Leonardo's Brain Read online

  Visionaries are those in the field of art and science who recognize novel patterns. They see beauty before the rest of us do. Then we catch up with them and agree that the innovation they imagined is, indeed, something marvelous to behold. That is why scientists speak of elegant equations and why artists can rearrange components of reality in countless new patterns that allow the rest of us to see the world in a new way.

  Chapter 11

  Leonardo/Theories

  Science is not a heartless pursuit of objective information. It is a creative human activity, its geniuses acting more as artists than as information processors. Changes in theory are not simply the derivative results of new discoveries, but are the work of creative imagination influenced by contemporary social and political forces.

  —Stephen Jay Gould

  The Earth is not in the center of the circle of the sun, nor in the center of the universe, but is in fact in the center of its elements which accompany it and are united to it. And if one were to be upon the moon, then to the extent to which it together with the sun is above us, so far below it would our Earth appear with the element of water, performing the same office.

  —Leonardo da Vinci

  More than any other single invention, writing has transformed human consciousness.

  —Walter Ong

  Let us now change the focus back to Leonardo. His name is ­featured prominently in all comprehensive art history books. Rarely does it surface in science history books. When it does, there always seems to be an asterisk next to it, as if to say, yes, this exceptional human being did indeed make some prescient notes in his private journals, but because he did not influence the forward movement of that collaboration called the “scientific endeavor,” his place among great scientists must be a mere footnote.

  Scientific luminaries of the stature of Albert Einstein and Stephen Jay Gould dismissed Leonardo’s contributions. Yet, if one carefully examines the record, one cannot fail to stand in awe of his accomplishments in the field of science—or, more appropriately, in various fields of science. One of Leonardo’s biographers, Edward MacCurdy, summed up his accomplishments thus:

  Before Copernicus or Galileo, before Bacon, Newton or Harvey, he uttered fundamental truths the discovery of which is associated with their names. “The sun does not move.” “Without experience there can be no certainty.” “A weight seeks to fall in the centre of the Earth by the most direct way.” “The blood which returns when the heart opens again is not the same as that which closes the valve.”

  Identifying the individual upon whom they would bestow the title of the first scientist has kindled a gentlemanly debate, with Galileo Galilei garnering the lion’s share of supporters. Until recently, Leonardo’s name has rarely surfaced as a candidate for the honor. Leonardo, however, was history’s first true scientist. He enthusiastically embraced the scientific method of observation, hypothesis, and experimental proof, adumbrating Galileo by a century. He was more exacting than Aristotle, more hands-on than Francis Bacon, and more relentlessly curious than Descartes. Newton seems to have channeled many of Leonardo’s earlier concepts.

  Leonardo can be credited with having initiated entirely new fields of scientific endeavor. He thoroughly investigated the fields of optics, botany, geology, anatomy, aeronautics, cartography, fluid dynamics, city planning, and mechanical engineering, to name but a handful. Using the scientific principles he either discovered or built upon the work of others, he invented myriad machines, military hardware, and measuring devices. Some sources credit Leonardo with having invented no less than three hundred of these marvels. So visionary were they that few ever actually became working models, because during the time in which he lived, the technology did not exist. In terms of the sheer volume of significant inventions based on scientific principles, only Thomas Edison can compare.

  Although Leonardo generously shared his knowledge concerning the finer points of painting and drawing with his students and disciples, he rarely divulged the information he had so painstakingly gathered concerning the workings of the natural world. The only cohesive “book” Leonardo ever assembled was his Treatise on Painting, and even this extended essay had to wait. His loyal disciple Francesco Melzi compiled an abridged version, and it was not published until 1651, well over a century after Leonardo’s death.

  His contemporaries, accustomed to reading about scientific matters in Latin or Greek, would have denigrated Leonardo’s use of what they dismissed as “the vulgar” language. His notebooks did not contain a clear linear narrative that clarified his thought processes. Leonardo made his comments on various subjects haphazardly; they resembled a stream of consciousness more than they did a coherent argument.

  Compounding the confusion, the keepers of Leonardo’s papers after Melzi’s death in 1572 often cut them up, or arbitrarily rearranged and shuffled them so as to obtain a higher price from the collectors who viewed them as extraordinary oddities without any understanding of the value these pages possessed. Extrapolating from what remains, experts speculate that two-thirds of his original notebooks have been lost. Correctly collating and sequencing his remaining pages and accurately dating them was something that had to wait until the end of the twentieth century.

  Further complicating the task: Leonardo had the habit of writing or drawing on a sheet of paper and then years later adding something else to the same page. This has bedeviled those Leonardisti attempting to follow the trajectory of his restless thoughts. An army of dogged researchers, however, using handwriting analysis, computers, and constant cross-referencing, have nearly completed the herculean task of rearranging his notebooks into a linear sequence. One benefit of this research was the discovery that around 1490, when Leonardo was thirty-eight, his notebooks moved from describing inventions to a more intense search for underlying principles.

  Comparable to an explorer on an unknown continent, Leonardo made many false starts, proposed many wrong hypotheses, and came to many erroneous conclusions regarding the workings of the natural world. He corrected some of these misperceptions through sustained research and experimentation. These redeeming findings have only recently come to light, making the present time propitious to reevaluate Leonardo’s record as a scientist.

  The nature of scientific exploration is its inherent sense of incompleteness. For Leonardo, there always remained a few unexamined phenomena that he believed were necessary to enfold into his theories before he could triumphantly explicate them. This obsession with perfection presented another obstacle to sharing his valuable scientific insights.

  Further complicating matters: He recognized his genius and appreciated that his greatest marketable resource was his imagination and creativity. He lived in a society without patents, in which one’s discoveries could be stolen and used for someone else’s monetary and prestigious advantage. Leonardo’s ability to promote himself as an engineer, architect, or designer depended on keeping much of his hard-won knowledge to himself.

  Leonardo sincerely believed, as he stated in various places throughout his scattered notes, that he would eventually get around to organizing his observations regarding anatomy, optics, botany, and mechanical engineering, and publish them in a proper book. It was an incredibly daunting goal to set for himself. His notes were a hodgepodge, and he refused to delegate this project to anyone else. The demands of organizing his writing would have been considerable, diverting him from his art and his scientific investigations. Adding to the problem was his need to make a living and deal with all the vicissitudes of life. Unfortunately, the sixty-nine years allotted to him by fate were insufficient, and he was unable to accomplish his goal.

  Secrecy is an anathema to science. In the years following Leonardo’s death, science slowly evolved into a cooperative venture that recognized it could only flourish if its practitioners shared their findings with each other. Many science historians are critical of Leonardo for hoarding his knowledge when it could have made a huge impact on subsequent scientific investigations. Le
st we be too hard on this Renaissance polymath, let us remember that the trend toward openness and the sharing of one’s discoveries was something that developed in fits and starts, and was in very short supply during the era in which he lived.

  Because of his failure to publish, Leonardo failed to excite the imagination of later scientists, nor did he ignite the interest of subsequent historians. In addition, art critics and the public had firmly established his reputation as a consummate artist. The barrier separating first-class art from first-class science was so formidable, it seemed almost excessive to accord him his due in the field of science. Nevertheless, history has a way of righting wrongs, and I will make the case that Leonardo should receive the honorific of history’s First Scientist.

  Let us begin by enumerating the many examples of Leonardo’s theories.

  Scientists generally accord physics the honorific of the “King of Sciences” because of its centrality to all the others. Leonardo made a number of astounding discoveries in this axial field. Of Newton’s Three Laws of Motion, Leonardo had elaborated both the first and the last. Newton framed his first law in 1687 thus:

  An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction, unless acted upon by an unbalanced force.

  Leonardo wrote in his notebook, “Nothing whatever can be moved by itself, but its motion is effected through another. There is no other force.” Elsewhere he wrote, “All movement tends to maintenance, or rather that all moved bodies continue to move as long as the impression of the force of their motors (original impetus) remains in them.” His explication was once known as the Principle of Leonardo until Newton restated it in mathematical terms.

  Leonardo also had expressed the idea behind Newton’s Third Law: For every action there is a reaction. In studying the effects of air and eagles, Leonardo wrote: “See how the wings, striking the air, sustain the heavy eagle in the thin air on high. As much force is exerted by the object against the air as by the air against the object.” Similarly, he grasped the principle of flight by determining that to understand how a bird’s wings keep it aloft, one must also understand the action of winds that press upward under the bird’s wings.

  The number of important principles of physics that Leonardo either noted in words or graphically illustrated, long before the essential groundwork had been laid, was astonishing. He intuited Torricelli’s law, propounded by Evangelista Torricelli in 1643, which enumerated the factors that affect the rate a liquid flows through an opening. Torricelli expressed the law in an elegant equation that factored in all the variables. Nearly two hundred years earlier, using his astute observations of flowing water, Leonardo arrived at a remarkably similar conclusion using words and images.

  In his extensive study of the preconditions for flight, Leonardo grasped the great principle laid out in Bernoulli’s law, expounded in 1738 by Dutch mathematician Daniel Bernoulli. The speed of air flowing above a plane’s wing in contrast to the slower speed flowing below the wing creates a pressure differential that is the crux of Bernoulli’s law. This simple aerodynamic is what supplies the “lift” necessary for flight, and allows massive airliners to take off and stay aloft. More than two centuries earlier, a lone investigator uncovered this great principle without the benefit of higher mathematics.

  The peculiar sound of a train’s whistle as it approaches and then recedes as it passes is a familiar phenomenon. The German mathematician Christian Doppler in 1840 explained in refined mathematical detail how the phenomenon is due to lengthening concentric ovals of sound waves due to the movement of the source of sound past the hearer. For his discovery, this hee-haw sound has been christened the “Doppler effect.” Leonardo observed the oblong wave patterns created on moving water by a pebble tossed into a stream. Extrapolating from water waves to sound waves, Leonardo described and illustrated the auditory phenomenon Doppler described in equations three hundred years later.

  Leonardo’s intuitive grasp of exceedingly complex concepts in physics without the benefit of a deep knowledge of the underlying mathematics makes his discoveries all the more impressive.

  When Descartes invented the field of analytical geometry in the mid-seventeenth century, demonstrating how algebraic relationships could be expressed visually on a graph, he was unaware that an unschooled genius working practically alone 150 years earlier had converted abstract mathematical relationships into visual representations with stunning results.

  The French lawyer/politician and renowned mathematician Pierre de Fermat had the habit of not publishing his extraordinary mathematical findings. He wrote in a letter to a friend in 1657 that light must travel in the shortest path in the least amount of time. Fermat’s principle, as it has come to be called, states that nature (with few exceptions) chooses the shortest direction to accomplish any transit in the least amount of time. To demonstrate the proof of this principle, Fermat needed an entire page of equations. The brilliant twelfth-century Arab mathematician—and hero of Alexandria—Alhazen had expressed Fermat’s principle, but in a less-rigorous manner. We find in Leonardo’s notebooks that he, too, had arrived at this fundamental principle of physics. He discussed its relation to light traveling through space and time, but his observation can be generalized to nearly all natural phenomena. Again, Leonardo’s insights occurred nearly two hundred years before Fermat came to his conclusions.

  The law of conservation of mass states that a given quantity of mass at the beginning of an experiment will exactly equal the amount of mass at the end. It is of no consequence how many transformations, deformations, or reformations the mass experiences during the experiment. Leonardo became intrigued with this subject when he met the geometer and mathematician Luca Pacioli when Leonardo was in his forties. Together they published a book about the principles of geometry in 1509, with Leonardo supplying the illustrations of Pacioli’s principles and conclusions. It would be the only book Leonardo had a hand in publishing during his lifetime. Without stating the conservation of mass law as definitively as Newton did in his 1687 Principia, Leonardo realized that despite the many deformations of geometrical shapes moving through space, their mass always remained the same. Had he had the mathematical background, I am convinced that he would have also announced the conservation of mass law.

  While working with Pacioli, Leonardo did in fact immerse himself in the study of mathematics and geometry. Leonardo toyed with an idea that became the heart of the integral calculus: “[S]pace is a continuous quantity and that any continuous quantity is infinitely divisible.” Though he did not come up with the equations themselves, this is still impressive. One cannot overemphasize the important role that the discovery of integral calculus has played in the advancement of physics and mathematics

  One of the disarming questions parents must address is the one posed by their young child: “Why is the sky blue?” Physicists have struggled to find the correct answer to what would seem at first glance to be a simple conundrum. Not until Lord Rayleigh in the late nineteenth century explained that it was due to the scattering of sunlight off atoms and molecules in the atmosphere did a scientist propose an explanation that appeared to lay the question to rest. Rayleigh won the Nobel Prize in Physics in 1904 for this work. Several decades later, Albert Einstein, using equations derived from his 1905 theory of special relativity, expanded upon Rayleigh’s work, and produced the definitive explanation for why the sky was blue.

  And, yet, the solitary Leonardo, using nothing more than his considerable powers of observation and deductive reasoning, arrived at the same conclusion as to why the sky is blue:

  I say that the blueness we see in the atmosphere is not intrinsic color, but is caused by warm vapour evaporated in minute and insensible atoms on which the solar rays fall, rendering them luminous against the infinite darkness of the fiery sphere which lies beyond and includes it.

  Leonardo’s foray into matters relating to the atmosphere, as well as his other observations con
cerning the nature of clouds, makes him the appropriate candidate for the title of history’s first meteorologist.

  Leonardo challenged the classical notions of Plato and Aristotle, who taught that the sun and the moon were perfect spheres. Using only deductive reasoning, Leonardo concluded that the blotchy complexion of the Man in the Moon’s face was due to surface mountains and valleys, and therefore the moon could not be a perfect sphere.

  Again, using his keen sense of observation, he correctly surmised that the reason the portion of the moon hidden during the slivery appearance of a new moon remains faintly visible to observers on Earth is because sunlight reflects off of Earth’s oceans and mountains’ snowcaps and back into space, illuminating that darkened portion of the moon. Using deductive reasoning, and without the aid of any scientific instruments, Leonardo noted that the sunlight reflected off the moon’s surface during its full phase is sufficient to venture out in nighttime and still discern the features of the earthly landscape. Michael Maestlin, Kepler’s teacher, gave exactly the same explanation over one hundred years later.

  Though he lacked algebraic language, as science historians point out, his explorations in geometry and his fascination with cartography led him to create some of the most arresting and accurate maps of his times.

  Author Fritjof Capra outlines the story of Henri Poincaré, a mathematical genius, who had discovered a complicated principle concerning geometry that he called topology at the turn of the twentieth century. Earlier, in the seventeenth century, Gottfried Wilhelm von Leibniz had attempted to assemble these geometrical concepts, but did not complete his efforts. Then, in the nineteenth century, mathematical insights and important additions exploded, giving Poincaré the accessory information that would help him in his calculations. The Frenchman used delicate geometric inserts that could subtly influence the drawing of maps.