Capra, however, points out that in the Renaissance, Leonardo’s map of the Val di Chiana [Fig. 15] used graphic sleight of hand that resembled the method outlined in Poincaré’s equations. Leonardo’s astonishing accomplishment would not be seen again for nearly half a millennium. In his map detailing the watercourses of the Val di Chiana, he distorted the map so as to highlight the salient features shown in the center of the map while scrunching the periphery in a clever and revolutionary manner. This distortion had the effect of making the map appear realistic yet more readable. Poincaré was unaware that Leonardo, five hundred years earlier, had expressed topological principles graphically.
Capra also points out that despite Leonardo’s limited familiarity with sophisticated algebra, Leonardo, the civil engineer and painter, routinely used a kind of mental algebra to calculate proportions and loads for fulcrums, levers, and pulleys. This field of modern physics is known as statics. Leonardo accurately estimated lever arm length, position of fulcrums, and the amount of weights and accurate distances using his super-refined artistic sense of proportion. This should not be surprising, as he considered painting a science, and utilized his calculations concerning the correct proportions of objects to paint them faithfully.
Leonardo was not entirely unfamiliar with algebra and trigonometry. Leonardo the military specialist, without using the symbols of these complex forms of higher mathematics, was able to calculate the trajectories of cannon- and mortar-fired projectiles.
His study of water presaged the branch of physics called chaos theory (later renamed complexity theory). The Swiss mathematician Leonhard Euler in 1755 made the first attempt to express turbulence mathematically. Heinrich Helmholz, 350 years after Leonardo’s initial observations, was the next physicist to study water vortices and their turbulence in a systematic fashion. Fluid dynamics initiated the field of complexity theory. Rarely do science textbooks mention Leonardo’s primacy in this important modern field.
Leonardo’s interest in fluid dynamics and his careful study of the manner in which water flows led him to one of his most dramatic discoveries concerning physics and its subfield of optics. He studied wave motion of water by scattering kernels of grain or bits of straw on the still surface of a pond. He then disturbed the surface by throwing pebbles into the pond and observed that, although the waves he created diminished in intensity the farther they traveled from the point of impact, the kernels and straw remained bobbing in the same location.
He thus was able to conclude that a wave moved through the medium of water in a manner that did not cause the water molecules (particles) to move. This was the critical observation that laid the foundation for wave theory. He then extrapolated from his study of water waves and proposed that invisible sound waves traveled through the air in the same manner. Leonardo wrote:
Just as a stone thrown into the water becomes the center and cause of various circles, sound spreads circles in the air. Thus every body placed in the light spreads out in circles and fills the surrounding space with infinite likenesses of itself and appears all in all in every part.
In an age when almost everyone believed that light transfer was instantaneous, his next daring leap was to proceed to light, and conclude that it traveled through space and time in a similar manner.
Two hundred years later, Newton proposed that light consisted of little bits of light he called “corpuscles,” and there was an interval of darkness between each tiny piece of light. Because of his immense stature after his publication of Principia, Newton’s view of the nature of light was generally accepted by the scientific community.
But two hundred years earlier, Leonardo had arrived at a very different conclusion concerning the nature of light. In 1690, the Dutch mathematician Christiaan Huygens published a paper on light that hit the scientific community like a thunderbolt. Huygens overturned the reigning belief that light was particlelike in nature. Huygens’s remarkable contrarian view—that light was wavelike—has earned him an honored place in the annals of science. While Huygens proved that light moved through space as a wave, his description was incomplete. He failed to describe what happened when two waves intersect, giving rise to transverse waves. This phenomenon, however, was described by Leonardo.
In 1697, the Danish astronomer Olaus Roemer discovered that light moved through space with a finite velocity. This finding, coming quickly on the heels of Huygens’s paper, overturned another cherished belief among those in the scientific community: that light did not have a particular speed because its transfer from the moment it emanated from its source was the precise moment it arrived at its destination. Roemer’s calculation posited that it took a finite amount of time for light to travel from here to there.
In 1803, Thomas Young published a paper on the wave theory of light in which he extrapolated from water waves to light waves, just as Leonardo had done, and demonstrated in a series of experiments similar to those performed by Leonardo that light indisputably traveled through space and time as a wave. For their work, science historians credit Huygens, Roemer, and Thomas with experimentally proving the wave theory of light conclusively.
Imagine how much more quickly science would have advanced had the community of investigators been made aware that a fifteenth-century genius had proposed that light moved through space in the form of a wave and, further, that it produced transverse waves upon intersecting with another wave form, traveling with a finite velocity.
Leonardo also took a lively interest in the comings and goings of celestial objects. He outright rejected astrology, calling it “that deceptive opinion by means of which (begging your pardon) a living is made from fools.” His stand was, for its time, exceedingly nonconformist. The age was infected with a deeply ingrained belief that the positions of the stars determined whether undertaking earthly ventures on a particular date was propitious or foolhardy. He grasped that Earth was a spherical globe and not the flat tabletop imagined by so many of his contemporaries. One of his notebooks contains the entry “The sun does not move,” strongly suggesting that he knew that the sun, not the Earth, was the center of the solar system. He had a grander vision of our place in the cosmos when he declared that “the Earth was but a speck in the universe.”
Leonardo’s interest included the age of the Earth, which he estimated was markedly older than the four thousand years that had been proposed by the followers of the Bible. Georges-Louis Leclerc, Comte de Buffon, a French naturalist writing in 1778, estimated that the Earth was 74,832 years old. His work influenced the young Scotsman, Charles Lyell, who published the Principles of Geology in 1830. Lyell calculated that geological processes were immensely older, and that the Earth was in the process of evolving.
The young Charles Darwin brought this book with him on his now-famous voyage on the HMS Beagle, during which he hit upon his grand idea concerning natural selection, which he laid out in considerable detail in his 1859 The Origin of Species. Lyell had provided the young naturalist with the missing piece. For Darwin’s theory to be plausible, he needed the age of the Earth to extend far back into the distant past, so that species would have the requisite long stretches of time during which they could adapt to changing environmental challenges and evolve into entirely new phyla and species.
But Leonardo had also speculated that the various species, like the Earth itself, were the product of ongoing processes. He rejected the view held for the subsequent four hundred years—that the Earth was unchanging and that an omnipotent Creator had lavished all the diverse species of plants and animals upon the Earth in just a few days.
A key attribute of life is the presence of mechanisms that allow an organism to correct any internal imbalances created by a changing environment. Physiologists name this self-correcting mechanism homeostasis—the state at which all the organisms’ enzyme systems operate optimally. In the 1970s, James Lovelock, an independent scientist working with NASA, introduced a heretical idea. The sea, the mountains, the atmosphere, and all living organisms on Earth were
part of a superorganism consisting of the whole Earth. He reached this hypothesis because he noted a close resemblance between the macrosystems that maintain the constancy of the mix of gases in the atmosphere, the temperature of the earth, and the salinity of the oceans and the homeostatic mechanisms that microscopic unicellular critters use. Lovelock’s daring conclusion: The Earth was one gigantic self-sustaining organism. With the assistance of Lynn Margulis, he named his idea the Gaia theory, after the mythological mother of all the gods and living things. Radical for its time, it was dismissed by many in academia, and attacked by such luminaries as Stephen Jay Gould and Richard Dawkins. However, since its introduction, the Gaia theory has proven its predictive value in many experiments and is now considered mainstream science.
Leonardo had arrived at a conclusion similar to Lovelock’s. He conceptualized the Earth as a single, exceedingly large, living organism whose forests, rivers, animals, mountains, and oceans each contributed to the planet’s overall health. Leonardo adumbrated Lovelock by five hundred years. In the interim, no other significant thinker, philosopher, or scientist had embraced a similar holistic vision.
Chapter 12
Leonardo/Inventions
If they disparage me as an inventor, how much more they, who never invented anything but are trumpets and reciters of the works of others, are open to criticism.
—Leonardo da Vinci
So many of the insights and inventions of the notebooks prefigure the developments and discoveries of the following three hundred years. Had they been available to others in Leonardo’s time, the progress of science and technology would have been accelerated dramatically.
—Bülent Atalay
The dead Master [Leonardo] is alive, and speaks to us, to me, directly, unmediated, his greatness confirmed once again because I, so different, so distant, separated by class, race, language, and above all by time, communicate directly with this great creator.
—Donald Sassoon
Leonardo’s inventions prefigure a future that the inhabitants of the Renaissance could neither appreciate nor comprehend. As an apprentice in Verrocchio’s studio, Leonardo learned how to grind lenses to such a high polish that they could be used to concentrate sunlight to generate the heat necessary to weld and anneal metals. But he also discovered that using a concave lens to focus light to a central focal point had the effect of transmitting a greatly enlarged image. In his words:
In order to observe the nature of the planets, open the roof and bring the image of a single planet onto the base of a concave mirror. The image of the planet reflected by the base will show the surface of the planet much magnified.
Reflecting telescopes are large, unwieldy devices. A debate currently smolders among science historians concerning who was the first person to invent the much-easier-to-use handheld telescope. The introduction of this simple tube fitted with lenses at each end brought distant objects closer. Considered one of history’s transformative inventions, its profound effect on military engagements, commerce, astronomy, and world navigation cannot be overemphasized. The credit for its discovery generally goes to a Dutch spectacle maker, Hans Lippershey, who in 1608 applied for a patent for his device. There were several other northern Europeans whose names surface as having preceded Lippershey.
And yet, there remain tantalizing clues that link Leonardo with its invention. In one place, he wrote a reminder to himself to “make glasses to see the moon enlarged.” His notebooks abound with detailed drawings of how light rays interact with objects, and how the absence of light creates penumbras and shadows. His interest in the subject led him to invent a prototype of the modern photometer, a device used to measure the intensity of light (not seen again until Robert Wilhelm Bunsen reinvented this device in 1844). He even devised a table lamp that could be adjusted for variable intensity. His suggestion of the possibility of contact lenses to correct distortions in the eye’s cornea was half a millennium ahead of his time. He sketched an instrument to record the intensity of light that differed little from the one developed by Benjamin Thompson, an American, three centuries later.
Leonardo invented the first camera, and described its principles in his invention of the camera obscura. He invented an octagonal room, each surface of which contained a polished mirror. Sitting in the center of this room, a subject can visualize his or her three-quarter profile. Art historians speculate that the famous red chalk drawing of an old sage drawn from off center is a self-portrait of Leonardo, done while seated in his octagonal room.
As previously noted, most science historians credit Galileo with being the first real scientist. It is a supreme irony that Galileo went blind using his naked eye to look at the sun. He mused, over his predicament:
This universe, that I have extended a thousand times . . . has now shrunk to the narrow confines of my own body. Thus God likes it; so I too must like it.
Had he read Leonardo’s recommendation, made a hundred years earlier—to view the sun through a pinprick made in a piece of thick paper—the “first scientist” would have not suffered the loss of his sight.
Leonardo took walks through the countryside and imagined a windmill that would serve as a power generator fifty years before the Dutch invented their picturesque but efficient windmills. He deduced the function of invisible oxygen: “Where flame cannot live, no animal that draws breath can live.” Leonardo designed the first double-hulled transport ship; it was never built, but in the twentieth century, it became the standard design for oil tankers. He invented everything from common scissors to folding furniture and made significant contributions to civil engineering and city planning. He even put his mind to the field of landscape and garden design, creating the layout for some of the most stunning and innovative gardens in Europe.
Inventing weapons is not usually paired with fine-tuning innovative musical instruments. However, one of the contradictions of this complicated man was the celerity with which a youthful Leonardo could switch from designing the former to polishing the latter. As the city-states of Italy were in an almost constant state of war with each other, the young man’s attempt to promote himself as an accomplished armament designer would have increased his value to his potential patrons.
Putting aside the gruesome purpose behind his military inventions and considering them for their sheer innovation, we witness another side of his genius. Leonardo invented the flamethrower, the machine gun, the first breech-loaded gun, a gun boring device, the first steam-powered gun, and a gigantic crossbow that required several men to operate. He improved on catapults and mortars, and designed rope ladders to storm high walls. History’s first tank appears among his drawings.
Considerable evidence has accumulated that he invented the wheel-lock firing device that permitted the miniaturization of the gun. Leonardo’s invention of the wheel lock sent a miniature wheel made of flint (wound tightly beforehand by a spring mechanism) spinning when the gunner pulled the trigger. The whirling flint—striking a fixed post opposite the wheel, also made of flint—sent a shower of sparks into a much smaller-sized pan containing the gunpowder. The economy of this system made it possible for gunsmiths to reduce the size of the weapon to one that could be carried and fired in one hand—the pistol.
The scope of Leonardo’s military inventiveness ranged from the minute to the grandiose. He could move from designing the miniaturized pistol to creating defensive and offensive plans that included diverting rivers from their natural beds to deprive rival city-states of their life-sustaining water. Later in his life, after serving with Borgia, he abandoned his interest in designing weapons. For example, he had invented the submarine, but did not want the plans known because he was convinced it would be used for warfare.*
* According to researchers, Leonardo da Vinci inserted a series of deliberate flaws into his inventions, perhaps to prevent their being put to military use. “Da Vinci war machines ‘designed to fail’ ” by Tom Leonard; The Age, December 14, 2002.
Leonardo, the consummate musici
an, designed many innovative musical instruments. For a prospective patron, his facility at composing, singing, choreographing, and playing an instrument added considerable luster to his desirability as a potential employee. The primary reason that the Duke of Sforza initially hired Leonardo was for his musical talent. Leonardo made improvements to the most popular musical instrument of the day, the pianoforte. There remains a controversy in the Leonardo literature as to whether or not he invented the precursor to the violin.
From his notebooks historians know that Leonardo knew how to read and write musical notation. Demonstrating his agility with musical notation, in one place in his notebooks he uses rebuses (icons that represent words) to stand in for the symbols of the musical notes!
Always the scientist, Leonardo’s interest in music led him to study how sound propagates through space and time. His detailed anatomical examination of the human larynx and its twin vocal cords led him to the origins of human speech and song. And his attention to the anatomy of the ear displayed his curiosity concerning how we hear.
His fascination with flight led him to invent the parachute, the glider, and the helicopter. The Russian-born inventor of the modern helicopter, Igor Sikorsky, acknowledges his debt to Leonardo, who half a millennium earlier had discovered the principle of flight, drawn the first propeller, and conceptualized the first helicopter.
The design for a bicycle and a spring-operated automobile appear among the pages of Leonardo’s notebooks. He invented the universal joint that would become the critical component for the drivetrain of modern cars and conceived of the ball bearing to reduce friction and increase the speed and ease by which a land vehicle could continue to roll along. The Englishman Philip Vaughan obtained the first patent for the invention of ball bearings in 1791, nearly 350 years later.
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