Beauty as Symmetry (Part II)

The Education of Vitruvius’ Architect and Raphael’s Stanza della Segnatura

by Robert E. Proctor

Raphael (Raffaello Sanzio), School of Athens, c. 1510–12 Stanza dela Segnatura, Stanze di Raffaelo, Vatican Palace, Vatican StateIf I had to show through images Vitruvius’ understanding of beauty as both true mathematical symmetry and the appearance of such symmetry, I would choose Raphael’s fresco the School of Athens in his Stanza della Segnatura in the Vatican. Raphael (1483–1520) portrays Plato and Aristotle equal in height and standing side by side. Plato is holding a copy of his work on cosmology, the Timaeus, and is pointing up to the heavens. Aristotle holds a copy of hisNichomachean Ethics and points down to the earth. Raphael’s pairing of Aristotle and Plato as equals is the culmination of centuries of discussion in Western Christianity concerning the differences between the philosophies of Plato and Aristotle. “And so it appears,” St. Bonaventure (1221–74) observed, “that, of the philosophers, it was given to Plato to speak of wisdom, to Aristotle of science. The former looked mainly toward the higher things, the latter mainly toward the lower.”1 According to Raphael’s contemporary Marsilio Ficino (1433–99), “Plato deals with natural things divinely, while Aristotle treats divine things naturally.”2 These remarks concern Plato’s and Aristotle’s philosophies in general, not their particular orientations toward transcendental as opposed to aesthetic beauty. Nor is there any reason to believe that, in portraying Plato and Aristotle as equals, Raphael had our specific question of beauty in mind, or even that Vitruvius was thinking of Plato and Aristotle as he was defining symmetry and eurhythmy. My use of Raphael’s School of Athens is directed to those who may have trouble understanding how, for Vitruvius, a material form, such as a symmetrical colonnade, can be linked to the cosmos. Raphael’s pairing of Plato and Aristotle, with Plato pointing to the heavens and Aristotle to the earth, can be a powerful pedagogical visualization of a theory of beauty that seeks to link the visible to the invisible, the individual sensuous form to a transcendent truth. But Raphael’s Stanza della Segnatura does more than provide an attractive teaching tool. It enacts an understanding of beauty very similar to Vitruvius’.
As we have seen, Vitruvius begins his description of the architect’s broad education with this statement: “The architect’s knowledge (scientia) is equipped (ornata) with many disciplines (disciplinae) and various forms of learning (eruditiones), and all the works achieved (perficiuntur) by the other arts (artes) are demonstrated (probantur) according to its judgment.” (1. 1. 1) In her book on Vitruvius, Ingrid McEwen makes a strong case for translatingprobantur in the sense of to “make [a thing] credible, show, prove, demonstrate.”3 The Stanza della Segnatura does something similar: it uses formal symmetries to prove theological assertions, and thus equates beauty with truth. In his book on Raphael’s paintings, Konrad Oberhuber gives the title “The Master of Harmony” to his chapter on the Stanza della Segnatura.4 The harmony Raphael strives to achieve in this room is both intellectual and artistic—in a sense, both Platonic and Aristotelian. In Raphael’s School of Athens, Plato and Aristotle face the Disputa, the fresco on the west wall opposite them. It is commonly observed that since the center of the Disputa is an altar, Plato and Aristotle appear to be walking through the nave of a church toward this altar, as if to show that classical Greek philosophy leads to and achieves its full realization in Roman Catholic theology. Aristotle’s right hand is outstretched exactly between him and Plato and constitutes the vanishing point of the fresco’s perspective, as can be seen by extending the vertical lines of the pavement at the bottom of the painting. In the fresco of the Disputa on the opposite wall, the lines of the pavement meet in the sacred host in the monstrance on the altar. In her discussion of the Disputa, Christiane Joost-Gaugier points to the fresco’s three clearly defined horizontal levels: the angelic host, the smallest hemicycle of the painting; the second and larger hemicycle of figures from the Hebrew Bible and the New Testament; and the earthly stratum below, composed of the four Doctors of the Latin Church and other figures. These three hemicycles are cut exactly in half by the strong vertical line that goes from God the Father through Christ the Son and the Holy Ghost down to the sacred host in the monstrance placed exactly in the middle of the altar. Joost-Gaugier observes:

[i]n no other painting of the Vatican stanze, indeed in no other painting by Raphael, are order and symmetry stated in so absolute a form. . . [T]he three-in-one theme of the Disputa is extended from the Trinity to the three distinct and separate worlds it brings together in the center.5

She adds:

[t]he imaginary architecture of the Disputa bears a close relationship with the actual structure of the School of Athens on the opposite wall, with whose constructional layout and symmetry it is coordinated. The horizontal, or transversal, emphases and the equality of figure scales in both frescoes appear to have been calculated in relation to each other, a point that is reflected as well . . . in the balanced pairing of their central subject matter.6

Vitruvius, who wrote on architecture in Agrippa’s day, had speculated about proportions in both architecture and the human figure, and their sympathetic relationships, in something quite like these circle-and-square terms: Leonardo da Vinci’s drawing of these Vitruvian suppositions is famous. In it, reciprocities are suggested between the circle and the square, on the one hand, and the reach and theoretical spatial envelope of an idealized human figure, on the other. These concepts appear dramatically enlarged in the Pantheon, where the sweep of the limbs of the Vitruvian figure are expanded to colossal dimensions. This sympathy between the forms of Roman vaulted architecture and the spatial potential of the human figure is perhaps one of the principal keys to understanding the long life and continuing influence of that architecture.12These two frescoes, both separately and in their relationship to one another—since the partially enclosed space of the School of Athens seems to lead to the open space of theDisputa—are based on geometric and therefore mathematical symmetries. What distinguishes these symmetries from classical symmetries is the restless dynamism of the human bodies, which express individual character through gestures and movements. The strong one-point perspective, along with the monumental classical architecture in the School of Athens, and the three hemicycles in the Disputa, holds all of these frescoes together in one symmetrical whole. Raphael’s symmetry is much more dynamic than the symmetry Vitruvius describes. In fact, Raphael’s School of Athens and Disputa match a definition of beauty given by Roald Hoffmann, a Nobel laureate in chemistry, who, having described organic molecules as beautiful, was asked to define beauty. “Beauty,” he said, “resides at some tense edge where order and disorder, symmetry and asymmetry contend with each other in our soul, with both emotion and cognition entering into that struggle.”7

When Oberhuber writes that, not too long ago, Raphael’s Stanza was experienced as one of the “most sacred” works of post-medieval art,8 he points to what assuredly must have been the intention of Raphael and the humanists he consulted in planning the room: to give people an experience of beauty as harmony that would “prove” the truth of what seems to be the overarching belief behind all the images in the room. The reality of harmony in this case means the actual harmony of all the intellectual disciplines, the harmony between all the schools of ancient Greek philosophy and Catholic theology, and, within Catholic theology itself, the beauty and therefore the truth of the Trinity, the deepest mystery of the Christian faith, and perhaps also the harmony between thought and action, between speculative and pastoral theology. In his bookSymbolic Images, E.H. Gombrich observes in regard to Raphael’s Stanza della Segnatura that the modern dichotomy between form and content, beauty and meaning, is “inapplicable to works of High Renaissance.” Raphael and his friends, Gombrich observes, were brought up in the tradition of rhetoric: “They naturally accepted the theory of Decorum, the doctrine demanding that a noble content should be matched by noble forms….”9 
In his treatise on the ideal orator, Cicero has Crassus proclaim that, since all being is one, words and things are one, so that the more honorable the things the orator lights up with his words, the more eloquent his words will be.10 The frescoes of the Stanza della Segnatura visualize Pico della Mirandola’s vision of a harmonious synthesis between divine wisdom and all the areas of human learning. Pico, in fact, appears both in the School of Athens and in the Disputa, as the tall man on the left welcoming us into the fresco. From a Renaissance point of view, this symmetry of ideas is the highest truth imaginable. This affirmation of symmetry also had a papal political purpose.
William MacDonald says that what he calls the “new architecture” of the Roman empire, beginning around Vitruvius’ time, was based upon the “concept of monumental interior space” and defined by a “compelling symmetry.” This architecture proclaimed “the Roman stewardship of all antiquity and the imperial hope of one inclusive society.”11 Add “Catholic” to the word Roman and “papal” to the word imperial and you have in a nutshell the intended message of the Stanza della Segnatura Raphael painted for the warrior pope Julius II: “the Roman Catholic stewardship of all antiquity and the papal imperial hope of one inclusive society.”
Did Raphael succeed in persuading his contemporaries through the beauty of this room in the truth of Julius’s hope? Does he succeed in persuading us? One thing is certain concerning Raphael’s perception of the relationship between beauty and symmetry. He loved the Pantheon and asked to be buried there. The Pantheon, probably dedicated 126 A.D. and perhaps designed by the Emperor Hadrian himself, is the single most influential example of the beauty of symmetry in Western art. Its design is based on the relationship between the circle and the square, now expanded into three dimensions to become a sphere, a cylinder and a cube. In William MacDonald’s words, “the theoretical evolution of the interior surfaces of the rotunda is that of half a sphere—the dome—and a cylinder—the inner vertical wall below—all inscribed and tangent to the surfaces of an enclosing cube.” MacDonald writes of Vitruvius:

In Raphael’s School of Athens, Plato and Aristotle have passed through a great domed space and are standing under a high vaulted arch, as if they had paused for a moment as they were walking toward the Disputa. Classical antiquity is moving toward Christianity. If they were standing under the dome of the Pantheon, they would be still, for they would be at the center of the empire. But the figurative meaning I have tried to draw from Plato and Aristotle would be the same: as in Vitruvius’ understanding of mathematical and geometrical symmetry, and visual eurhythmy, the Pantheon is a concrete form perceived by the eye. But the initial moment of perception induces the experience of surprise, wonder and awe—the sense of being part of something greater than ourselves. From Vitruvius’ point of view, we have left ourselves, if only for a moment, and joined the cosmos.


1. “Et ideo videtur, quod philosophos datus sit Platoni sermo sapientiae, Aristoteli vero sermo scientiae. Ille enim principaliter aspiciebat ad superior, hic vero principaliter ad inferior.” Quoted in Konrad Oberhuber,Raphael: The Paintings (Munich and New York: Prestel, 1999), p. 102.
2. “Plato de naturalibus agit divine, quemadmodum Aristoteles, vel de divinbus naturaliter agit.” Quoted in Oberhuber, p. 102.
3. Indra Kagis McEwen, Vitruvius: Writing the Body of Architecture (Cambridge, Mass.: MIT Press, 2003), p. 319, n. 88.
4. Oberhuber, p. 85.
5. Christiane Joost-Gaugier, Raphael’s Stanza della Segnatura: Meaning and Invention (Cambridge, UK and New York: Cambridge University Press, 2002), p. 67.
6. Ibid., p. 66.
7. Skidmore College ScopeOnline Accessed 27 July 2009.
8. Oberhuber, p. 85.
9. E.H. Gombrich, Symbolic Images (London: Phaidon, and New York: Praeger, 1972), p. 100.
10. De Oratore 3. 19–20.
11. William Lloyd MacDonald, The Architecture of the Roman Empire, rev. ed. (New Haven: Yale University Press, 1982), pp. 167, 169.
12. Ibid., pp. 68–70.

 American Arts Quarterly, Spring 2010, Volume 27, Number 2.