members of a philosophical circle in Rome that was intent on reconciling the philosophies of Plato and Aristotle, whose differences threatened to persist into the Renaissance, dividing the moderns as they had the ancients. Florence, for example, was then a hotbed of Platonism, whereas Milan was proud of its Aristotelian worldliness and encyclopaedic collection of scientists and engineers. And it is still said that everyone is born either a Platonist or an Aristotelian.

But Raphael and his friends held that the ancient dispute between idealism and realism was only a semantic one: that Plato and Aristotle "agree in substance while they disagree in words." On matters of substance, any point in Plato could be translated into a proposition of Aristotle, and vice versa. The verbal difference was that Plato wrote in poetic images, while Aristotle used his new logic and four-cause analysis.*
Keeping in mind its underlying unity and spirit of dialogue, let us return to the main division of forms and ideas in Raphael's picture.

Above the figures arrayed on Plato's side stands, in his niche, a naked statue of Apollo, patron god of poetry and the fine arts. Note Apollo's pose: he stands in the classical contraposto pose that goes way back to the Greek "Canon" of Polycleitus. But this Apollo, like his lyre, exhibits also a limpness, a curvaceous softness, that suggests something epicene: something hermaphroditic and at least as dionysian as apollonian, as feminine as masculine. Equally androgynous, on Aristotle's side, is the figure in the opposite niche: Athena, goddess of reason, clad in her traditional full battle dress, complete with spear, helmet and Gorgon-headed shield, which turns to stone all who gaze upon it.

Another curious criss-cross involves the heads of the two philosophers. When seen as the end points of the main diagonal axes of the painting, the heads of Apollo and Athena line up with the heads of Plato and Aristotle. Apollo lines up with Plato's head, and Athena with Aristotle's. The point where those diagonals intersect is the "divine center" between the two philosophers; the other ends of the diagonals lie at the foot of the kneeling figure by the Stanze doors to the left, and at an equal distance in from the right hand corner. But (and especially from this right side) the eye wants to see another strong pair of diagonals starting from the extreme lower corners of the picture: and along these diagonals the heads of the gods line up with their "opposite" philosophical heads: Apollo's with Aristotle's, and Athena's with Plato's. Thus the dialectical interplay of ideas goes on.

Arrayed on either side of Plato or Aristotle are the main thinkers of the classical world. The philosophers, poets and abstract thinkers are allied on Plato's side. The physical scientists and more empirical thinkers are on the side of Aristotle. Only a few of these ancient thinkers can be identified with much success. But the fresco's great variety is constructed out of many discrete groups of figures, each group with its own center and focal point. And within most of these, the central thinker is identifiable.

To the left of Plato the woman with the child is said to be the poet Sappho. The yellow-robed figure further left is said to be Plato's teacher Socrates.

The intense little school in the left foreground is huddled around another of Plato's masters, the Greek mathematician and mystic Pythagoras. Here he is demonstrating, not his famous Pythagorean Theorem, but his theory that ultimate reality consists of numbers and harmonic ratios.

Pythagoras held that the "best" numbers were the "triangular" numbers — those that are simple sums of successive integers or whole numbers. The best of these, the "perfect" number, is 1 + 2 + 3 + 4 = 10. This he called the "divine tetraktys," the holy four-foldness, which he held to be the number of Justice. Raphael has drawn a picture of this mystical number on the bottom half of the slate being held before Pythagoras by a young assistant. Drawn in Roman numerals, it looks like this: Now you can see why the number 10, and each of the four numbers that compose it, are called "triangular" numbers. The diagram shows how each of the successive integers, like a row of blocks on the face of a pyramid, contains the numbers above it, to create bigger and bigger "triangles."

On the same slate, right above this magic number, Raphael has drawn a beautiful diagram of Pythagoras' theory of the harmonic ratios. These are the ratios that determine not only those heard harmonies such as Apollo's lyre produces, but also the inaudible harmonies of the celestial spheres. Raphael's diagram shows how a single string can be divided into three different lengths to tune or produce the four most harmonious strings of the seven-stringed lyre to the musical intervals of the octave, the fifth and the fourth (labelled by Raphael in Greek: diatessaron, diapente, and diapason).

Here is how Pythagoras discovered the mathematical ratios underlying these harmonic intervals, and what that discovery meant for him, for Plato, and for Raphael and the Renaissance:

Upon hearing the musical intervals produced by a series of hammers in a blacksmith shop, Pythagoras rushed home to experiment with lyre strings and flute pipes. What he learned is that the most harmonious musical intervals or chords such as the octave, fifth, and fourth correspond to strict mathematical ratios — those created by dividing or stopping the string or pipe at its mid-point, at two-thirds of its length, or at three-fourths of its length. The ratio between the half-stopped string or pipe and the unstopped full-length string or pipe is 1:2, and the musical interval between the two tones those produce is an octave. The ratio between a string or pipe stopped at two-thirds of its length and the whole string or pipe is 2:3, and the interval between the tones these produce is a musical "fifth." The ratio between a string or pipe stopped at three-fourths of its length and the unstopped whole length is 3:4, and the interval between the tones these produce is a musical "fourth."

So the mathematical ratios that underlie the physical basis (hammers, lyre-strings, flute-pipes) of the sounds that strike our ear as in beautiful harmony are these: for the octave l:2, for the fifth 2:3, for the fourth 3:4.

But — wonder of wonders — these numbers correspond to the first three "triangular" numbers, to the first four rows or "triangles" of the Pythagorean tetraktys. Is something mystical as well as musical and mathematical going on here? Pythagoras and his followers thought so.

Inspired by this discovery, the Pythagoreans now made a tremendous intellectual leap: they extrapolated from the physical and mathematical ratios underlying musical harmony to similar ratios or harmonic patterns underlying the cosmos, the entire universe. Just as different vibrating strings in a lyre create a musical harmony, they reasoned, so the sun, moon and planets travelling along in their circular orbits vibrate in a celestial harmony. The lowest note is produced by the innermost orbital motion of the moon; and the highest by the outermost circle of the fixed stars. For Pythagoras, the whole universe was thus like an enormous lyre — a lyre with circular strings or cords, producing the chords of a celestial concert.

Later, with Plato and the Renaissance, these planetary orbits were transformed from circles into hollow spheres, and then into hollow crystalline spheres. Hence the Harmony or Music of the Spheres.

Why can't we hear the music of the spheres? Because our souls are too gross and impure. Like a rock fan whose eardrums are too damaged to hear Mozart, the ports of our spiritual ears are so contaminated and plugged up with the noise and clamor of sensations and passions that we simply cannot hear the pure music of the cosmos. Here is how Shakespeare puts it:

... look, how the floor of heaven
Is thick inlaid with patines of bright gold;
There's not the smallest orb which thou behold'st
But in his motion like an angel sings,
Still quiring to the young-eyed cherubins;
Such harmony is in immortal souls;
But, whilst this muddy vesture of decay
Doth grossly close it in, we cannot hear it.
— The Merchant of Venice, Act V, scene I.

Some said, nevertheless, that a select few, whose souls were pure enough, could hear the music of the spheres even here below. Others said No, only Pythagoras himself could hear the music of the universe.

Plato, by the way, held that there is no actual music of the spheres. Otherwise, he bought most of the Pythagorean system of a world created out of numbers, the five regular ("Platonic") solids, and the Pythagorean concept of the cosmos as a set of concentric circles or hollow spheres nestled onc inside the other. This is the cosmic geometry that was explained in Plato's TIMAEUS, and which inspires the geometric design of Raphael's painting.

The dark-skinned scholar in the white turban and green robe who leans over Pythagoras is the Arabic philosopher Averroes. It is thanks to him that the philosophies of Plato and Aristotle were transmitted to the west.

In the right foreground are concentrated two groups. An absorbed group of students huddles around the stooped figure of Euclid (or maybe Archimedes), who is demonstrating some geometric proposition with a pair of compasses upon a slate. Behind him, in yellow robes, stands the Greek astronomer and geographer Ptolemy, holding his globe of the earth. Behind him is the Persian astronomer and philosopher Zoroaster, holding a sphere of the fixed stars. Just to the right of these two is Raphael himself, [the only figure in the School of Athens] who gazes directly back at the viewer.

Somebody important seems to be the impressive white-haired figure standing over behind Zoroaster's star-studded sphere. But neither he nor any of the remaining classical figures in the picture have been identified. Except the two isolated figures in the center.

Sprawled in solitude on the steps before Aristotle is the Cynic philosopher Diogenes, who lived like an unwashed hippie in his rented barrel on the streets and who, when visited by Alexander the Great and offered anything he wanted, replied: "Please move out of the sunlight in front of my barrel!"

Counterweight to the anti-social Diogenes is the brooding figure on Plato's side, the dark-bearded, purple-robed figure meditating on the marble block down front, skewed out from the rigid geometric system of the floor pattern. This is supposed to be Heraclitus, the pre-Socratic philosopher whose enigmatic utterances fit into nobody's System: "Strife is Justice," "No man can step into the same stream twice," and "The way up and the way down are one and the same."

There is an interesting story or two behind this solitary "Heraclitus" figure. In the first place, he is the sole figure in the whole "School" who is totally absent from Raphael's preliminary working drawing or "cartoon" of the painting. Technical examination of the fresco confirms that Heraclitus was painted in later, as an afterthought, on an area of fresh plaster put on after the adjacent figures were completed. This block-like figure plugged up a visual hole, a tunnel of white light and marble that streamed out in front of Plato and Aristotle. But there is a more interesting explanation for Raphael's last-minute addition.

Heraclitus looks a lot like Michelangelo, who was at this time slaving away next door on the Sistine Chapel ceiling. It is said that despite Michelangelo's efforts to keep his work in total secrecy, Raphael managed to sneak into the Chapel to see what his anti-social older rival was up to. And sure enough, not only does the Heraclitus figure look like Michelangelo; in its block-like sculptural solidity, it looks like it was painted by Michelangelo.

They say imitation is the sincerest form of flattery. And Raphael's inclusion of Michelangelo along with himself and his friends among the immortals is also a great tribute to him. For it was part of the Renaissance's neoPlatonic mystique that immortality in this world could be acquired by becoming the reincarnation, however brief, of some immortal deity or hero of antiquity. The doctrine of reincarnation itself came to them from Pythagoras via Plato; and it was believed in at the revival of Plato's Academy in Florence, whose founder was rumored to be a reincarnation of Plato.

What other contemporaries did Raphael idealize and immortalize by using their portraits in the School of Athens to reincarnate ancient philosophers and scientists? The white-robed young man with the angelic face standing above Pythagoras is said to be . Standing next to Raphael on the extreme right is his friend the painter Sodoma — he whose frescoes Pope Julius ordered Raphael to obliterate to make way for his own. The model for Zoroaster is said to be the humanist scholar Pietro Bembo — probably a prime source of many of Raphael’s ideas.

But the greatest influence on Raphael was his friend and mentor, the architect Bramante, portrayed here as Euclid (or Archimedes). It was from the older, more experienced Bramante that Raphael probably got most of the secret geometry and architectural composition of his painting, as well as many of the philosophical ideas in it. Though the vaults overarching the figures could have been studied by Raphael during visits to the Roman ruins of the Baths of Caracalla, these and the half-hidden central dome beyond were also part of Bramante’s design for the new St. Peters, already under construction.

As a painter, however, Raphael owed most to his teacher Leonardo da Vinci. If the viewer can recall Leonardo’s red-chalk self-portrait, he should be able to recognize him here in the School of Athens. It is Leonardo who is painted here as the reincarnated Plato. But why Leonardo? Leonardo had found Florence such a stuffy hothouse of otherworldly Platonism that he left it to join the more congenial circle of “Aristotelian” scholars, scientists and engineers at Milan. True, Leonardo made “extraordinary and most beautiful figures” of the five Platonic solids for the mathematician Pacioli to illustrate his book, Divine Proportions. But that does not make Leonardo a Platonist. Was it Raphael’s admiration and preference for the thought of Plato, combined with his respect for his teacher, that led him to identify the two men? Was this part of his strategy for re-uniting the philosophies of Plato and Aristotle? Perhaps. But it is also true that in Leonardo himself there was a certain dreamy and romantic quality — his visionary schemes hardly ever being realized in the real world. And perhaps it is that slightly quixotic quality which makes him, as it makes each of us, a Platonist?