Fritjof Capra (33 page)

Even though Leonardo did not state explicitly that the velocity of light is finite, it is clear from his Notebooks that he held that view. This is quite extraordinary, since the traditional view, handed down from antiquity, was that the propagation of light is instantaneous. Even Huygens and Descartes subscribed to that traditional view, and it was not until the end of the seventeenth century that the finite velocity of light was established.
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Leonardo was well aware of the phenomenon of refraction (the deflection of a light ray upon passing obliquely from air into glass, for instance). He performed several ingenious experiments to explore it, without, however, relating the effect to the wave-nature of light as Descartes and others would do some 150 years later. Leonardo even used refraction in a primitive prism to split white light into components of different colors, as Isaac Newton would do again in a celebrated experiment during the 1660s. But unlike Newton, Leonardo did not go much further than accurately recording the effect.
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On the other hand, Leonardo found the correct explanation for a phenomenon that had intrigued people throughout history—the blue color of the sky. In the years of his optical experiments, he climbed one of the giant peaks of Monte Rosa and noticed the deep blue of the sky at high altitude.
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During the long climb, he apparently pondered the age-old question, “Why is the sky blue?”—and with amazing intuition came up with the correct answer:

The blue displayed by the atmosphere is not its own color, but is caused by moisture that has evaporated into minute and imperceptible atoms on which the solar rays fall, rendering them luminous against the immense darkness of the region of fire that forms a covering above them. And this may be seen, as I myself saw it, by anyone who climbs Monte Rosa.
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The modern explanation of this phenomenon was given about four hundred years later by Lord Rayleigh, and the effect is now known as Rayleigh scattering. Sunlight is scattered by the molecules of the atmosphere (Leonardo’s “minute and imperceptible atoms”) in such a way that blue light is absorbed much more than other frequencies and is then radiated in different directions all around the sky. Hence, whichever way we look, we will see more of the scattered blue light than light of any other color. It is evident that Leonardo’s explanation of solar rays falling on the molecules and “rendering them luminous” is a perfectly accurate qualitative description of the effect. This must certainly rank among his finest achievements in optics.

SOUND WAVES

Leonardo also explored the nature of sound, and from experiments with bells, drums, and other musical instruments, he observed that sound is always produced by “a blow on a resonant object.” He correctly deduced that this causes an oscillating movement in the surrounding air, which he called “fanning movement”
(moto ventilante)
in association with the oscillating movement of a handheld fan.
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“There cannot be any sound,” he concluded, “where there is not movement and percussion of air; there cannot be percussion of that air where there is no instrument.”
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Leonardo then proposed that, as in water, the initial percussion propagates in the form of circular waves, “since in all cases of movement water has great conformity with air.”
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As noted earlier, he was unaware that sound travels via longitudinal waves, but he noticed the phenomenon of resonance, demonstrating it with small pieces of straw, as he had demonstrated the transverse movement of water waves:

The blow given to the bell will make another bell similar to it respond and move somewhat. And the string of a lute, as it sounds, produces response and movement in another similar string of similar tone in another lute. And this you will perceive by placing a straw on the string which is similar to that sounded.
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The observations of resonating bells and lute strings suggested to Leonardo the general mechanism for the propagation and perception of sound—from the initial percussion and the resulting waves in the air to the resonance of the eardrum.

Lacking the appropriate mathematical language, Leonardo was not able to develop a proper wave theory of light, nor a corresponding wave theory of sound.
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He observed that the loudness of the sound generated depended on the power of percussion, but he failed to associate it with the amplitude of the sound wave; nor did he relate the pitch of sound to the wave’s frequency. However, many years later, during the time he was reviewing the contents of all his Notebooks,
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he came close to understanding the relation between pitch and frequency by studying the sound made by flies and other insects.

Whereas the common belief in his time was that flies produce sound with their mouths, Leonardo correctly observed that the sound is generated by their wings and proceeded with a clever experiment: “That flies have their voice in the wings,” he recorded, “you will see by…daubing them with a little honey in such a way that they are not entirely prevented from flying. And you will observe that the sound made by the movement of their wings…will change from high to low pitch in direct proportion to the degree that their wings are more impeded.”
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One of Leonardo’s most impressive discoveries in the field of acoustics was his observation that, “If you tap a board covered with dust, that dust will collect in diverse little hills.”
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Having enhanced the vibrations of lute strings by putting small pieces of straw on them, he now concluded correctly that the dust was flying off the vibrating parts of the board and settling at the nodes, that is, in the areas that were not vibrating. He did not stop at that observation, but carefully continued tapping the vibrating surface while observing the fine movements of the little hills of dust. Next to a sketch representing one such hillock as a pyramid, he recorded his observations. “The hills will always pour down that dust from the tips of their pyramids to their base,” he wrote. “From there, it will re-enter underneath, ascend through the center, and fall back again from the top of that little hill. And so the dust will circulate again and again…as long as the percussion continues.”
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The attention to detail in these observations is truly remarkable. The phenomenon of nodal lines of dust or sand on vibrating plates was rediscovered in 1787 by the German physicist Ernst Chladni. They are now commonly called “Chladni patterns” in physics textbooks, where it is generally not mentioned that Leonardo da Vinci discovered them almost three hundred years earlier.

VISION AND THE EYE

To complete his science of perspective, Leonardo studied not only the external pathways of light rays, together with various optical phenomena, but also followed them right into the eye. Indeed, during the 1480s, he pursued his anatomical studies of the eye and the physiology of vision simultaneously with his investigations of perspective and the interplay of light and shadow.

At that time there was a debate among Renaissance artists and philosophers about the exact location of the tip of the visual pyramid in the eye. Most artists followed Alberti, who paid little attention to the actual physiology of vision and located the apex of the visual pyramid in a geometric point at the center of the pupil. Most philosophers, by contrast, took the position of Alhazen, who asserted that the eye’s visual faculty must reside in a finite area rather than in an infinitely small point.
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In the beginning of his investigations of perspective and the anatomy of the eye, Leonardo adopted Alberti’s view, but during the 1490s, as his research became more sophisticated, he came to embrace Alhazen’s position, arguing that “if all the images that come to the eye converged in a mathematical point, which is proved to be indivisible, then all the things seen in the universe would appear as one, and that one would be indivisible.”
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In his late optical writings in Manuscript D, finally, he asserted repeatedly and confidently that “every part of the pupil possesses the faculty of vision
(virtù visiva),
and…this faculty is not reduced to a point, as the perspectivists wish.”
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In this Notebook, Leonardo offers three simple but very elegant experiments, involving the shadowy perception of small objects held near the eye, as persuasive proofs of Alhazen’s position.
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From then on he distinguished between two kinds of perspective. The first, “perspective made by art,” is a geometric technique for representing objects located in three-dimensional space on a flat surface, while the second, “perspective made by nature,” needs a proper science of vision to be understood.
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Having convinced himself that in such a science of vision, the geometric apex of the visual pyramid in the eye needs to be replaced by much more complex pathways of the sensory impressions, Leonardo then traced these pathways through the lens and the eyeball to the optic nerve, and from there all the way to the center of the brain where he believed he had found the seat of the soul.

NINE

The Eye, the Senses, and the Soul

T
he structure of the eye and the process of vision were natural wonders for Leonardo that never ceased to amaze him. “What language can express this marvel?” he writes about the eyeball, before continuing with a rare expression of religious awe: “Certainly none. This is where human discourse turns directly to the contemplation of the divine.”
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In the
Treatise on Painting
, Leonardo waxes enthusiastic about the human eye:

Don’t you see that the eye embraces the beauty of the whole world? It is the master of astronomy, it practices cosmography, it counsels and corrects all human arts; it transports man to different parts of the world. [The eye] is the prince of mathematics; its sciences are most certain. It has measured the heights and sizes of the stars, it has discovered the elements and their locations…. It has created architecture, perspective, and divine painting…. [The eye] is the window of the human body, through which [the soul] contemplates and enjoys the beauty of the world.
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It is not surprising that Leonardo spent more than twenty years investigating the anatomy and physiology of the eye by carefully dissecting the eyeball and associated muscles and nerves. One of his earliest drawings, made around 1487, shows the human head and brain surrounded by several membranes, like layers of an onion (Fig. 9-1). In fact, this onion analogy was widely used by leading medieval anatomists.
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Beneath the layers of the scalp Leonardo shows two membranes (known today as dura mater and pia mater) surrounding the brain and then extending to form the eyeball, which contains a round lens. The pupil is formed by a transparent gap in the membranes in front of the lens, which appears to lie unattached, presumably floating in some clear fluid. This crude drawing is a faithful illustration of the medieval view of the eye, which was based almost entirely on imagination rather than on empirical knowledge.

With his own anatomical dissections, Leonardo soon progressed far beyond these traditional ideas. The “onion drawing” already shows one of his discoveries, the frontal sinus above the eyeball, and in the subsequent years he would gradually add many fine details concerning the anatomy of the eye and the pathways of visual perception.

He was well aware of the novelty of his discoveries. “The eye has until now been defined by countless writers in a certain way,” he noted in the Codex Atlanticus, “but I find through experience that it works in a different manner.”
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LEONARDO’S ANATOMY OF THE EYE

Leonardo’s study of visual perception was an extraordinary program of scientific investigation, combining optics, anatomy of the eye, and neuroscience. He explored these fields without any inhibitions, applying the same meticulous empirical method to them that he used to explore everything else in nature, never fearing that some phenomenon might be beyond his grasp.

Figure 9-1: Leonardo’s illustration of the medieval view of the scalp, brain, and eyeball, Anatomical Studies, folio 32r

One of the first things Leonardo noticed when he studied the structure of the eye in detail was its ability to change the size of the pupil according to its exposure to light. He first observed this phenomenon while painting a portrait, and then tested it in a series of experiments in which he exposed subjects to varying amounts of light. “The pupil of the eye,” he concluded, “changes to as many different sizes as there are differences in the degrees of brightness and darkness of the objects which present themselves before it…. Nature has equipped the visual faculty, when irritated by excessive light, with the contraction of the pupil…, and here nature works like someone who, having too much light in his house, closes half of a window, and more or less according to necessity.” And then he added: “You can observe that in nocturnal animals such as cats, screech owls, tawny owls and others, which have the pupil small at midday and very large at night.”
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When he investigated the mechanism of these contractions and dilations in his dissections of the eyeball, Leonardo discovered the delicate sphincter of the pupil. “I find by experiment,” he recorded, “that the black, or nearly black, crinkled rough color, which appears around the pupil, serves no other function than to increase or decrease the size of that pupil.”
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In another passage, he likened the action of the radial folds of the sphincter to the closing of a purse with a string.
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Leonardo’s detailed description of the “nearly black, crinkled rough color” of the pupillary muscles is amazingly accurate. Indeed, it is almost identical to that of modern medical textbooks, in which the muscles on the central opening of the iris, the so-called “pupillary ruff,” are described as a dark brown, wrinkled rim.
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In the Middle Ages and the Renaissance, most natural philosophers believed that vision involved the emission of “visual rays” by the eye, which were then reflected back by the perceived objects. This view was first proposed by Plato and was supported by Euclid, Ptolemy, and Galen. Only the great experimental philosopher Alhazen expounded the opposite view—that vision was triggered when visual images, carried by light rays, entered the eye.

Leonardo debated the merits of both points of view at great length before agreeing with Alhazen.
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His principal argument in favor of the theory of “intromission” was based on his discovery of the pupil’s adaptation to changing illumination. In particular, he saw the fact that sudden bright sunlight produces pain in the eye as decisive proof that light not only enters the eye, but can also cause harm to it and, in extreme cases, even its destruction. An additional argument for the entry of light into the eye was Leonardo’s observation of afterimages. “If you look at the sun or another luminous body and then shut your eyes,” he noted, “you will see it similarly inside your eye for a long space of time. This is evidence that images enter the eye.”
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After a hiatus of almost twenty years, Leonardo returned to the study of vision around 1508 to explore further details of the eye’s anatomy and its visual pathways.
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This time, he also made use of his new technique of embedding the eyeball in egg white during dissections.
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He recognized the cornea as a transparent membrane and noticed its prominent curvature, concluding correctly that this extends the visual field beyond 180 degrees: “Nature made the surface of the cornea in the eye convex in order to allow surrounding objects to imprint their images at greater angles.”
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Leonardo realized that the extension of the visual field by the prominence of the cornea’s curvature is due to the refraction of light rays when they pass from the air into the denser medium of the cornea, and he carefully illustrated this phenomenon in several sketches. In addition, he tested the refractions experimentally by building a crystal model of the cornea.
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Leonardo was quite familiar with lenses from his optical experiments as well as from his own use of spectacles, which he had to wear by the time he studied the lens of the eye.
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Naturally, he applied his knowledge of refraction to his investigations of both the cornea and the lens. However, he always presented the lens, which he called the “crystalline humor,” as spherical and located in the center of the eyeball, suspended in a clear fluid, rather than right behind the pupil. Kenneth Keele has pointed out that Leonardo’s sophisticated technique of dissection of the eyeball, developed around 1509, would certainly have enabled him to recognize the true shape and location of the lens, and Keele has speculated that Leonardo either did not continue his dissections of the eye after that time, or that more accurate drawings have been lost.
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The detailed optics of the light rays inside the eyeball presented great difficulties for Leonardo, as they did for all his contemporaries. Today we know that the rays are refracted by the convex lens in such a way that they cross each other behind the lens and form an inverted image of the perceived object on the retina. How the brain then corrects the inversion to produce normal vision is still not fully understood.

Since Leonardo could not know that a second inversion of the image is performed in the brain, he had to construct two consecutive inversions of the light rays within the eyeball to produce an upright image. He came up with a brilliant though incorrect idea. The first inversion of the rays, he postulated, occurs between the pupil and the lens, caused by the small opening of the pupil, which turns the image upside down like a camera obscura.
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The inverted rays then enter the lens where they are inverted a second time, resulting in an upright image at the end. Leonardo built a simple but very ingenious model of the eye to test this idea and illustrated it clearly with a charming drawing in Manuscript D (Fig. 9-2). In the lower part of the drawing, he has sketched the visual pathways according to his theory. The light rays, entering the eye from below, are slightly refracted by the cornea (except for the central ray), proceed through the small opening of the pupil and, as in a camera obscura, produce an inverted image on the spherical lens. There, the rays are inverted again before they form a proper image on the back of the lens, from where they would enter the optic nerve.

The upper part of the drawing shows Leonardo’s model. He has filled a transparent globe, representing the eyeball, with water and at the front has fitted a plate with a small hole in the middle, representing the pupil. Suspended in the center of the globe is a “ball of thin glass,” representing the lens, behind which Leonardo places his own eye underwater in the position of the optic nerve. “Such an instrument,” he explains in the accompanying text, “will send the images…to the eye just as the eye sends them to the visual faculty.”
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Leonardo’s construction of the visual pathways was certainly ingenious, but it also had some serious problems. The camera-obscura effect would work only if the size of the pupil were much smaller and its distance from the lens greater than they actually are. And even if that were the case, the images of objects on the retina would be affected by the contractions and dilations of the pupil in response to varying exposures to light. Leonardo considered that possibility and also experimented with alternative visual paths, but he was never able to resolve the inconsistencies inherent in his construction.
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Nevertheless, his discoveries of many fine details of the eye’s anatomy are truly remarkable.

Leonardo was the first to distinguish between central and peripheral vision. “The eye has a single central line,” he observed, “and all the things that come to the eye along this line are seen well. Around this central line, there are an infinite number of other lines, which are of less value the further they are from the central line.”
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He was also the first to explain binocular vision—the way in which we see things stereoscopically by fusing the separate images of the visual field formed in each eye. To explore the details of binocular vision, he placed objects of various sizes at varying distances from the eyes, from very close to very far, and looked at them alternatively with the right and left eye and with both eyes. His conclusion was unequivocal and correct: “One and the same object is clearly comprehended when seen with two concordant eyes. These eyes refer it to one and the same point inside the head…. But if you displace one of those eyes with the finger, you will see one perceived object converted into two.”
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