Fritjof Capra (20 page)

Leonardo fully embraced the humanist passion for exploration, in both the physical and mental realms. He was one of the first European mountaineers
¹²
and traveled frequently within Italy, exploring the vegetation, waterways, and geological formations of the regions he visited. In addition, he delighted in composing fictitious tales of journeys to mountains and deserts in faraway countries.
¹³

These few examples from Leonardo’s many interests and activities show us that he was well aware of the intellectual, technological, and cultural achievements of his time. From his early days as an apprentice in Verrocchio’s workshop through the years he spent at various European courts, he was in regular contact with leading artists, engineers, philosophers, historians, and explorers, and thus thoroughly familiar with the wide range of ideas and practices that we now associate with the Renaissance.

THE ANCIENT VIEW OF THE UNIVERSE

The foundation of the Renaissance worldview was the conception of the universe that had been developed in classical Greek science: that the world was a
kosmos
, an ordered and harmonious structure. From its beginnings in the sixth century
B.C.
, Greek philosophy and science understood the order of the cosmos to be that of a living organism rather than a mechanical system. This meant that all its parts had an innate purpose to contribute to the harmonious functioning of the whole, and that objects moved naturally toward their proper places in the universe. Such an explanation of natural phenomena in terms of their goals, or purposes, is known as teleology, from the Greek
telos
(purpose). It permeated virtually all of Greek philosophy and science.

The view of the cosmos as an organism also implied for the Greeks that its general properties are reflected in each of its parts. This analogy between macrocosm and microcosm, and in particular between the Earth and the human body, was articulated most eloquently by Plato in his
Timaeus
in the fourth century
B.C.
, but it can also be found in the teachings of the Pythagoreans and other earlier schools. Over time, this idea acquired the authority of common knowledge, which continued throughout the Middle Ages and into the Renaissance.

In early Greek philosophy, the ultimate moving force and source of all life was identified with the soul, and its principal metaphor was that of the breath of life. Indeed, the root meaning of both the Greek
psyche
and the Latin
anima
is “breath.” Closely associated with that moving force—the breath of life that leaves the body at death—was the idea of knowing. For the early Greek philosophers, the soul was both the source of movement and life, and that which perceives and knows. Because of the fundamental analogy between micro-and macrocosm, the individual soul was thought to be part of the force that moves the entire universe, and accordingly the knowing of an individual was seen as part of a universal process of knowing. Plato called it the
anima mundi
, the “world soul.”

As far as the composition of matter was concerned, Empedocles in the fifth century
B.C.
claimed that the material world was composed of varying combinations of four elements—earth, water, air, and fire. When left to themselves, the elements would settle into concentric spheres with the earth at the center, surrounded successively by the spheres of water, air, and fire. Farther outside were the spheres of the planets and beyond them was the sphere of the stars.

According to the four-element theory, the great variety of qualities we observe in material objects is the result of combinations of four pairs of qualities associated with the elements: cold and dry (earth), hot and dry (fire), cold and wet (water), and hot and wet (air). Half a century after Empedocles, an alternative theory of matter was proposed by Democritus, who taught that all material objects are composed of atoms of numerous shapes and sizes, and that all observable qualities are derived from the particular combinations of atoms inside the objects. His theory was so antithetical to the traditional teleological views of matter that it was pushed into the background, where it remained throughout the Middle Ages and the Renaissance. It would surface again only in the seventeenth century, with the rise of Newtonian physics.
¹⁴

Even if the properties of material objects could be seen as arising from various combinations of the basic qualities inherent in the four elements, the Greek philosophers still faced the problem of how these combinations of elements acquired the specific forms we see in nature. The first philosopher to address the problem of form was Pythagoras in the sixth century
B.C.
, who founded a cultlike school of mathematics, known as Pythagoreans. He and his disciples believed that numerical patterns and ratios were at the origin of all forms. With this association between the concrete world of natural forms and the abstract realm of numerical relationships began the link between science and mathematics that would become the foundation of classical physics in the seventeenth century.

The Pythagoreans divided the universe into two realms: the heavens, in which the stars revolve in celestial spheres according to perfect, unchanging mathematical laws; and the Earth, in which phenomena are complex, ever changing, and imperfect. Plato added his own refinement to this picture. Since the circle is the most perfect geometrical figure, he argued, the planets, like the stars, must move in circles.

ARISTOTLE’S SYNTHESIS OF SCIENCE

For science at the time of the Renaissance, the most important Greek philosopher was Aristotle. A student of Plato, Aristotle was by far the most brilliant in Plato’s Academy. But he was quite different not only from his teacher, but also from all his predecessors. Aristotle was the first philosopher to write systematic, professorial treatises about the main branches of learning of his time. He synthesized and organized the entire scientific knowledge of antiquity in a scheme that would remain the foundation of Western science for two thousand years. And when this body of knowledge was fused with Christian theology in the Middle Ages, it acquired the status of religious dogma.

To integrate the main disciplines of his time—biology, physics, metaphysics, ethics, and politics—into a coherent theoretical framework, Aristotle created a formal system of logic and a set of unifying principles. He stated explicitly that the goal of his logic was to learn the art of scientific investigation and reasoning. It was to serve as the rational instrument for all scientific work.

As a scientist, Aristotle was first and foremost a biologist, whose observations of marine life were unsurpassed until the nineteenth century. Like Pythagoras, he distinguished between matter and form, but as a biologist he knew that living form is more than shape, more than a static configuration of component parts.
¹⁵
His highly original approach to the problem of form was to posit that matter and form are linked through a process of development. In contrast with Plato, who believed in an independent realm of ideal forms, Aristotle held that form has no separate existence but is immanent in matter. Nor can matter exist separately from form. By means of form, the essence of matter becomes real, or actual. Aristotle called this process of the self-realization of matter
entelechy
(self-completion). Matter and form, in his view, are the two sides of this process of development, separable only through abstraction.

Aristotle associated his
entelechy
with the traditional Greek concept of the soul as the source of life.
¹⁶
The soul, for him, is the source not only of bodily motion but also of the body’s formation: It is the form that realizes itself in the changes and movements of the organic body. Leonardo, as I shall show, adopted the Aristotelian concept of the soul, expanded it, and transformed it into a scientific theory based on empirical evidence.
¹⁷

Aristotle conceived of the soul as being built up in successive levels, corresponding to levels of organic life. The first level is the “vegetative soul,” which controls, as we would say today, the mechanical and chemical changes of the body’s metabolism. The soul of plants is restricted to this metabolic level of a vital force. The next higher form is the “animal soul,” characterized by autonomous motion in space and by sensation, that is, feelings of pleasure and pain. The “human soul,” finally, includes the vegetable and animal souls, but its main characteristic is reason.

In terms of physics and astronomy, Aristotle adopted the Pythagorean antithesis between the terrestrial and the heavenly worlds. From the Earth to the sphere of the Moon, he taught, all things constantly change, generating new forms and then decaying again; above the Moon, the crystalline spheres of the planets and stars revolve in eternal, unchanging motions. He subscribed to the Platonic idea that the perfection of the celestial realm implies that the planets and stars move in perfect circles. Aristotle also accepted Plato’s view that divine souls reside in the heavenly bodies, and that they influence life on Earth. This idea lies at the root of medieval astrology, which was still very popular during the Renaissance. Leonardo, however, emphatically rejected it.
¹⁸

Following Empedocles, Aristotle maintained that all forms in the world arise from various combinations of the four elements—earth, water, air, and fire—and he saw the ever-changing mixtures of elements as the source of the imperfection and accidental nature of material forms. The four elements did not always remain in their assigned realms, he stated, but were constantly disturbed and being pushed into neighboring spheres, whereupon they would naturally try to return to their proper places. With this argument, Aristotle tried to explain why rain falls downward through the air, while air drifts upward in water, and the flames of fire rise up into the air. He strongly opposed the attempt by Democritus to reduce the qualities of matter to quantitative relations between atoms. It was because of Aristotle’s great authority that the atomism of Democritus was eclipsed by teleological explanations of physical phenomena throughout antiquity and the Middle Ages.

For Aristotle, all activities that occurred spontaneously were natural, guided by the goals inherent in physical phenomena, and hence observation was the proper means of investigating them. Experiments that altered natural conditions in order to bring to light some hidden properties of matter were unnatural. As such, they could not be expected to reveal the essence of the phenomena. Experiments, Aristotle taught, were therefore not proper means of investigation, and indeed the experimental method was not essential to Greek science.

Aristotle’s treatises were the foundation of philosophical and scientific thought in the Renaissance. But the humanist scholars also read Plato and various texts from the earlier traditions of Greek natural philosophy as well as the more recent treatises by Arab scientists. Thus, different schools of thought soon arose that followed one or another of the ancient philosophers. In particular, there was a lively debate between the Platonists, for whom only ideas were real and the world of the senses was illusory, and the Aristotelians, for whom the senses provided reality and ideas were mere abstractions.

Florence under the Medici was the center of Platonism. Milan, under the influence of the universities of Padua and Bologna, was predominantly Aristotelian. Leonardo, who spent many years in both cities, was well aware of the philosophical debates between the two schools. Indeed, the tension between the Platonic fascination with mathematical precision and the Aristotelian attention to qualitative forms and their transformations surfaces again and again in his writings.
¹⁹

Renaissance science as a whole was characterized by a literary rather than an empirical approach. Instead of observing nature, the Italian humanists preferred to read the classical texts. In the words of historian of science George Sarton, “To study geometry was to study Euclid; a geographical atlas was an edition of Ptolemy; the physician did not study medicine, he studied Hippocrates and Galen.”
²⁰

The classical treatises rediscovered in the Renaissance covered a wide range of subjects, from art and literature to philosophy, science, architecture, and engineering. As far as science, or “natural philosophy,” was concerned, the Renaissance scholars studied Greek and Arabic texts within three broad areas: mathematics and astronomy, natural history, and medicine and anatomy.

MATHEMATICS AND ASTRONOMY AT THE TIME OF LEONARDO

Greek theoretical mathematics began during the lifetime of Plato, in the fifth and fourth centuries
B.C.
The Greeks tended to geometrize all mathematical problems and seek answers in terms of geometrical figures. For example, they represented quantities by lengths of lines and products of two quantities by the area of rectangles. These methods even enabled them to deal with irrational numbers,
²¹
representing the number
2, for example, by the diagonal of a square with sides of length 1.