In the Notebooks, Leonardo repeatedly commented on how a good experiment should be conducted, and in particular he stressed the need for careful repetitions and variations. Thus we read in Manuscript A: “Before you make a general rule of this case, test it two or three times and observe whether the tests produce the same effects.” In Manuscript M he notes: “This experiment should be made several times, so that no accident may occur to hinder or falsify the test.”14
Being a brilliant inventor and mechanical engineer, Leonardo was able to design ingenious experiments with the simplest means. For example, grains of millet or sprigs of straw, thrown into flowing water, helped him visualize and draw the shapes of the flow lines; specially designed floats, suspended at different depths of a flowing river, allowed him to measure the water’s speed at different levels and at different distances from the banks.15 He built glass chambers with their bases lined with sand and rear walls painted black for observing fine details of water movements in a controlled laboratory setting.16
Leonardo had to invent and design most of his measuring instruments. These included a device for measuring wind speed, a hygrometer to measure the humidity of the air, and various types of odometers to record distances traveled. In the course of surveying land, Leonardo would sometimes attach a pendulum to his thigh, which moved the teeth in a cogwheel to count the number of his steps. At other times he would use a cart with a cogwheel, and the cogwheel was designed to advance one cog with every ten braccia (about twenty feet) traveled, until a pebble audibly dropped into a metal basin at a distance of one mile.17 In addition, he made many attempts to improve clock mechanisms for time measurement, which was still in its infancy in his day.18
In his scientific observations and experiments, Leonardo showed the same patience and subtle attention to detail that he practiced as a painter. This is especially noticeable in his anatomical research. For example, in one dissection he poured wax into the cavities of the brain known as cerebral ventricles to determine their shape. “Make two vent holes in the horns of the greater ventricles and insert melted wax with the syringe,” he noted in his Anatomical Studies. “Then, when the wax has set, dissect off the brain and you will see the shape of the three ventricles exactly.”19 He invented an equally ingenious technique for dissecting the eye. As physician Sherwin Nuland describes it:
In dissecting the eye, a notoriously difficult organ to cut, Leonardo hit upon the idea of first immersing it in egg white and then boiling the whole, so as to create a coagulum [thickened mass] before cutting into the tissue. Similar embedding techniques are routinely used today to enable accurate slicing of fragile structures.20
The systematic approach and careful attention to detail that Leonardo applied to his observations and experiments are characteristic of his entire method of scientific investigation. He would usually start from commonly accepted concepts and explanations, often summarizing what he had gathered from the classical texts before proceeding to verify it with his own observations. Sometimes he jotted down these summaries in the form of quick sketches, or even as elaborate drawings. Before the accurate dating of the Notebooks, these drawings were often seen as indications of Leonardo’s own lack of scientific knowledge rather than as the “citations” of received opinion that they are.
For example, the well-known “coitus figure” in the Windsor Collection of anatomical drawings, which shows the male reproductive organs with anatomies that are mostly erroneous, was long viewed as reflecting Leonardo’s poor understanding of anatomy. More recently, however, the drawing was recognized by the historian of medicine and Leonardo scholar Kenneth Keele as Leonardo’s illustration of what he had read in Plato’s Timaeus. He had used it as the starting point for his own anatomical explorations of human reproductive processes.21
After testing the traditional ideas repeatedly with careful observations and experiments, Leonardo would either adhere to tradition if he found no contradictory evidence or would formulate his own alternative explanations. Sometimes he would dispense with comments altogether, relying entirely on the persuasive power of his drawings.
Leonardo generally worked on several problems simultaneously and paid special attention to similarities of forms and processes in different areas of investigation—for example, between the forces transmitted by pulleys and levers and those transmitted by muscles, tendons, and bones; between patterns of turbulence in water and in air; between the flow of sap in a plant or tree and the flow of blood in the human body.
When he made progress in his understanding of natural phenomena in one area, he was always aware of the analogies and interconnecting patterns to phenomena in other areas and would revise his theoretical ideas accordingly. This method led him to tackle many problems not just once but several times during different periods of his life, modifying his theories in successive steps as his scientific thought evolved over his lifetime.
Leonardo’s method of repeatedly reassessing his theoretical ideas in various areas meant that he never saw any of his explanations as “final.” Even though he believed in the certainty of scientific knowledge, as did most philosophers and scientists for the next three hundred years, his successive theoretical formulations in many fields are quite similar to the theoretical models that are characteristic of modern science. For example, he proposed several different models for the functioning of the heart and its role in maintaining the flow of blood, including one that pictured the heart as a stove housing a central fire, before he concluded that the heart is a muscle pumping blood through the arteries.22 Leonardo also used simplified models—or approximations, as we would say today—to analyze the essential features of complex natural phenomena. For instance, he represented the flow of water through a channel of varying cross sections by using a model of rows of men marching through a street of varying width.23
Like modern scientists, Leonardo was always ready to revise his models when he felt that new observations or insights required him to do so. In his art as in his science, he always seemed to be more interested in the process of exploration than in the completed work or final results. Thus many of his paintings and all of his science remained unfinished work in progress.
This is a general characteristic of the modern scientific method. Although scientists publish their work in various stages of completion in papers, monographs, and textbooks, science as a whole is always work in progress. Old models and theories continue to be replaced by new ones, which are judged superior but are nevertheless limited and approximate, destined to be replaced in their turn as knowledge progresses.
Since the Scientific Revolution in the seventeenth century, this progress in science has been a collective enterprise. Scientists continually exchanged letters, papers, and books, and discussed their theories at various gatherings. This continual exchange of ideas is well documented and thus makes it fairly easy for historians to follow the progress of science through the centuries. With Leonardo, the situation is quite different. He worked alone and in secrecy, did not publish any of his findings, and only rarely dated his notes. In addition, he frequently copied excerpts from scholarly works into his Notebooks without proper attribution, even without identifying them as quotations, so that historians long took some of those copied passages for Leonardo’s own original ideas.
Having pioneered the scientific method in solitude, Leonardo did not see science as a collective, collaborative enterprise. During his lifetime, therefore, any progress in his science was evident to him alone. Scholars today have had to engage in meticulous detective work to reconstruct the evolution of his scientific thought.
THE NOTEBOOKS
Leonardo recorded the results of his observations and experiments, his theoretical models, and his philosophical speculations in thousands of pages of notes, some in the form of well-organized treatises in various stages of completion, but most of them as disjointed notes and drawings without any apparent order, sometimes scribbled on the same folio at different times. Even though scholarly editions wit
h clear transcriptions of all the Notebooks are now available, and most of the pages have been carefully dated, Leonardo’s notes and drawings are so extensive, and their topics so diverse, that much work remains to be done to fully analyze their scientific contents and evaluate their significance.
The original text is difficult to read not only because it is written in mirror writing and is often disjointed, but also because Leonardo’s spelling and syntax are highly idiosyncratic. He always seems to be in a hurry to jot down his thoughts, makes plenty of banal slips and errors, and often strings words together without any spaces between them. Punctuation is practically absent in his handwriting. The period (the only punctuation he uses) may occur very frequently in some manuscripts and be totally absent in others. In addition, like anyone used to taking regular and extensive personal notes, he employs his own code of abbreviations and shorthand notations.
In the fifteenth century, standard Italian spelling had not yet been established,24 and scribes allowed themselves considerable variations. Accordingly, Leonardo varies his spellings quite indiscriminately, recording the sound of the spoken word in his own idiosyncratic ways rather than following any written tradition.
Taken together, these idiosyncrasies present considerable obstacles to the reader of Leonardo’s original text. Fortunately, however, scholars have provided us with two kinds of transcriptions which, reproduced side by side, solve all these problems while following Leonardo’s words as closely as possible.25 The so-called “diplomatic” transcription gives a printed version of the text exactly the way Leonardo wrote it, with all the abbreviations, idiosyncratic spellings, errors, crossed-out words, and other anomalies. The “critical” transcription next to it is a cleaned-up version of the text in which the abbreviations and errors have been eliminated, and Leonardo’s archaic and erratic spellings have been replaced by their modern Italian counterparts, including modern punctuation, whenever this could be done without affecting the original Florentine pronunciation.
Figure 6-1: Spiraling foliage of Star of Bethlehem, c. 1508, Windsor Collection, Landscapes, Plants, and Water Studies, folio 16r
From these critical transcriptions emerges a flowing text, liberated from the obstacles mentioned, which anybody who is reasonably fluent in Italian can read without too many difficulties. Such reading makes it evident that Leonardo’s language is highly eloquent, often witty, and at times movingly beautiful and poetic. It is worth reading his writings aloud to appreciate their beauty, because Leonardo’s medium was the spoken word rather than the carefully composed written text. To make his arguments, he used the persuasive power of his drawings as well as the elegant cadences of his native Tuscan.
Let me now turn to the key characteristics of the science Leonardo discussed and developed in his Notebooks.
A SCIENCE OF LIVING FORMS
From the very beginning of Western philosophy and science, there has been a tension between mechanism and holism, between the study of matter (or substance, structure, quantity) and the study of form (or pattern, order, quality).26 The study of matter was championed by Democritus, Galileo, Descartes, and Newton; the study of form by Pythagoras, Aristotle, Kant, and Goethe. Leonardo followed the tradition of Pythagoras and Aristotle, and he combined it with his rigorous empirical method to formulate a science of living forms, their patterns of organization, and their processes of growth and transformation. He was deeply aware of the fundamental interconnectedness of all phenomena and of the interdependence and mutual generation of all parts of an organic whole, which Immanuel Kant in the eighteenth century would define as “self-organization.”27 In the Codex Atlanticus, Leonardo eloquently summarized his profound understanding of life’s basic processes by paraphrasing a statement by the Ionian philosopher Anaxagoras: “Everything comes from everything, and everything is made of everything, and everything turns into everything, because that which exists in the elements is made up of these elements.”28
The Scientific Revolution replaced the Aristotelian worldview with the concept of the world as a machine. From then on the mechanistic approach—the study of matter, quantities, and constituents—dominated Western science. Only in the twentieth century did the limits of Newtonian science become fully apparent, and the mechanistic Cartesian worldview begin to give way to a holistic and ecological view not unlike that developed by Leonardo da Vinci.29 With the rise of systemic thinking and its emphasis on networks, complexity, and patterns of organization, we can now more fully appreciate the power of Leonardo’s science and its relevance for our modern era.
Leonardo’s science is a science of qualities, of shapes and proportions, rather than absolute quantities. He preferred to depict the forms of nature in his drawings rather than describe their shapes, and he analyzed them in terms of their proportions rather than measured quantities. Proportion was seen by Renaissance artists as the essence of harmony and beauty. Leonardo filled many pages of his Notebooks with elaborate diagrams of proportions between the various parts of the human figure, and he drew corresponding diagrams to analyze the body of the horse.30 He was far less interested in absolute measurements, which, in any case, were not as accurate, nor as important, in his time as they are in the modern world. For example, the standard units of length and weight—the braccio (arm) and the pound—both varied in different Italian cities from Florence to Milan to Rome, and they had different values in neighboring European countries.31
Leonardo was always impressed by the great diversity and variety of living forms. “Nature is so delightful and abundant in its variations,” he wrote in a passage about how to paint trees, “that among trees of the same kind there would not be found one plant that resembles another nearby, and this is so not only of the plant as a whole, but among the branches, the leaves, and the fruit, not one will be found that looks precisely like another.”32
Leonardo recognized this infinite variety as a key characteristic of living forms, but he also tried to classify the shapes he studied into different types.
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.33 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.”34 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.35 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 hum
an 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.”36 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
The Science of Leonardo: Inside the Mind of the Great Genius of the Renaissance Page 18