The Science of Leonardo: Inside the Mind of the Great Genius of the Renaissance

by Fritjof Capra

  If the painter wants to see beauties that make him fall in love, he is the lord who can generate them, and if he wants to see monstrous things that frighten, or funny things that make him laugh, or things that truly arouse compassion, he is their lord and God…. In fact, whatever there is in the universe, by essence, presence, or imagination, he has it first in his mind and then in his hands.8

  For Leonardo, the artist’s imagination always remains closely linked to his intellectual understanding of nature. “The inventions of his fantasia,” explains Martin Kemp, “are never out of harmony with universal dynamics as rationally comprehended; they are fabulous yet not implausible, each element in their composition deriving from the causes and effects of the natural world.”9 At the same time, Leonardo insisted on the divine quality of the painter’s creativity. “The godlike nature of the science of painting,” he declared, “transforms the painter’s mind into a resemblance of the divine mind.”10

  Leonardo realized that fantasia is not limited to artists, but rather is a general quality of the human mind. He called all human creations—artifacts as well as works of art—“inventions,” and he made an interesting distinction between human inventions and the living forms created by nature. “Nature encompasses only the production of simple things,” he argued, “but man from these simple things produces an infinity of compounds.”11

  From the modern scientific perspective, this distinction no longer holds, because we know that in the process of evolution, nature, too, produces living forms through an infinity of new compounds from cells and molecules. However, in a broader sense, Leonardo’s distinction is still valid as a distinction between forms that emerge through evolution and forms created by human design. In contemporary scientific language, Leonardo’s term “simple things” would be replaced by “emergent structures” and his notion of “compounds” by “designed structures.”12

  Throughout his life, Leonardo referred to himself as an inventor. In his view, an inventor was someone who created an artifact or work of art by assembling various elements into a new configuration that did not appear in nature. This definition comes very close to our notion of a designer, which did not exist in the Renaissance. (Leonardo’s term disegnatore, sometimes incorrectly translated as “designer,” always means “draftsman” a better equivalent of “designer” is his term compositore.) The concept of design as a distinct profession emerged only in the twentieth century as a consequence of mass production and industrial capitalism.13 During the preindustrial era, design was always an integral part of a larger process that included problem solving, innovation, form giving, decoration, and manufacturing. This process traditionally took place in the domains of engineering, architecture, crafts, and the fine arts.

  Accordingly, Leonardo did not separate the design process—the abstract configuration of multiple elements—from the process of material production. However, he always seemed to be more interested in the process of design than in its physical realization. It is worthwhile to recall that most of the machines and mechanical devices he invented, designed, and presented in superb drawings were not built; most of his military inventions and schemes of civil engineering were not realized; and although he was famous as an architect, his name is not connected with any known building. Even as a painter he often seemed to be more interested in the solution of compositional problems—the discorso mentale—than in the actual completion of the painting.

  It seems to me, then, that the wide-ranging activities and achievements of Leonardo da Vinci, the archetypal uomo universale, are best examined within the three categories of artist, designer, and scientist. In his own synthesis, the activities of the inventor, or designer, like those of the artist, are inextricably linked to scientia, the knowledge of natural principles. He referred to himself, in one of his most arresting expressions, as “inventor and interpreter between nature and humans.”14

  THE SUBLIME LEFT HAND

  In practice, it was Leonardo’s exceptional drawing facility that formed the link between the three domains of art, design, and science, as he himself recognized:

  Drawing, [the foundation of painting], teaches the architect to render his building agreeable to the eye; this is what teaches potters, goldsmiths, weavers, embroiderers. It has found the characters by which different languages are expressed; it has given the arithmeticians their ciphers and has taught geometers how to represent their figures; it instructs the experts in perspective, astronomers, machine builders, and engineers.15

  With his acute powers of observation and his “sublime left hand” (as his friend, the mathematician Luca Pacioli, called it), Leonardo was able to draw, in exquisite detail, flowers, birds in flight, whirlpools, muscles and bones, and human expressions with unparalleled accuracy (see Fig. 2-1). Writing about the studies for his early Madonnas, Kenneth Clark comments, “They show his matchless quickness of vision, which allowed him to convey every movement or gesture with the certainty and unconscious grace of a great dancer performing a familiar step.”16

  Figure 2-1: Madonna and Child and other studies, c. 1478–80, Drawings and Miscellaneous Papers, Vol. III, folio 162r

  Leonardo’s anatomical drawings were so radical in their conception that they remained unrivaled until the end of the eighteenth century, nearly three hundred years later. Indeed, they have been praised as the beginning of modern anatomical illustration.17 To present the knowledge he had gathered from his extensive anatomical dissections, Leonardo introduced numerous innovations: drawing structures from several perspectives; drawing in cross sections and “exploded” views; showing the removal of muscles in successive layers to expose the depths of an organ or anatomical feature. None of his predecessors or contemporaries came close to him in anatomical detail and accuracy.

  To the few of his contemporaries who were privileged to see them, Leonardo’s anatomical manuscripts must have seemed almost miraculous. When the Cardinal of Aragon visited the old master in France in 1517, his secretary, Antonio de Beatis, wrote in his journal: “This gentleman has written a treatise on anatomy, showing the limbs, muscles, nerves, veins, joints, intestines, and everything that can be explained in the body of men and women, in a way that has never been done by anyone before.”18

  Leonardo called his anatomical drawings “demonstrations,” adopting a terminology typically used by mathematicians to refer to their diagrams, and he proudly asserted that they gave “true knowledge of [various] shapes, which is impossible for either ancient or modern writers…without an immense, tedious and confused amount of writing and time.”19 Indeed, when looking through the Anatomical Studies, it is evident that Leonardo’s main focus is on the drawings. The accompanying text is secondary, and sometimes absent altogether. In a way, these manuscripts are reminiscent of modern scientific papers in which the main statements are the mathematical equations, with a few explanatory lines between them (see Fig. 2-2).

  Leonardo used the same innovative techniques that he perfected in his anatomical drawings in his vast collection of technical drawings of mechanisms and machines. A multitude of mechanical elements in different combinations are presented in cutaway or exploded views and from many sides, with great mastery of visual perspective and subtle renderings of light and shade (see Fig. 2-3). Drawings of similar machines were produced by other Renaissance engineers. However, as art historian Daniel Arasse points out, while theirs are merely explanatory, Leonardo’s are convincing, persuading the viewer of the feasibility and soundness of the author’s designs:

  Figure 2-2: Muscles of the arm and shoulder in rotated views, c. 1510, Anatomical Studies, folio 141v

  Figure 2-3: Two-wheeled hoist, Codex Atlanticus, folio 30v

  His working drawings not only possess a rare elegance; they are visually put in context, and they have the concrete appearance of objects which exist: the angle or angles of view, the subtlety of the shadows and the treatment of the background itself on which they are drawn gives them an extraordinarily persuasive…effectiveness.20
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  As an artist, Leonardo introduced a novelty into the practice of preparatory drawing, which forms an intriguing counterpoint to the precision of his scientific and technical drawings.21 In many studies for his paintings, he would go over the outlines of a figure again and again, sketching several alternative lines and variations of the figure’s position, until he found the ideal form. These preparatory sketches have an extraordinary dynamic quality. One can almost feel the rhythm of Leonardo’s “sublime left hand” as he tries out different possibilities, translating his discorso mentale into a blur of lines. In Leonardo’s time, this technique was unprecedented, as Martin Kemp describes:

  Never before had any artist worked out his compositions in such a welter of alternative lines. The pattern-book drawing techniques of the fourteenth and fifteenth centuries, which Verrocchio had relaxed in some measure, have here been overthrown in a “brain storm” of dynamic sketching. Such flexibility of preparatory sketching became the norm for later centuries; it was introduced almost single-handedly by Leonardo.22

  Sometimes—as, for example, in a study for his famous Madonna and Child with Saint Anne—Leonardo would push his technique of dynamic sketching to an extreme, producing what Arasse describes as “an unreadable blur. Nothing can any longer be distinguished in this chaos, but his eye has perceived in the movement of his hand the hidden, buried, latent form, straining to become a figure. Leonardo marks this with a stylus and, turning the sheet over, makes it visible with a distinct line.”23

  To me, this is a fascinating visual illustration of the process known to complexity theorists as “emergence”—the spontaneous emergence of new forms of order out of chaos and confusion.24 According to complexity theory, creativity—the generation of new forms—is a key property of all life, and it involves the very process that Leonardo revealed in his exquisite preparatory drawings. I would argue that our most creative insights emerge from such states of uncertainty and confusion.

  THE SOUL OF PAINTING

  Although he kept his scientific ideas to himself, Leonardo freely shared his views on painting with his students and fellow artists. At his death he left over six hundred pages of detailed instructions for painters, covering all aspects of his science and art of painting. From this vast collection, scattered through eighteen of Leonardo’s Notebooks (over half of which, as noted earlier, are now lost), his friend and disciple Francesco Melzi compiled the famous anthology known as Trattato della pittura (Treatise on Painting).25 First published in 1651, it was soon translated throughout Europe, and remained a standard text for art students for three centuries.

  The first part of the Trattato, known as the “Paragone” (“Comparison”), is a long polemical “debate” comparing painting to poetry, music, and sculpture.26 This kind of polemic was fashionable in the fifteenth century, and Leonardo’s highly original arguments in favor of painting are so lively and witty that we can easily imagine him presenting them in an actual debate.

  “Painting serves a more noble sense than poetry,” he argues, “and renders the figures of the works of nature with more truth than the poet does.” He continues in a lighter vein: “Take a poet who describes the beauties of a lady to her lover, and take a painter who represents her, and you will see where nature will turn the enamored judge.”27 Music ought to be called “the younger sister of painting,” Leonardo suggests, “since it composes harmony from the conjunctions of its proportional parts…. Yet painting excels and rules over music, because it does not immediately die after its creation the way the unfortunate music does.”28 What about sculpture? Surely, no painting endures as well as marble or bronze? True, he admits, “sculpture has the greatest resistance to time.” Nevertheless, painting is far superior, because sculpture “will not produce lucid and transparent bodies like the veiled figures that show the nude flesh under the veils laid against it. It will not produce the minute pebbles of varied colors below the surface of transparent waters.” Sculptors, he continues, “cannot represent…mirrors and similar lustrous things, nor mists, nor bad weather, nor infinite other things that I need not mention because it would be too tedious.”29

  The deeper purpose of Leonardo’s lively polemic was to advance persuasive arguments for considering painting as a mental activity and a science, far above the rank of a mere craft. At the beginning of the Renaissance, painting was classified as a “mechanical art,” together with crafts like gold and metal work, jewelry, tapestry, and embroidery. None of these mechanical arts stood out in terms of prestige, and their practitioners remained relatively anonymous. Commissions would typically specify the quality of the raw materials (gold leaf, lapis lazuli, etc.), which was more important to the patron than the name of the artist.30

  When Florence became a major artistic center in the fourteenth century, its painters began to share their knowledge and experience, and collectively developed many technical innovations. They perfected the fresco technique (the art of painting al fresco, that is, on freshly spread moist plaster), introduced panel painting, and, a century later, pioneered perspective and oil painting. The Florentine painters and sculptors also established an elaborate apprenticeship system, with strict quality control under the supervision of professional guilds, all of which enhanced their prestige and gradually elevated their professions above the anonymous world of craftsmen.

  Leonardo committed himself to advancing this process of emancipation, to convince society that painting should be considered an intellectual enterprise, a true liberal art. To distinguish painting from manual labor, Alberti, in his 1435 book De Pictura (On Painting), had already discussed the importance of mathematics, one of the liberal arts of the time, as the foundation of perspective and the geometry of shadows, and by implication as the intellectual core of painting as a whole.31 Leonardo followed in Alberti’s footsteps but then went beyond him by promoting painting as an intellectual discipline based not only on mathematics but on the theoretical knowledge of “all the qualities of forms.”32

  As a painter, Leonardo excelled especially in modeling subtle gradations of light and dark, known to art historians as chiaroscuro. He revolutionized painting by completely reconceptualizing traditional techniques. “In his use of light and shade, Leonardo was the precursor of all subsequent European painting,” writes Kenneth Clark.”33

  The essence of Leonardo’s innovation lies in his use of shadow as a unifying element, a theme that brings out different qualities of tone and color. As Martin Kemp explains in his discerning analysis of Leonardo’s Virgin of the Rocks,

  From [the] soft substratum of velvety shadow emerge the colors, revealed only by the presence of light…. Within this unity of shadow an infinite subtle series of adjustments are made to accommodate the inherent tonal values of different colors, from the lightest yellow to the deepest of blues.34

  One of the hallmarks of a master painter in the Florentine tradition was the ability to represent figures in apparent three-dimensional relief. “The first task of the painter,” writes Leonardo, “is to make a flat surface appear as a body in relief, standing out from that surface, and he who surpasses the others in that skill deserves most praise.”35 As Kenneth Clark explains, Leonardo was not content to achieve this effect by “the subtle combination of drawing and surface modeling which the painters of the quattrocento [fifteenth century] had brought to perfection. He wished to achieve relief through the scientific use of light and shade.”36 According to Leonardo, such an achievement is “the soul of painting.”37

  Leonardo’s technique of using light and shade to give his figures “great vigor and relief,” as Vasari put it, culminated in his celebrated creation of sfumato, the subtle melting of shades that eventually became the unifying principle of his paintings. “Leonardo’s sfumato was the power behind the poetry of his paintings,” Arasse claimed, “and the mystery that seems to emanate from them.”38

  It is clear from Leonardo’s writings on the use of light and shade that he derived his knowledge from a series of systematic experim
ents with lamps shining on a variety of geometrical solids. He drew numerous complex diagrams showing the formation, projection, intersections, and gradations of shadows in endless combinations. As I will show later in the book, his detailed investigations of vision, the nature of light and shadow, and the appearance of forms were the gateway to his science of painting.39

  Leonardo’s earliest existing notes on shadow and light date from around 1490,40 but it is evident from his Virgin of the Rocks (1483–86) that he had thoroughly mastered the basic concepts several years earlier. His power of observation, combined with his intuitive understanding of light, allowed him to render not only the most subtle gradations of chiaroscuro, but also complex secondary effects of light—reflected sheens, areas of diffused light, subtle glows, and the like—with unprecedented mastery. According to Kemp, “No one until the nineteenth century was to achieve a comparable level of intensity in depicting the elusive complexities of visual phenomena.”41

  DISCORSO MENTALE

  Leonardo could not have developed his mastery of chiaroscuro, nor his characteristic sfumato style, without a major advance in Renaissance painting—the use of oil-based paints. Oil painting makes it possible to put layers of paint on top of each other without blurring the colors (provided the layers are allowed to dry individually), to go back over work again and again, and to mix paints at ease, all of which were essential for Leonardo to achieve his special effects of relief and sfumato.