Piero's Light

by Larry Witham

  Beginning with this work, the influence of Cusanus’s Platonist writings would have a lasting impact in three areas: his view of human knowledge, his picture of a mathematical universe, and his interest in making artworks a part of theological discussions. It was this smorgasbord of ideas that would have appealed to someone like Piero, who, for all we know, may have seen a copy of On Learned Ignorance being passed around in Rome in those days.

  By “learned ignorance” (docta ignorantia), Cusanus meant the wisdom that comes with recognizing the limits of human knowledge about the physical world and about the infinite. This was an idea he found in the “divine Plato” and an idea that was a precursor to the modern philosopher Immanuel Kant.11 Given human finiteness, the most reliable knowledge came by mathematics. Indeed, God had ordered the world by number, “the principal exemplar of things,” Cusanus said. “For if number is removed, the distinctness, order and comparative relation, and harmony of things cease.”12

  As a form of measurement, number allowed a method of comparison in an otherwise indeterminate world of flux, where “all perceptible things are in a state of continual instability.” Except for mathematics, Cusanus suggested, “Precise truth is inapprehensible.” The human mind makes do by creating mental categories or “conjectures” to organize the world.13 In his many writings, Cusanus is not exactly consistent in whether he is saying mathematics is a divine and tran­scen­dent system behind the world, or a numerical system of conjectures that humans invent to organize their perceptions. He may be suggesting that the Platonist Ideas and human conjectures should be matched up as closely as possible, this being a point of true human insight and knowledge. Either way, in his ambiguity, Cusanus foreshadows the modern debate on mathematics—is it ultimate, or is it relative? By his concept of conjecture, Cusanus also foreshadows a modern hypothetical approach to science: in this method, scientists adopt a plausible conjecture, and then test it as rigorously as possible to see whether it is true enough, or useful enough, to be called a theory about how nature works. And if applied to art, Cusanus’s notion of conjectures was similar to the emerging medieval idea of “imagination.” In the imagination (or intuition), the finite human mind mingles with the divine mind or the Platonist Ideas, such as the Idea of Beauty.14

  As a second feature of Cusanus’s thought, he offered a view of the cosmos derived from Plato. Amid the many versions of Renaissance Platonism, he argued for a return to the more original. Cusanus rejected Neoplatonism’s idea of gradations in the physical universe between God and created things. Such comparative measures, according to Cusanus, were impossible to use in relationship to an infinite Being such as the deity: measurable gradations and ladders to the infinite are not possible. The finite and infinite are entirely different in nature. As a consequence, Cusanus said, all things are “immediate to God.”15 This not only helped break down a universe of hierarchical structures; it also proposed a kind of independence of all things, tethered to God, yet in their motion they are relative to other things in motion (the essence of Einstein’s future theory of relativity). This outlook allowed Cusanus to say the unsayable for his time: “the earth, which cannot be the center, cannot be devoid of all motion.”16 Though he dabbled in science, Cusanus was not a scientist, and his logic was based in metaphysics. Nonetheless, future thinkers in science, from Giordano Bruno to Galileo and René Descartes, cited Cusanus as they pushed back scientific frontiers.17

  Cusanus’s political fortunes in Germany, alas, had never been something he could be sanguine about. The northern cardinals and the emperor were resistant to the papal will. As the clash between imperial and papal power thickened, Cusanus, a cardinal since 1448, pulled up his northern roots and headed for Rome. By the time Pius II was elected, Cusanus was a leading theologian around the Vatican. The new pope turned to him, as to Bessarion, for help in the affairs of state. Soon after taking office, Pius began to travel. He had called for a three-year crusade against the Turks and summoned the Council of Mantua. During his absences, Cusanus served as vicar-general of the papal territories, adding to his already considerable influence.

  Perhaps remarkably, both Bessarion and Cusanus avoided charges of heresy for the way they opened Christian doctrine to both a Platonist metaphysics and a new universalism (and tolerance) among religions. Cusanus was the last breath of a Roman theology of universal natural religion among all people. It was an ecumenical and interfaith idea that became modern, but it did not survive the Reformation and Counter-Reformation, and their new subcultures of intolerance, which came in the generation after Cusanus’s death.18

  Bessarion and Cusanus offered a picture of God and the universe that was sufficiently dualistic to avoid the problem of pantheism, in which God is the material universe. By contrast, the apostate Dominican Giordano Bruno, an ardent pantheist, had insisted that natural philosophy, on its way to becoming modern science, must separate itself from theology. The idea of such a separation, endorsed also by Galileo and Descartes, was attacked by the Counter-Reformation’s Inquisition, which threatened the writings of Bruno, Galileo, and Descartes. Bruno refused to give up his pantheistic, self-existing, and infinite universe and was burned at the stake; Galileo was put on trial for saying the Earth moved; Descartes kept his Earth-moves theory quiet to avoid censure.

  Both Bessarion and Cusanus, by their time and place, and probably by their suave ability to bypass ultimate showdowns (in which Bruno and Galileo seemed to specialize), avoided all of this unpleasantness. Even so, both had virulent critics from the Aristotelian camp, for Cusanus in Germany and for Bessarion in Rome: with a strong preference for Aristotle, these critics found Plato too ethereal and illogical.19 Nevertheless, related to science, Cusanus and Bessarion had nurtured a Platonist subculture that would break with Aristotelian orthodoxy. This would influence the rise of a new astronomy and the inclusion of mathematics in experimental science.

  When Piero arrived in Rome in 1458, there was no reason that he could not have shown up in the humanist circles hosted by Bessarion and Cusanus. With Bessarion, Piero may have had common acquaintances in Tuscany or through the Camaldolese order, with which they were both on fairly intimate terms. Cusanus in particular was known to take an interest in meeting with painters. In such a setting, Alberti probably found opportunities to draw upon Cusanus’s thought about God’s numerical world being a basis for artistic design and proportion.20 In his writings, Cusanus used examples of paintings, such as by Rogier van der Weyden. He was perhaps the first theologian to speak, metaphorically, of God as an artist.

  Piero had been in humanist courts before, of course. But if he had picked up on the new mental skepticism espoused by Cusanus, it must have satisfied the soul of a world-weary painter. He knew well the difficulties of achieving precision and perfection in art, and now he was hearing some of the early scientific debates about how physical appearances often obscure deeper law-like principles. This dualism suited his religious outlook, but it was also proving fruitful in how he viewed mathematics and painting (which modern commentators have inferred from his work).21 In mathematics, perfect formulas are found below the world’s rough surfaces. Some of this can be brought to the surface, he realized, by geometric harmonies that convey a feeling of spiritual harmony. The idealized world he tried to produce in paint would always fall short. Nevertheless, a painting could give viewers a tran­scen­dent moment with Beauty as an essence. Many of Piero’s paintings prior to this Rome trip already evoked this dual sense. But the Christian Platonists in Rome must have deepened his thinking on how this applied to his craft.

  On his arrival in Rome, the church officials under Pius II gave Piero painting tasks in the Vatican complex and in one of the city’s basilicas, Santa Maria Maggiore. He probably painted two frescos in rooms of the Apostolic Palace, rooms used by popes as chapels, libraries, or reception areas. As it turned out, sixty years after Piero completed one of those frescos, Raphael would paint over it when Pope Julius II wanted one of
the rooms—now called the Stanza d’ Eliodoro—redecorated.22 Piero’s Vatican project was well enough along by April 12, 1459, that the papal household made a substantial payment to him. Its record books note that it was for “paintings made in the room of his Holiness our Lord the Pope.”23 Piero may have brought one of his most talented students with him, Luca Signorelli, who would go on to become a prominent painter in his own right.

  By painting in Santa Maria Maggiore, Piero was putting his mark on a historic religious setting. Standing on the other side of Rome from the Vatican, the church was founded by the papacy in the fifth century. At this location, it was said, God had produced miraculous snow in August. Now it was a pilgrimage site that drew many rising stars to paint its interior surfaces. For his part, Piero produced ceiling frescos of the four evangelists, just one of which survives. He is St. Luke, a blond young man on a cloud. He holds his writing instrument over an ink cup, producing his Gospel. For this painting, Piero improved on the normal plaster by using a paste of pulverized marble. This gave him a hard and smooth surface, as if a panel, more amenable to painting detail.

  Piero’s projects in Rome lasted no more than a year and a half, from fall 1458 to the end of 1459, an apparent break from projects he had already begun in Arezzo and San­sepol­cro. He returned home after hearing of his mother’s death, which came on November 6, 1459. As far as we know, Piero never returned to Rome, and he probably left the work for his assistants to complete. When Piero had arrived in Rome, many of the churches had the ambiance of Fra Angelico’s starry ceilings. After Piero worked in Rome, according to some art historians, paintings done in the papal city departed further from old medieval conventions, taking on the more geometrical and light-filled look of Piero.24 It was a style later brought to perfection by Raphael. In turn, Piero’s sojourn in Rome surely left a lasting impression on his own life as an artist. In one historian’s assessment: “the Platonic and mathematical inspiration of his mature works … were fostered by his meetings in Rome … with the humanists of Pius II’s court—perhaps with Bessarion himself.”25

  After his year and a half in Rome, Piero did not have anything specific to say about Platonism, except by way of his brush. But he felt it was time to write something more about mathematics and art. He was persuaded that the artist could aspire to be a humanist, and this required the application of painting as a true science. Such were his thoughts when he decided to write a second treatise, this one directly tied to painting and going under the title On Perspective for Painting (De prospectiva pingendi). His first treatise, on abacus, had been geared to practical mathematics, such as calculating the price of a fish at the market, and offered nothing directly useful to the painter. Now, his On Perspective tried to guide the artist in his workshop, if such a painter was willing to endure a good deal of technical precision.

  To move ahead on this second treatise, Piero needed a patron, not only for possible funding, but, even more important, to have the cover of legitimacy. During the Renaissance, labored-over treatises needed an audience, which might amount to just a single patron.26 Wealthy merchants and Italian courts valued original manuscripts to fill their libraries. Works of polished rhetoric were most popular, though anything about devices, mechanics, astronomy, or anatomy were valued for collectors’ shelves.

  By now, Piero could read enough Latin to see how the more traditional, high-tone treatises of the humanists were done (as compared to the simple abacus tracts used in schools and written in the Tuscan vernacular). But over his lifetime, Piero would never master the writing of Latin in full, sequential sentences. When he put pen to parchment sometime in the 1460s, Piero would write On Perspective in the popular tongue. There was no shame in this, of course. Dante, the exemplar poet of medieval Italy, had elevated Tuscan to middle-brow eloquence a century before Piero’s birth, and even Alberti, seeking a wider reading audience, had written a version of his On Painting in the vernacular.

  When On Perspective was done, however, Piero still felt it was below humanist standards, or not appealing enough to a high-ranking patron. Forthwith, he had it translated into Latin, the language of the learned. At some point, he organized a small shop, probably in San­sepol­cro, to bring this Latin transformation about, setting up what one Piero scholar calls “a scriptorium with all the equipment and assistance, a scribe and at least one translator, necessary to produce at least eight manuscripts, most notably five copies of his On Perspective.”27

  Piero addresses On Perspective to painters. Its most insistent emotion is that painting in perspective is a “true science.”28 He wants to demonstrate the “power of lines and angles produced by perspective.” Before the book is over, in fact, he will declare: “Many painters are against perspective… . Therefore it seems to me that I ought to show how necessary this science is to painting.”29 By “against perspective,” Piero must have been speaking of vying attitudes within his profession, for some painters would have been skeptical of, or intimidated by, the introduction of highfalutin mathematics to produce effects they had estimated well enough by the skill of the eye and hand (as even Michelangelo would later suggest).

  Piero divides his treatise into three parts (again, “books”) and opens each with a brief essay of a few paragraphs. His first states simply that “Painting has three parts”—perspective, composition, and color—but he will address only the first of these in this treatise.30 As ever, Piero is a man of few written words. He uses these mainly to explain Euclidian propositions and define some of his terms, such as the names for basic shapes, from the triangle and circle to the hexagon, and so on. He works directly from Euclid’s Elements and must have known about Euclid’s theories in Optics, for, like Alberti, Piero explains that as the visual angle in the eye grows smaller, distant objects also shrink, this being the basic reason for optical perspective.

  The three books build upon one another, showing methods that match the difficulty of the object: flat space, three-dimensional objects, and then objects that are irregular. The first is easiest and is demonstrated with floor tiles, much as Alberti had done in On Painting with diagonals, a center point, and what would later be called a “distant point.” Piero builds on these to construct, in perspective, examples of architectural objects such as a simple square house. By the time he is done with the first two books, he has demonstrated perspective constructions with methods that range across optics, geometry, and surveying.31

  The third and final book opens with an overview. “In the first [book], I demonstrated the diminution of plane surfaces in a number of ways,” Piero writes. “In the second I demonstrated the diminution of square bodies… .” He concludes: “But as I now intend in this third book to deal with the diminution of bodies which are more difficult, I shall describe another way and another means of diminishing them… .”32 This alternative will avoid the drawing of a “multiplicity of lines” typical of the floor-tile approach, and will help “the eye and the intellect” avoid being deceived by such diagrammatic confusion.33

  The third book, in other words, will be about drawing irregular bodies in perspective—“heads, capitals … and other bodies positioned in diverse ways”—and to do this, Piero will use a method that modern architects now call “plan and elevation.” Back when the method was explained by Alberti and Piero, it instead evoked the idea of finding points on an object as they are seen intersecting a visual plane, such as a window. Piero applies this method to the drawing of human heads, buildings, column bases, column capitals, coffered domes, goblets, rings, hats, baptismal fonts, and wells. It is a practical form of drawing, requiring the tracing of lines from points on objects. Piero even offers some hands-on advice for transferring the points by using “a nail with a very fine silken thread; the hair of a horse’s tail would be good,” and also introduces the use of paper and wooden rulers.34

  In completing On Perspective, Piero summarizes the two basic Renaissance approaches to drawing in perspective. The first, being more th
eoretical, organizes the visual space by laying down a geometric floor plan with a horizon, diagonals, and visual rays; the other is the practical method of tracing a “perfect” image so that it takes on its “diminished” form in perspective as it intersects a visual plane, such as a window (an approach that in later decades would be done by mechanical devices for drawing objects in perspective).35 Invariably, though, On Perspective was complex and tedious enough that it was destined for a humanist library or an interested mathematician, not necessarily a street-side artisan workshop.

  In hindsight, mathematicians have pointed out that Piero actually attempted a geometrical proof of perspective. From Euclid onward, proof had been a central idea to geometry; and to the extent that Piero had studied Euclid, he would have picked up the Greek method of making a formal argument to prove the veracity of a geometrical or mathematical principle. To prove that a triangle with one right angle would have a determinate third side, for instance, Euclid defined its geometric parts, stated axioms, and then offered a step-by-step demonstration that the law of the third side is always valid. In On Perspective, Piero seems to do something similar. Based on a complex diagram, he points to the mathematical equivalency of some of its lines. Modern-day mathematicians look back on this aspect of Piero’s work and applaud it as an early accomplishment in geometry. Unfortunately, Piero does not explain his thinking, as the Greeks so often did verbally. Admirers of Piero have had to presume what his true intentions had been regarding a proof of perspective.36

  In On Perspective, Piero once more deals with what seem to be the outspoken critics of academic perspective in his day. At one point, Piero speaks of a group of “detractors” who have more specifically pointed out that perspective lines actually distort forms at the wide angles of a picture. These people claim that a draftsman’s perspective, therefore, could not be correct. On the curvature problem, these critics are actually correct, since this distortion is a property in the curvature of the eye (or of the visual ambiguity that arises when humans try to judge curved surfaces). Undeterred, Piero claims that the geometry of straight lines is nevertheless true. The distortion, he wrongly suggests, is based on limits to the eye’s angle of vision.37