Fritjof Capra (24 page)

Figure 6-2: Flow of water and flow of human hair, c. 1513, Windsor Collection, Landscapes, Plants, and Water Studies, folio 48r

He made lists of different body parts, such as lips and noses, and identified different types of human figures, varieties of plant species, and even classes of water vortices.
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Whenever he observed natural forms, he recorded their essential features in drawings and diagrams, classified them into types if possible, and tried to understand the processes and forces underlying their formation.

In addition to the variations within a particular species, Leonardo paid attention to similarities of organic forms in different species and to similarities of patterns in different natural phenomena. The Notebooks contain countless drawings of such patterns—anatomical similarities between the leg of a man and that of a horse, spiraling whirlpools and spiraling foliages of certain plants (Fig. 6-1), the flow of water and the flow of human hair (Fig. 6-2), and so on. On a folio of anatomical drawings, he notes that the veins in the human body behave like oranges, “in which, as the skin thickens, so the pulp diminishes the older they become.”
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Among his studies for
The Battle of Anghiari
, we find a comparison of expressions of fury in the faces of a man, a horse, and a lion (Fig. 6-3).

These frequent comparisons of forms and patterns are usually described as analogies by art historians, who point out that explanations in terms of analogies were common among artists and philosophers in the Middle Ages and the Renaissance.
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This is certainly true. But Leonardo’s comparisons of organic forms and processes in different species are much more than simple analogies. When he investigates similarities between the skeletons of different vertebrates, he studies what biologists today call homologies—structural correspondences between different species, due to their evolutionary descent from a common ancestor.

The similarities of expressions of fury in the faces of animals and humans are homologies as well, derived from commonalities in the evolution of face muscles. Leonardo’s analogy between the skin of human veins and the skin of oranges during the process of aging is based on the fact that in both cases he was observing the behavior of living tissues. In all these cases, he realized intuitively that living forms in different species exhibit similarities of patterns. Today we explain these patterns in terms of microscopic cellular structures and of metabolic and evolutionary processes. Leonardo, of course, did not have access to those levels of explanation, but he correctly perceived that throughout the creation (or evolution, as we would say today) of the great diversity of forms, nature used again and again the same basic patterns of organization.

Leonardo’s science is utterly dynamic. He portrays nature’s forms—in mountains, rivers, plants, and the human body—in ceaseless movement and transformation.

Form, for him, is never static. He realizes that living forms are continually being shaped and transformed by underlying processes. He studies the multiple ways in which rocks and mountains are shaped by turbulent flows of water, and how the organic forms of plants, animals, and the human body are shaped by their metabolism. The world Leonardo portrays, both in his art and in his science, is a world in development and flux, in which all configurations and forms are merely stages in a continual process of transformation. “This feeling of movement inherent in the world,” writes art historian Daniel Arasse, “is absolutely central to Leonardo’s work, because it reveals an essential aspect of his genius, thereby defining his uniqueness among his contemporaries.”
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At the same time, Leonardo’s dynamic understanding of organic forms reveals many fascinating parallels to the new systemic understanding of life that has emerged at the forefront of science over the past twenty-five years.

Figure 6-3: Fury in the faces of a man, a horse, and a lion, c. 1503–4, Windsor Collection, Horses and Other Animals, folio 117r

In Leonardo’s science of living forms, life’s patterns of organization and its fundamental processes of metabolism and growth were the unifying conceptual threads that interlinked his knowledge of macro-and microcosm. 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 birds in flight.

THE MOVEMENTS OF WATER

Leonardo was fascinated by water in all its manifestations. He recognized its fundamental role as life’s medium and vital fluid, as the matrix of all organic forms. “It is the expansion and humor of all living bodies,” he wrote. “Without it nothing retains its original form.”
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Throughout his life, he strove to understand the mysterious processes underlying the creation of nature’s forms by studying the movements of water through earth and air.

As an engineer, Leonardo worked extensively on schemes of canalization, irrigation, the drainage of marshes, and the uses of waterpower for pumping, milling, and sawing. Like other noted engineers in the Renaissance, he was very familiar with the beneficial as well as the destructive effects of the power of water. But he was the only one to go beyond empirical rules of hydraulic engineering and embark on sustained theoretical studies of the flow of water. His examinations and exquisite drawings of the flows of rivers, eddies, spiraling vortices, and other patterns of turbulence establish Leonardo as a pioneer in a field that did not even exist in his time—the discipline known today as fluid dynamics.

Throughout his life, Leonardo observed the flows of rivers and tides, drew beautiful and accurate maps of entire watersheds, and investigated currents in lakes and seas, flows over weirs and waterfalls, and the movement of waves as well as flows through pipes, nozzles, and orifices. His observations, drawings, and theoretical ideas would fill hundreds of pages in his Notebooks.

Through this lifelong study, Leonardo gained a full understanding of the main characteristics of fluid flow. He recognized the two principal forces operating in flowing water—the force of gravity and the fluid’s internal friction, or viscosity—and he correctly described many phenomena generated by their interplay. He also realized that water is incompressible and that, even though it assumes an infinite number of shapes, its mass is always conserved.

In a branch of science that did not even exist before him, Leonardo’s deep insights into the nature of fluid flow must be ranked as a momentous achievement. That he also drew many turbulent structures erroneously and imagined some flow phenomena that do not occur in reality does not diminish his great accomplishments, especially in view of the fact that even today scientists and mathematicians encounter considerable difficulties in their attempts to predict and model the complex details of turbulent flows.

At the center of Leonardo’s investigations of turbulence lies the water vortex, or whirlpool. Throughout the Notebooks, there are countless drawings of eddies and whirlpools of all sizes and types—in the currents of rivers and lakes, behind piers and jetties, in the basins of waterfalls, and behind objects of various shapes immersed in flowing water. These often very beautiful drawings are testimony to Leonardo’s endless fascination with the ever-changing and yet stable nature of this fundamental type of turbulence. I believe that this fascination came from a deep intuition that the dynamics of vortices, combining stability and change, embody an essential characteristic of living forms.
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Leonardo was the first to understand the detailed motions of water vortices, often drawing them accurately even in complex situations. He correctly distinguished between flat circular eddies in which the water essentially rotates as a solid body, and spiral vortices (such as the whirlpool in a bathtub) that form a hollow space, or funnel, at their center. “The spiral or rotary movement of every liquid,” he noted, “is so much swifter as it is nearer to the center of its revolution. What we are here proposing is a fact worthy of admiration, since the circular movement of the wheel is so much slower as it is nearer to the center of the rotating object.”
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Such detailed studies of vortices in turbulent water were not taken up again for another 350 years, until the physicist Hermann von Helmholtz developed a mathematical analysis of vortex motion in the mid-nineteenth century.

Figure 6-4: Turbulent wakes behind a rectangular plank, c. 1509–11, Windsor Collection, Landscapes, Plants, and Water Studies, folio 42r

Leonardo produced several elaborate drawings of highly complex patterns of turbulence, generated by placing various obstacles into flowing water. Figure 6-4, from the Windsor Collection, shows the turbulent flows around a rectangular plank inserted at two different angles. (Additional variations are suggested in the small sketches to the right of the main drawing.) The upper drawing clearly shows a pair of counter-rotating vortices at the head of a stream of random wake. The essential details of this complex pattern of turbulence are completely accurate—an amazing testimony to Leonardo’s powers of observation and conceptual clarity.

THE FORMS AND TRANSFORMATIONS OF THE LIVING EARTH

Leonardo saw water as the chief agent in the formation of the Earth’s surface. “Water wears away the mountains and fills up the valleys,” he wrote, “and if it could, it would like to reduce the Earth to a perfect sphere.”
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This awareness of the continual interaction of water and rocks impelled him to undertake extensive studies in geology, which informed the fantastic rock formations that appear so often in the shadowy backgrounds of his paintings.

His geological observations are stunning not only by their great accuracy, but also because they led him to formulate general principles that were rediscovered only centuries later and are still used by geologists today.
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Leonardo recognized temporal sequences in the strata of soil and rock, and corresponding sequences in the fossils deposited in those strata, and he recorded many fine details concerning erosion and deposits by rivers.

He was the first to postulate that the forms of the Earth are the result of processes taking place over long epochs of what we now call geological time. With this view he came close to an evolutionary perspective more than three hundred years before Charles Darwin, who also found inspiration for evolutionary thought in geology. For Leonardo, geological time began with the formation of the living Earth, a process to which he alluded in his paintings with a sense of awe and mystery.

“Describe a landscape with wind and water,” Leonardo exhorted his fellow painters, “and at the setting and rising of the sun.”
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He was a true master in rendering these atmospheric effects. Like his predecessors and contemporaries, he frequently introduced flowers and herbs into his paintings for their symbolic meanings, but unlike most of his fellow painters, he was always careful to present plants in their proper ecological habitats with seasonal appropriateness and great botanical accuracy.
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