by The Science of Leonardo: Inside the Mind of the Great Genius of 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.
Several centuries earlier the Babylonians had developed a different approach to solving mathematical problems, now known as algebra, which began with simple arithmetic operations and then evolved into more abstract formulations with numbers represented by letters. The Greeks learned these numerical and algebraic methods together with Babylonian astronomy, but they transformed them into their geometrical language and continued to see mathematical problems in terms of geometry. Plato’s Academy, the principal Greek school of natural philosophy for nine centuries, is said to have had a sign above its entrance, “Let no one enter here who does not know geometry.”
The culmination of the early phase of Greek mathematics was reached around 300 B.C. with Euclid, who presented all of the geometry and other mathematics known in his day in a systematic, orderly sequence in his celebrated Elements. The thirteen volumes of this classical textbook were not only widely read during the Renaissance, but remained the foundation for the teaching of geometry until the end of the nineteenth century. About one hundred years after Euclid, Greek mathematics reached its final climax with Archimedes, a brilliant mathematician who wrote many important treatises in what we would now call mathematical physics. But he was never as popular as Euclid. His mathematical work was so advanced that it was not understood until many centuries later, and his great fame as an inventor eclipsed his reputation as a mathematician.
With the rise of Islam during the seventh and subsequent centuries, the Arab world became the center of mathematical studies. Arab mathematicians translated and synthesized the Greek texts and also commented on important influences from Mesopotamia and India. Of particular importance was the work of Muhammad al-Khwarzimi in the ninth century, whose Kitab al jabr was the most influential work on algebra from this period. The Arabic al jabr (binding together) in its title is the root of our modern word “algebra.”22
Two centuries later, Persia produced an outstanding algebraist in the poet Omar Khayyam, the world-renowned author of the Rubaiyat, who was famous in his time for classifying cubic equations and solving many of them. Another Islamic scholar of that period who was very influential in the Renaissance was the Arab mathematician Alhazen (Ibn al-Haitham), who wrote a brilliant treatise on the “science of perspective,” which included detailed discussions of geometrical optics and of the geometrical principles of vision and the eye’s anatomy.
In the Renaissance, thus, mathematicians had access to two different approaches for solving mathematical problems, geometry and algebra. However, until the seventeenth century, geometry was considered to be more fundamental. All algebraic reasoning was justified in terms of geometrical figures in the tradition of Greek mathematics. In the seventeenth century, this dependence of algebra on geometry was reversed by René Descartes, the founder of modern philosophy and a brilliant mathematician, who invented a method for associating algebraic equations with curves and surfaces.23 This method, now known as analytic geometry, involves using Cartesian coordinates, the system invented by Descartes and named after him. Long before Descartes, however, the fields of geometry and algebra were related because both of them were necessary for the development of an accurate science of astronomy.
For astronomy was surely the principal physical science throughout antiquity. The Babylonians successfully applied their numerical methods to compile astronomical tables. The Greeks used their geometrical approach to construct elaborate cosmological models, involving the use of trigonometry—which the Greek astronomers had learned from Hindu mathematicians—to determine the distances between celestial bodies from their observed angular positions.
When the conquests of Alexander the Great made the observations and mathematical methods of the Babylonian astronomers available to the Greeks, they found it impossible to reconcile this improved data with their Platonic idea of circular planetary orbits. Several Greek astronomers therefore abandoned the Platonic-Aristotelian view and began to devise complex geocentric systems of cycles and epicycles to account for the movements of the sun, moon, and planets. The culmination of this development was reached in the second century A.D. with the Ptolemaic system, which predicted the motion of the planets with considerable accuracy.
Ptolemy’s thirteen-volume treatise, He mathematike syntaxis (The Mathematical Collection) summarized much of this ancient astronomical knowledge. It remained the authoritative text on astronomy for fourteen centuries. (It is indicative of the prestige of Islamic science that the text was known throughout the Middle Ages and the Renaissance under its Arabic title, Almagest.) Ptolemy also published the Geography, which contained detailed discussions of cartographic techniques and an elaborate map of the known world. The book was printed in the fifteenth century under the title Cosmography and became the most popular geographical book printed from movable type during the Renaissance.
NATURAL HISTORY
Throughout antiquity and in the centuries that followed, the study of the living world was known as natural history, and those who pursued it were known as naturalists. This was often an amateur activity rather than a professional occupation. It was only in the nineteenth century that the term “biology” began to be widely used, and even then, biologists often continued to be called “naturalists.”
In the fifteenth century, books about natural history still tended to display some fascination with the fabulous, often imaginary beasts that had populated medieval bestiaries. At the time of Leonardo, the rediscovery of classical natural history texts, together with the explorations of new floras and faunas in the Americas, began to stimulate more serious interest in the study of living things. The ideas of the ancient natural philosophers about plants and animals were represented in great detail in the encyclopedic works of Aristotle, Theophrastus, Pliny the Elder, and Dioscorides.24
Aristot
le was the classical author most widely available to Renaissance scholars. His numerous works included several treatises on animals, including the Historia animalium (History of Animals) and De anima (Of the Soul). While Aristotle’s observations of plants were less accurate than his observations of animals, his disciple and successor Theophrastus was a keen botanical observer. His treatise De historia plantarum (Of the History of Plants) was a pioneering work that made Theophrastus famous as the “father of botany.”
In the first century A.D., the Roman naturalist Pliny the Elder (Gaius Plinius) wrote a monumental encyclopedia titled Natural History, comprising 37 books in which almost 500 Greek and Roman authors are cited. It became the favorite scientific encyclopedia in the Middle Ages, not only because of its rich content but also because it was written in an informal style. While it lacked scientific rigor, it was much easier and more pleasant to read than the learned volumes of Aristotle and the other Greek philosophers. For most Renaissance humanists, Pliny’s name meant natural history itself. And his encyclopedia was the most convenient entry point to further research.
Botany, from ancient times up to the end of the sixteenth century, was often considered a subdiscipline of medicine, since plants were mainly studied for their use in the healing arts. For centuries the authoritative text in this field was the Materia Medica by the Greek physician Dioscorides, who was a contemporary of Pliny.
MEDICINE AND ANATOMY
In prehistoric cultures around the world, the origin of illness and the process of healing were associated with forces belonging to the spirit world, and a great variety of healing rituals and practices were developed to deal with illness accordingly.25 In Western medicine, a revolutionary change occurred in Greece in the fifth century B.C., with the emergence of the scientific medical tradition associated with Hippocrates. There is no doubt that a famous physician by that name practiced and taught medicine around 400 B.C. on the island of Cos, but the voluminous writings attributed to him, known as the Hippocratic Corpus, were probably written by several authors at different times.