Piero's Light

by Larry Witham

  Within the writings of Albrecht Dürer, Giorgio Vasari, and Daniele Barbaro, art historians have found the modern origin of what today is called “art theory,” which is distinct from art-practice manuals and, in turn, is essentially derived from the theoretical (and speculative) Platonist tradition. Barbaro spoke of the Platonic “secret intelligence” behind mathematical forms, but Dürer and Vasari went further. Their writings proposed two alternative ways to reconcile the Platonic Idea of Beauty with the finite world of the artist, his inventive mind, and his materials.24 Vasari in effect said that the artist’s mental idea can merge with the Platonic Idea, thus giving art an improvement on nature plus a quality of divinity (something that Plato had not quite allowed). This was the origin of the modern neoclassical definition of Beauty: beautiful creations enhance or perfect nature and participate in a divine Idea by way of their images and aesthetic effects.

  By contrast, Albrecht Dürer had offered a more brooding solution to how the Platonist Idea of Beauty could make contact with earthly art. Dürer, perhaps in the tradition of German mysticism, offered a bridge that was something like the modern idea of intuition, an innate ability of the human mind to be in the tran­scen­dent world and the physical world. As Dürer said, “A good painter is inwardly full of figures [images], and if it were possible that he live forever, he would have from the inner ideas, of which Plato writes, always something new to pour out of his works.”25 From the days when the revival of Platonism had introduced concerns about mathematics and geometry into Renaissance art, its influence had grown and spread. Both art theory and the perennial debate on the nature of Beauty may be seen as two of its children. To take a step further, Platonism did more than influence the psychology of art. It would also play a role in the coming Scientific Revolution, and this by way of Platonist cosmology.

  It has always been tempting to place two such prominent features of the Renaissance as Platonism and linear perspective at the threshold of the Scientific Revolution. Historians disagree on the exact causes of scientific progress. But the arguments for the influence of Platonism, mathematics, and the new visualization of the arts have been made often enough.26 If Platonism gave early scientists a new model of the cosmos (an alternative to Aristotle), the arts gave new tools: visualization and quantification. The tools of the new artisans drove progress in architecture and mapmaking, for example, and in inventing the two characteristic devices of the Renaissance, the telescope and the microscope.27

  More generally, the growing use of artistic perspective had generated a more confident foundation for observing the real world. The arts may have led to the “rationalization of space,” which would prove to be a key feature of modern physics.28 It was also realized that diagrams, drawn based on perspective, could be matched up with mathematical calculations or measurements. In this, the modern scientific method was born. It became a method with a two-part dynamic. The scientist produced both a visual model and a mathematical equation, trying to fit the two together exactly, or to refute either one in the process of scientific hypothesis and testing. By this approach, early modern astronomy and physics made their first great strides, and the same model-and-equation method would be applied to the biological sciences in the far future.

  The chief obstacle for the new astronomy in the age from Copernicus to Galileo—a span across the sixteenth and seventeenth centuries—was not necessarily religion or the church. It was the dominance of an Aristotelian cosmology, and by extension the church’s adoption of the Ptolemaic astronomical calendar, both of which placed Earth at the hub of things. Renaissance Platonism would question the age-old Aristotelian cosmology, helping to open the way for new thinking in science and astronomy. At the end of Piero’s generation, the figure who established Platonism as major school of thought was not a scientist, but a theologian, Marsilio Ficino. His voluminous Theologia Platonica (completed in 1482, a decade before Piero’s death), along with his many commentaries on the texts of Plato, allowed for a learned Platonist subculture to develop within the Aristotelian world of science. Anyone interested in mathematics, light, optics, astrology, and astronomy read Ficino’s translations and commentaries. Those readers would include the standard-bearers of the new science, Nicolaus Copernicus, Johannes Kepler, and Galileo Galilei.

  There are two ways that Ficino’s Platonism set the stage for new thinking in science. First was his discussion of the Sun and light, and second was his mathematical universe. Ficino perpetuated the tradition of “light cosmology.” For many Platonists, including Copernicus, the metaphysical centrality of the Sun—as in Ficino’s claim that “all celestial things appear by divine law to lead back to the Sun”—was plausibly a more impressive idea in Platonism than the contrary assertion in Plato’s Timaeus that the Sun orbited the Earth like a planet.29

  Ficino also promoted a “light psychology.” It was a parallel to the kind of Platonist art theory found in Dürer and Vasari and, similarly, Ficino’s thought was a prelude to more modern notions of intuition. For instance, this role of intuition or insight was suggested by Ficino’s Platonist psychology of optics. “When anyone sees a man with his eyes,” Ficino wrote, “he creates an image of the man in his imagination and then ponders for a long time, trying to judge that image. Then he raises the eye of his intellect to look up to the Reason of Man which is present in the divine light. Then suddenly from the divine light a spark shines forth to his intellect and the true nature of Man is understood.”30

  Ficino did not know the mechanism by which light rays stimulated the retina, sending signals to the physical brain with its one thousand trillion neural connections. But he essentially was accurate in the two-step process. The first is purely mechanical, while the second—interpreting sense data—is mentally subjective for each individual, subject also to divine illumination if one cares to add that theological element.

  Ficino’s second contribution to undermining the Aristotelian hegemony in science was his literary explication of Plato’s most basic work on the physical cosmos and natural world, Timaeus. Plato extolled number, unlike Aristotle, who preferred to put things in various categories, such as substance and accident as one example, or mineral, plant, and animal as another. “Plato, in the manner of the Pythagoreans, seems to build natural phenomena on the principles of mathematics,” Ficino wrote. “Natural phenomena dissolve into shapes and numbers as if into their limits.”31 Ficino’s commentary, called Compendium in Timaeum (1484), was owned by Galileo and would frequently be used in lectures at Italian universities.

  Plato and Aristotle differed in one other important respect. Aristotle’s system said that the higher elements in the cosmos are different from the lower, and, being unchanging, the higher move only in circular motion while the lower move in a rectilinear (straight) fashion. In the Platonist cosmos, as summarized by Ficino, all the elements in the universe are homogenous (not higher and lower), and therefore the rectilinear motion of things can be translated, by mathematical calculations, into circular motion, which becomes the basis for calculating orbits, momentum, and other central concepts in physics.32

  By the time of Kepler (born in 1571) and Galileo (born in 1564), the Platonist subculture that had been nurtured by Ficino was affecting their scientific outlook. Kepler spoke for both himself and Galileo when he wrote: “The Creator, the true first cause of geometry … as Plato says, always geometrizes… . [His] laws lie within the power of understanding of the human mind.”33 Temperamentally, Kepler and Galileo took different approaches to their work, of course. Mystically drawn to the Sun, Kepler was more willing to extend Platonic geometry and mathematics into the heavens. Galileo, by contrast, was a down-to-earth character.34 He jettisoned the dreamy world of the stars to focus only on objects he could see or touch, as illustrated by his building a case for heliocentricity on seeing the Moon, interpreting tides (though wrongly), and, in part, rolling objects down inclines. His feet firmly on the Earth, Galileo also was willing to debate the Church
’s Aristotelian theologians, who insisted that the Earth did not move.

  If the theologians were being stubborn, it was not just for stubbornness’s sake. They had their own doctrinal dilemmas to deal with. Foremost was that Aristotle’s philosophy allowed Catholic theology to explain the Eucharist—the body and blood of Christ in bread and wine—under the categories of substance and accident. Aristotle’s Earth-centered world came with the package, so questioning Aristotle’s cosmology also questioned the Eucharist, the basis of the priesthood’s role in the Church. After Thomas Aquinas, “Aristotle’s philosophical vocabulary becomes the basic idiom of Scholastic theology and philosophy … waxing and waning with Scholasticism,” according to one Catholic authority.35 In Galileo’s era of the Counter-Reformation, Rome made the Earth-centered universe a kind of doctrinal litmus test as it revived scholastic Aristotelian theology and reasserted its use of the Bible to counter Protestants; in both the Bible and Aristotle, the Earth did not move.

  Thanks to the Renaissance artists, there was more than just Aristotle, Plato, or the Bible by which to visualize the world. In the tradition of Piero (followed by Leonardo and Pacioli), Albrecht Dürer would draw page upon page of polyhedra, and this at a time when book publishing made such illustrations widely available. Kepler studied Dürer’s precise drawings; by this he surely learned something about the art of visualization of the heavens. Such visualizing became a new rage of the times. A growing number of mathematicians and decorative draftsmen used perspective and polyhedra as a great analytical plaything.36 Other books followed in the Dürer tradition, stuffed with diagrams of visual rays, extreme perspective on many shapes, architectural decorations, Platonic solids, multifaceted polyhedra, and star-like crystalline structures that seemed to come from another world.

  As his own contribution, Kepler would chart the basic system of the thirteen Archimedean polyhedra, drawing and naming each. He felt that the older humanist geometers in Italy, by their imprecision, were “in a dream.”37 Still, Kepler was indebted to their revival of visual geometry, and, to be sure, Kepler was dreaming a bit himself at this early stage of his work. He began his scientific quest by believing that the five Platonic solids defined the orbits of heavenly bodies. He gave up that mystical chimera when he discovered the mathematics of elliptical orbits.

  Galileo, in turn, if not particularly interested in the technicalities of linear perspective, was attracted to the power of drawing in three dimensions. Galileo taught drawing, since perspective had become part of humanist studies in the Italian universities; he famously drew the changing shadows on the Moon’s surface. It has been argued, furthermore, that Galileo’s aesthetic preference for perfect circles prompted him to view planetary orbits that way, despite Kepler’s new theory of elliptical orbits.38

  Ellipses notwithstanding, Galileo may have followed other pointers by Kepler, pointers to Plato’s Timaeus. It was in that book and in Ficino’s Platonist writings that Galileo found the poetically expressed ideas that God had made the universe by turning rectilinear motion into curved motion. Whether for rhetorical or scientific reasons, Galileo famously evoked Plato on the topic of motion in the Italian astronomer’s two major works, Concerning the Two Chief World Systems (1632) and Two New Sciences (1638).39

  There is no easy way to translate Plato’s poetically stated cosmology in Timaeus into the precise mechanics of Galileo’s final theories. Poetry aside, the Platonic subculture in Italian science was an important prod for the new direction: the universe was one substance, motion was mathematically continuous, and the key to science was matching a visual model (an experiment or drawing) with a mathematical law.

  The new astronomy, meanwhile, had turned attention to problems of sight. Kepler recognized that human error in judging the night sky properly originated in the error of the eye. Over the century that separated Piero from Kepler and Galileo, the science of classical “perspectiva”—the most comprehensive idea of seeing—remained unchanged. This is made evident by the fact that the texts that artists such as Ghiberti, Piero, and Leonardo had read, those by John Pecham (Perspectiva communis) and Erasmus Witelo (Perspectiva), were the same ones found in the libraries of Kepler and Galileo.

  Then Kepler tipped the scales. He took the first major step in understanding how the eye collected so many visual rays and focused them into a remarkably accurate and singular image.

  Kepler had the advantage of higher-quality lenses for his experiments on how light refracts and focuses. With this, he set out to simulate how the eye might operate. The most perplexing puzzle of optics was this: If light rays went in all directions from objects, this meant the rays entered the eye not only at perfectly perpendicular points, but also at many angles. Therefore, how did the eye choose the perfect points of light, eliminating all the blur of the other angled rays?

  Kepler began his inquiry with a fairly common observation, known since the invention of the camera obscura. In that device, which is a pinhole in a dark box, the small aperture sent the image to the back of the box. Remarkable as this was, the image was weak, fuzzy, and upside down. Kepler asked: How did the eye make a clear image, first, and then make the image right side up? New anatomical discoveries of his age helped Kepler determine that the “seeing” part of the eye was indeed its retina, for, as one medical report said in 1583:

  The primary organ of vision, namely the optic nerve, expands when it enters the eye into a hollow retiform hemisphere. It receives and judges the species and colors of external objects, which, along with brightness, fall into the eye through the pupil and are manifest to it through its looking glass.40

  With this knowledge, Kepler could approach that crystalline lens of the eye as the “looking glass,” a mechanism of focus much like an eyeglass, telescope, or microscope. He combined lens experiments with ray geometry and calculated that it was the special shape of the lens in the eye that allowed it to gather up all the light rays—perpendicular and angled—into a focused impression. It produced a package of optimum light, unlike a fuzzy camera obscura. The inversion of the image, Kepler discovered, resulted from the way light passed through the lens. A ray coming in at the top of the eye was refracted, in other words, to the bottom of the retina, and vice versa. “That which is to the right on the outside is portrayed on the left side of the retina,” and so forth, Kepler explained.41

  Much about the mystery of light remained, so Kepler stopped while he was ahead. He stayed with a tradition that viewed light rays as colorless, noncorporeal mysteries. How the mind or soul captured vision was still too deep. Kepler stopped at the edge of that precipice. “How the image or picture is composed by the visual spirits that reside in the retina … I leave to be disputed by the physicists [medical practitioners],” he said.42 The nature of the “visual spirits” would be the great dispute of psychology and neuro­science, which were both generations to come in the future. In the short run, optics was brought under a new outlook that marked every kind of modern science, a mechanistic outlook.

  During the Renaissance, neither Aristotle nor Plato provided a direct model for the world as a machine, although Plato’s geometry was approaching that threshold. The pushing of geometry into quantified modules, whether in architecture or mechanical devices, opened the way to do the same with nature. When addressing nature, however, the mechanistic view had to become a theoretical abstraction, unlike a real, tactile machine. The mechanical outlook, using the tools of mathematics, abstracted the universe into predictable, moving, interacting parts. This vision, nurtured by the Renaissance and even by some of its art, finally was personified in the central figure of the Scientific Revolution, the Englishman Isaac Newton, an unrepentant Platonist in his own way.

  Of his many accomplishments, Newton would revolutionize the way the Renaissance had approached the question of beauty by presenting the first scientific theory of color. To do this, Newton began not with art, but with a “triangular glass Prisme, to try therewith the celebrat
ed phenomena of Colours,” as he said in 1666.43

  A classic tool of optical experiments for centuries, the prism was used in a new way by Newton. He transformed his room into a kind of camera obscura: he shut out all the light except a beam that he allowed through a crack in the window shutter. When the beam hit the prism, it divided the white light into colors. Each field of color was bent at a different angle, being “variously refrangible,” as Newton said.44 These colors could not be further divided by refraction; and when he merged the colors back to a common point, they recombined into white light.

  In the past, white had been considered a color that gave brightness to other colors, but Newton discovered that in physical reality all the colors originate in, and return to, white. Since light originated in the Sun, he extrapolated his theory to a higher physics: pure light is made up of a limited number of “primary colors,” all of which refract differently when viewed by the eye and thus create the consistent spectrum found in sunlight and the visible world. Newton presented his findings to the Royal Society in 1672, and then elaborated in his monumental work, Opticks (1704).

  There still were anomalies in Newton’s theory to be swept under the rug for the time being. To name just a few, light rays seemed to produce an almost infinite number of colors, and Newton could not explain how this occurred if there were a distinct number of “colorific rays,” presumably just seven. He conceded furthermore that all seven colors were not necessary to produce white light. As few as three, or even two, primary colors (as beams of light) could produce white, according to experiments. For the world of art and the painter, meanwhile, Newton would not make the important distinction between color in pure sunlight and color mixed from pigments. This would continue to be the great conundrum for another century: Why do colors mix differently in sunlight and in colored materials such as paint?