The Science of Leonardo

Leonardo intended to eventually present the results of his scientific research as a coherent, integrated body of knowledge. He never managed to do so, because throughout his life he always felt more compelled to expand, refine, and document his investigations than to organize them in a systematic way. loc: 107

Leonardo’s systematic studies of living and nonliving forms amounted to a science of quality and wholeness that was fundamentally different from the mechanistic science of Galileo and Newton. At the core of his investigations, it seemed to me, was a persistent exploration of patterns, interconnecting phenomena from a vast range of fields. loc: 128

The image that emerges from my account is, in contemporary scientific terms, one of Leonardo as a systemic thinker, ecologist, and complexity theorist; a scientist and artist with a deep reverence for all life, and as a man with a strong desire to work for the benefit of humanity. loc: 141

“Painting,” he declares, “embraces within itself all the forms of nature.”3 This statement, in fact, is the key to understanding Leonardo’s science. He asserts repeatedly, especially in his early manuscripts, that painting involves the study of natural forms, and he emphasizes the intimate connection between the artistic representation of those forms and the intellectual understanding of their intrinsic nature and underlying principles. loc: 186

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 loc: 208

Understanding a phenomenon, for him, meant connecting it with other phenomena through a similarity of patterns. loc: 216

For Leonardo, drawing was the perfect vehicle to formulate his conceptual models—a perfect “mathematics” for his science of organic forms.11 loc: 250

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 loc: 269

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 loc: 271

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, loc: 276

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. loc: 282

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. loc: 296

in the painting of a human figure, the most important task was to “express in gesture the passion of its soul.”18 loc: 305

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 loc: 310

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 loc: 319

Leonardo’s synthesis of art and science is infused with a deep awareness of ecology and systems thinking. loc: 326

ONE Infinite Grace loc: 341

Leonardo da Vinci, an artist of outstanding physical beauty who displayed infinite grace in everything he did and who cultivated his genius so brilliantly that all problems he studied he solved with ease. He possessed great strength and dexterity; he was a man of regal spirit and tremendous breadth of mind; loc: 363   • Delete this highlight

Note: Vasari's opening paragraphs on Leonardo Edit

love of animals was also the reason Leonardo became a vegetarian—something loc: 438

animals are sensitive to pain because they are capable of movement, and he did not want to cause them pain and suffering by killing them loc: 441

a man of unusual tenderness. He had tremendous compassion for the suffering of people and animals. loc: 447

Leonardo did not see science as a collective enterprise the way we see it now. In the words of art historian and classicist Charles Hope, “He had…no real understanding of the way in which the growth of knowledge was a cumulative and collaborative process, loc: 536

The Latin word genius originated in Roman religion, where it denoted the spirit of the gens, the family. It was understood as a guardian spirit, first associated with individuals and then also with peoples and places. The extraordinary achievements of artists or scientists were attributed to their genius, or attendant spirit. loc: 552

mental attributes that seem to be distinctive signs of genius, in addition to exceptional talent in a particular field.27 loc: 570

first is an intense curiosity and great enthusiasm for discovery and understanding. loc: 571

extraordinary capacity for intense concentration over long periods of time. loc: 573

ability to memorize large amounts of information in the form of a coherent whole, a single gestalt. loc: 587

TWO The Universal Man loc: 612

new human ideal—l’uomo universale, the infinitely versatile “universal” man, educated in all branches of knowledge and capable of producing innovations in many of them. loc: 621

he went much farther than anyone else in his inquiries, asking questions nobody had asked before, loc: 634

he transcended the disciplinary boundaries of his time. He did so by recognizing patterns that interconnected forms and processes in different domains and by integrating his discoveries into a unified vision of the world. loc: 635

For Leonardo, in other words, being universal meant to recognize similarities in living forms that interconnect different facets of nature—in loc: 643

“the pattern which connects.”5 loc: 648   • Delete this highlight

Note: Is that also the gist of fractal? Edit

“systemic thinking.” loc: 651

Leonardo insisted again and again that the “art,” or skill, of painting must be supported by the painter’s “science,” or sound knowledge of living forms, by his intellectual understanding of their intrinsic nature and underlying principles. loc: 657

The third element in Leonardo’s synthesis, in addition to arte (skill) and scientia (knowledge), is fantasia, the artist’s creative imagination. loc: 667

the artist’s imagination always remains closely linked to his intellectual understanding of nature. loc: 675

“The godlike nature of the science of painting,” he declared, “transforms the painter’s mind into a resemblance of the divine mind.”10 loc: 679

fantasia is not limited to artists, but rather is a general quality of the human mind. loc: 681

Leonardo referred to himself as an inventor. In his view, an inventor was someone who created an artifact or work of art by assembling various elements into a new configuration that did not appear in nature. This definition comes very close to our notion of a designer, loc: 690

the wide-ranging activities and achievements of Leonardo da Vinci, the archetypal uomo universale, are best examined within the three categories of artist, designer, and scientist. loc: 702

Leonardo’s exceptional drawing facility that formed the link between the three domains loc: 708

In many studies for his paintings, he would go over the outlines of a figure again and again, sketching several alternative lines and variations of the figure’s position, until he found the ideal form. loc: 749

illustration of the process known to complexity theorists as “emergence”—the spontaneous emergence of new forms of order out of chaos and confusion.24 loc: 762

our most creative insights emerge from such states of uncertainty and confusion. loc: 765

purpose of Leonardo’s lively polemic was to advance persuasive arguments for considering painting as a mental activity and a science, far above the rank of a mere craft. loc: 786

Leonardo excelled especially in modeling subtle gradations of light and dark, known to art historians as chiaroscuro. loc: 802

shadow as a unifying element, a theme that brings out different qualities of tone and color. loc: 805

He wished to achieve relief through the scientific use of light and shade.”36 loc: 814

creation of sfumato, the subtle melting of shades that eventually became the unifying principle of his paintings. loc: 817

His power of observation, combined with his intuitive understanding of light, allowed him to render not only the most subtle gradations of chiaroscuro, but also complex secondary effects of light—reflected sheens, areas of diffused light, subtle glows, and the like—with unprecedented mastery. loc: 826

It is clear from Leonardo’s notes that he saw the city as a kind of living organism in which people, material goods, food, water, and waste needed to move and flow with ease for the city to remain healthy. loc: 1036

For the most elaborate performances, Leonardo combined his skills of painting, costume design, musical composition, and engineering to create a complete spectacle, with moving scenery and “special effects” produced by his stage machines. To his contemporaries, these performances were awe-inspiring, bordering on magic. loc: 1062

THREE The Florentine loc: 1117

He always sought to find stable situations with regular incomes that allowed him to engage in his intellectual pursuits relatively undisturbed, rather than relying on infrequent commissions for works of art. loc: 1127

living quite comfortably for most of his life. loc: 1129

Being an illegitimate child, Leonardo was barred from attending university, and hence was not sent to a scuola di lettere. Instead he began his apprenticeship in the arts. This had a decisive influence on his further education and intellectual development. Being “unlettered” meant that he knew almost no Latin and was therefore unable to read the scholarly books of his time, loc: 1173

he also realized that not being constrained by the rules of classical rhetoric was an advantage because it made it easier for him to learn directly from nature, especially when his observations contradicted conventional ideas. loc: 1179

Leonardo left Vinci to live with his father in Florence. A few years later he began his apprenticeship with the renowned artist and craftsman Verrocchio. loc: 1206

Brunelleschi’s magnificent dome, crowning the shining marble of Santa Maria del Fiore, the cathedral of Florence, was newly finished and already being admired as a wonder of the modern world. loc: 1222

supported by a huge number of workshops in which artists and artisans produced the required materials, works of art, loc: 1227

Andrea del Verrocchio, who was about the same age as Leonardo’s uncle Francesco, was a brilliant teacher. Originally trained as a goldsmith, he was a skilled craftsman, an accomplished painter, and a noted sculptor. He also had considerable engineering skills. He had excellent connections to the Medici family and a solid reputation, and hence received a steady stream of commissions. loc: 1236

Leonardo spent the next twelve years in this creative environment, during which he diligently followed the rigorous course of a traditional apprenticeship.12 loc: 1251

The Florentine bottega of the fifteenth century fostered a unique synthesis of art, technology, and science, which found its highest expression in Leonardo’s mature work. loc: 1263

One important influence on Leonardo’s future work habits was the use of a libro di bottega (“workbook”), which all apprentices had to keep.14 It was a journal in which they recorded technical instructions or procedures, personal reflections, solutions to problems, and drawings and diagrams of their ideas. loc: 1268

the Medici never extended to Leonardo their vast patronage of the arts. loc: 1341

Florence declared war on the pope. But Lorenzo resolved the crisis with a daring move. He traveled to Naples and negotiated a peace agreement with King Ferrante, thus depriving the pope of his strongest ally. Shortly thereafter, Florence and Rome were reconciled again, and in 1481—three years after conspiring to kill him—Pope Sixtus IV asked Lorenzo to lend him his best painters to decorate the Sistine Chapel, which he had just built and which had been named after him. loc: 1372

conspicuously ignored by Lorenzo, loc: 1376

Leonardo’s Adoration as “the first mature and independent statement of his genius.”35 loc: 1392

when Leonardo was thirty years old, the Magnifico sent him to present a lyre to the Duke of Milan, with a certain Atalante Migliorotti, for he played upon this instrument exceptionally well.”37 loc: 1399

When Leonardo arrived in Milan, the city had no renowned painters or sculptors, although the Sforza court was filled with doctors, mathematicians, and engineers. Its culture was linked to that of the great universities of northern Italy, whose emphasis was on the study of the physical world rather than on moral philosophy, loc: 1414

Leonardo soon transcended his Florentine workshop culture and turned toward a more analytic and theoretical approach to the understanding of nature. loc: 1418

he offered his services as a military and civil engineer, and also mentioned his skills as an architect, sculptor, and painter. Leonardo began his letter with a telling reference to his “secrets,” revealing a taste for secrecy that became a characteristic trait of his personality loc: 1423

“In short,” he concluded his list, “whatever the situation, I can invent an infinite variety of machines for both attack and defense.” Then he added, almost as an afterthought, “In peacetime, I think I can give perfect satisfaction and be the equal of any man in architecture, in the design of public and private buildings, and in conducting water from one place to another. Furthermore, I can carry out sculpture in marble, bronze, or clay; and likewise in painting I can do any kind of work as well as any man….” loc: 1434

collaboration with the brothers Ambrogio and Evangelista Predis, loc: 1450

result was his second masterpiece, the Virgin of the Rocks, loc: 1457

The confraternity may have had good reasons to be dissatisfied with the Virgin of the Rocks, but in the botteghe and intellectual circles of Milan, Leonardo’s masterpiece caused a sensation. loc: 1465

He was attempting to be accepted as an intellectual in a culture that was in close contact with the leading universities, a culture dominated by the written word, in which Latin was used almost exclusively. loc: 1476

“he embarks on an intense and in some ways obsessive program of self-education. The years between 1483 and 1489 are dedicated largely to this obstinate attempt of cultural emancipation.”51 loc: 1480

his full personal library would have included about 200 books—a substantial library even for a Renaissance scholar.56 loc: 1496

Over half of them dealt with scientific and philosophical matters. loc: 1498

The beginning of Leonardo’s systematic studies in 1484, not surprisingly, coincides with the first entries in his Notebooks. Once he embarked on his interdisciplinary program of research, he regularly recorded all new ideas and observations. loc: 1504

deepened his theoretical investigations beyond his needs as an artist and inventor. loc: 1506

interested in the physiology of vision, and then went on to study the other senses. loc: 1513

allowed him to discuss his ideas about the tiburio, as well as his views on architecture in general, with the other competitors, especially with Bramante and Francesco di Giorgio, loc: 1532

portrait of the Moor’s mistress, the young and lovely Cecilia Gallerani. loc: 1544

Lady with an Ermine, loc: 1546

Masque was a huge success and made Leonardo famous throughout Italy, even more so than his paintings had done. From that point on he was in great demand loc: 1556

FOUR A Well-Employed Life loc: 1560

Leonardo had become the Moor’s favorite court artist. He was given a large space for his workshop and living quarters in the Corte Vecchia, the old ducal palace next to the cathedral, loc: 1565

1490s were a period of intense creative activity. With two major projects—the equestrian statue and The Last Supper—his artistic career was at its peak, loc: 1571

Leonardo’s discussions with Cardano and his studies in the library ignited a passion for mathematics, especially geometry, and fueled his subsequent research. Immediately after his return to Milan, he began two new Notebooks, now known as Manuscripts A and C, in which he applied his new knowledge of geometry to a systematic study of perspective and optics as well as to elementary problems involving weights, force, and movement—the loc: 1586

In the midst of his studies and experimentation, and his final preparations for the casting of the giant bronze horse, Leonardo received the commission from Ludovico to paint The Last Supper—the masterpiece that most would argue stands at the climax of his career as a painter. loc: 1603

Leonardo contrived a series of visual paradoxes to create an elaborate illusion—a complex perspective that made the room of the Last Supper look like an extension of the refectory itself, loc: 1614

when he had made up his mind, he went to places where he knew that people of that kind assembled and observed their faces, their manners, dresses, and gestures; and when he found what fitted his purpose, he noted it in a little book which he was always carrying in his belt. After repeating this procedure many times, and being satisfied with the material thus collected for the figure which he wished to paint, he would proceed to give it shape.”8 loc: 1633

Leonardo and Fra Luca decided to collaborate on a book, titled De divina proportione, to be written by Pacioli and illustrated by Leonardo. The book, presented to Ludovico as a lavish manuscript and eventually published in Venice, contains an extensive review of the role of proportion in architecture and anatomy—and in particular of the golden section, or “divine proportion”—as well as detailed discussions of the five regular polyhedra known as the Platonic solids.10 loc: 1648

the new French king, Louis XII, declared himself duke of Milan and prepared to conquer the city. In the summer of 1499, Louis formed a secret alliance with Venice and invaded Lombardy to attack its capital, Milan, while the Venetians attacked from the east. Ludovico, in panic, fled to Innsbruck, Austria, with his family to seek the protection of his relative, Emperor Maximilian. In September, Milan capitulated without a shot being fired.23 loc: 1699

When he returned to Florence, where he would spend the next six years, Leonardo, now forty-eight, was at the beginning of what was then considered old age. However, his artistic and scientific creativity continued undiminished. Over the next fifteen years he would paint several more masterpieces and produce his most substantial scientific work. loc: 1712

In 1502, Leonardo was hired by Cesare to travel throughout central Italy, inspect the ramparts, canals, and other fortifications of the newly conquered cities, and make suggestions for their improvements. loc: 1806

A brilliant intellectual, Machiavelli was also a renowned poet and playwright; Leonardo was likely fascinated by him, and they remained on friendly terms for many years. loc: 1822

While he drew his maps of the Arno watershed, Leonardo studied the smooth and turbulent flows of water in rivers, the erosion of rocks, and the deposits of gravel and sand. On a larger scale, he speculated about the formation of the earth out of the waters of the sea and the movement of the “watery humors” through the macrocosm. He studied strata of rock formations and their fossil contents, which he recognized as telltale signs of life in the distant geological past. loc: 1848

with the horrors of Cesare Borgia’s massacres still fresh in his mind, his Battle of Anghiari would not be a celebration of the military glory of Florence, as the city fathers expected. Instead, it would stand for all the world to see as his definitive condemnation of that pazzia bestialissima, the madness of war.43 loc: 1864

the French king, Louis XII, who was a great admirer of the artist, requested Leonardo’s presence at his court in Milan from the Signoria. loc: 1894

In May 1506, abandoning his fresco, Leonardo left once more for an extended sojourn in Milan. loc: 1897

The sympathetic understanding and generosity of Charles d’Amboise gave him the freedom to dedicate as much time as he desired to his studies and to pursue them in any direction he wished. This unprecedented freedom, combined with his mature age, brought forth a period of broad systemic reflection, of revision and synthesis, allowing him to map out comprehensive treatises on many of his favorite subjects: the flow of water, the geometry of transformations, the movement of the human body, the growth of plants, and the science of painting. loc: 1913

The six years Leonardo spent at the French court in Milan marked a stage of maturity both in his science and his art. loc: 1916

In 1507, Leonardo met a young man, Francesco Melzi, who became his pupil, personal assistant, and inseparable companion. loc: 1924

Leonardo’s main activity in Martelli’s house, however, was of a far more serious nature. He used his ample free time to bring some order into his vast collection of notes, dating from the previous twenty years. loc: 1943

During the next four years he performed more dissections than ever before, and his anatomical drawings reached their highest degree of accuracy. loc: 1953

concentrated on the grand theme of the human body in motion. loc: 1956

Leonardo was able to perform a postmortem on an old man he met by chance at the hospital of Santa Maria Nuova, where he had done his earlier anatomical studies, and who died in his presence. This dissection became a milestone in his anatomical work and led him to some of his most important medical discoveries. loc: 1981

Soon after his brother ascended to the papacy, Giuliano de’ Medici invited Leonardo to the papal court in Rome. The two had likely met at the court in Milan, and Giuliano was well aware of Leonardo’s reputation as a military engineer. Giuliano de’ Medici was also an eager student of natural philosophy. loc: 2030

And yet, for Leonardo, this was not a happy time. At sixty-one, he was now an old man. His long beard was white, his eyesight was failing. And though he was well respected—even venerated—as a great sage, he was no longer in fashion as an artist. loc: 2040

Leonardo’s studies included highly original speculations about the origin of the embryo’s cognitive processes or, in his terminology, of the embryo’s soul.66 Unfortunately, these speculations contradicted the official Church doctrine about the divine nature of the human soul and were thus considered heretical by Pope Leo X. As a result, Leonardo was banned from conducting further autopsies or human dissections.67 loc: 2056

Having kept his sexual feelings private throughout his life, Leonardo, it seems to me, finally declares himself to the world in his last painting. Saint John the Baptist is his personal genius and embodies his desire, which is fully revealed in its androgynous haunting beauty, grace, and transcendence. loc: 2100

Soon after he was crowned king, François crossed the Alps with his troops to reconquer Lombardy. The French army swept aside the Italian troops and Swiss mercenaries, and in July, François I captured Maximiliano Sforza and entered Milan in triumph. loc: 2112

king may have personally offered him the position of peintre du Roy (royal painter) at his court in France. loc: 2128

François also granted his famous guest a generous income. In return, he asked nothing but the pleasure of his company, which he enjoyed almost every day. loc: 2146

François I was now tutored by Leonardo da Vinci, the great sage and genius of the Renaissance. He never tired of hearing Leonardo explain to him the subtleties of his science of living forms—the complexities of turbulent water and air, the formation of rocks and the origin of fossils, the intricacies of human movement and the flight of birds, the nature of light and perspective, the canons of beauty and proportion, the pathways of the senses and the vital spirits that sustain our life, and the origin of human will and power in the seat of the soul. loc: 2150

Art historians surmise that Leonardo’s paralysis, probably as a result of a stroke, did not prevent him from writing and drawing, which he did with his left hand. But it would have affected the nuanced painting he was famous for, which would have required the freedom to move both arms. loc: 2166

Leonardo spent most of his working time at Cloux systematically reorganizing his Notebooks, most likely in view of future publication. loc: 2174

After Melzi’s death in 1570, his son Orazio, who did not share his father’s reverence for the great Leonardo, carelessly stuffed the Notebooks into several chests in the villa’s attic. When it became known that batches of Leonardo’s exquisite drawings could easily be obtained from Orazio, souvenir hunters turned up at Vaprio; they were allowed to take whatever they wanted. loc: 2230

FIVE Science in the Renaissance loc: 2273

by the end of the century Venice boasted around one hundred printers, who turned this city of great wealth into the foremost printing center of Europe. It has been estimated that the Venetian printers alone produced about 2 million volumes during the fifteenth century.6 loc: 2339

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. loc: 2384

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, loc: 2389

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. loc: 2393

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). loc: 2431

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. loc: 2434

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. loc: 2456

Florence under the Medici was the center of Platonism. Milan, under the influence of the universities of Padua and Bologna, was predominantly Aristotelian. loc: 2464

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. loc: 2467

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. loc: 2480

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. loc: 2485

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. loc: 2499

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, loc: 2506

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. loc: 2509

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. loc: 2525

For most Renaissance humanists, Pliny’s name meant natural history itself. And his encyclopedia was the most convenient entry point to further research. loc: 2536

At the core of Hippocratic medicine was the conviction that illnesses are not caused by supernatural forces, but are natural phenomena that can be studied scientifically and influenced by therapeutic procedures and wise management of one’s life.26 loc: 2546

One of the most important volumes in the Hippocratic Corpus, the book on Airs, Waters and Places, represents what we might now call a treatise on human ecology. It shows in great detail how the well-being of individuals is influenced by environmental factors—the quality of air, water, and food, the topography of the land, and general living habits. loc: 2552

Medical teaching at the great universities was based on the classical texts of Hippocrates, Galen, and Avicenna, and concentrated on interpreting the classics, without questioning them or comparing them with clinical experience. loc: 2566

Pacioli helped Leonardo deepen his understanding of mathematics, particularly geometry, by guiding him through the complete Latin edition of Euclid’s Elements.32 loc: 2587

Having thoroughly studied the three principal medical authorities of his time—Galen, Avicenna, and Mondino—Leonardo had a solid foundation in classical and medieval anatomy, on which he built his own extraordinary accomplishments. loc: 2600

SIX Science Born of Experience loc: 2607

Twentieth-century science has shown repeatedly that all natural phenomena are ultimately interconnected, and that their essential properties, in fact, derive from their relationships to other things. Hence, in order to explain any one of them completely, we would have to understand all the others, loc: 2634

In science, to put it bluntly, we never deal with truth, in the sense of a precise correspondence between our descriptions and the described phenomena. We always deal with limited and approximate knowledge. loc: 2637

Five hundred years before the scientific method was recognized and formally described by philosophers and scientists, Leonardo da Vinci single-handedly developed and practiced its essential characteristics—study of the available literature, systematic observations, experimentation, careful and repeated measurements, the formulation of theoretical models, and frequent attempts at mathematical generalizations. loc: 2644   • Delete this highlight

Note: Is this the book's thesis? Edit

relentless reliance on direct observation of nature. loc: 2662

critical importance of methodical observation and experimentation. loc: 2666

empirical approach came naturally to Leonardo. He was gifted with exceptional powers of observation and a keen visual memory, complemented by his great drawing skills.11 loc: 2688

What turned Leonardo from a painter with exceptional gifts of observation into a scientist was his recognition that his observations, in order to be scientific, needed to be carried out in an organized, methodical fashion. loc: 2691

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. loc: 2739

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, loc: 2760

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. loc: 2798

deeply aware of the fundamental interconnectedness of all phenomena and of the interdependence and mutual generation of all parts of an organic whole, loc: 2799

The Scientific Revolution replaced the Aristotelian worldview with the concept of the world as a machine. loc: 2804   • Delete this highlight

Note: These awe the kind if statements that I object to in this book--sweeping generalizations and over simplifications of tha arguments and ideas criticized. It's just too simplified. Edit

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. loc: 2809

similarities of organic forms in different species and to similarities of patterns in different natural phenomena. loc: 2829

biologists today call homologies—structural correspondences between different species, due to their evolutionary descent from a common ancestor. loc: 2838

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. loc: 2844

living forms are continually being shaped and transformed by underlying processes. loc: 2847

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. loc: 2849

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. loc: 2857

At the center of Leonardo’s investigations of turbulence lies the water vortex, or whirlpool. loc: 2882

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.38 loc: 2886

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 loc: 2906

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 loc: 2910

first great theorist in botany.44 loc: 2928

proportion in painting, sculpture, and architecture as the essence of harmony and beauty, and there were many attempts to establish a canon of proportions for the human figure. Leonardo threw himself into this project with his usual vigor and attention to detail, taking a wealth of measurements to establish a comprehensive system of correspondences between all parts of the body. loc: 2944

Leonardo’s science of living forms is a science of movement and transformation, loc: 2950

in order to understand the movements of the animal body, he needed to explore the laws of mechanics. loc: 2958

The classical law of the lever, in particular, appears repeatedly in the Notebooks. loc: 2967

applied this law to calculate the forces and weights necessary to establish equilibria in numerous simple and compound systems involving balances, levers, pulleys, and beams hanging from cords.53 loc: 2970

Leonardo applied his knowledge of mechanics not only to his investigations of the movements of the human body, but also to his studies of machines. Indeed, the uniqueness of his genius lay in his synthesis of art, science, and design.54 loc: 2982

All the great Renaissance engineers were aware of the effects of friction, but Leonardo was the only one who undertook systematic empirical studies of frictional forces. loc: 3007

meticulous records of his investigations and analyses of the resistance of water and air to moving solid bodies, as well as of water and fire moving in air.63 loc: 3026

His “science of flight” involved numerous disciplines—from fluid dynamics to human anatomy, mechanics, the anatomy of birds, and mechanical engineering. He diligently pursued these studies throughout most of his life, loc: 3036

His observations led Leonardo to speculate that, even though human beings would not be able to fly by flapping mechanical wings, “soaring flight,” or gliding, might be possible, since this required much less force. During his last years in Florence he began to experiment with designs of flying machines that had fixed wings, not unlike a modern hang glider. loc: 3070

The third grand theme in Leonardo’s anatomical research (in addition to the themes of harmony and proportion, and the body in motion) is his persistent quest for understanding the nature of life. loc: 3084

understood and pictured the heart like no one before him, but also observed subtleties in its actions and in the flow of blood that would elude medical researchers for centuries. loc: 3089

Leonardo’s success in cardiac anatomy [is] so great that there are aspects of the work which are not yet equaled by modern anatomical illustration…. loc: 3100

Leonardo developed a theory of the functioning of the heart and the flow of blood that allowed him to understand some of the essential features of biological life. loc: 3108

He described the life processes of the fetus in the womb, including its nourishment through the umbilical cord, in astonishing detail, and he also made a series of measurements on animal fetuses to determine their rates of growth. loc: 3120

Leonardo knew very well that, ultimately, the nature and origin of life would remain a mystery, no matter how brilliant his scientific mind was. “Nature is full of infinite causes that have never occurred in experience,”80 he declared in his late forties, and as he got older his sense of mystery deepened. loc: 3126

Nearly all the figures in his last paintings have that smile that expresses the ineffable, often combined with a pointing finger. “Mystery to Leonardo,” wrote Kenneth Clark, “was a shadow, a smile and a finger pointing into darkness.”81 loc: 3129

SEVEN Geometry Done with Motion

Leonardo then used this geometric figure—the isosceles triangle (i.e., a triangle with two equal sides)—to represent arithmetic progressions and linear algebraic relationships, thus establishing a visual link between the proportions of perspective and quantitative relationships loc: 3168

For most of his life, Leonardo believed that his “pyramidal” progression was a universal mathematical law describing all quantitative relationships between physical variables. He discovered only late in life that there are other kinds of functional relationships between physical variables, and that some of those, too, could be represented by pyramids. loc: 3189

Leonardo’s scientific drawings—whether they depict elements of machines, anatomical structures, geological formations, turbulent flows of water, or botanical details of plants—were never realistic representations of a single observation. Rather, they are syntheses of repeated observations, crafted in the form of theoretical models. loc: 3210

It was evident to Leonardo that a mathematics of continuous quantities would be needed to describe the incessant movements and transformations in nature. In the seventeenth century, mathematicians developed the theory of functions and the differential calculus for that very purpose.21 loc: 3230

Leonardo uses geometry to study trajectories and various kinds of complex motions in natural phenomena; on the other hand, he uses motion as a tool to demonstrate geometrical theorems. loc: 3249

The second, highly original branch of Leonardo’s geometry is a geometry of continuous transformations of rectilinear and curvilinear shapes, loc: 3261

Leonardo saw this conservation of volume as a general principle governing all changes and transformations of natural forms, whether solid bodies moving in space or pliable bodies changing their shapes. loc: 3265

Leonardo evidently thought that, by developing a “geometry done with motion,” based on the conservation of volume, he might be able to describe the continual movements and transformations of water and other natural forms with mathematical precision. He methodically set out to develop such a geometry, and in doing so anticipated some important developments in mathematical thought that would not occur until several centuries later. loc: 3273

When we look at Leonardo’s geometry from the point of view of present-day mathematics, and in particular from the perspective of complexity theory, we can see that he developed the beginnings of the branch of mathematics now known as topology. loc: 3363

topology is a geometry of continuous transformations, or mappings, in which certain properties of geometric figures are preserved. loc: 3366

The transformations of Leonardo’s “geometry done with motion” are early forms of this important field of mathematics—three hundred years before Leibniz and five hundred years before Poincaré. loc: 3385

Leonardo worked from the basic premise that the physical universe is fundamentally ordered and that its causal relationships can be comprehended by the rational mind and expressed mathematically.54 He used the term “necessity” to express the stringent nature of those ordered causal relationships. loc: 3422

new mathematics, naturally, is far more abstract and sophisticated than anything Leonardo could have imagined in the fifteenth and sixteenth centuries. But it is used in the same spirit in which he developed his “geometry done with motion”—to show with mathematical rigor how complex natural phenomena are shaped and transformed by the “necessity” of physical forces. The mathematics of complexity has led to a new appreciation of geometry and to the broad realization that mathematics is much more than formulas and equations. loc: 3435

EIGHT Pyramids of Light loc: 3442

He explored the geometry of light rays, the interplay of light and shadow, and the very nature of light, and he also studied the anatomy of the eye, the physiology of vision, and the pathways of sensory impressions along the nerves to the “seat of the soul.” loc: 3449

the geometry of perspective developed by the Florentine artists was the first scientific conception of three-dimensional space: loc: 3476

artists were the first to conceive a generalized mathematical model of space and that it constituted an essential step in the evolution from medieval symbolism to the modern image of the universe.8 loc: 3479

Leonardo derived a theory of perspective that went well beyond Alberti, Piero della Francesca, and other leading artists of the early Renaissance. “There are three kinds of perspective,” he declared. “The first is concerned with the reason for the diminution [of] things as they recede from the eye. The second contains the way in which colors vary as they recede from the eye. The third and last encompasses the declaration of how objects should appear less distinct the more distant they are.” loc: 3530

By far the largest part of Leonardo’s optical studies concerned the effects of light falling on objects and the nature of different kinds of shadows. loc: 3576

shadow is the central element in the science of painting. It allows the painter to effectively represent solid bodies in relief, emerging from the backgrounds of the painted surface. loc: 3582

His starting point was the accepted contemporary knowledge that light is emitted by luminous objects in straight lines. loc: 3645

in essence, Leonardo identifies three basic properties of light rays: They are rays of energy generated at the center of luminous bodies; they are infinitely thin and without material substance; and they always travel in straight lines. loc: 3661

the concept of pyramids of light filling the air with images of solid objects: loc: 3670

the pyramids of light “intersect and interweave” without interfering with each other. loc: 3676

he concludes that light spreads in circles, and he immediately associates this circular pattern with the circular spread of ripples of water and the spread of sound in air: loc: 3684

He recognized the essence of wave motion—that the water particles do not move along with the wave but merely move up and down as the wave passes by.57 What is transported along the wave is the disturbance causing the wave phenomenon—the “tremor,” loc: 3712

this is the reason, he concludes correctly, why the circular waves intersect smoothly without disturbing each other: loc: 3716

This smooth intersection of water waves is the key property that suggests to Leonardo that light and sound, too, propagate in waves. loc: 3719

From these observations, Leonardo draws the momentous conclusion that both light and sound are waves. loc: 3726

extends his insight to elastic waves in the earth and concludes that wave motion, caused by initial vibrations (or “tremors”), is a universal form of propagation of physical effects. loc: 3727

realization that wave motion is a universal phenomenon in all four elements—earth, water, air, and fire (or light)—was a revolutionary insight in Leonardo’s time. loc: 3731

he also realized that, however fast light moves, its velocity is not infinite. He asserted that the speed of sound is greater than that of elastic waves in earth, and that light moves faster than sound, but that the mind moves even faster than light. “The mind jumps in an instant from the East to the West,” he noted, “and all the other immaterial things have velocities that are by a long way inferior.”64 loc: 3746

it was not until the end of the seventeenth century that the finite velocity of light was established.65 loc: 3752

Sunlight is scattered by the molecules of the atmosphere (Leonardo’s “minute and imperceptible atoms”) in such a way that blue light is absorbed much more than other frequencies and is then radiated in different directions all around the sky. loc: 3766

he observed that sound is always produced by “a blow on a resonant object.” He correctly deduced that this causes an oscillating movement in the surrounding air, which he called “fanning movement” loc: 3772

attention to detail in these observations is truly remarkable. loc: 3803   • Delete this highlight

Note: This is rea lly the heart of Leonardo's science--attention to details by close observation, even without the mathematical language to express it. Edit

NINE The Eye, the Senses, and the Soul loc: 3828

Leonardo’s construction of the visual pathways was certainly ingenious, but it also had some serious problems. loc: 3913

Nevertheless, his discoveries of many fine details of the eye’s anatomy are truly remarkable. loc: 3918

the first to distinguish between central and peripheral vision. loc: 3919

the first to explain binocular vision—the loc: 3922

Leonardo’s neurological theory of visual perception must be ranked as one of his greatest scientific achievements. loc: 3947

the optic nerve is pictured as expanding gradually where it enters the eyeball and attaching itself directly to the back of the spherical lens, forming a kind of restricted retina. This is where the visual images are transformed into nerve impulses. He saw this process as a percussion of the optic nerve by the light rays, which triggers sensory impulses (sentimenti) that travel through the nerves in the form of waves, loc: 3950

Leonardo paid special attention to the pathways of the sensory nerves in the human skull, in particular the optic nerve. loc: 3968

In the anterior ventricle, Leonardo located a special organ not mentioned by anyone before him, which he called the receptor of impressions (impressiva).32 He saw it as a relay station that collects the wave patterns of sensory impressions, makes selections by some process of resonance, and organizes them into harmonious rhythmic forms that are then passed on to the senso comune, where they enter consciousness. loc: 3982

investigated the anatomy and physiology of the entire vocal apparatus to understand the formation of the voice, but extended his studies to phonetics, musical theory, and the functioning and design of musical instruments.34 loc: 3996

Leonardo’s dissections of the cranial nerves and the central nervous system convinced him that all five senses are associated with special nerves that carry sensory impressions to the brain, where they are selected and organized by the receptor of impressions (impressiva) and passed on to the senso comune. There, in the central ventricle of the brain, the integrated sensory impressions are judged by the intellect and influenced by the imagination and memory. loc: 4014

The senso comune is the seat of the soul, the memory is its store, and the receptor of impressions is its informant.”39 loc: 4021

During the period of Hellenistic-Roman philosophy, Alexandrian thought gradually separated the two characteristics that had originally been united in the Greek conception of the soul—that of a vital force and that of the activity of consciousness. Side by side with the soul, which moves the body, now appears “spirit” as an independent principle expressing the essence of the individual, and also of the divine personality. Alexandrian philosophers introduced the triple division of the human being into body, soul, and spirit, but the boundaries between “soul” and “spirit” were fluctuating. The soul was situated somewhere between the two extremes, matter and spirit. loc: 4029

empirically. In his delicate dissections of the brain and the nervous system, he traced the sensory perceptions from the initial impressions on the sense organs, especially the eye, through the sensory nerves to the center of the brain. He also followed the nerve impulses for voluntary movement from the brain down the spinal cord, and through the peripheral motor nerves out to the muscles, tendons, and bones; and he illustrated all these pathways in precise anatomical drawings loc: 4036

From his thorough investigations of the brain and the nervous system, Leonardo concluded that the soul evaluated sensory impressions and transferred them to the memory, and that it was also the origin of voluntary bodily movement, which he associated with reason and judgment. loc: 4040

The decisive advance has been to reject the view of mind as a thing; to realize that mind and consciousness are not entities but processes. loc: 4058

One of the central insights of cognitive science is the identification of cognition, the process of knowing, with the process of life. Cognition, according to this view, is the organizing activity of living systems at all levels of life. Accordingly, the interactions of a living organism—plant, animal, or human—with its environment are understood as cognitive interactions. loc: 4064

the identification of mind, or cognition, with the process of life, although a novel idea in science, comes very close to Leonardo’s concept of the soul. loc: 4070

Leonardo saw the soul not only as the source of all bodily movements, but also as the force underlying the body’s formation. loc: 4086

consistent with the views of today’s cognitive scientists who understand cognition as a process involving the self-generation and self-organization of living organisms. loc: 4088

Body and soul formed one indivisible whole for Leonardo. “The soul desires to stay with its body,” he explained, “because without the organic instruments of that body it can neither carry out nor feel anything.”49 loc: 4100

In Leonardo’s view, the essential unity of body and soul arises at the very beginning of life, and it dissolves with the demise of both at death. loc: 4110

“While I thought I was learning how to live, I have been learning how to die,” Leonardo wrote movingly late in his life.53 loc: 4118

Leonardo da Vinci never expressed a belief that the soul would survive the body after death. loc: 4120

EPILOGUE “Read me, O reader, if in my words you find delight” loc: 4143

He fully recognized and extensively studied the mechanical aspects of the human and animal bodies, but he always saw them as instruments, used by the soul for the organism’s self-organization. Trying to understand those processes of self-organization—the growth, movements, and transformations of nature’s living forms—was at the very core of Leonardo’s science. loc: 4148

Life’s patterns of organization, its organic structures, and its fundamental processes of metabolism and growth are the unifying conceptual threads that interlink his knowledge of macro-and microcosm. loc: 4175

Instead of trying to dominate nature, as Francis Bacon advocated in the seventeenth century, Leonardo’s intent was to learn from her as much as possible. He was in awe of the beauty he saw in the complexity of natural forms, patterns, and processes, and aware that nature’s ingenuity was far superior to human design. loc: 4204

nature as a model and mentor is now being rediscovered in the practice of ecological design. loc: 4209

ecodesigners today study the patterns and flows in the natural world and try to incorporate the underlying principles into their design processes.10 loc: 4210

When spirituality is understood as a way of being that flows from a deep sense of oneness with all, a sense of belonging to the universe as a whole, it becomes clear that ecological awareness is spiritual in its deepest essence.16 loc: 4235

Leonardo da Vinci’s view of the world had that kind of spiritual dimension. loc: 4237

the underlying conception of the living world as being fundamentally interconnected, highly complex, creative, and imbued with cognitive intelligence loc: 4263