All the notes were taken directly from the source mentioned.

– – –

Together they served his driving passion, which was nothing less than knowing everything there was to know about the world, including how we fit into it. He had a reverence for the wholeness of nature and a feel for the harmony of its patterns, which he saw replicated in phenomena large and small.

Over and over again, year after year, Leonardo lists things he must do and learn. Some involve the type of close observation most of us rarely pause to do.

Others involve why-is-the-sky-blue questions about phenomena so commonplace that we rarely pause to wonder about them. Why is the fish in the water swifter than the bird in the air when it ought to be the contrary since the water is heavier and thicker than the air?

Best of all are the questions that seem completely random.

The reason he wanted to know was because he was Leonardo: curious, passionate, and always filled with wonder.

Did learn from Leonardo how a desire to marvel about the world that we encounter each day can make each moment of our lives richer.

There are three major early accounts of Leonardo by writers who were almost contemporaries. The painter Giorgio Vasari, born in 1511 (eight years before Leonardo died), wrote the first real art history book, Lives of the Most Eminent Painters, Sculptors, and Architects, in 1550 and came out with a revised version in 1568 that included corrections based on further interviews with people who knew Leonardo, including his pupil Francesco Melzi.

An anonymous manuscript written in the 1540s, known as the Anonimo Gaddiano after the family that once owned it, contains colorful details about Leonardo and other Florentines.

A third early source is by Gian Paolo Lomazzo, a painter who became a writer when he went blind. He wrote an unpublished manuscript called Dreams and Arguments in about 1560 and then published a voluminous treatise on art in 1584.

In addition, there are shorter accounts contained in writings by two Leonardo contemporaries, Antonio Billi, a Florentine merchant, and Paolo Giovio, an Italian physician and historian.

Notoriously, he left many of his paintings unfinished, most notably the Adoration of the Magi, Saint Jerome in the Wilderness, and the Battle of Anghiari.

In short, it was a time like our own. That is why we have much to learn from Leonardo. His ability to combine art, science, technology, the humanities, and imagination remains an enduring recipe for creativity. So, too, was his ease at being a bit of a misfit: illegitimate, gay, vegetarian, left-handed, easily distracted, and at times heretical.

The man who has intercourse aggressively and uneasily will produce children who are irritable and untrustworthy, he wrote, but if the intercourse is done with great love and desire on both sides, the child will be of great intellect, witty, lively, and lovable.

The nineteenth-century cultural historian Jacob Burckhardt went so far as to label Renaissance Italy a golden age for bastards.

Among the poets, artists, and artisans born out of wedlock were Petrarch, Boccaccio, Lorenzo Ghiberti, Filippo Lippi, his son Filippino, Leon Battista Alberti, and of course Leonardo.

Leonardo was mainly self-taught.

His lack of reverence for authority and his willingness to challenge received wisdom would lead him to craft an empirical approach for understanding nature that foreshadowed the scientific method developed more than a century later by Bacon and Galileo. His method was rooted in experiment, curiosity, and the ability to marvel at phenomena that the rest of us rarely pause to ponder after we’ve outgrown our wonder years.

In 1452 Johannes Gutenberg had just opened his publishing house, and soon others were using his moveable-type press to print books that would empower unschooled but brilliant people like Leonardo.

It was a good time for a child with such ambitions and talents to be born. In 1452 Johannes Gutenberg had just opened his publishing house, and soon others were using his moveable-type press to print books that would empower unschooled but brilliant people like Leonardo. Italy was beginning a rare forty-year period during which it was not wracked by wars among its city-states. Literacy, numeracy, and income were rising dramatically as power shifted from titled landowners to urban merchants and bankers, who benefited from advances in law, accounting, credit, and insurance. The Ottoman Turks were about to capture Constantinople, unleashing on Italy a migration of fleeing scholars with bundles of manuscripts containing the ancient wisdom of Euclid, Ptolemy, Plato, and Aristotle. Born within a year of Leonardo were Christopher Columbus and Amerigo Vespucci, who would lead an era of exploration. And Florence, with its booming merchant class of status-seeking patrons, had become the cradle of Renaissance art and humanism.

Leonardo da Vinci is sometimes incorrectly called da Vinci, as if that were his last name rather than a descriptor meaning from Vinci.

He lived primarily with his grandparents and his idle uncle Francesco in the family house in the heart of Vinci.

His notebooks have many other maxims praising the countryside and solitude. Leave your family and friends and go over the mountains and valleys into the country, he instructed aspiring painters. While you are alone you are entirely your own master.3 These paeans to country living are romantic and, for those who cherish the image of lonely genius, quite appealing. But they are infused with fantasy. Leonardo would spend almost all of his career in Florence, Milan, and Rome, crowded centers of creativity and commerce, usually surrounded by students, companions, and patrons. He rarely retreated alone to the countryside for an extended period of solitude. Like many artists, he was stimulated by being with people of diverse interests and (willing to contradict himself in his notebooks) declared, Drawing in company is much better than alone.4 The impulses of his grandfather and uncle, who both practiced the quiet country life, were imprinted in Leonardo’s imagination but not practiced in his life.

Fully a third of Florence’s population was literate, the highest rate in Europe. By embracing trade, it became a center of finance and a cauldron of ideas.

Exercising power from behind its façade was the Medici family, the phenomenally wealthy bankers who dominated Florentine politics and culture during the fifteenth century without holding office or hereditary title. (In the following century they became hereditary dukes, and lesser family members became popes.) After Cosimo de’ Medici took over the family bank in the 1430s, it became the largest in Europe. By managing the fortunes of the continent’s wealthy families, the Medici made themselves the wealthiest of them all. They were innovators in bookkeeping, including the use of debit-and-credit accounting that became one of the great spurs to progress during the Renaissance. By means of payoffs and plotting, Cosimo became the de facto ruler of Florence, and his patronage made it the cradle of Renaissance art and humanism.

A collector of ancient manuscripts who had been schooled in Greek and Roman literature, Cosimo supported the rebirth of interest in antiquity that was at the core of Renaissance humanism. He founded and funded Florence’s first public library and the influential but informal Platonic Academy, where scholars and public intellectuals discussed the classics. In art, he was a patron of Fra Angelico, Filippo Lippi, and Donatello. Cosimo died in 1464, just as Leonardo arrived in Florence from Vinci.

He was succeeded by his son and then, five years later, his famous grandson, Lorenzo de’ Medici, aptly dubbed Lorenzo the Magnificent. Lorenzo had been tutored in humanist literature and philosophy under the watchful eye of his mother, an accomplished poet, and he patronized the Platonic Academy, launched by his grandfather. He was also an accomplished sportsman, distinguishing himself in jousting, hunting, falconry, and breeding horses. All of this made him a better poet and patron than he was a banker; he took more delight in using wealth than in making it. During his twenty-three-year reign, he would sponsor innovative artists, including Botticelli and Michelangelo, as well as patronize the workshops of Andrea del Verrocchio, Domenico Ghirlandaio, and Antonio del Pollaiuolo, which were producing paintings and sculptures to adorn the booming city.

The culture rewarded, above all, those who mastered and mixed different disciplines.

The legacy of two such polymaths had a formative influence on Leonardo. The first was Filippo Brunelleschi (13771446), the designer of the cathedral dome.

Brunelleschi showed how parallel lines seemed to converge in the distance toward a vanishing point. His formulation of linear perspective transformed art and also influenced the science of optics, the craft of architecture, and the uses of Euclidean geometry.

Brunelleschi’s successor as a theorist of linear perspective was another of the towering Renaissance polymaths, Leon Battista Alberti (1404‰1472), who refined many of Brunelleschi’s experiments and extended his discoveries about perspective. An artist, architect, engineer, and writer, Alberti was like Leonardo in many ways: both were illegitimate sons of prosperous fathers, athletic and good-looking, never-married, and fascinated by everything from math to art.

Leonardo was not strongly motivated by the goal of furthering human knowledge by openly disseminating and publishing his findings; Alberti, on the other hand, was dedicated to sharing his work, gathering a community of intellectual colleagues who could build on each other’s discoveries, and promoting open discussion and publication as a way to advance the accumulation of learning.

By applying mathematics to art, Alberti elevated the painter’s status and advanced the argument that the visual arts deserve a standing equal to that of other humanist fields, a cause that Leonardo would later champion.

One skill that was emphasized was how to draw analogies between cases, a method that Leonardo would use repeatedly in his later science. Analogies and spotting patterns became for him a rudimentary method of theorizing.

Vasari also noted that Leonardo was interested in so many things that he got easily distracted. He turned out to be good in geometry, but he never mastered the use of equations or the rudimentary algebra that existed at the time. Nor did he learn Latin. In his thirties he would still be trying to remedy this deficiency by drawing up lists of Latin words, painstakingly writing out awkward translations, and wrestling with grammar rules.14 A left-hander, Leonardo wrote from right to left on a page, the opposite direction of the words on this and other normal pages, and drew each letter facing backward.

He wrote that way because when using his left hand he could glide leftward across the page without smudging the ink.

Being left-handed also affected Leonardo’s method of drawing. As with his writing, he drew from right to left so as not to smudge the lines with his hand.

One of Verrocchio’s most captivating sculptures was a four-foot bronze of the young warrior David standing in triumph over the head of Goliath

For Leonardo, the drapery studies helped foster one of the key components of his artistic genius: the ability to deploy light and shade in ways that would better produce the illusion of three-dimensional volume on a two-dimensional surface.

Chiaroscuro, from the Italian for light/dark, is the use of contrasts of light and shadow as a modeling technique for achieving the illusion of plasticity and three-dimensional volume in a two-dimensional drawing or painting. Leonardo’s version of the technique involved varying the darkness of a color by adding black pigments rather than making it a more saturated or richer hue. In his Benois Madonna, for example, he painted the Virgin Mary’s blue dress in shades ranging from almost white to almost black.

Leonardo also pioneered sfumato, the technique of blurring contours and edges. It is a way for artists to render objects as they appear to our eye rather than with sharp contours.

The Compagnia was not a guild but a club-like mutual aid society or fraternity. Other members who registered and paid dues in 1472 included Botticelli, Pietro Perugino, Ghirlandaio, Pollaiuolo, Filippino Lippi, and Verrocchio himself.

The culmination of Leonardo’s collaborations with Verrocchio came in the mid-1470s with the completion of the Baptism of Christ,

Leonardo painted the radiant, turning angel on the far left of the scene, and Verrocchio was so awed when he beheld it that he resolved never again to touch a brushor

Afterward Verrocchio never completed any new painting on his own.

Leonardo took care to observe the real world, and he noticed the opposite: when we look at three-dimensional objects, we don’t see sharp lines. Paint so that a smoky finish can be seen, rather than contours and profiles that are distinct and crude, he wrote. When you paint shadows and their edges, which cannot be perceived except indistinctly, do not make them sharp or clearly defined, otherwise your work will have a wooden appearance. Verrocchio’s angel has this wooden appearance. Leonardo’s does not.

In addition to the collaborations he did with Verrocchio in the 1470s, the twenty something Leonardo produced at least four paintings primarily on his own while working at the studio: an Annunciation, two small devotional paintings of the Madonna and Child, and a pioneering portrait of a Florentine woman, Ginevra de’ Benci.

Leonardo was experimenting with the trick known as anamorphosis, in which some elements of a work may look distorted when viewed straight on but appear accurate when viewed from another angle.

Ginevra de’ Benci is not the Mona Lisa, not even close. But it is recognizably the work of the man who would paint it.

Homosexuality was not uncommon in the artistic community of Florence or in Verrocchio’s circle. Verrocchio himself never married, nor did Botticelli, who was also charged with sodomy. Other artists who were gay included Donatello, Michelangelo, and Benvenuto Cellini (who was twice convicted of sodomy). Indeed, l’amore masculino, as Lomazzo quoted Leonardo calling it, was so common in Florence that the word Florenzer became slang in Germany for gay.

The Church considered homosexual acts a sin. A 1484 papal bull likened sodomy to carnal knowledge with demons, and preachers regularly railed against it. Dante, whose Divine Comedy was beloved by Leonardo and illustrated by Botticelli, consigned sodomites, along with blasphemers and usurers, to the seventh circle of hell.

Nevertheless, unlike Michelangelo, Leonardo was a master at painting women. From Ginevra de’ Benci to the Mona Lisa, his portraits of women are deeply sympathetic and psychologically insightful.

We are again lucky that Leonardo described in his notebook the artistic principles that he put into practice, in this case the use of light sketching and revisions to capture mental states. It helps us better appreciate his works as well as the thinking that went into them. Do not draw the limbs of your figure with hard contours or the same fate will happen to you as has happened to many painters who wished every little stroke of charcoal to be definite, he advised. By drawing fixed lines, these artists create figures that do not move their limbs in a manner that reflects the motions of their mind.

We are again lucky that Leonardo described in his notebook the artistic principles that he put into practice, in this case the use of light sketching and revisions to capture mental states. It helps us better appreciate his works as well as the thinking that went into them. Do not draw the limbs of your figure with hard contours or the same fate will happen to you as has happened to many painters who wished every little stroke of charcoal to be definite, he advised. By drawing fixed lines, these artists create figures that do not move their limbs in a manner that reflects the motions of their mind. A good painter, he continued, should decide broadly upon the position of the limbs and attend first to the movement appropriate to the mental attitudes of the creatures in the narrative.

Portraying the motions of the mind was not a new concept. Pliny the Elder complimented the fourth-century BC painter Aristides of Thebes by saying he was the first to express the mentality, sentiments, character, and passions of a subject.

Leonardo was deeply influenced by Alberti’s book, and he repeatedly echoed that injunction in his own notebooks. The good painter has to paint two principal things, man and the intention of his mind, he wrote. The first is easy and the second is difficult, because the latter has to be represented through gestures and movements of the limbs.44 He expanded on this concept in a long passage in his notes for his planned treatise on painting: The movement which is depicted must be appropriate to the mental state of the figure. The motions and postures of figures should display the true mental state of the originator of these motions, in such a way they can mean nothing else. Movements should announce the motions of the mind.

As he approached his thirtieth birthday, Leonardo had established his genius but had remarkably little to show for it publicly.

Rucellai introduced the term balance of power to describe the continuous conflicts and shifting alliances involving Florence, Milan, other Italian city-states, plus a pride of popes, French kings, and Holy Roman emperors. The competition among the various rulers was not only military but cultural,

Unlike Florence, Milan was not well-stocked with master artists. That made it more fertile territory for Leonardo. Because he was an aspiring polymath, he also enjoyed that Milan was filled with scholars and intellectuals in a wide variety of fields, partly due to the esteemed university in nearby Pavia, which was officially founded in 1361 but had roots stretching back to 825. It boasted some of Europe’s best lawyers, philosophers, medical researchers, and mathematicians.

Leonardo cast himself as an engineer because he was going through one of his regular bouts of being bored or blocked by the prospect of picking up a brush. As his mood swung between melancholy and exultation, he fantasized and boasted about being an accomplished weapons designer. These boasts were aspirational. He had never been to a battle nor actually built any of the weapons he described. All he had produced thus far were some elegant sketches of concepts for weapons, many of them more fanciful than practical.

Leonardo would be known for paintings, monuments, and inventions that he conceived but never brought to fruition.

Only one of Leonardo’s military conceptions is known to have made it off the pages of his notebooks and onto the battlefield, and he arguably deserves priority as its inventor. The wheellock, or wheel lock, which he devised in the 1490s, was a way to create a spark for igniting the gunpowder in a musket or similar hand-carried weapon. When the trigger was pulled, a metal wheel was set spinning by a spring. As it scraped against a stone, it sparked enough heat to ignite the gunpowder.

Leonardo’s wondrously imaginative giant crossbows and turtle-like tanks show his ability to let fantasy drive invention. But he had not lashed his imagination to practicality.

He pursued his architectural interests the way he did his military interests: mainly on paper as imaginative visions never to be implemented.

He applied the classic analogy between the microcosm of the human body and the macrocosm of the earth: cities are organisms that breathe and have fluids that circulate and waste that needs to move. He had recently begun studying blood and fluid circulation in the body. Thinking by analogy, he considered what would be the best circulation systems for urban needs, ranging from commerce to waste removal. The glory of Milan was that it had an ample water supply and a long tradition of channeling the flow of mountain streams and melting snows. Leonardo’s idea was to combine the streets and canals into a unified circulation system. The utopian city he envisioned would have two levels: an upper level designed for beauty and pedestrian life, and a level hidden below for canals, commerce, sanitation, and sewage.

As the offspring of a long line of notaries, Leonardo da Vinci had an instinct for keeping records. Jotting down observations, lists, ideas, and sketches came naturally.

One purpose of these notebooks was to record interesting scenes, especially those involving people and emotions.

These little books on his belt, along with the larger sheets in his studio, became repositories for all of his manifold passions and obsessions, many of them sharing a page. As an engineer, he honed his technical skills by drawing mechanisms he encountered or imagined. As an artist, he sketched ideas and made preparatory drawings. As a court impresario, he jotted down designs for costumes, contrivances for moving scenery and stages, fables to be enacted, and witty lines to be performed.

Over the years, as his scientific study got more serious, he filled pages with outlines and passages for treatises on topics such as flight, water, anatomy, art, horses, mechanics, and geology.

He became interested not only in how things work but why.6 Because good paper was costly, Leonardo tried to use every edge and corner of most pages, cramming as much as possible on each sheet and jumbling together seemingly random items from diverse fields. Often he would go back to a page, months or even years later, to add another thought, just as he would go back to his painting of Saint Jerome, and later his other paintings, to refine his work as he evolved and matured.

He was not great at algebra or even arithmetic, but he had a feel for how geometry could be used to transform one shape into another while keeping the area constant.

What Leonardo probably began as four distinct elements ended up woven together in a way that illustrates a fundamental theme in his art and science: the interconnectedness of nature, the unity of its patterns, and the analogy between the workings of the human body and those of the earth.

Leonardo had originally come to the Sforza court partly as a musical envoy bearing his own specially designed version of an instrument that was popular among court entertainers. It was a type of lyre to be held like a fiddle, with five strings meant to be played with a bow and two that were to be plucked.

There are no musical compositions in his notebooks. Rather than reading music or composing lyrics, he improvised when performing at the Sforza court. Since by nature he possessed a lofty and graceful spirit, Vasari explained, he sang divinely, improvising his own accompaniment on the lyre.

Leonardo recommended to young artists this practice of walking around town, finding people to use as models, and recording the most interesting ones in a portable notebook: Take a note of them with slight strokes in a little book which you should always carry with you, he wrote. The positions of the people are so infinite that the memory is incapable of retaining them, which is why you should keep these sketches as your guides.

But even though he did not consider physiognomy a science, he did believe that facial expressions indicate underlying causes. Characteristics of the face partly reveal the character of men, their vices and temperaments, he wrote. If the features which separate the cheeks from the lips, or the nostrils from the cavities of the eyes, are strongly pronounced, they belong to cheerful and good-humored men.

Gypsies from the Balkans had spread throughout Europe in the fifteenth century and become such a nuisance in Milan that they were banished by a decree in 1493.

Because of his love for animals, Leonardo was a vegetarian for much of his life, although his shopping lists show that he often bought meat for others in his household.

Marcus Vitruvius Pollio, born around 80 BC, served in the Roman army under Caesar and specialized in the design and construction of artillery machines.

His most important work was literary, the only surviving book on architecture from classical antiquity: De Architectura, known today as The Ten Books on Architecture.

His most important work was literary, the only surviving book on architecture from classical antiquity: De Architectura, known today as The Ten Books on Architecture.13 For many dark centuries, Vitruvius’s work had been forgotten, but in the early 1400s it was one of the many pieces of classical writing, including Lucretius’s epic poem On the Nature of Things and Cicero’s orations, that were rediscovered and collected by the pioneering Italian humanist Poggio Bracciolini.

What made Vitruvius’s work appealing to Leonardo and Francesco was that it gave concrete expression to an analogy that went back to Plato and the ancients, one that had become a defining metaphor of Renaissance humanism: the relationship between the microcosm of man and the macrocosm of the earth.

Vitruvius’s descriptions of human proportions would inspire Leonardo, as part of the anatomy studies he had just begun in 1489, to compile a similar set of measurements. More broadly, Vitruvius’s belief that the proportions of man are analogous to those of a well-conceived temple and to the macrocosm of the world became central to Leonardo’s worldview.

There are two key differences that distinguish Leonardo’s version of Vitruvian Man from those done around the same time by his two friends, Francesco di Giorgio and Giacomo Andrea.

Before he began, he had determined exactly how the circle would rest on the base of the square but extend out higher and wider. Using a compass and a set square, he drew the circle and the square, then allowed the man’s feet to rest comfortably on them. As a result, per Vitruvius’s description, the man’s navel is in the precise center of the circle, and his genitals are at the center of the square.

Leonardo’s Vitruvian Man embodies a moment when art and science combined to allow mortal minds to probe timeless questions about who we are and how we fit into the grand order of the universe. It also symbolizes an ideal of humanism that celebrates the dignity, value, and rational agency of humans as individuals. Inside the square and the circle we can see the essence of Leonardo da Vinci, and the essence of ourselves, standing naked at the intersection of the earthly and the cosmic.

When Leonardo drew his Vitruvian Man, he had a lot of interrelated ideas dancing in his imagination. These included the mathematical challenge of squaring the circle, the analogy between the microcosm of man and the macrocosm of earth, the human proportions to be found through anatomical studies, the geometry of squares and circles in church architecture, the transformation of geometric shapes, and a concept combining math and art that was known as the golden ratio or divine proportion.

Unlike Michelangelo and some other anguished artists, Leonardo enjoyed being surrounded by friends, companions, students, assistants, fellow courtiers, and thinkers. In his notebooks we find scores of people with whom he wanted to discuss ideas. His closest friendships were intellectual ones.

Ideas are often generated in physical gathering places where people with diverse interests encounter one another serendipitously. That is why Steve Jobs liked his buildings to have a central atrium and why the young Benjamin Franklin founded a club where the most interesting people of Philadelphia would gather every Friday. At the court of Ludovico Sforza, Leonardo found friends who could spark new ideas by rubbing together their diverse passions.

Leonardo da Vinci liked to boast that, because he was not formally educated, he had to learn from his own experiences instead. It was around 1490 when he wrote his screed about being a man without letters and a disciple of experience, with its swipe against those who would cite ancient wisdom rather than make observations on their own.

We can see a turning point in the early 1490s, when he undertook to teach himself Latin, the language not only of the ancients but also of serious scholars of his era. He copied page after page of Latin words and conjugations from textbooks of his time, including one that was used by Ludovico Sforza’s young son.

By 1492 Leonardo had close to forty volumes. A testament to his universal interests, they included books on military machinery, agriculture, music, surgery, health, Aristotelian science, Arabian physics, palmistry, and the lives of famous philosophers, as well as the poetry of Ovid and Petrarch, the fables of Aesop, some collections of bawdy doggerels and burlesques, and a fourteenth-century operetta from which he drew part of his bestiary. By 1504 he would be able to list seventy more books, including forty works of science, close to fifty of poetry and literature, ten on art and architecture, eight on religion, and three on math.

As with so many things, this empirical approach put him ahead of his time. Scholastic theologians of the Middle Ages had fused Aristotle’s science with Christianity to create an authorized creed that left little room for skeptical inquiry or experimentation. Even the humanists of the early Renaissance preferred to repeat the wisdom of classical texts rather than test it. Leonardo broke with this tradition by basing his science primarily on observations, then discerning patterns, and then testing their validity through more observations and experiments.

When he began absorbing knowledge from books in the 1490s, it helped him realize the importance of being guided not only by experiential evidence but also by theoretical frameworks. More important, he came to understand that the two approaches were complementary, working hand in hand.

As a result, Leonardo became one of the major Western thinkers, more than a century before Galileo, to pursue in a persistent hands-on fashion the dialogue between experiment and theory that would lead to the modern Scientific Revolution. Aristotle had laid the foundations, in ancient Greece, for the method of partnering inductions and deductions: using observations to formulate general principles, then using these principles to predict outcomes. While Europe was mired in its dark years of medieval superstition, the work of combining theory and experiment was advanced primarily in the Islamic world. Muslim scientists often also worked as scientific instrument makers, which made them experts at measurements and applying theories. The Arab physicist Ibn al-Haytham, known as Alhazen, wrote a seminal text on optics in 1021 that combined observations and experiments to develop a theory of how human vision works, then devised further experiments to test the theory. His ideas and methods became a foundation for the work of Alberti and Leonardo four centuries later. Meanwhile, Aristotle’s science was being revived in Europe during the thirteenth century by scholars such as Robert Grosseteste and Roger Bacon. The empirical method used by Bacon emphasized a cycle: observations should lead to a hypothesis, which should then be tested by precise experiments, which would then be used to refine the original hypothesis. Bacon also recorded and reported his experiments in precise detail so that others could independently replicate and verify them. Leonardo had the eye and temperament and curiosity to become an exemplar of this scientific method. Galileo, born 112 years after Leonardo, is usually credited with being the first to develop this kind of rigorous empirical approach and is often hailed as the father of modern science, the historian Fritjof Capra wrote. There can be no doubt that this honor would have been bestowed on Leonardo da Vinci had he published his scientific writings during his lifetime, or had his Notebooks been widely studied soon after his death.

That goes a step too far, I think. Leonardo did not invent the scientific method, nor did Aristotle or Alhazen or Galileo or any Bacon. But his uncanny abilities to engage in the dialogue between experience and theory made him a prime example of how acute observations, fanatic curiosity, experimental testing, a willingness to question dogma, and the ability to discern patterns across disciplines can lead to great leaps in human understanding.

In lieu of possessing abstract mathematical tools to extract theoretical laws from nature, the way Copernicus and Galileo and Newton later did, Leonardo relied on a more rudimentary method: he was able to see patterns in nature, and he theorized by making analogies.

In addition to his instinct for discerning patterns across disciplines, Leonardo honed two other traits that aided his scientific pursuits: an omnivorous curiosity, which bordered on the fanatical, and an acute power of observation, which was eerily intense. Like much with Leonardo, these were interconnected.

In his notebook, he described his method almost like a trick for closely observing a scene or object: look carefully and separately at each detail. He compared it to looking at the page of a book, which is meaningless when taken in as a whole and instead needs to be looked at word by word. Deep observation must be done in steps: If you wish to have a sound knowledge of the forms of objects, begin with the details of them, and do not go on to the second step until you have the first well fixed in memory.

For more than two decades, beginning around 1490, Leonardo investigated, with an unusual degree of diligence, the flight of birds and the possibility of designing machines that would enable humans to fly. He produced more than five hundred drawings and thirty-five thousand words scattered over a dozen notebooks on these topics. The endeavor wove together his curiosity about nature, his observational skills, and his engineering instincts. It was also an example of his method of using analogy to discover nature’s patterns. But in this case the analogy process extended even further: it took him closer than most of his other investigations into the realm of pure theory, including fluid dynamics and the laws of motion.

But like much of Leonardo’s work, the treatise remained unfinished. He was more interested in nailing concepts than he was in polishing them for publication.

Leonardo increasingly came to realize that mathematics was the key to turning observations into theories. It was the language that nature used to write her laws. There is no certainty in sciences where mathematics cannot be applied, he declared.

Pacioli’s book focused on the golden ratio, or divine proportion, an irrational number that expresses a ratio that pops up often in number series, geometry, and art. It is approximately 1.61803398, but (being irrational) has decimals that stretch on randomly forever. The golden ratio occurs when you divide a line into two parts in such a way that the ratio between the whole length and the longer part is equal to the ratio between the longer part and the shorter part. For example, take a line that’s 100 inches long and divide it into two parts of 61.8 inches and 38.2 inches. That comes close to the golden ratio, because 100 divided by 61.8 is about the same as 61.8 divided by 38.2; in both cases, it’s approximately 1.618.

Nevertheless, Leonardo’s interest in harmonic ratios was reflected in his intense studies of the ways that ratios and proportions are manifest in anatomy, science, and art. It led him to search for analogies between the proportions of the body, the notes of musical harmonies, and other ratios that underpin the beauty manifest in the works of nature.

Like his other treatises, it produced brilliant notebook pages but not a published book.

As a young painter in Florence, Leonardo studied human anatomy primarily to improve his art. His forerunner as an artist-engineer, Leon Battista Alberti, had written that anatomical study was essential for an artist because properly depicting people and animals requires beginning with an understanding of their insides.

The most basic anatomical knowledge for a painter is the understanding of muscles, and in this Florence’s artists were pioneers.

In anatomy, as in so many of his studies, he saw the art and science as interwoven. Art required a deep understanding of anatomy, which in turn was aided by a profound appreciation for the beauty of nature. As with his study of the flight of birds, Leonardo went from seeking knowledge that could be of practical use and began seeking knowledge for its own sake, out of pure curiosity and joy.

More important, his fascination with the connection between the mind and the body became a key component of his artistic genius: showing how inner emotions are manifest in outward gestures. In painting, the actions of the figures are, in all cases, expressive of the purpose of their minds.

The distance from the top of the nose to the bottom of the chin is two-thirds of the face… The width of the face is equal to the space between the mouth and the roots of the hair and is one-twelfth of the whole height… From the top of the ear to the top of the head is equal to the distance from the bottom of the chin to the duct of the eye and also equal to the distance from the angle of the chin to that of the jaw… The hollow of the cheek bone occurs half way between the tip of the nose and the top of the jaw bone… The great toe is the sixth part of the foot, taking the measure in profile… From the joint of one shoulder to the other is the length of two faces… From the navel to the genitals is a face’s length. I am tempted to quote him at even greater length because the enormity of his feat, and what it says about his compulsive mind, is evident not in each measurement but in the staggering accumulation of them.

The distance from the top of the nose to the bottom of the chin is two-thirds of the face… The width of the face is equal to the space between the mouth and the roots of the hair and is one-twelfth of the whole height… From the top of the ear to the top of the head is equal to the distance from the bottom of the chin to the duct of the eye and also equal to the distance from the angle of the chin to that of the jaw… The hollow of the cheek bone occurs half way between the tip of the nose and the top of the jaw bone… The great toe is the sixth part of the foot, taking the measure in profile… From the joint of one shoulder to the other is the length of two faces… From the navel to the genitals is a face’s length.

Leonardo had set for himself the most magnificent of all tasks for the mind of mankind: nothing less than knowing fully the measure of man and how he fits into the cosmos. In his notebook, he proclaimed his intention to fathom what he called universale misura del huomo, the universal measure of man.17 It was the quest that defined Leonardo’s life, the one that tied together his art and his science.

Leonardo later wrote that observing how the deaf communicate was a good way to study the relation between human gestures and thoughts: Let your figures have actions appropriate to what they are intended to think or say, and these will be well learned by imitating the deaf, who by the motion of their hands, eyes, eyebrows, and the whole body, endeavor to express the sentiments of their mind.

Leonardo wove an argument that was integral to understanding his genius: that true creativity involves the ability to combine observation with imagination, thereby blurring the border between reality and fantasy. A great painter depicts both, he said.

Leonardo explained. Intuition needs nurturing. Men of lofty genius sometimes accomplish the most when they work least, he told the duke, for their minds are occupied with their ideas and the perfection of their conceptions, to which they afterwards give form.

But his life became unsettled in the late 1490s, after Caterina’s death and the completion of The Last Supper.

In most of his portraits, and all of those that were fully painted, Leonardo avoided the conventional approach of the period, which was to portray subjects in profile. Instead, he preferred to show his subjects facing the viewer or in three-quarters view, which allowed him to imbue them with a sense of motion and psychological engagement. Ginevra de’ Benci, Cecilia Gallerani, Lucrezia Crivelli, and Mona Lisa are posed this way.

Most significant, the painting conveys the paramount theme in Leonardo’s art: the spiritual connection and analogy between the earth and humans. Echoing so many of his paintings Ginevra de’ Benci, Virgin of the Rocks, Madonna of the Yarnwinder, and of course the Mona Lisaa river curls from the distant horizon of the macrocosm of the earth and seems to flow into the veins of the Holy Family, ending with the lamb that foreshadows the Passion. The curving flow of the river connects to the flowing composition of the characters.

For three months during the winter of 15023, as if in a historical fantasy movie, three of the most fascinating figures of the Renaissance brutal and power-crazed son of a pope, a sly and amoral writer-diplomat, and a dazzling painter yearning to be an engineer were holed up in a tiny fortified walled town that was approximately five blocks wide and eight blocks long.

For three months during the winter of 15023, as if in a historical fantasy movie, three of the most fascinating figures of the Renaissance brutal and power-crazed son of a pope, a sly and amoral writer-diplomat, and a dazzling painter yearning to be an engineer were holed up in a tiny fortified walled town that was approximately five blocks wide and eight blocks long.

In a larger sense, Leonardo’s maps are another example of one of his greatest, though under appreciated, innovations: devising new methods for the visual display of information.

Amerigo Vespucci, whose cousin Agostino worked with Machiavelli in the Florentine chancery, helped supply Columbus’s third voyage in 1498, and the following year he made his own voyage across the Atlantic, landing in what is now Brazil. Unlike Columbus, who thought he was finding a route to India, Vespucci correctly reported to his Florentine patrons that he had arrived at a new land which for many reasons . . . we observed to be a continent. His correct surmise led to its being named America, after him.

Leonardo would end up pitted against his personal and professional young rival, Michelangelo, who was chosen in early 1504 to paint the other large mural in the hall. Even though neither painting was finished like Leonardo’s, Michelangelo’s work is known to us only through copies and preparatory drawings the saga provides a fascinating look at how the contrasting styles of Leonardo, then fifty-one, and Michelangelo, twenty-eight, each transformed the history of art.

The result would have been neither a commemoration of conquest like the Bayeux Tapestry nor an antiwar statement like Picasso’s Guernica. In his own nature and in his art, Leonardo’s attitude toward war was complex.

When Leonardo left Florence for Milan in 1482, Michelangelo was only seven years old.

During the seventeen years that Leonardo was away in Milan, Michelangelo became Florence’s hot new artist. He was apprenticed to the thriving Florence workshop of the painter Domenico Ghirlandaio, won the patronage of the Medici, and traveled to Rome in 1496, where he carved his Pietà, showing Mary grieving over the body of Jesus.

By 1500 the two artists were back in Florence. Michelangelo, then twenty-five, was a celebrated but petulant sculptor, and Leonardo, forty-eight, was a genial and generous painter who had a following of friends and young students.

Whereas Leonardo was disinterested in personal religious practice, Michelangelo was a pious Christian who found himself convulsed by the agony and the ecstasy of faith. They were both gay, but Michelangelo was tormented and apparently imposed celibacy on himself, whereas Leonardo was quite comfortable and open about having male companions.

Leonardo was not generally prudish about nudity. From his Vitruvian Man to his portraits of Salai, he merrily drew naked men, and in his notebooks he once wrote that the penis should be displayed unashamedly.

Therein lay another difference between the two artists. Michelangelo tended to specialize in muscular male nudes; even when he painted the ceiling of the Sistine Chapel a few years later he included twenty ignudi, athletic nude males, as corner figures. Leonardo, on the contrary, prided himself on the universal nature of his subjects. He believed The painter should aim at universality, because there is a great want of self-respect in doing one thing well and another badly, as many do who study only the nude figure and do not seek after variety, Leonardo wrote.

Their divergent approaches represent two schools in Florentine art: that of Leonardo, Andrea del Sarto, Raphael, Fra Bartolomeo, and others who emphasized the use of sfumato and chiaroscuro, and the more traditional approach taken by Michelangelo, Agnolo Bronzino, Alessandro Allori, and others who favored a disegno based on outlined contours.

We should pause to imagine the dandy-dressing Leonardo, now in his mid-fifties and at the height of his fame as a painter, spending his night hours at an old hospital in his neighborhood talking to patients and dissecting bodies. It is another example of his relentless curiosity that would astonish us if we had not become so used to it.

In most of his studies of nature, Leonardo theorized by making analogies. His quest for knowledge across all the disciplines of arts and sciences helped him see patterns. Occasionally this mode of thinking misled him, and it sometimes substituted for reaching more profound scientific theories. But this cross-disciplinary thinking and pattern-seeking was his hallmark as the quintessential Renaissance Man, and it made him a pioneer of scientific humanism.

He was mainly motivated by his own curiosity. He may have considered, as well, that he was making a contribution to public knowledge, but here it gets murky. He wrote that he intended his findings to be published, but when it came to editing and organizing his notes he was once again dilatory rather than diligent. He was more interested in pursuing knowledge than in publishing it.

He wanted to accumulate knowledge for its own sake, and for his own personal joy, rather than out of a desire to make a public name for himself as a scholar or to be part of the progress of history.

As a painter who marveled at nature’s patterns, Leonardo embraced the microcosm-macrocosm connection as more than merely an analogy. He viewed it as having a spiritual component, which he expressed in his drawing of Vitruvian Man. As we have seen, this mystical connection between humans and the earth is reflected in many of his masterpieces, from Ginevra de’ Benci to Saint Anne to Madonna of the Yarnwinder and eventually the Mona Lisa.

His goal was the one that Renaissance thinkers, himself foremost among them, bequeathed to the subsequent ages of science and enlightenment: understanding the causes and effects that rule.

The analogy helped him look at the earth in a pioneering way. Rather than assuming that it had been static since its creation, Leonardo realized that the earth had a dynamic history in which powerful forces caused it to change and mature over the centuries.

Leonardo pondered a question that seems so ordinary and mundane that most of us forget to marvel about it after age eight or so. But the greatest geniuses, from Aristotle to Leonardo, Newton, Rayleigh, and Einstein, have studied it: Why is the sky blue?

Vasari was referring to Lisa del Giocondo, who was born in 1479 into a minor branch of the distinguished Gherardini family, whose roots as landowners stretched from feudal times but whose money had not survived quite so long.

The most obvious evidence that he was human rather than superhuman is the trail of projects he left unfinished. Among them were a horse model that archers reduced to rubble, an Adoration scene and battle mural that were abandoned, flying machines that never flew, tanks that never rolled, a river that was never diverted, and pages of brilliant treatises that piled up unpublished.

Each moment incorporates what came right before and what is coming right after. Similarly, he looked upon his art and engineering and his treatises as a part of a dynamic process, always receptive to a refinement by the application of a new insight.

His facility for combining observation with fantasy allowed him, like other creative geniuses, to make unexpected leaps that related things seen to things unseen.

His curiosity impelled him to become among the handful of people in history who tried to know all there was to know about everything that could be known.

Leonardo was a genius, but more: he was the epitome of the universal mind, one who sought to understand all of creation, including how we fit into it.

Be curious, relentlessly curious. I have no special talents, Einstein once wrote to a friend. I am just passionately curious.

He wanted to know what causes people to yawn, how they walk on ice in Flanders, methods for squaring a circle, what makes the aortic valve close, how light is processed in the eye and what that means for the perspective in a painting. He instructed himself to learn about the placenta of a calf, the jaw of a crocodile, the tongue of a woodpecker, the muscles of a face, the light of the moon, and the edges of shadows.

Seek knowledge for its own sake. Not all knowledge needs to be useful. Sometimes it should be pursued for pure pleasure. Leonardo did not need to know how heart valves work to paint the Mona Lisa, nor did he need to figure out how fossils got to the top of mountains to produce Virgin of the Rocks. By allowing himself to be driven by pure curiosity, he got to explore more horizons and see more connections than anyone else of his era.

Retain a childlike sense of wonder. At a certain point in life, most of us quit puzzling over everyday phenomena. We might savor the beauty of a blue sky, but we no longer bother to wonder why it is that color. Leonardo did. So did Einstein, who wrote to another friend, You and I never cease to stand like curious children before the great mystery into which we were born.5 We should be careful to never outgrow our wonder years, or to let our children do so.

Observe. Leonardo’s greatest skill was his acute ability to observe things. It was the talent that empowered his curiosity, and vice versa. It was not some magical gift but a product of his own effort.

Start with the details. In his notebook, Leonardo shared a trick for observing something carefully: Do it in steps, starting with each detail. A page of a book, he noted, cannot be absorbed in one stare; you need to go word by word. If you wish to have a sound knowledge of the forms of objects, begin with the details of them, and do not go on to the second step until you have the first well fixed in memory.

See things unseen. Leonardo’s primary activity in many of his formative years was conjuring up pageants, performances, and plays. He mixed theatrical ingenuity with fantasy. This gave him a combinatory creativity.

Go down rabbit holes. He filled the opening pages of one of his notebooks with 169 attempts to square a circle. In eight pages of his Codex Leicester, he recorded 730 findings about the flow of water; in another notebook, he listed sixty-seven words that describe different types of moving water. He measured every segment of the human body, calculated their proportional relationships, and then did the same for a horse.

If we want to be more like Leonardo, we have to be fearless about changing our minds based on new information.

Let the perfect be the enemy of the good. When Leonardo could not make the perspective in the Battle of Anghiari or the interaction in the Adoration of the Magi work perfectly, he abandoned

Jobs embraced a counter maxim, Real artists ship,

Think visually. Leonardo was not blessed with the ability to formulate math equations or abstractions. So he had to visualize them, which he did with his studies of proportions, his rules of perspective, his method for calculating reflections from concave mirrors, and his ways of changing one shape into another of the same size. Too often, when we learn a formula or a rule even one so simple as the method for multiplying numbers or mixing a paint color we no longer visualize how it works. As a result, we lose our appreciation for the underlying beauty of nature’s laws.

Let your reach exceed your grasp. Imagine, as he did, how you would build a human-powered flying machine or divert a river. Even try to devise a perpetual-motion machine or square a circle using only a ruler and a compass. There are some problems we will never solve. Learn why.

Create for yourself, not just for patrons.

Collaborate. Genius is often considered the purview of loners who retreat to their garrets and are struck by creative lightning. Like many myths, that of the lone genius has some truth to it. But there’s usually more to the story. The Madonnas and drapery studies produced in Verrocchio’s studio, and the versions of Virgin of the Rocks and Madonna of the Yarnwinder and other paintings from Leonardo’s studio, were created in such a collaborative manner that it is hard to tell whose hand made which strokes. Vitruvian Man was produced after sharing ideas and sketches with friends. Leonardo’s best anatomy studies came when he was working in partnership with Marcantonio della Torre. And his most fun work came from collaborations on theatrical productions and evening entertainments at the Sforza court.

Take notes, on paper. Five hundred years later, Leonardo’s notebooks are around to astonish and inspire us. Fifty years from now, our own notebooks, if we work up the initiative to start writing them, will be around to astonish and inspire our grandchildren, unlike our tweets and Facebook posts.

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