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

by Fritjof Capra

  For Leonardo, painting is both an art and a science—a science of natural forms, of qualities, quite different from the mechanistic science that would emerge two hundred years later. Leonardo’s forms are living forms, continually shaped and transformed by underlying processes. Throughout his life he studied, drew, and painted the rocks and sediments of the earth, shaped by water; the growth of plants, shaped by their metabolism; and the anatomy of the animal (and human) body in motion.

  THE NATURE OF LIFE

  Nature as a whole was alive for Leonardo. He saw the patterns and processes in the microcosm as being similar to those in the macrocosm. He frequently drew analogies between human anatomy and the structure of the Earth, as in the following beautiful passage from the Codex Leicester:

  We may say that the Earth has a vital force of growth, and that its flesh is the soil; its bones are the successive strata of the rocks which form the mountains; its cartilage is the porous rock, its blood the veins of the waters. The lake of blood that lies around the heart is the ocean. Its breathing is the increase and decrease of the blood in the pulses, just as in the Earth it is the ebb and flow of the sea.5

  While the analogy between microcosm and macrocosm goes back to Plato and was well known throughout the Middle Ages and the Renaissance, Leonardo disentangled it from its original mythical context and treated it strictly as a scientific theory. Today we know that some of the analogies in the passage quoted above are flawed, and in fact Leonardo himself corrected some of them late in his life.6 However, we can easily recognize Leonardo’s statement as a forerunner of today’s Gaia theory—a scientific theory that views the earth as a living, self-organizing, and self-regulating system.7

  At the most fundamental level, Leonardo always sought to understand the nature of life. This has often escaped earlier writers, because until recently the nature of life was defined by biologists only in terms of cells and molecules, to which Leonardo, living two centuries before the invention of the microscope, had no access. But today, a new systemic understanding of life is emerging at the forefront of science—an understanding in terms of metabolic processes and their patterns of organization. And those are precisely the phenomena Leonardo explored throughout his life.

  A SYSTEMIC THINKER

  Leonardo da Vinci was what we would call, in today’s scientific parlance, a systemic thinker.8 Understanding a phenomenon, for him, meant connecting it with other phenomena through a similarity of patterns. When he studied the proportions of the human body, he compared them to the proportions of buildings in Renaissance architecture. His investigations of muscles and bones led him to study and draw gears and levers, thus interlinking animal physiology and engineering. Patterns of turbulence in water led him to observe similar patterns in the flow of air; and from there he went on to explore the nature of sound, the theory of music, and the design of musical instruments.

  This exceptional ability to interconnect observations and ideas from different disciplines lies at the very heart of Leonardo’s approach to learning and research. At the same time, it was also the reason why he often got carried away and extended his investigations far beyond their original role in the formulation of a “science of painting,” exploring almost the entire range of natural phenomena known at his time as well as many others previously unrecognized.

  Leonardo’s scientific work was virtually unknown during his lifetime and remained hidden for over two centuries after his death in 1519. His pioneering discoveries and ideas had no direct influence on the scientists who came after him, although during the subsequent 450 years his conception of a science of living forms would emerge again at various times. During those periods, the problems he had struggled with were revisited with increasing levels of sophistication, as scientists advanced in their understanding of the structure of matter, the laws of chemistry and electromagnetism, cellular and molecular biology, genetics, and the critical role of evolution in shaping the forms of the living world.

  Today, from the vantage point of twenty-first-century science, we can recognize Leonardo da Vinci as an early precursor of an entire lineage of scientists and philosophers whose central focus was the nature of organic form. They include Immanuel Kant, Alexander von Humboldt, and Johann Wolfgang von Goethe in the eighteenth century; Georges Cuvier, Charles Darwin, and D’Arcy Thompson in the nineteenth; Alexander Bogdanov, Ludwig von Bertalanffy, and Vladimir Vernadsky in the early twentieth; and Gregory Bateson, Ilya Prigogine, and Humberto Maturana in the late twentieth century; as well as contemporary morphologists and complexity theorists like Brian Goodwin, Ian Stewart, and Ricard Solé.

  Leonardo’s organic conception of life has continued as an undercurrent of biology throughout the centuries, and during brief periods came to the fore and dominated scientific thought. However, none of the scientists in that lineage were aware that the great genius of the Renaissance had already pioneered many of the ideas they were exploring. While Leonardo’s manuscripts were gathering dust in ancient European libraries, Galileo Galilei was being celebrated as the “father of modern science.” I cannot help but argue that the true founder of modern science was Leonardo da Vinci, and I wonder how Western scientific thought would have developed had his Notebooks been known and widely studied soon after his death.

  SYNTHESIS OF ART AND SCIENCE

  To describe nature’s organic forms mathematically, we cannot use Euclidean geometry, nor the classical equations of Newtonian physics. We need a new kind of qualitative mathematics. Today, such a new mathematics is being formulated within the framework of complexity theory, technically known as nonlinear dynamics.9 It involves complex nonlinear equations and computer modeling, in which curved shapes are analyzed and classified with the help of topology, a geometry of forms in movement. None of this was available to Leonardo, of course. But amazingly, he experimented with a rudimentary form of topology in his mathematical studies of “continuous quantities” and “transmutations,” long before this important branch of modern mathematics was developed by Henri Poincaré in the early twentieth century.10

  Leonardo’s principal tool for the representation and analysis of nature’s forms was his extraordinary facility of drawing, which almost matched the quickness of his vision. Observation and documentation were fused into a single act. He used his artistic talent to produce drawings that are stunningly beautiful and at the same time serve as geometric diagrams. For Leonardo, drawing was the perfect vehicle to formulate his conceptual models—a perfect “mathematics” for his science of organic forms.11

  The dual role of Leonardo’s drawings—as art and as tools of scientific analysis—shows us why his science cannot be understood without his art, nor his art without his science. His assertion that “painting embraces in itself all the forms of nature” cuts both ways. In order to practice his art, he needed the scientific understanding of the forms of nature; in order to analyze the forms of nature, he needed the artistic ability to draw them.

  In addition to his keen intellect and powers of observation, his experimental ingenuity, and his great artistic talents, Leonardo also had a very practical bent. As he pursued his investigations of nature’s forms, beholding them with the eye of a scientist and painter, the useful applications of his discoveries were never far from his mind. He spent a major part of his life conceiving machines of all kinds, inventing numerous mechanical and optical devices, and designing buildings, gardens, and cities.

  When he studied water, he saw it not only as the medium of life and the driving force of nature, but also as a source of power for industrial systems, similar to the role that steam—another form of water—would play in the Industrial Revolution three centuries later. His extensive investigations of the flows of air and wind and the flight of birds led him to invent various flying machines, many of them based on sound aerodynamic principles. Indeed, Leonardo’s achievements as a designer and engineer are on a par with his accomplishments as an artist and scientist.

  THE EYE AND THE APPEARANCE OF FORMSr />
  In his Treatise on Painting, Leonardo makes clear that painting is the unifying perspective and integrating thread that runs through all his fields of study. From this work, a coherent conceptual structure emerges, which he might have intended to use for the eventual publications of his Notebooks.

  Like all true scientists, Leonardo based his science on systematic observation. Hence his starting point is the human eye. His careful investigations of the anatomy of the eye and the origin of vision were unparalleled in his time. He paid particular attention to the connections between the eye and the brain, which he demonstrated in a series of beautiful drawings of the human skull. Using brilliant anatomical dissections, Leonardo displayed for the first time the complete path of vision through the pupil and lens to the optic nerve, and all the way to a specific cavity in the brain, known to neurologists today as the third cerebral ventricle.12

  This is where he located the “seat of the soul,” where all sense impressions meet. Leonardo’s concept of the soul comes very close to what cognitive scientists today call “cognition,” the process of knowing.13 His theory of how sensory impulses travel along the nerves from the sense organs to the brain is so ingenious that I doubt if neuroscientists today could conceive of anything better, were they given the restrictions of having to work without any knowledge of electromagnetism, biochemistry, and microbiology.

  Leonardo saw his discoveries in optics and the physiology of vision as the grounding of his science of painting, beginning with the science of perspective, the outstanding innovation of Renaissance art. “Painting is based on perspective,” he explains, “and perspective is nothing else than a thorough knowledge of the function of the eye.”14 From perspective, he moved on to explore the geometry of light rays (known today as geometrical optics), the effects of light falling on spheres and cylinders, the nature of shadow and of contrasts, and the juxtaposition of colors.

  These systematic studies, illustrated in long series of intricate drawings, were the scientific basis of Leonardo’s extraordinary artistic ability to understand and render the most subtle visual complexities. Most renowned was his invention and mastery of a special art of shading—a melting of shades, known as sfumato—which delicately blurs the outlines of bodies. In the words of art historian Daniel Arasse,

  The supreme expression of the science of painting and of its divine character, Leonardo’s sfumato was the power behind the poetry of his paintings and the mystery that seems to emanate from them.15

  Eventually, these sophisticated studies of the effects of light and shade led Leonardo to thoroughly investigate the very nature of light. With only the most rudimentary instruments, he used his phenomenal powers of observation, his ability to recognize similarities of patterns, and the great intuitive understanding of light he had acquired as a painter to formulate concepts that were diametrically opposed to the ideas of his contemporaries, but were almost identical to those Christian Huygens would propose two hundred years later in his famous wave theory of light.16

  THE LIVING FORMS OF NATURE

  Leonardo’s studies of living forms began with their appearance to his painter’s eye, and then proceeded to detailed investigations of their intrinsic nature. In the macrocosm, the main themes of his science were the movements of water and air, the geological forms and transformations of the Earth, and the botanical diversity and growth patterns of plants. In the microcosm, his main focus was on the human body—its beauty and proportions, the mechanics of its movements, and how it compared to other animal bodies in motion, in particular the flight of birds.

  The science of living forms, for Leonardo, is a science of movement and transformation, whether he studies mountains, rivers, plants, or the human body. To understand the human form means to understand the body in motion. Leonardo demonstrated in countless elaborate and beautiful drawings how nerves, muscles, tendons, bones, and joints work together to move the limbs; how limbs and facial expressions perform gestures and actions.

  As always, Leonardo used the insights he gained from this extensive research in his paintings. In the words of Daniel Arasse,

  From the early Madonnas, through the portraits, to St. John the Baptist, Leonardo caught the figure in motion. The immediate and exceptional impact of The Last Supper was largely due to the fact that Leonardo replaced the traditional arrangement with a rhythmical composition that considerably changed the very idea of the subject.17

  As a painter, Leonardo felt that he should use gestures to portray the frames of mind and emotions that provoked them. He asserted that, in the painting of a human figure, the most important task was to “express in gesture the passion of its soul.”18 Indeed, to portray the body’s expression of the human spirit was the artist’s highest aspiration, in Leonardo’s view. And it was one in which he himself excelled, as the paintings of his mature period attest. As art historian Irma Richter explains in the introductory comments to her classic selections from the Notebooks, for Leonardo, “the human body was an outward and visible expression of the soul; it was shaped by its spirit.”19 We shall see that this view of soul and spirit, unmarred by the mind-body split that René Descartes would introduce in the seventeenth century, is perfectly consistent with the conception of the “embodied mind” in today’s cognitive science.20

  Figure I-1: The Mechanisms of the Arm, c. 1510, Anatomical Studies, folio 135v

  Unlike Descartes, Leonardo never thought of the body as a machine, even though he was a brilliant engineer who designed countless machines and mechanical devices. He clearly recognized, and documented in superb renderings, that the anatomies of animals and humans involve mechanical functions (see Fig. I-1). “Nature cannot give movement to animals without mechanical instruments,” he explained.21 But that did not imply for him that living organisms were machines. It only implied that, in order to understand the movements of the animal body, he needed to explore the principles of mechanics, which he did for many years in a thorough and systematic way. He clearly understood that the means of the body’s movements were mechanical. But for Leonardo, their origin lay in the soul, the nature of which was not mechanical but spiritual.22

  LEONARDO’S LEGACY

  Leonardo did not pursue science and engineering to dominate nature, as Francis Bacon would advocate a century later. He had a deep respect for life, a special compassion for animals, and great awe and reverence for nature’s complexity and abundance. While a brilliant inventor and designer himself, he always thought that nature’s ingenuity was vastly superior to human design. He felt that we would be wise to respect nature and learn from her. It is an attitude that has reemerged today in the practice of ecological design.23

  Leonardo’s synthesis of art and science is infused with a deep awareness of ecology and systems thinking. It is not surprising that he spoke with great disdain of the so-called “abbreviators,” the reductionists of his time:

  The abbreviators of works do injury to knowledge and to love…. Of what value is he who, in order to abbreviate the parts of those things of which he professes to give complete knowledge, leaves out the greater part of the things of which the whole is composed?…Oh human stupidity!…You don’t see that you are falling into the same error as one who strips a tree of its adornment of branches full of leaves, intermingled with fragrant flowers or fruit, in order to demonstrate that the tree is good for making planks.24

  This statement is revealing testimony of Leonardo’s way of thinking and is also ominously prophetic. Reducing the beauty of life to mechanical parts and valuing trees only for their lumber is an eerily accurate characterization of the mind-set that dominates our world today. In my view, this makes Leonardo’s legacy all the more relevant to our time.

  Our sciences and technologies have become increasingly narrow in their focus, and we are unable to understand our multifaceted problems from an interdisciplinary perspective. We urgently need a science that honors and respects the unity of all life, that recognizes the fundamental interdependence of all natural phen
omena, and reconnects us with the living earth. What we need today is exactly the kind of thinking and science Leonardo da Vinci anticipated and outlined five hundred years ago, at the height of the Renaissance and the dawn of the modern scientific age.

  ONE

  Infinite Grace

  The earliest literary portrait of Leonardo da Vinci, and to me still the most moving, is that by the Tuscan painter and architect Giorgio Vasari in his classic book Lives of the Artists, published in 1550.1 Vasari was only eight years old when Leonardo died, but he gathered information about the master from many artists who had known him and remembered him well, most notably Leonardo’s close friend and disciple Francesco Melzi. An acquaintance of Leonardo, the surgeon and art collector Paolo Giovio, wrote a short eulogy, but it is unfinished and merely a page long.2 Vasari’s chapter, “Life of Leonardo da Vinci,” there fore, is as close as we can come to a contemporary account.

  Besides being an accomplished painter and architect, Vasari was a keen collector of drawings by famous masters and of stories about them. The idea of writing a book on the history of Italian art from the thirteenth to the sixteenth centuries was suggested to him by Giovio during a dinner party in Rome.3 The book became a bestseller when it was first published, and its wide popular appeal has endured over the centuries due to the author’s lively and colorful portraits, replete with charming anecdotes. Through a series of engaging stories about the lives of its greatest artists, Vasari’s Lives conveyed the revolutionary nature of the Italian Renaissance. In spite of many inaccuracies and a tendency toward referring to legends and idolizing, Vasari’s work remains the principal source for anyone interested in that period of European art and culture.