Leonardo’s Legacy: How Da Vinci Reimagined the World

Reviewed by: 

Stefan Klein has written such a beautiful book that the reader can easily remain unaware that the original language was German. This transparency is due in large part to the translation into English by Shelley Frisch that, except for a few odd turns of phrase here and there, is nothing short of immaculate.

Klein’s diligent exploration of what is known about Leonardo di ser Piero da Vinci is clearly a labor of love. From the detailed analysis of Leonardo’s painting style, to visiting the places where Leonardo lived, to interviews with Da Vinci aficionados about the design on his various machines, this work is truly encompassing and a must read for anyone who has even the slightest interest in the intellect of Leonardo da Vinci.

Leonardo’s Legacy is very much directed at a lay audience rather than a scholarly one. As Klein himself expresses it, this book “is not intended as a standard biography of a masterful artist as much as an attempt to get inside the mind of one of the most extraordinary individuals who ever lived—and to see the world through his eyes.”

Because of the sheer historical distance, as well as the loss of much of Leonardo’s writings, many aspects of Leonardo remain inscrutable. Churchill’s description of Russia seems apt: Leonardo is a puzzle, wrapped by a mystery, inside an enigma. Undeterred by this historical inscrutability, Klein strives to attain a fresh perception of Leonardo; no easy task given the historical baggage carried by this iconic and popular figure.

Moreover, such a laudable endeavor is always fraught with the difficulty of trying to detach oneself from our own modern milieu. We tend to think they thought the way we think. Klein is fully aware of this problem and tries hard to avoid the pitfalls. Even if he is not always successful in maintaining that dissociation, he does make some new inroads into Leonardo’s style of thinking. In general, the emphasis of this book is on the scientific rather than the artistic. Indeed, as Klein reveals in his opening chapter, Leonardo’s art is governed in large measure by his self-acquired scientific and engineering knowledge.

For me, as a lay reader but one with a scientific background, the value of Klein’s book lies in the way it evokes certain questions and subsequent revelations about Leonardo. These questions may not have always been the ones the author intended, but that simply serves to demonstrate the engaging style of Klein’s writing.

The first of these revelations was to clarify my otherwise vague perspective on the extraordinarily early period in which Leonardo lived relative to the development of western scientific thought. Merely repeating that Leonardo was born 560 years ago captures neither how advanced was his thinking nor how inevitable were its limitations. One way to get a better handle on Leonardo’s life is to note who were his Renaissance contemporaries, e.g., Michelangelo, Machievelli, and Copernicus, as well as those who followed in his footsteps during the Age of Reason and the early Enlightenment, e.g., Galileo, Kepler, and Newton, to develop the foundations of modern science.

Since the book was no help in this respect, I resorted to creating the timelines. Only by this means did I come to realize that Leonardo had already lived more than a quarter of his life before Copernicus and Machievelli were born and that he had been dead almost as long as he had been alive when Galileo was born.

It may be helpful for the prospective reader to see a list of other questions and revelations about Leonardo that occurred to me as I read Klein’s book.

• Dissecting cadavers. Last summer, I was unfortunate enough to have a rodent die under my living room. The stench at times was almost unbearable and that from something only a few inches long. As Klein reminds us, it is almost inconceivable how Leonardo could have accomplished his detailed anatomical drawings of cadavers by candlelight in unrefrigerated caverns. I was also surprised by certain errors in some of these drawings that were not a result of poor lighting conditions. Some mistakes are due to the influence of accepted Renaissance views on Leonardo (the milieu problem I mentioned earlier), while others are due to Leonardo conceiving of the human body as a machine. Klein’s point is that Leonardo drew what he thought, not just what he saw.

• Backward writing. Leonardo’s use of backward cursive script is legendary. What I had not fully appreciated is that the act of writing reversed cursive letters is difficult, even for a southpaw (although it’s thought that Leonardo was actually ambidextrous). Klein refers to it throughout as “mirror writing,” but did Leonardo actually use a mirror? It seems reasonable to assume that he did use as mirror, at least early on, but that he may also have become accustomed enough over time to abandon it. And what was the point of this mirror writing? The ultimate purpose cannot have been serious encryption, because it can easily be decoded with a mirror or any shiny flat surface. Klein does not delve into how Leonardo’s mirror writing was accomplished or why.

• Stroboscopic vision. His super-human eyesight impresses everyone who studies Leonardo. It allowed him to draw the wing motion of dragonflies and birds, as well as eddies in whirlpools. As Klein puts it, “It is amazing that he was able to detect the phases of the wing movement with the naked eye at all. Normally we do not perceive even movements that are eight times slower.” Personally, I am inclined to think that people like Leonardo had a few tricks up their sleeve that we would no longer think of because we have come to rely on technology like high-speed cameras. I can imagine that Leonardo might have used the simple expedient of blinking his eyes in rapid succession to make a stroboscope. In this way, with enough repeated blinks under the right conditions, you can build up a series of “freeze frames” in your mind. After all, this is the man who wrote backwards.

• The opportunist. Part of the iconic Leonardo involves the pacifist who bought caged birds merely in to set them free. In contrast, Klein writes that “Leonardo earned a living by promising his employers spectacular works of art and technology.” Because of protracted local wars during that period, Klein makes it clear that Leonardo was enough of an opportunist to be employed by some very undesirable but very powerful patrons—Cesare Borgia foremost among them. And that he was adept enough to switch allegiances when necessary.

• Optics. Various technical drawings in Leonardo’s notebooks suggest that he carried out a variety of optical experiments aimed at understanding how vision works. The possible ramifications for his artwork would have provided sufficient motivation. Thus, Leonardo knew that the image formed in the eye is inverted. All his life, “he could never get over his astonishment that man sees everything right side up even though the images in the eye ought to be upside down the way they are in a camera obscura,” according to Klein.

Quite apart from the fact that he drew the anatomy of the eyeball incorrectly (the milieu problem again), Leonardo could not have known that optics and vision are different things. Nor could he have known the true laws of refraction. Even Descartes (100 years later) and Newton (150 years later) got the physics of refraction wrong. But Leonardo is remarkable for attempting to understand optical phenomena through experiment. In this, he predates Galileo.

• Electric water. Water and canals were for Leonardo what electricity and the electric grid are for us. Modern phrases like “the flow of electrical current,” have inherited this association. Hydraulics was as vital in the sixteenth century as electric power is for us today and hence, it formed the basis of many of Leonardo’s mechanical conceptions. Klein also underscores the degree to which hydraulics also defined what Leonardo could not conceive: “steam engines and motors lay so far beyond the capabilities of the technology that even Leonardo could not picture them.”

• Innumeracy. Klein tells us that Leonardo’s “limited education had never allowed him to master even the basics of arithmetic.” To put things in perspective, Leonardo Fibonacci predated Leonardo da Vinci by about two hundred and fifty years while contemporaneous mathematicians were busy finding solutions to cubic equations. For me, this lies at the heart of the Leonardo enigma. He seems to have been able to devise highly novel solutions to engineering problems using geometry—presumably because it has a very visual component—but he must have been severely hampered when it came to engineering calculations.

In this respect, Klein appropriately quotes Daniel Arasse who calls Leonardo the “thinker without a system of thought.” It also struck me that very few of Leonardo’s engineering sketches contain numerical annotations. The incredibly detailed map of Imola comes with no legend or scale markings, yet we knew that he measured distances accurately with his cyclometer. In many ways, the Imola map seems emblematic of Leonardo’s mind. According to Klein, “Leonardo thought in pictures. He owed his highly significant discoveries to this pictorial approach, though it also led him astray at time, because looks can be deceiving.” By way of contrast, one of the hallmarks of Einstein’s thinking style was that he also tended to develop his insights visually. The difference being that he often spent much longer testing his visual intuition against the rigors of mathematics—something Leonardo could not do.

• Computing engines. Chapter V is entitled “Robots,” and even though that word does not appear in the English lexicon until 1920, what better Leonardo metaphysical juxtaposition could there be than machines with a life: living machines. Leonardo’s biggest hit seems to have been the mechanical lion he constructed for a banquet in honor of the king of France. Klein speculates, “people wondered whether the engineer had breathed a soul into his creation.” Leonardo may also have been the James Randy of his day, because Klein tells us that his interest in automata “was also fueled by his aversion to charlatans and superstitions of all kinds.” The highlight of this chapter, however, is “Leonardo’s Computer” or bell-ringing machine—a type of digital clock.

Once again water is the analog of electricity in this automaton. To call it “man’s oldest digital computer” is a bit of a stretch. As Klein himself says, “It could count.” But counting is merely the operation of incrementing by one or adding one (+1). There was no carry operation, so it could not add two different numbers together. There was no accumulator, so it could not store numbers, and there was no multiply operation. Even an ancient Chinese abacus could perform multiplication. The bell-ringing digital clock is really a water-driven ratchet and ratchets were something with which Leonardo was intimately familiar, e.g., his cyclometer. This is not to take away from Leonardo’s innovative engineering skills, rather just to keep things in perspective.

• Simulations. Although it is highly unlikely that Leonardo saw any direct military action, Klein states that his “close ties to the tyrants of his day offer a case study of the early symbiosis of science and the military.” In this respect many of Leonardo’s artillery designs were most likely based on simulations with water jets substituting for projectiles. This strikes me as a revelatory point because the sketch of saturation bombing likely derives from such simulations. Despite the erroneous depiction of the trajectories as semicircular instead of parabolae, the shot from the battery of canon look like fountains of water rather than discrete canon balls.

Why is this significant? There is a huge conceptual leap between seeing a discrete cannonball in flight and depicting its locus as a continuous path. In fact, the concept of motion as a continuum of infinitesimal epochs, did not really take hold until Newton and the development of the calculus; some two hundred years later. On the other hand, if you are simulating cannonballs with arcs of water, this is precisely how it looks.

• The grounded aeronaut. Leonardo was an intuitive engineer. Intuition is a seductive siren who will gladly allow you to crash on the rocks of misunderstanding. Better to tie yourself to the mast of mathematics but, unfortunately, this is something that Leonardo could not do. As a consequence, Leonardo arguably had the best intuition in the world regarding the mechanics of flight, but he never flew.

Klein points out that Leonardo thought all forces were pyramidal, i.e., they follow the proportions of similar triangles. This principle does appear to be valid in certain static situations. For example, the static pressure at a water spigot doubles in proportion to the height of the water above it, although Leonardo’s drawing of water jets issuing from holes in a cask, is incorrect. Moreover, the pyramidal principle breaks down when it comes to analyzing motion. The horizontal velocity of the water jet is proportional to the square root of the water level. Square roots would have troubled Leonardo. Quoting Klein, “He tackled mathematics for years without ever getting the hang of long division.”

Trying to resolve Leonardo da Vinci from a distance of five hundred years is a formidable task. Most of his own written record has been destroyed, so that today we would say Leonardo suffers from a zero citation index. To make resolving him even more confounded, we know that Leonardo borrowed liberally from others without attribution, as did his peers. We also know that many of his mechanical drawings were intended to impress rather than work. One of the more infamous examples is the giant crossbow illustration. The British Army tried to construct this weapon from Leonardo’s drawings, but it could never be made to fire successfully.

Rather then focusing on this outward confusion, Klein has tried to bring Leonardo closer to us by looking inside his mind. What emerges is the Audubon of automata, who gives rise to exquisite artistic and scientific representations of his sixteenth century universe.

Long Description: 

Stefan Klein has written such a beautiful book that the reader can easily remain unaware that the original language was German. This transparency is due in large part to the translation into English by Shelley Frisch that, except for a few odd turns of phrase here and there, is nothing short of immaculate.

Klein’s diligent exploration of what is known about Leonardo di ser Piero da Vinci is clearly a labor of love. From the detailed analysis of Leonardo’s painting style, to visiting the places where Leonardo lived, to interviews with Da Vinci aficionados about the design on his various machines, this work is truly encompassing and a must read for anyone who has even the slightest interest in the intellect of Leonardo da Vinci.

Leonardo’s Legacy is very much directed at a lay audience rather than a scholarly one. As Klein himself expresses it, this book “is not intended as a standard biography of a masterful artist as much as an attempt to get inside the mind of one of the most extraordinary individuals who ever lived—and to see the world through his eyes.”

Because of the sheer historical distance, as well as the loss of much of Leonardo’s writings, many aspects of Leonardo remain inscrutable. Churchill’s description of Russia seems apt: Leonardo is a puzzle, wrapped by a mystery, inside an enigma. Undeterred by this historical inscrutability, Klein strives to attain a fresh perception of Leonardo; no easy task given the historical baggage carried by this iconic and popular figure.

Moreover, such a laudable endeavor is always fraught with the difficulty of trying to detach oneself from our own modern milieu. We tend to think they thought the way we think. Klein is fully aware of this problem and tries hard to avoid the pitfalls. Even if he is not always successful in maintaining that dissociation, he does make some new inroads into Leonardo’s style of thinking. In general, the emphasis of this book is on the scientific rather than the artistic. Indeed, as Klein reveals in his opening chapter, Leonardo’s art is governed in large measure by his self-acquired scientific and engineering knowledge.

For me, as a lay reader but one with a scientific background, the value of Klein’s book lies in the way it evokes certain questions and subsequent revelations about Leonardo. These questions may not have always been the ones the author intended, but that simply serves to demonstrate the engaging style of Klein’s writing.

The first of these revelations was to clarify my otherwise vague perspective on the extraordinarily early period in which Leonardo lived relative to the development of western scientific thought. Merely repeating that Leonardo was born 560 years ago captures neither how advanced was his thinking nor how inevitable were its limitations. One way to get a better handle on Leonardo’s life is to note who were his Renaissance contemporaries, e.g., Michelangelo, Machievelli, and Copernicus, as well as those who followed in his footsteps during the Age of Reason and the early Enlightenment, e.g., Galileo, Kepler, and Newton, to develop the foundations of modern science.

Since the book was no help in this respect, I resorted to creating the timelines. Only by this means did I come to realize that Leonardo had already lived more than a quarter of his life before Copernicus and Machievelli were born and that he had been dead almost as long as he had been alive when Galileo was born.

It may be helpful for the prospective reader to see a list of other questions and revelations about Leonardo that occurred to me as I read Klein’s book.

• Dissecting cadavers. Last summer, I was unfortunate enough to have a rodent die under my living room. The stench at times was almost unbearable and that from something only a few inches long. As Klein reminds us, it is almost inconceivable how Leonardo could have accomplished his detailed anatomical drawings of cadavers by candlelight in unrefrigerated caverns. I was also surprised by certain errors in some of these drawings that were not a result of poor lighting conditions. Some mistakes are due to the influence of accepted Renaissance views on Leonardo (the milieu problem I mentioned earlier), while others are due to Leonardo conceiving of the human body as a machine. Klein’s point is that Leonardo drew what he thought, not just what he saw.

• Backward writing. Leonardo’s use of backward cursive script is legendary. What I had not fully appreciated is that the act of writing reversed cursive letters is difficult, even for a southpaw (although it’s thought that Leonardo was actually ambidextrous). Klein refers to it throughout as “mirror writing,” but did Leonardo actually use a mirror? It seems reasonable to assume that he did use as mirror, at least early on, but that he may also have become accustomed enough over time to abandon it. And what was the point of this mirror writing? The ultimate purpose cannot have been serious encryption, because it can easily be decoded with a mirror or any shiny flat surface. Klein does not delve into how Leonardo’s mirror writing was accomplished or why.

• Stroboscopic vision. His super-human eyesight impresses everyone who studies Leonardo. It allowed him to draw the wing motion of dragonflies and birds, as well as eddies in whirlpools. As Klein puts it, “It is amazing that he was able to detect the phases of the wing movement with the naked eye at all. Normally we do not perceive even movements that are eight times slower.” Personally, I am inclined to think that people like Leonardo had a few tricks up their sleeve that we would no longer think of because we have come to rely on technology like high-speed cameras. I can imagine that Leonardo might have used the simple expedient of blinking his eyes in rapid succession to make a stroboscope. In this way, with enough repeated blinks under the right conditions, you can build up a series of “freeze frames” in your mind. After all, this is the man who wrote backwards.

• The opportunist. Part of the iconic Leonardo involves the pacifist who bought caged birds merely in to set them free. In contrast, Klein writes that “Leonardo earned a living by promising his employers spectacular works of art and technology.” Because of protracted local wars during that period, Klein makes it clear that Leonardo was enough of an opportunist to be employed by some very undesirable but very powerful patrons—Cesare Borgia foremost among them. And that he was adept enough to switch allegiances when necessary.

• Optics. Various technical drawings in Leonardo’s notebooks suggest that he carried out a variety of optical experiments aimed at understanding how vision works. The possible ramifications for his artwork would have provided sufficient motivation. Thus, Leonardo knew that the image formed in the eye is inverted. All his life, “he could never get over his astonishment that man sees everything right side up even though the images in the eye ought to be upside down the way they are in a camera obscura,” according to Klein.

Quite apart from the fact that he drew the anatomy of the eyeball incorrectly (the milieu problem again), Leonardo could not have known that optics and vision are different things. Nor could he have known the true laws of refraction. Even Descartes (100 years later) and Newton (150 years later) got the physics of refraction wrong. But Leonardo is remarkable for attempting to understand optical phenomena through experiment. In this, he predates Galileo.

• Electric water. Water and canals were for Leonardo what electricity and the electric grid are for us. Modern phrases like “the flow of electrical current,” have inherited this association. Hydraulics was as vital in the sixteenth century as electric power is for us today and hence, it formed the basis of many of Leonardo’s mechanical conceptions. Klein also underscores the degree to which hydraulics also defined what Leonardo could not conceive: “steam engines and motors lay so far beyond the capabilities of the technology that even Leonardo could not picture them.”

• Innumeracy. Klein tells us that Leonardo’s “limited education had never allowed him to master even the basics of arithmetic.” To put things in perspective, Leonardo Fibonacci predated Leonardo da Vinci by about two hundred and fifty years while contemporaneous mathematicians were busy finding solutions to cubic equations. For me, this lies at the heart of the Leonardo enigma. He seems to have been able to devise highly novel solutions to engineering problems using geometry—presumably because it has a very visual component—but he must have been severely hampered when it came to engineering calculations.

In this respect, Klein appropriately quotes Daniel Arasse who calls Leonardo the “thinker without a system of thought.” It also struck me that very few of Leonardo’s engineering sketches contain numerical annotations. The incredibly detailed map of Imola comes with no legend or scale markings, yet we knew that he measured distances accurately with his cyclometer. In many ways, the Imola map seems emblematic of Leonardo’s mind. According to Klein, “Leonardo thought in pictures. He owed his highly significant discoveries to this pictorial approach, though it also led him astray at time, because looks can be deceiving.” By way of contrast, one of the hallmarks of Einstein’s thinking style was that he also tended to develop his insights visually. The difference being that he often spent much longer testing his visual intuition against the rigors of mathematics—something Leonardo could not do.

• Computing engines. Chapter V is entitled “Robots,” and even though that word does not appear in the English lexicon until 1920, what better Leonardo metaphysical juxtaposition could there be than machines with a life: living machines. Leonardo’s biggest hit seems to have been the mechanical lion he constructed for a banquet in honor of the king of France. Klein speculates, “people wondered whether the engineer had breathed a soul into his creation.” Leonardo may also have been the James Randy of his day, because Klein tells us that his interest in automata “was also fueled by his aversion to charlatans and superstitions of all kinds.” The highlight of this chapter, however, is “Leonardo’s Computer” or bell-ringing machine—a type of digital clock.

Once again water is the analog of electricity in this automaton. To call it “man’s oldest digital computer” is a bit of a stretch. As Klein himself says, “It could count.” But counting is merely the operation of incrementing by one or adding one (+1). There was no carry operation, so it could not add two different numbers together. There was no accumulator, so it could not store numbers, and there was no multiply operation. Even an ancient Chinese abacus could perform multiplication. The bell-ringing digital clock is really a water-driven ratchet and ratchets were something with which Leonardo was intimately familiar, e.g., his cyclometer. This is not to take away from Leonardo’s innovative engineering skills, rather just to keep things in perspective.

• Simulations. Although it is highly unlikely that Leonardo saw any direct military action, Klein states that his “close ties to the tyrants of his day offer a case study of the early symbiosis of science and the military.” In this respect many of Leonardo’s artillery designs were most likely based on simulations with water jets substituting for projectiles. This strikes me as a revelatory point because the sketch of saturation bombing likely derives from such simulations. Despite the erroneous depiction of the trajectories as semicircular instead of parabolae, the shot from the battery of canon look like fountains of water rather than discrete canon balls.

Why is this significant? There is a huge conceptual leap between seeing a discrete cannonball in flight and depicting its locus as a continuous path. In fact, the concept of motion as a continuum of infinitesimal epochs, did not really take hold until Newton and the development of the calculus; some two hundred years later. On the other hand, if you are simulating cannonballs with arcs of water, this is precisely how it looks.

• The grounded aeronaut. Leonardo was an intuitive engineer. Intuition is a seductive siren who will gladly allow you to crash on the rocks of misunderstanding. Better to tie yourself to the mast of mathematics but, unfortunately, this is something that Leonardo could not do. As a consequence, Leonardo arguably had the best intuition in the world regarding the mechanics of flight, but he never flew.

Klein points out that Leonardo thought all forces were pyramidal, i.e., they follow the proportions of similar triangles. This principle does appear to be valid in certain static situations. For example, the static pressure at a water spigot doubles in proportion to the height of the water above it, although Leonardo’s drawing of water jets issuing from holes in a cask, is incorrect. Moreover, the pyramidal principle breaks down when it comes to analyzing motion. The horizontal velocity of the water jet is proportional to the square root of the water level. Square roots would have troubled Leonardo. Quoting Klein, “He tackled mathematics for years without ever getting the hang of long division.”

Trying to resolve Leonardo da Vinci from a distance of five hundred years is a formidable task. Most of his own written record has been destroyed, so that today we would say Leonardo suffers from a zero citation index. To make resolving him even more confounded, we know that Leonardo borrowed liberally from others without attribution, as did his peers. We also know that many of his mechanical drawings were intended to impress rather than work. One of the more infamous examples is the giant crossbow illustration. The British Army tried to construct this weapon from Leonardo’s drawings, but it could never be made to fire successfully.

Rather then focusing on this outward confusion, Klein has tried to bring Leonardo closer to us by looking inside his mind. What emerges is the Audubon of automata, who gives rise to exquisite artistic and scientific representations of his sixteenth century universe.

Reviewed by: 

Stefan Klein has written such a beautiful book that the reader can easily remain unaware that the original language was German. This transparency is due in large part to the translation into English by Shelley Frisch that, except for a few odd turns of phrase here and there, is nothing short of immaculate.

Klein’s diligent exploration of what is known about Leonardo di ser Piero da Vinci is clearly a labor of love. From the detailed analysis of Leonardo’s painting style, to visiting the places where Leonardo lived, to interviews with Da Vinci aficionados about the design on his various machines, this work is truly encompassing and a must read for anyone who has even the slightest interest in the intellect of Leonardo da Vinci.

Leonardo’s Legacy is very much directed at a lay audience rather than a scholarly one. As Klein himself expresses it, this book “is not intended as a standard biography of a masterful artist as much as an attempt to get inside the mind of one of the most extraordinary individuals who ever lived—and to see the world through his eyes.”

Because of the sheer historical distance, as well as the loss of much of Leonardo’s writings, many aspects of Leonardo remain inscrutable. Churchill’s description of Russia seems apt: Leonardo is a puzzle, wrapped by a mystery, inside an enigma. Undeterred by this historical inscrutability, Klein strives to attain a fresh perception of Leonardo; no easy task given the historical baggage carried by this iconic and popular figure.

Moreover, such a laudable endeavor is always fraught with the difficulty of trying to detach oneself from our own modern milieu. We tend to think they thought the way we think. Klein is fully aware of this problem and tries hard to avoid the pitfalls. Even if he is not always successful in maintaining that dissociation, he does make some new inroads into Leonardo’s style of thinking. In general, the emphasis of this book is on the scientific rather than the artistic. Indeed, as Klein reveals in his opening chapter, Leonardo’s art is governed in large measure by his self-acquired scientific and engineering knowledge.

For me, as a lay reader but one with a scientific background, the value of Klein’s book lies in the way it evokes certain questions and subsequent revelations about Leonardo. These questions may not have always been the ones the author intended, but that simply serves to demonstrate the engaging style of Klein’s writing.

The first of these revelations was to clarify my otherwise vague perspective on the extraordinarily early period in which Leonardo lived relative to the development of western scientific thought. Merely repeating that Leonardo was born 560 years ago captures neither how advanced was his thinking nor how inevitable were its limitations. One way to get a better handle on Leonardo’s life is to note who were his Renaissance contemporaries, e.g., Michelangelo, Machievelli, and Copernicus, as well as those who followed in his footsteps during the Age of Reason and the early Enlightenment, e.g., Galileo, Kepler, and Newton, to develop the foundations of modern science.

Since the book was no help in this respect, I resorted to creating the timelines. Only by this means did I come to realize that Leonardo had already lived more than a quarter of his life before Copernicus and Machievelli were born and that he had been dead almost as long as he had been alive when Galileo was born.

It may be helpful for the prospective reader to see a list of other questions and revelations about Leonardo that occurred to me as I read Klein’s book.

• Dissecting cadavers. Last summer, I was unfortunate enough to have a rodent die under my living room. The stench at times was almost unbearable and that from something only a few inches long. As Klein reminds us, it is almost inconceivable how Leonardo could have accomplished his detailed anatomical drawings of cadavers by candlelight in unrefrigerated caverns. I was also surprised by certain errors in some of these drawings that were not a result of poor lighting conditions. Some mistakes are due to the influence of accepted Renaissance views on Leonardo (the milieu problem I mentioned earlier), while others are due to Leonardo conceiving of the human body as a machine. Klein’s point is that Leonardo drew what he thought, not just what he saw.

• Backward writing. Leonardo’s use of backward cursive script is legendary. What I had not fully appreciated is that the act of writing reversed cursive letters is difficult, even for a southpaw (although it’s thought that Leonardo was actually ambidextrous). Klein refers to it throughout as “mirror writing,” but did Leonardo actually use a mirror? It seems reasonable to assume that he did use as mirror, at least early on, but that he may also have become accustomed enough over time to abandon it. And what was the point of this mirror writing? The ultimate purpose cannot have been serious encryption, because it can easily be decoded with a mirror or any shiny flat surface. Klein does not delve into how Leonardo’s mirror writing was accomplished or why.

• Stroboscopic vision. His super-human eyesight impresses everyone who studies Leonardo. It allowed him to draw the wing motion of dragonflies and birds, as well as eddies in whirlpools. As Klein puts it, “It is amazing that he was able to detect the phases of the wing movement with the naked eye at all. Normally we do not perceive even movements that are eight times slower.” Personally, I am inclined to think that people like Leonardo had a few tricks up their sleeve that we would no longer think of because we have come to rely on technology like high-speed cameras. I can imagine that Leonardo might have used the simple expedient of blinking his eyes in rapid succession to make a stroboscope. In this way, with enough repeated blinks under the right conditions, you can build up a series of “freeze frames” in your mind. After all, this is the man who wrote backwards.

• The opportunist. Part of the iconic Leonardo involves the pacifist who bought caged birds merely in to set them free. In contrast, Klein writes that “Leonardo earned a living by promising his employers spectacular works of art and technology.” Because of protracted local wars during that period, Klein makes it clear that Leonardo was enough of an opportunist to be employed by some very undesirable but very powerful patrons—Cesare Borgia foremost among them. And that he was adept enough to switch allegiances when necessary.

• Optics. Various technical drawings in Leonardo’s notebooks suggest that he carried out a variety of optical experiments aimed at understanding how vision works. The possible ramifications for his artwork would have provided sufficient motivation. Thus, Leonardo knew that the image formed in the eye is inverted. All his life, “he could never get over his astonishment that man sees everything right side up even though the images in the eye ought to be upside down the way they are in a camera obscura,” according to Klein.

Quite apart from the fact that he drew the anatomy of the eyeball incorrectly (the milieu problem again), Leonardo could not have known that optics and vision are different things. Nor could he have known the true laws of refraction. Even Descartes (100 years later) and Newton (150 years later) got the physics of refraction wrong. But Leonardo is remarkable for attempting to understand optical phenomena through experiment. In this, he predates Galileo.

• Electric water. Water and canals were for Leonardo what electricity and the electric grid are for us. Modern phrases like “the flow of electrical current,” have inherited this association. Hydraulics was as vital in the sixteenth century as electric power is for us today and hence, it formed the basis of many of Leonardo’s mechanical conceptions. Klein also underscores the degree to which hydraulics also defined what Leonardo could not conceive: “steam engines and motors lay so far beyond the capabilities of the technology that even Leonardo could not picture them.”

• Innumeracy. Klein tells us that Leonardo’s “limited education had never allowed him to master even the basics of arithmetic.” To put things in perspective, Leonardo Fibonacci predated Leonardo da Vinci by about two hundred and fifty years while contemporaneous mathematicians were busy finding solutions to cubic equations. For me, this lies at the heart of the Leonardo enigma. He seems to have been able to devise highly novel solutions to engineering problems using geometry—presumably because it has a very visual component—but he must have been severely hampered when it came to engineering calculations.

In this respect, Klein appropriately quotes Daniel Arasse who calls Leonardo the “thinker without a system of thought.” It also struck me that very few of Leonardo’s engineering sketches contain numerical annotations. The incredibly detailed map of Imola comes with no legend or scale markings, yet we knew that he measured distances accurately with his cyclometer. In many ways, the Imola map seems emblematic of Leonardo’s mind. According to Klein, “Leonardo thought in pictures. He owed his highly significant discoveries to this pictorial approach, though it also led him astray at time, because looks can be deceiving.” By way of contrast, one of the hallmarks of Einstein’s thinking style was that he also tended to develop his insights visually. The difference being that he often spent much longer testing his visual intuition against the rigors of mathematics—something Leonardo could not do.

• Computing engines. Chapter V is entitled “Robots,” and even though that word does not appear in the English lexicon until 1920, what better Leonardo metaphysical juxtaposition could there be than machines with a life: living machines. Leonardo’s biggest hit seems to have been the mechanical lion he constructed for a banquet in honor of the king of France. Klein speculates, “people wondered whether the engineer had breathed a soul into his creation.” Leonardo may also have been the James Randy of his day, because Klein tells us that his interest in automata “was also fueled by his aversion to charlatans and superstitions of all kinds.” The highlight of this chapter, however, is “Leonardo’s Computer” or bell-ringing machine—a type of digital clock.

Once again water is the analog of electricity in this automaton. To call it “man’s oldest digital computer” is a bit of a stretch. As Klein himself says, “It could count.” But counting is merely the operation of incrementing by one or adding one (+1). There was no carry operation, so it could not add two different numbers together. There was no accumulator, so it could not store numbers, and there was no multiply operation. Even an ancient Chinese abacus could perform multiplication. The bell-ringing digital clock is really a water-driven ratchet and ratchets were something with which Leonardo was intimately familiar, e.g., his cyclometer. This is not to take away from Leonardo’s innovative engineering skills, rather just to keep things in perspective.

• Simulations. Although it is highly unlikely that Leonardo saw any direct military action, Klein states that his “close ties to the tyrants of his day offer a case study of the early symbiosis of science and the military.” In this respect many of Leonardo’s artillery designs were most likely based on simulations with water jets substituting for projectiles. This strikes me as a revelatory point because the sketch of saturation bombing likely derives from such simulations. Despite the erroneous depiction of the trajectories as semicircular instead of parabolae, the shot from the battery of canon look like fountains of water rather than discrete canon balls.

Why is this significant? There is a huge conceptual leap between seeing a discrete cannonball in flight and depicting its locus as a continuous path. In fact, the concept of motion as a continuum of infinitesimal epochs, did not really take hold until Newton and the development of the calculus; some two hundred years later. On the other hand, if you are simulating cannonballs with arcs of water, this is precisely how it looks.

• The grounded aeronaut. Leonardo was an intuitive engineer. Intuition is a seductive siren who will gladly allow you to crash on the rocks of misunderstanding. Better to tie yourself to the mast of mathematics but, unfortunately, this is something that Leonardo could not do. As a consequence, Leonardo arguably had the best intuition in the world regarding the mechanics of flight, but he never flew.

Klein points out that Leonardo thought all forces were pyramidal, i.e., they follow the proportions of similar triangles. This principle does appear to be valid in certain static situations. For example, the static pressure at a water spigot doubles in proportion to the height of the water above it, although Leonardo’s drawing of water jets issuing from holes in a cask, is incorrect. Moreover, the pyramidal principle breaks down when it comes to analyzing motion. The horizontal velocity of the water jet is proportional to the square root of the water level. Square roots would have troubled Leonardo. Quoting Klein, “He tackled mathematics for years without ever getting the hang of long division.”

Trying to resolve Leonardo da Vinci from a distance of five hundred years is a formidable task. Most of his own written record has been destroyed, so that today we would say Leonardo suffers from a zero citation index. To make resolving him even more confounded, we know that Leonardo borrowed liberally from others without attribution, as did his peers. We also know that many of his mechanical drawings were intended to impress rather than work. One of the more infamous examples is the giant crossbow illustration. The British Army tried to construct this weapon from Leonardo’s drawings, but it could never be made to fire successfully.

Rather then focusing on this outward confusion, Klein has tried to bring Leonardo closer to us by looking inside his mind. What emerges is the Audubon of automata, who gives rise to exquisite artistic and scientific representations of his sixteenth century universe.

Long Description: 

Stefan Klein has written such a beautiful book that the reader can easily remain unaware that the original language was German. This transparency is due in large part to the translation into English by Shelley Frisch that, except for a few odd turns of phrase here and there, is nothing short of immaculate.

Klein’s diligent exploration of what is known about Leonardo di ser Piero da Vinci is clearly a labor of love. From the detailed analysis of Leonardo’s painting style, to visiting the places where Leonardo lived, to interviews with Da Vinci aficionados about the design on his various machines, this work is truly encompassing and a must read for anyone who has even the slightest interest in the intellect of Leonardo da Vinci.

Leonardo’s Legacy is very much directed at a lay audience rather than a scholarly one. As Klein himself expresses it, this book “is not intended as a standard biography of a masterful artist as much as an attempt to get inside the mind of one of the most extraordinary individuals who ever lived—and to see the world through his eyes.”

Because of the sheer historical distance, as well as the loss of much of Leonardo’s writings, many aspects of Leonardo remain inscrutable. Churchill’s description of Russia seems apt: Leonardo is a puzzle, wrapped by a mystery, inside an enigma. Undeterred by this historical inscrutability, Klein strives to attain a fresh perception of Leonardo; no easy task given the historical baggage carried by this iconic and popular figure.

Moreover, such a laudable endeavor is always fraught with the difficulty of trying to detach oneself from our own modern milieu. We tend to think they thought the way we think. Klein is fully aware of this problem and tries hard to avoid the pitfalls. Even if he is not always successful in maintaining that dissociation, he does make some new inroads into Leonardo’s style of thinking. In general, the emphasis of this book is on the scientific rather than the artistic. Indeed, as Klein reveals in his opening chapter, Leonardo’s art is governed in large measure by his self-acquired scientific and engineering knowledge.

For me, as a lay reader but one with a scientific background, the value of Klein’s book lies in the way it evokes certain questions and subsequent revelations about Leonardo. These questions may not have always been the ones the author intended, but that simply serves to demonstrate the engaging style of Klein’s writing.

The first of these revelations was to clarify my otherwise vague perspective on the extraordinarily early period in which Leonardo lived relative to the development of western scientific thought. Merely repeating that Leonardo was born 560 years ago captures neither how advanced was his thinking nor how inevitable were its limitations. One way to get a better handle on Leonardo’s life is to note who were his Renaissance contemporaries, e.g., Michelangelo, Machievelli, and Copernicus, as well as those who followed in his footsteps during the Age of Reason and the early Enlightenment, e.g., Galileo, Kepler, and Newton, to develop the foundations of modern science.

Since the book was no help in this respect, I resorted to creating the timelines. Only by this means did I come to realize that Leonardo had already lived more than a quarter of his life before Copernicus and Machievelli were born and that he had been dead almost as long as he had been alive when Galileo was born.

It may be helpful for the prospective reader to see a list of other questions and revelations about Leonardo that occurred to me as I read Klein’s book.

• Dissecting cadavers. Last summer, I was unfortunate enough to have a rodent die under my living room. The stench at times was almost unbearable and that from something only a few inches long. As Klein reminds us, it is almost inconceivable how Leonardo could have accomplished his detailed anatomical drawings of cadavers by candlelight in unrefrigerated caverns. I was also surprised by certain errors in some of these drawings that were not a result of poor lighting conditions. Some mistakes are due to the influence of accepted Renaissance views on Leonardo (the milieu problem I mentioned earlier), while others are due to Leonardo conceiving of the human body as a machine. Klein’s point is that Leonardo drew what he thought, not just what he saw.

• Backward writing. Leonardo’s use of backward cursive script is legendary. What I had not fully appreciated is that the act of writing reversed cursive letters is difficult, even for a southpaw (although it’s thought that Leonardo was actually ambidextrous). Klein refers to it throughout as “mirror writing,” but did Leonardo actually use a mirror? It seems reasonable to assume that he did use as mirror, at least early on, but that he may also have become accustomed enough over time to abandon it. And what was the point of this mirror writing? The ultimate purpose cannot have been serious encryption, because it can easily be decoded with a mirror or any shiny flat surface. Klein does not delve into how Leonardo’s mirror writing was accomplished or why.

• Stroboscopic vision. His super-human eyesight impresses everyone who studies Leonardo. It allowed him to draw the wing motion of dragonflies and birds, as well as eddies in whirlpools. As Klein puts it, “It is amazing that he was able to detect the phases of the wing movement with the naked eye at all. Normally we do not perceive even movements that are eight times slower.” Personally, I am inclined to think that people like Leonardo had a few tricks up their sleeve that we would no longer think of because we have come to rely on technology like high-speed cameras. I can imagine that Leonardo might have used the simple expedient of blinking his eyes in rapid succession to make a stroboscope. In this way, with enough repeated blinks under the right conditions, you can build up a series of “freeze frames” in your mind. After all, this is the man who wrote backwards.

• The opportunist. Part of the iconic Leonardo involves the pacifist who bought caged birds merely in to set them free. In contrast, Klein writes that “Leonardo earned a living by promising his employers spectacular works of art and technology.” Because of protracted local wars during that period, Klein makes it clear that Leonardo was enough of an opportunist to be employed by some very undesirable but very powerful patrons—Cesare Borgia foremost among them. And that he was adept enough to switch allegiances when necessary.

• Optics. Various technical drawings in Leonardo’s notebooks suggest that he carried out a variety of optical experiments aimed at understanding how vision works. The possible ramifications for his artwork would have provided sufficient motivation. Thus, Leonardo knew that the image formed in the eye is inverted. All his life, “he could never get over his astonishment that man sees everything right side up even though the images in the eye ought to be upside down the way they are in a camera obscura,” according to Klein.

Quite apart from the fact that he drew the anatomy of the eyeball incorrectly (the milieu problem again), Leonardo could not have known that optics and vision are different things. Nor could he have known the true laws of refraction. Even Descartes (100 years later) and Newton (150 years later) got the physics of refraction wrong. But Leonardo is remarkable for attempting to understand optical phenomena through experiment. In this, he predates Galileo.

• Electric water. Water and canals were for Leonardo what electricity and the electric grid are for us. Modern phrases like “the flow of electrical current,” have inherited this association. Hydraulics was as vital in the sixteenth century as electric power is for us today and hence, it formed the basis of many of Leonardo’s mechanical conceptions. Klein also underscores the degree to which hydraulics also defined what Leonardo could not conceive: “steam engines and motors lay so far beyond the capabilities of the technology that even Leonardo could not picture them.”

• Innumeracy. Klein tells us that Leonardo’s “limited education had never allowed him to master even the basics of arithmetic.” To put things in perspective, Leonardo Fibonacci predated Leonardo da Vinci by about two hundred and fifty years while contemporaneous mathematicians were busy finding solutions to cubic equations. For me, this lies at the heart of the Leonardo enigma. He seems to have been able to devise highly novel solutions to engineering problems using geometry—presumably because it has a very visual component—but he must have been severely hampered when it came to engineering calculations.

In this respect, Klein appropriately quotes Daniel Arasse who calls Leonardo the “thinker without a system of thought.” It also struck me that very few of Leonardo’s engineering sketches contain numerical annotations. The incredibly detailed map of Imola comes with no legend or scale markings, yet we knew that he measured distances accurately with his cyclometer. In many ways, the Imola map seems emblematic of Leonardo’s mind. According to Klein, “Leonardo thought in pictures. He owed his highly significant discoveries to this pictorial approach, though it also led him astray at time, because looks can be deceiving.” By way of contrast, one of the hallmarks of Einstein’s thinking style was that he also tended to develop his insights visually. The difference being that he often spent much longer testing his visual intuition against the rigors of mathematics—something Leonardo could not do.

• Computing engines. Chapter V is entitled “Robots,” and even though that word does not appear in the English lexicon until 1920, what better Leonardo metaphysical juxtaposition could there be than machines with a life: living machines. Leonardo’s biggest hit seems to have been the mechanical lion he constructed for a banquet in honor of the king of France. Klein speculates, “people wondered whether the engineer had breathed a soul into his creation.” Leonardo may also have been the James Randy of his day, because Klein tells us that his interest in automata “was also fueled by his aversion to charlatans and superstitions of all kinds.” The highlight of this chapter, however, is “Leonardo’s Computer” or bell-ringing machine—a type of digital clock.

Once again water is the analog of electricity in this automaton. To call it “man’s oldest digital computer” is a bit of a stretch. As Klein himself says, “It could count.” But counting is merely the operation of incrementing by one or adding one (+1). There was no carry operation, so it could not add two different numbers together. There was no accumulator, so it could not store numbers, and there was no multiply operation. Even an ancient Chinese abacus could perform multiplication. The bell-ringing digital clock is really a water-driven ratchet and ratchets were something with which Leonardo was intimately familiar, e.g., his cyclometer. This is not to take away from Leonardo’s innovative engineering skills, rather just to keep things in perspective.

• Simulations. Although it is highly unlikely that Leonardo saw any direct military action, Klein states that his “close ties to the tyrants of his day offer a case study of the early symbiosis of science and the military.” In this respect many of Leonardo’s artillery designs were most likely based on simulations with water jets substituting for projectiles. This strikes me as a revelatory point because the sketch of saturation bombing likely derives from such simulations. Despite the erroneous depiction of the trajectories as semicircular instead of parabolae, the shot from the battery of canon look like fountains of water rather than discrete canon balls.

Why is this significant? There is a huge conceptual leap between seeing a discrete cannonball in flight and depicting its locus as a continuous path. In fact, the concept of motion as a continuum of infinitesimal epochs, did not really take hold until Newton and the development of the calculus; some two hundred years later. On the other hand, if you are simulating cannonballs with arcs of water, this is precisely how it looks.

• The grounded aeronaut. Leonardo was an intuitive engineer. Intuition is a seductive siren who will gladly allow you to crash on the rocks of misunderstanding. Better to tie yourself to the mast of mathematics but, unfortunately, this is something that Leonardo could not do. As a consequence, Leonardo arguably had the best intuition in the world regarding the mechanics of flight, but he never flew.

Klein points out that Leonardo thought all forces were pyramidal, i.e., they follow the proportions of similar triangles. This principle does appear to be valid in certain static situations. For example, the static pressure at a water spigot doubles in proportion to the height of the water above it, although Leonardo’s drawing of water jets issuing from holes in a cask, is incorrect. Moreover, the pyramidal principle breaks down when it comes to analyzing motion. The horizontal velocity of the water jet is proportional to the square root of the water level. Square roots would have troubled Leonardo. Quoting Klein, “He tackled mathematics for years without ever getting the hang of long division.”

Trying to resolve Leonardo da Vinci from a distance of five hundred years is a formidable task. Most of his own written record has been destroyed, so that today we would say Leonardo suffers from a zero citation index. To make resolving him even more confounded, we know that Leonardo borrowed liberally from others without attribution, as did his peers. We also know that many of his mechanical drawings were intended to impress rather than work. One of the more infamous examples is the giant crossbow illustration. The British Army tried to construct this weapon from Leonardo’s drawings, but it could never be made to fire successfully.

Rather then focusing on this outward confusion, Klein has tried to bring Leonardo closer to us by looking inside his mind. What emerges is the Audubon of automata, who gives rise to exquisite artistic and scientific representations of his sixteenth century universe.