Leonardo’s genius was a human one, wrought by his own will and ambition. It did not come from being the divine recipient, like Newton or Einstein, of a mind with so much processing power that we mere mortals cannot fathom it. Leonardo had almost no schooling and could barely read Latin or do long division. His genius was of the type we can understand, even take lessons from. It was based on skills we can aspire to improve in ourselves, such as curiosity and intense observation. He had an imagination so excitable that it flirted with the edges of fantasy, which is also something we can try to preserve in ourselves and indulge in our children.
At first I thought that his susceptibility to fantasia was a failing, revealing a lack of discipline and diligence that was related to his propensity to abandon artworks and treatises unfinished. To some extent, that is true. Vision without execution is hallucination. But I also came to believe that his ability to blur the line between reality and fantasy, just like his sfumato techniques for blurring the lines of a painting, was a key to his creativity. Skill without imagination is barren. Leonardo knew how to marry observation and imagination, which made him history’s consummate innovator.
There was no place then, and few places ever, that offered a more stimulating environment for creativity than Florence in the 1400s. Its economy, once dominated by unskilled wool-spinners, had flourished by becoming one that, like our own time, interwove art, technology, and commerce. It featured artisans working with silk makers and merchants to create fabrics that were works of art. In 1472 there were eighty-four wood-carvers, eighty-three silk workers, thirty master painters, and forty-four goldsmiths and jewelry craftsmen working in Florence. It was also a center of banking; the florin, noted for its gold purity, was the dominant standard currency in all of Europe, and the adoption of double-entry bookkeeping that recorded debits and credits permitted commerce to flourish. Its leading thinkers embraced a Renaissance humanism that put its faith in the dignity of the individual and in the aspiration to find happiness on this earth through knowledge. Fully a third of Florence’s population was literate, the highest rate in Europe. By embracing trade, it became a center of finance and a cauldron of ideas.
“Beautiful Florence has all seven of the fundamental things a city requires for perfection,” the essayist Benedetto Dei wrote in 1472, when Leonardo was living there. “First of all, it enjoys complete liberty; second, it has a large, rich, and elegantly dressed population; third, it has a river with clear, pure water, and mills within its walls; fourth, it rules over castles, towns, lands and people; fifth, it has a university, and both Greek and accounting are taught; sixth, it has masters in every art; seventh, it has banks and business agents all over the world.”6 Each one of those assets was valuable for a city, just as they are today: not only the “liberty” and “pure water,” but also that the population was “elegantly dressed” and that the university was renowned for teaching accounting as well as Greek.
Homosexuality was not uncommon in the artistic community of Florence or in Verrocchio’s circle. Verrocchio himself never married, nor did Botticelli, who was also charged with sodomy. Other artists who were gay included Donatello, Michelangelo, and Benvenuto Cellini (who was twice convicted of sodomy). Indeed, l’amore masculino, as Lomazzo quoted Leonardo calling it, was so common in Florence that the word Florenzer became slang in Germany for “gay.” When Leonardo worked for Verrocchio, a cult of Plato was arising among some Renaissance humanists, and it included an idealized view of erotic love for beautiful boys. Homosexual love was celebrated in both uplifting poems and bawdy songs.
Nevertheless, sodomy was a crime, as Leonardo became painfully aware, and it was sometimes prosecuted. During the seventy years following the creation of the Officers of the Night in 1432, an average of four hundred men per year were accused of sodomy, and about sixty per year were convicted and sentenced to prison, exile, or even death.8 The Church considered homosexual acts a sin. A 1484 papal bull likened sodomy to “carnal knowledge with demons,” and preachers regularly railed against it.
Even unfinished, the Adoration of the Magi and Saint Jerome show that Leonardo was pioneering a new style that treated narrative paintings and even portraits as psychological expositions. This approach to art was partly informed by his love of pageants, theatrical productions, and court amusements; he knew how actors feign sentiments, and he recognized the tells on the lips and in the eyes of audience members that indicate their reactions. It probably also helped that the Italians, then as now, were expressive in their gestures, which Leonardo loved to capture in his notebooks.
He sought to portray not only moti corporali, the motions of the body, but also how they related to what he called “atti e moti mentali,” the attitudes and motions of the mind. More important, he was a master at connecting the two. This is most noticeable in his action-packed and gesture-filled narrative works, such as the Adoration and The Last Supper. But it is also the genius behind his most serene portraits, most notably the Mona Lisa.
He came to understand that the use of shadows, not lines, was the secret to modeling three-dimensional objects on a two-dimensional surface. The primary goal of a painter, Leonardo declared, “is to make a flat surface display a body as if modeled and separated from this plane.” This crowning achievement of painting “arises from light and shade.” He knew that the essence of good painting, and the key to making an object look three-dimensional, is getting the shadows right, and that’s why he spent more time studying and writing about shadows than he did on any other artistic topic.
He felt that shadows were so important to art that, in the outline for his treatise, he planned that the longest section would be on that topic. “Shadows appear to me to be of supreme importance in perspective, because, without them opaque and solid bodies will be ill defined,” he wrote. “Shadow is the means by which bodies display their form. The forms of bodies could not be understood in detail but for shadow.”
This emphasis on the use of shadows as the key to modeling three-dimensional objects in a painting was a break from common practice of the time. Following Alberti, most artists emphasized the primacy of contour lines. “Which is the most important, the Shadows or Outlines in Painting?” Leonardo asked in his notes for his treatise. The correct answer, he believed, was the former. “It requires much more observation and study to perfect the shadowing of a picture than in merely drawing the lines of it.” Typically he used an experiment to show why shading is more subtle than line drawing. “The proof of this is that the lines may be traced upon a veil or a flat glass placed between the eye and the object to be imitated. But that cannot be of any use in shadowing, because of the infinite gradation of shades and the blending of them, which does not allow of any precise borders.”
Leonardo proceeded to write obsessively about shadows. A torrent of more than fifteen thousand words on the topic, which would fill thirty pages of a book, still survives, and that is probably less than half of what he originally wrote. His observations, charts, and diagrams became increasingly complex. Using his feel for proportional relations, he calculated the effects of light striking contoured objects at varying angles. “If the body is larger than the light, the shadow resembles a truncated and inverted pyramid, and its length has also no defined termination. But if the body is smaller than the light, the shadow will resemble a pyramid and come to an end, as is seen in eclipses of the moon.”
The deft use of shadows became a unifying force in Leonardo’s paintings, distinguishing them from those of other artists of the time. He was especially ingenious in the way he used gradations of color tones to create shadows. The parts of a scene that get the most direct light have the greatest saturated color. This understanding of the relationship between shadows and color tones created a unified coherence to his art.
Having become, by now, a lover of received knowledge as well as a disciple of experience, Leonardo studied Aristotle’s work on shadows and combined it with a variety of ingenious experiments involving different sizes of lamps and objects. He came up with multiple categories of shadows and plotted chapters on each: primary shadows that are caused by direct light hitting an object, derived shadows that result from ambient light diffused through the atmosphere, shadows that are subtly tinged with light reflected from nearby objects, compound shadows cast by multiple sources of light, shadows made by the subdued light at dawn or sunset, shadows made by light that has been filtered through linen or paper, and many other variations. With each category, he included striking observations, such as this: “There is always a space where the light falls and then is reflected back towards its cause; it meets the original shadow and mingles with it and modifies it somewhat.”
Reading his studies on reflected light provides us with a deeper appreciation for the subtleties of the light-dappled shadow on the edge of Cecilia’s hand in Lady with an Ermine or the Madonna’s hand in Virgin of the Rocks, and it reminds us why these are innovative masterpieces. Studying the paintings, in turn, leads to a more profound understanding of Leonardo’s scientific inquiry into rebounding and reflected light. This iterative process was true for him as well: his analysis of nature informed his art, which informed his analysis of nature.
Leonardo’s reliance on shadows, rather than contour lines, to define the shape of most objects stemmed from a radical insight, one that he derived from both observation and mathematics: there was no such thing in nature as a precisely visible outline or border to an object. It was not just our way of perceiving objects that made their borders look blurred. He realized that nature itself, independent of how our eyes perceive it, does not have precise lines.
In his mathematical studies, he made a distinction between numerical quantities, which involve discrete and indivisible units, and continuous quantities of the sort found in geometry, which involve measurements and gradations that are infinitely divisible. Shadows are in the latter category; they come in continuous, seamless gradations rather than in discrete units that can be delineated. “Between light and darkness there is infinite variation, because their quantity is continuous,” he wrote.
That was not a radical proposition. But Leonardo then took a further step. Nothing in nature, he realized, has precise mathematical lines or boundaries or borders. “Lines are not part of any quantity of an object’s surface, nor are they part of the air which surrounds this surface,” he wrote. He realized that points and lines are mathematical constructs. They do not have a physical presence. They are infinitely small. “The line has in itself neither matter nor substance and may rather be called an imaginary idea than a real object; and this being its nature it occupies no space.”
This theory—based on a Leonardesque blend of observation, optics, and mathematics—reinforced his belief that artists should not use lines in their paintings. “Do not edge contours with a definite outline, because the contours are lines, and they are invisible, not only from a distance, but also close at hand,” he wrote. “If the line and also the mathematical point are invisible, the outlines of things, also being lines, are invisible, even when they are near at hand.” Instead an artist needs to represent the shape and volume of objects by relying on light and shadow. “The line forming the boundary of a surface is of invisible thickness. Therefore, O painter, do not surround your bodies with lines.” This was an upending of the Florentine tradition known as disegno lineamentum, praised by Vasari, which was founded on linear precision in drawing and the use of lines to create forms and designs.
Leonardo’s insistence that all boundaries, both in nature and in art, are blurred led him to become the pioneer of sfumato, the technique of using hazy and smoky outlines such as those so notable in the Mona Lisa. Sfumato is not merely a technique for modeling reality more accurately in a painting. It is an analogy for the blurry distinction between the known and the mysterious, one of the core themes of Leonardo’s life. Just as he blurred the boundaries between art and science, he did so to the boundaries between reality and fantasy, between experience and mystery, between objects and their surroundings.
Machiavelli arrived on October 7, sent by Florence to be an emissary and informant. In his daily dispatches back to Florence, which he knew were being read by Borgia’s intelligence agents, Machiavelli apparently refers to Leonardo only as “another who is also acquainted with Cesare’s secrets” and as a “friend” whose knowledge is “worthy of attention.”17 Imagine the scene. For three months during the winter of 1502–3, as if in a historical fantasy movie, three of the most fascinating figures of the Renaissance—a brutal and power-crazed son of a pope, a sly and amoral writer-diplomat, and a dazzling painter yearning to be an engineer—were holed up in a tiny fortified walled town that was approximately five blocks wide and eight blocks long.
This inability to ground his fantasies in reality has generally been regarded as one of Leonardo’s major failings. Yet in order to be a true visionary, one has to be willing to overreach and to fail some of the time. Innovation requires a reality distortion field. The things he envisioned for the future often came to pass, even if it took a few centuries. Scuba gear, flying machines, and helicopters now exist. Suction pumps now drain swamps. Along the route of the canal that Leonardo drew there is now a major highway. Sometimes fantasies are paths to reality.
Leonardo and Michelangelo had become luminaries, paving the way for other artists—who until then had rarely even signed their work—to do the same. When the pope summoned Michelangelo, and when the Milanese vied with the Florentines over the services of Leonardo, it was recognition that super-artists had their own recognizable style, artistic personality, and individual genius. Instead of being treated as somewhat interchangeable members of the craftsman’s class, the best artists were now treated as singular stars.
Leonardo’s studies of water movements also led him to understand the concept of waves. He realized that waves do not actually involve water moving forward. Waves in the sea and ripples emanating from a pebble falling into a pond progress in a certain direction, but these “tremors,” as he called them, merely cause the water to move up for a moment before returning to where it had been. He compared them to waves caused by a breeze in a field of grain. By the time he wrote the Codex Leicester and other, concurrent notebook pages on the movement of water, Leonardo had a deep feel for how waves propagate in a medium, and he correctly assumed that sound and light travel in waves. With his gift for analogy and ability to notice movement, he even viewed emotions as traveling in waves. At the core of the narrative in The Last Supper are the waves of emotion that emanate from the disturbance caused by the utterance of Jesus.
As always with Leonardo, in his art and in his life, in his birthplace and now even in his death, there is a veil of mystery. We cannot portray him with crisp sharp lines, nor should we want to, just as he would not have wanted to portray Mona Lisa that way. There is something nice about leaving a little to our imagination. As he knew, the outlines of reality are inherently blurry, leaving a hint of uncertainty that we should embrace. The best way to approach his life is the way he approached the world: filled with a sense of curiosity and an appreciation for its infinite wonders.
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