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Copyright © 2006 Trinh Xuan Thuan
All right reserved.
Truth and Beauty
A MAN AND A WOMAN
It is a beautiful spring day in Paris. At a sidewalk café, a man is enjoying a glass of beer while reading a newspaper. At the next table, a woman is sipping coffee while watching passersby. They haven't noticed each other yet. Suddenly, the man turns his head and his gaze meets the woman's. At that instant, a remarkable series of events is set in motion. The golden light of the sun reflects off the woman's slender body and penetrates the man's eyes. Traveling at a speed of 300,000 kilometers per second, 10,000 billion particles of light (called photons) rush in through his pupils. First they traverse an oval-shaped body called the lens, then a transparent and gelatinous substance, before they strike the retina.
THE DANCE IN THE RETINA
In the retina, more than 100 million rod- and cone-shaped cells go to work. Covering the retina like darts bristling out of a dartboard, some of these rods receive large amounts of light from the bright areas of the woman's body, such as her moist lips highlighted by vivid red lipstick. Others receive less light, because it comes from more subdued parts of the woman, suchas her discreetly made-up cheeks. While rods are sensitive to very dim light, cones require brighter light. Both rods and cones contain light-sensitive pigments that respond differently to different levels of light coming from the woman's body. All rods have the same type of pigment. Cones, however, come in three types, each containing a different visual pigment. One type absorbs best in the blue, another in the green-yellow, and the third in the orange-red. Visual pigment molecules are each composed of 20 carbon atoms, 28 hydrogen atoms, and 1 oxygen atom. They respond to light by engaging in a kind of strange ballet. When at rest, in the absence of light, each such molecule is attached to a protein and is all crumpled up. But as soon as light strikes it (the light reflected by the woman hits 30 million billion molecules in the man's eye every second), the molecule in the retina separates from the protein and straightens out. After a while, it crumples back up until the next photon arrives.
NEURONS SPRING INTO ACTION
All these events took less than 1/1,000 of a second since the moment the man's gaze met the woman's. But the man is still not "conscious" of the woman's presence, because the information carried by the particles of light has yet to reach his brain. The frenetic dance of the molecules in his retina must fire up neurons, first in his eyes and then in his brain. Molecules on the surface of neurons also change shape, blocking the flow of sodium ions (particles with a positive electrical charge) in the surrounding liquid, which triggers an electrical current propagating from neuron to neuron, from the eye all the way to the brain. In the cerebral cortex, each neuron processes the information transmitted by thousands of neurons before relaying it in turn to thousands of other neurons farther up the chain. A great many of the hundreds of billions of neurons in the man's brain, interconnected in an incredibly complex network, participate in relaying the information. The flow of potassium and sodium stops depending on whether or not it is blocked by neurons. Electrical currents race furiously through neural networks, exciting swarms of neurons relaying signals that go on to excite yet more neurons. Current crackles everywhere. After a few thousandths of a second, an image is reconstructed in the man's brain: He finally sees the woman. He notices her short blond hair, her deep blue eyes, her dark brown dress molding her body, her slightly tilted head with a pensive look.
The woman turns her head, meets the man's eyes, gives him a faint smile, and offers a cheerful "Hello." Instantly, a multitude of air molecules start jiggling about. The vibrations transmit the sound of the woman's vocal cords to the man's ears. Only two meters separate them, and the sound arrives in 1/150 of a second. The drum (a 1-millimeter-thick membrane) in each of the man's ears begins to vibrate. The vibrations are transmitted to the liquid in the cochlea, a structure shaped like a snail's shell. That is where sounds are decoded. A thin membrane starts oscillating in synchronism with the vibrating liquid. This membrane contains an array of fibers of various thicknesses, much like the strings of a harp. The harp resonates in unison with the woman's sensuous voice and reconstructs the relatively high pitch of the syllable "hel-" and the deeper one of the syllable "-lo." Eventually, the sounds are passed on to the auditory nerve, which conveys the information to the cerebral cortex. And the man finally hears the word "hello."
All theses processes are quite well understood. Neurobiology unveils more and more secrets of the brain each passing day. What remains a complete mystery is what causes the lightning-quick thought that crosses the man's mind: "She is so beautiful!"
NATURE IS BEAUTIFUL
What is beauty? Not only do we have no clue about how our brain apprehends beauty, but we are even less able to describe it in precise terms. It is even more of a challenge to speak of beauty in the context of science, which is exactly what I am going to attempt to do. The popular wisdom is that scientific work is a purely rational pursuit from which any emotion is banned. Physics is widely perceived as a precise and exact science in which there is no place for aesthetic contemplations. Aesthetic judgments are supposedly irrelevant in science; all that is left are cold and impersonal facts. The truth is that scientists are no less sensitive to Nature's beauty than artists. My frequent visits to various observatories have never dulled the intense and always renewed pleasure I experience when I find myself in sites of exceptional beauty, far removed from the lights of civilization. I am in absolute awe every time I see the majestic and arid splendor of the Arizona desert, where the Kitt Peak Observatory is located, or the desolation of the moonscape, stripped of any vegetation, on the summit of Mauna Kea, an extinct volcano in Hawaii where huge telescopes have popped up like mushrooms. My heart always starts racing when the spiral arms of a galaxy billions of light-years away take shape on a monitor screen hooked up to a telescope.
If Nature is so beautiful, why should the theories that describe it not be so too? Why should scientists be less prone than poets to letting themselves be guided by aesthetic considerations in addition to rational arguments? Some of the greatest scientists have answered the question unequivocally. The French mathematician Henri Poincaré (1854-1912), for one, stated: "Scientists do not study Nature for utilitarian reasons. They do it because they find it pleasurable; and they find it pleasurable because Nature is beautiful. If Nature were not beautiful, it would not be worth studying, and life would not be worth living." Poincaré even offered a definition of beauty to which I will return later on: "I speak of an inner beauty that stems from the harmonious order of the parts, which pure intelligence has the ability to grasp." A cri de coeur expanded upon later on by Werner Heisenberg (1901-1976), one of the fathers of quantum mechanics: "If Nature leads us to mathematical forms of great beauty and simplicity—by 'forms' I mean coherent systems of hypotheses, axioms, and the like—which nobody had foreseen before, we cannot help but think that they must be real, that they reveal a true side of Nature.... You must have experienced it too: The almost frightening simplicity and totality of the interconnections which Nature displays before us and for which we were not at all prepared." Albert Einstein (1879-1955) himself wrote at the end of his first paper on general relativity: "Anyone who understands the present theory could not miss its magic." "Harmonious order," "simplicity," "coherence," "magic": These are all words defining "beauty" in science, a concept which I will now try to further articulate.
THE THINGS OF LIFE AND THE RELATIVITY OF BEAUTY
The beauty a physicist speaks of is quite different from what a musician experiences when listening to a sonata by Mozart or a fugue by Bach. Nor is it the same as what an art lover reacts to when admiring the dancers of Degas, the apples of Cézanne, or the water lilies of Monet. It is not even the same as what our earlier character was feeling upon noticing the beautiful woman sitting at the next table. Feminine beauty obeys criteria that are notoriously dependent on cultural, psychological, or even biological contexts. The plump bodies of the women painted by Rubens or Renoir are no longer considered the paradigm of beauty. In the 1960s, Twiggy's skinny figure was considered attractive. The beauty of oriental women is different from that of their Western counterparts, even though massive advertising campaigns for cosmetic products have spread Western standards throughout the world, which has led to such absurd practices as some Asian women having the shape of their eyelids rounded. There are fashionable trends even in the world of art. Van Gogh died in poverty, unable to sell his canvases. Half a century later, people trip over one another buying his paintings at astronomical prices. Aesthetic perceptions change from one culture to another. The style of a painting of Mount Fuji by Hokusai has little in common with Cézanne's rendition of the Sainte-Victoire mountain. The timeless magnificence of the Taj Mahal in India is quite different from the splendor of the cathedral of Chartres. It would be downright presumptuous for anyone to define what constitutes beauty. Like love and hatred, we recognize it when it takes over our soul, no matter how difficult it may be to describe the experience in words.
Beauty is in the eye of the beholder. It is a cliché, perhaps, but so true. It can spring up around any street corner and find its way into ordinary objects in our everyday lives, provided we are receptive. A simple flower, a tree that only yesterday was completely unremarkable because we were preoccupied with other issues, suddenly evokes an overwhelming aesthetic sense. As the German philosopher Arthur Schopenhauer (1788-1860) put it so eloquently, at such times we consider "neither the place, nor the time, nor the why, nor the purpose of things, but quite simply and purely their essence"; we do so because we then allow "neither abstract thought nor any principle of reasoning to clutter our conscience; instead, we turn all the power of our mind toward intuition." Schopenhauer went on to argue: "When we are completely engrossed by it and our conscience is filled by a natural object, be it a landscape, a tree, a rock, a building, or anything else; ... the moment we forget our own individuality, our own will, and we remain as pure subject, as a clear mirror of the object, in such a way that everything happens as though the object existed in and of itself without anyone being able to perceive it, when it is impossible to distinguish between the object and intuition itself, when they both merge into a single entity, a single conscience completely filled and dominated by a unique and intuitive vision; in short, when we sever all ties with will: that is when what we grasp is no longer any particular thing in its individuality but, rather, the idea, the eternal form."
If there is no objective criterion for beauty in human creation, should we expect to discover one in scientific work? Is there a way to forge an aesthetic system in science to judge Nature's beauty and her organization? Perhaps the answer is yes, for unlike the relative beauty of women and things, the appeal of a physical theory is universal. It can be appreciated by any scientist, regardless of ethnic origin or cultural heritage. A Vietnamese physicist can extol the virtues of general relativity with as much passion as any of his French or American colleagues.
In spite of Schopenhauer's exhortations to disregard reason and let intuition be our guide in grasping beauty, I will in fact attempt the hazardous feat of trying to define the concept of beauty in a physical theory. I will refrain from offering a precise definition, which would be doomed to failure. I shall, instead, simply list and illustrate the characteristics a scientific theory must exhibit in order to be beautiful.
BEAUTY IN SCIENCE
To begin with, the word beautiful does not refer to the purely plastic beauty of equations carefully laid down on a piece of paper, even though I confess that even that sight elicits in me a certain sense of abstract beauty, similar to what I feel when I look at a page filled with characters lovingly drawn by a Chinese calligrapher. The poet and painter Henri Michaux made expert use of the plastic beauty of Chinese characters in his ink drawings. Nor is beauty the same thing as what physicists and mathematicians talk about when they use the word elegance. A mathematical proof or a result in physics are "elegant" when they are derived with a minimum number of steps. A theory can be beautiful without the benefit of elegant solutions. By any measure, the theory of general relativity is one the most beautiful intellectual constructs ever produced by the human mind. Yet, in most cases, its solutions hardly qualify as elegant. The mathematical derivations are extremely complicated. That does not prevent it from being perhaps the most beautiful theory ever devised. A theory is beautiful when it has an air of inevitability. It is the same feeling some people experience when listening to a fugue by Bach. Not a single note could be changed without upsetting the overall harmony. The same can be said of the Mona Lisa by Leonardo da Vinci. Not a single stroke of the brush could be altered without destroying the perfection of the painting. So it is for a theory. The moment Einstein accepted the physical principles at the basis of his theory of gravitation, he no longer had any choice: General relativity was inevitable. As he himself wrote: "The main appeal of the theory lies in the fact that it is self-contained. Should any of its conclusions be invalidated, the entire theory would have to be rejected. It is impossible to modify it without jeopardizing the entire structure" The inevitability of a beautiful theory is so overwhelming that when it bursts onto the scene, physicists often wonder how they could have missed it before.
The second quality of a beautiful theory is its simplicity. We are not talking here about the simplicity of the equations themselves, as measured for instance by the number of symbols they contain, but rather of the simplicity of the underlying ideas. As an example, Isaac Newton (1642-1727) needed only three equations—one for each dimension of space—while general relativity requires a total of fourteen. Yet the latter is more beautiful because it rests on simpler fundamental concepts, which we will discuss later on. The heliocentric universe of Copernicus (1473-1543), in which planets move in an orderly fashion along elliptical orbits around the Sun, is simpler than the geocentric model of Ptolemy (ca. 90—ca. 168), where Earth occupies a central place and the planets describe circles whose centers themselves describe other circles. A theory that is simple uses a minimum number of hypotheses. It does not carry excess baggage. It satisfies the postulate of simplicity stated by William of Occam (ca. 1285-1349): "What is not necessary is useless."
CONFORMITY WITH THE WHOLE
The final quality—the most important one, in my opinion—is to conform with Nature's intricacies. It must allow beauty and truth to merge into one. Indeed, a physical theory has no reason for existing unless it reveals new connections in Nature that can be verified by observations or laboratory experiments, unless it lays bare before our eyes "the almost frightening simplicity and totality of the interconnections of Nature," as Heisenberg put it so well. A theory that cannot be verified experimentally belongs not in the realm of science but of metaphysics. Intellectual speculations remain sterile as long as they are not rooted in the forms of Nature. Heisenberg defined beauty as it was perceived in antiquity as "conformity of the parts between themselves and with the whole." Relativity theory is beautiful because it managed to connect and unite fundamental physical concepts that until then had remained completely distinct—time, space, matter, and motion. Matter curves space, and the curvature of space dictates how motion proceeds. The Moon follows an elliptical trajectory around the Earth because Earth's mass causes the space around it to curve. In turn, motion determines the behavior of space-time. An elementary particle traveling at nearly the speed of light sees its time stretch out and its space shrink. The slowing down of time is not a utopian fountain of youth: Particles hurtling around accelerators, such as the one at CERN in Geneva, Switzerland, have been shown to indeed live longer than when they are at rest. And detailed observations have demonstrated that the path of starlight bends when it grazes the sun exactly as if space were curved in its vicinity.
The beauty of a theory is all the more compelling when it reveals a host of new and unexpected connections as researchers explore its deeper implications. General relativity meets this criterion to the utmost degree. Its richness never ceases to amaze us. Einstein himself was stunned when he realized that his equations implied an expanding universe. Just as a stone tossed in the air cannot remain frozen in place, the universe cannot be static: It must either expand or contract. Back in 1915, every astronomical observation suggested that the universe was static. That prompted Einstein to modify his equations so as to conform with the then-prevailing view. He would later regret this action and call it "the greatest blunder of my life" when the American astronomer Edwin Hubble (1889-1953) discovered in 1929 that the universe is in fact expanding. Einstein had failed to place enough trust in the beauty and truth of his own equations. General relativity has kept on delivering wonderful treasures ever since. It is the pillar on which the big bang theory rests. It has enabled cosmologists to go back in time and describe how the universe evolved out of a huge primordial explosion that also gave birth to space-time. It has allowed us to conceive of regions of space where gravity is so powerful and space so strongly curved that not even light can escape—these regions have been dubbed "black holes." It also tells us that massive galaxies can curve space so as to bend the light emitted by distant objects, creating cosmic mirages. Astronomers refer to these galaxies as "gravitational lenses," because they bend and focus light much as the lens in our eye does.
Inevitable, simple, congruent with the whole: Those are the hallmarks of a beautiful theory. It is, in fact, this aesthetic yearning for congruity with the whole that has spurred on physicists of the last two centuries to search for a Theory of Everything that could encompass all physical phenomena in the universe and unify the four fundamental forces of nature.
Before embarking on a search for the holy grail in physics—the Theory of Everything—with beauty as our guide, we must first become acquainted with the power of contingency. Beauty can lead to truth only if we learn to distinguish what is fundamental from what is fortuitous. Beauty alone cannot be a reliable guide in constructing a theory if we fail to take into account the intervention of chance. Nature is governed both by fundamental laws and by accidental events without deep significance. The history of the formation of the solar system is a perfect example to illustrate how random events can shape Nature. Accordingly, we are about to travel back 4.6 billion years to witness live the birth of the solar system. What happened then is of crucial importance not only because it eventually culminated in our own existence but also because it can teach us to distinguish necessity from contingency.
Excerpted from Chaos and Harmony by Trinh Xuan Thuan Copyright © 2006 by Trinh Xuan Thuan. Excerpted by permission.
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