Leonardo Da Vinci

the ability to make connections across disciplines—arts and sciences, humanities and technology—is a key to innovation, imagination, and genius.

“He saw beauty in both art and engineering,” Jobs said, “and his ability to combine them was what made him a genius.”4

His genius was of the type we can understand, even take lessons from. It was based on skills we can aspire to improve in ourselves, such as curiosity and intense observation. He had an imagination so excitable that it flirted with the edges of fantasy, which is also something we can try to preserve in ourselves and indulge in our children.

Vision without execution is hallucination. But I also came to believe that his ability to blur the line between reality and fantasy, just like his sfumato techniques for blurring the lines of a painting, was a key to his creativity.

Skill without imagination is barren. Leonardo knew how to marry observation and imagination, which made him history’s consummate innovator.

The cross-disciplinary brilliance whirls across every page, providing a delightful display of a mind dancing with nature.

His notebooks are the greatest record of curiosity ever created, a wondrous guide to the person whom the eminent art historian Kenneth Clark called “the most relentlessly curious man in history.”

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

“He who can go to the fountain does not go to the water-jar.”12

I 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.

His ability to combine art, science, technology, the humanities, and imagination remains an enduring recipe for creativity.

Above all, Leonardo’s relentless curiosity and experimentation should remind us of the importance of instilling, in both ourselves and our children, not just received knowledge but a willingness to question it—to be imaginative and, like talented misfits and rebels in any era, to think different.

“1452: There was born to me a grandson, the son of Ser Piero my son, on the 15th day of April, a Saturday, at the third hour of the night [about 10 p.m.]. He bears the name Leonardo.”2

He would have made a poor notary: he got bored and distracted too easily, especially when a project became routine rather than creative.14

took pride that his lack of formal schooling led him to be a disciple of experience and experiment.

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.

my intention is to consult experience first and then with reasoning show why such experience is bound to operate in such a way.”

Born within about a year of Leonardo were Christopher Columbus and Amerigo Vespucci, who would lead an era of exploration.

Its leading thinkers embraced a Renaissance humanism that put its faith in the dignity of the individual and in the aspiration to find happiness on this earth through knowledge.

“One must apply the greatest artistry in three things,” Alberti wrote, “walking in the city, riding a horse, and speaking, for in each of these one must try to please everyone.”12 Leonardo mastered all three.

“The first intention of the painter,” Leonardo later wrote, “is to make a flat surface display a body as if modeled and separated from this plane, and he who surpasses others in this skill deserves most praise. This accomplishment, with which the science of painting is crowned, arises from light and shade, or we may say chiaroscuro.”

The glory of being an artist, he realized, was that reality should inform but not constrain.

Other artists had drawn landscapes as backdrops, but Leonardo was doing something different: depicting nature for its own sake.

“Whoever does not curb lustful desires puts himself on the level of beasts.”

Adoration of the Magi (fig. 15). It was destined to remain unfinished, but it became the most influential unfinished painting in the history of art and, in the words of Kenneth Clark, “the most revolutionary and anti-classical picture of the fifteenth century.”

Thus one of history’s most creative artists found himself decorating a clock for firewood, borrowing money for paint, and cadging wine.

Leonardo at twenty-nine was more easily distracted by the future than he was focused on the present. He was a genius undisciplined by diligence.

Ginevra de’ Benci and the Mona Lisa, for example—were never delivered to clients. Leonardo clung to his favorite works, carried them with him when he moved, and returned to them when he had new ideas.

He did not like to let go. That is why he would die with some of his masterpieces still near his bedside.

As frustrating as it is to us today, there was a poignant and inspiring aspect to Leonardo’s unwillingness to declare a painting done and relinquish it: he knew that there was always more he might learn, new techniques he might master, and further inspirations that might strike him. And he was right.

Alberti, in On Painting, emphasized the importance of the idea in a clear and crisp sentence: “Movements of the soul are made known by movements of the body.”43

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.”

“While I thought that I was learning how to live, I have been learning how to die.”48

On another page is a quote from someone named Johannes: “There is no perfect gift without great suffering. Our glories and our triumphs pass away.”

transcription from Dante’s Inferno: “Put off this sloth,” the master said, “for shame! Sitting on feather-pillows, lying reclined Beneath the blanket is no way to fame— Fame, without which man’s life wastes out of mind, Leaving on earth no more memorial Than foam in water or smoke upon the wind.” 51

In 1482, the year he turned thirty, Leonardo da Vinci left Florence for Milan, where he would end up spending the next seventeen years.

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.

In addition, 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.

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.

The spread of printing presses helped Leonardo pursue additional military ideas after he arrived in Milan. He borrowed some of his concepts from a book by the thirteenth-century scientist Roger Bacon that had a list of ingenious weapons, including “carts and wagons that could move without animal power; devices used to walk on water and to move underneath the water, and contrivances capable of putting man in flight, having a person placed in the center of a mechanical device with artificial wings.”10 Leonardo embellished on all of these ideas.

On the far side he depicts two soldiers just at the moment they are being sliced in half. Here is our gentle and beloved Leonardo, who became a vegetarian because of his fondness for all creatures, wallowing in horrifying depictions of death. It is, perhaps, yet another glimpse of his inner turmoil. Within his dark cave was a demon imagination.

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

Another proposal he drew was for a machine with many cannons, one with racks of eleven cannons each. While one set of cannons was cooling off and being reloaded, the other sets could be firing. It was the precursor to the machine gun.17 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.

In collecting such a medley of ideas, Leonardo was following a practice that had become popular in Renaissance Italy of keeping a commonplace and sketch book, known as a zibaldone.

His notebooks have been rightly called “the most astonishing testament to the powers of human observation and imagination ever set down on paper.”

The more than 7,200 pages now extant probably represent about one-quarter of what Leonardo actually wrote,4 but that is a higher percentage after five hundred years than the percentage of Steve Jobs’s emails and digital documents from the 1990s that he and I were able to retrieve. Leonardo’s notebooks are nothing less than an astonishing windfall that provides the documentary record of applied creativity.

the Codex Leicester contains 72 pages, mainly on geology and water studies, that have remained together since Leonardo composed them around 1508 to 1510; it is now owned by Bill Gates.

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.

The juxtapositions can seem haphazard, and to some extent they are; we watch his mind and pen leap from an insight about mechanics, to a doodle of hair curls and water eddies, to a drawing of a face, to an ingenious contraption, to an anatomical sketch, all accompanied by mirror-script notes and musings. But the joy of these juxtapositions is that they allow us to marvel at the beauty of a universal mind as it wanders exuberantly in free-range fashion over the arts and sciences and, by doing so, senses the connections in our cosmos.

The beauty of a notebook is that it indulges provisional thoughts, half-finished ideas, unpolished sketches, and drafts for treatises not yet refined.

He occasionally declared an intent to organize and refine his notebook jottings into published works, but his failure to do so became a companion to his failure to complete artworks.

His notebooks show the interest he took in the mechanism of the automated props and scenery changes. The interplay of fantasy and machinery was something he was born to choreograph.

“No sooner is Virtue born than Envy comes into the world to attack it,”

he spent more time pursuing wisdom than working on jobs that would make him money beyond what he needed to support his growing household retinue.

“Often when passing the places where birds were sold, he would take them with his own hand out of their cages, and having paid to those who sold them the price that was asked, he let them fly away into the air, restoring to them their lost liberty.”

A Florentine traveler to India recorded that the people there “do not feed on anything that has blood, nor will they allow anyone to hurt any living thing, like our Leonardo da Vinci.”3

His rationale for avoiding meat derived from a morality based on science. Unlike plants, animals could feel pain, Leonardo realized.

“Nature has given sensibility to pain to living organisms that have the power of movement, in order to preserve those parts which might be destroyed by movement,” he surmised. “Pain is not necessary in plants.”5

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.

Francesco was composing. “All the arts and all the world’s rules are derived from a well-composed and proportioned human body,” he wrote in the foreword to his fifth chapter. “Man, called a little world, contains in himself all the general perfections of the whole world.”

Leonardo likewise embraced the analogy in both his art and his science. He famously wrote around this time, “The ancients called man a lesser world, and certainly the use of this name is well bestowed, because his body is an analog for the world.”

Leonardo once warned against falling prey to the axiom “Every painter paints himself,” but in a section in his proposed treatise on painting called “How Figures Often Resemble Their Masters,” he accepted that it was natural to do so.

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.

Conceiving ideas was for Leonardo, as it has been throughout history for most other cross-disciplinary thinkers, a collaborative endeavor.

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.

We can imagine what his studio looked like, in reality or at least in Leonardo’s imagination, from a description he wrote of an artist at work: “The painter sits in front of his work at perfect ease. He is well dressed and wields a very light brush dipped in delicate color. He adorns himself with the clothes he fancies; his home is clean and filled with delightful pictures, and he is often accompanied by music or by the reading of various beautiful works.”

Even though it was typical of him, we still should marvel that he would decide that before sculpting a horse he had to dissect one. Once again his compulsion to engage in anatomical investigations for his art eventually led him to pursue the science for its own sake.

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. “Though I have no power to quote from authors as they have,” he proclaimed almost proudly, “I shall rely on a far more worthy thing—on experience.”

In 1452 Johannes Gutenberg began selling Bibles from his new printing press, just when the development of rag processing was making paper more readily available. By the time Leonardo became an apprentice in Florence, Gutenberg’s technology had crossed the Alps into Italy. Alberti marveled in 1466 about “the German inventor who has made it possible, by certain pressings down of characters, to have more than two hundred volumes written out in a hundred days from the original, with the labor of no more than three men.”

A goldsmith from Gutenberg’s hometown of Mainz named Johannes de Spira (or Speyer) moved to Venice and started Italy’s first major commercial publishing house in 1469; it printed many of the classics, starting with Cicero’s letters and Pliny’s encyclopedic Natural History, which Leonardo bought. By 1471 there were printing shops also in Milan, Florence, Naples, Bologna, Ferrara, Padua, and Genoa. Venice became the center of Europe’s publishing industry, and by the time Leonardo visited in 1500, there were close to a hundred printing houses there, and two million volumes had come off their presses.3

Leonardo thus was able to become the first major European thinker to acquire a serious knowledge of science without being formally schooled in Latin or Greek.

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.

His appetite for soaking up information from books was voracious and wide-ranging.

Thus Leonardo became a disciple of both experience and received wisdom. More important, he came to see that the progress of science came from a dialogue between the two. That in turn helped him realize that knowledge also came from a related dialogue: that between experiment and theory.

He preferred to induce from experiments rather than deduce from theoretical principles. “My intention is to consult experience first, and then with reasoning show why such experience is bound to operate in such a way,” he wrote.

“Although nature begins with the cause and ends with the experience, we must follow the opposite course, namely begin with the experience, and by means of it investigate the cause.”

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.

Not comfortable wrestling with theory, he preferred dealing with knowledge that he could observe and draw.

But Leonardo did not remain merely a disciple of experiments. His notebooks show that he evolved. 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.

“Those who are in love with practice without theoretical knowledge are like the sailor who goes onto a ship without rudder or compass and who never can be certain whither he is going,” he wrote in 1510. “Practice must always be founded on sound theory.”

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.

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.

“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.”

As the philosopher Michel Foucault noted, the “protoscience” of Leonardo’s era was based on similarities and analogies.13

“All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk below them,” he wrote elsewhere. “All the branches of a river at every stage of its course, if they are of equal rapidity, are equal to the body of the main stream.”15 This conclusion is still known as “da Vinci’s rule,”

The connections that Leonardo made across disciplines served as guides for his inquiries. The analogy between water eddies and air turbulence, for example, provided a framework for studying the flight of birds.

“To arrive at knowledge of the motions of birds in the air,” he wrote, “it is first necessary to acquire knowledge of the winds, which we will prove by the motions of water.”

Any person who puts “Describe the tongue of the woodpecker” on his to-do list is overendowed with the combination of curiosity and acuity.

Einstein said he marveled about questions others found mundane because he was slow in learning to talk as a child.

For Leonardo, this talent may have been connected to growing up with a love of nature while not being overly schooled in received wisdom.

The acuteness of his observational skill was not some superpower he possessed. Instead, it was a product of his own effort.

“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.”23

“In rivers, the water that you touch is the last of what has passed, and the first of that which comes,” he observed. “So with time present.”

Observe the light,” he instructed. “Blink your eye and look at it again. That which you see was not there at first, and that which was there is no more.”

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.

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.

No scientist before Leonardo had methodically shown how birds stay aloft.

He also realized that the pressure the bird puts on the air is met by an equal and opposite pressure that the air puts on the bird. “See how the wings, striking against the air, sustain the heavy eagle in the thin air on high,” he noted,

“As much force is exerted by the object against the air as by the air against the object.”16 Two hundred years later, Newton would state a refined version of this as his third law of motion: “To every action there is always opposed an equal reaction.”

Leonardo accompanied this concept with a precursor to Galileo’s principle of relativity: “The effect of moving air on a stationary object is as great as it is when the object is moving and the air is stationary.”

Even more presciently, he had an intimation of what became known, more than two hundred years later, as Bernoulli’s principle: when air (or any fluid) flows faster, it exerts less pressure.

“The air above birds is thinner than the usual thinness of the other air,” he wrote.19 Leonardo thus realized, before other scientists, that a bird stays aloft not merely because the wings beat downward against the air but also because the wings propel the bird forward and the air lessens in pressure as it rushes over the wing’s curved top surface.

“A bird is an instrument working according to mathematical law, and it is in the capacity of man to reproduce such an instrument,” he wrote. “A man with wings large enough and duly attached might learn to overcome the resistance of the air and raise himself upon it.”20

“Every movement tends to maintain itself; or, rather, every body in motion continues to move so long as the influence of the force that set it in motion is maintained in it.”9 Leonardo’s insights were a precursor to what Newton, two hundred years later, would make his first law of motion: that a body in motion will stay in the same motion unless acted upon by another force.10

Once again, Leonardo was about three centuries ahead of his time. The first antifriction alloy is usually credited to the American inventor Isaac Babbitt, who patented an alloy containing copper, tin, and antimony in 1839.

All movements in the universe—of human limbs and of cogs in machines, of blood in our veins and of water in rivers—operate according to the same laws, he concluded. These laws are analogous; the motions in one realm can be compared to those in another realm, and patterns emerge. “Man is a machine, a bird is a machine, the whole universe is a machine,” wrote Marco Cianchi in an analysis of Leonardo’s devices.

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.1 He was correct.

Using geometry to understand the laws of perspective taught him how math could extract from nature the secrets of its beauty and reveal the beauty of its secrets.

What Leonardo liked about geometry, as opposed to arithmetic, was that geometric shapes are continuous quantities, whereas numbers are discrete digits and thus discontinuous units.

“Arithmetic deals with discontinuous quantities, geometry with continuous ones,” he wrote.3

“Arithmetic is a computational science in its calculation, with true and perfect units, but it is of no avail in dealing with continuous quantity.”4

One of Leonardo’s close friends at Milan’s court was Luca Pacioli, a mathematician who developed the first widely published system for double-entry bookkeeping.

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.

“The soul seems to reside in the judgment, and the judgment would seem to be seated in that part where all the senses meet; and this is called the senso comune,”

On one drawing from this period showing the bones and nerves of an arm, he drew a faint sketch of the spinal cord and nerves emerging from it. Appended is a note about his experience pithing a frog, the first scientist to record doing what is now a staple of biology classes.

he was neither fully original nor correct in his description of a senso comune, he was right in his general view that the human brain receives visual and other stimuli, processes them into perceptions, then transmits reactions through the nervous system to the muscles.

“In painting, the actions of the figures are, in all cases, expressive of the purpose of their minds,”

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.

In his notes for a treatise on painting, Leonardo explained, “Since the quality of color is revealed by means of light, where there is more light will be seen more of the true quality of the illuminated color.”

We tend to think of artists as lone creators, holed in a garret, waiting for inspiration to strike. But as evident in his notebooks and in the process that led to his drawing of Vitruvian Man, much of Leonardo’s thinking was collegial.

Leonardo incorrectly believed that the pupils of the eye dilate separately, when in fact they dilate in unison,