A Beautiful Question: Finding Nature's Deep Design
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Artists as well as scientists throughout human history have pondered this “beautiful question.” With Nobel laureate Frank Wilczek as your guide, embark on a voyage of related discoveries, from Plato and Pythagoras up to the present. Wilczek’s groundbreaking work in quantum physics was inspired by his intuition to look for a deeper order of beauty in nature. This is the deep logic of the universe—and it is no accident that it is also at the heart of what we find aesthetically pleasing and inspiring.
Wilczek is hardly alone among great scientists in charting his course using beauty as his compass. As he reveals in A Beautiful Question, this has been the heart of scientific pursuit from Pythagoras and the ancient belief in the music of the spheres to Galileo, Newton, Maxwell, Einstein, and into the deep waters of twentieth-century physics. Wilczek brings us right to the edge of knowledge today, where the core insights of even the craziest quantum ideas apply principles we all understand. The equations for atoms and light are almost the same ones that govern musical instruments and sound; the subatomic particles that are responsible for most of our mass are determined by simple geometric symmetries.
Gorgeously illustrated, A Beautiful Question is a mind-shifting book that braids the age-old quest for beauty and the age-old quest for truth into a thrilling synthesis. It is a dazzling and important work from one of our best thinkers, whose humor and infectious sense of wonder animate every page. Yes: The world is a work of art, and its deepest truths are ones we already feel, as if they were somehow written in our souls.
ISBN-13: 9780143109365
Media Type: Paperback(Reprint)
Publisher: Penguin Publishing Group
Publication Date: 07-12-2016
Pages: 448
Product Dimensions: 5.40(w) x 7.60(h) x 1.10(d)
Frank Wilczek won the Nobel Prize in Physics in 2004 for work he did as a graduate student. He was among the earliest MacArthur fellows, and has won many awards both for his scientific work and his writing. He is the author of Fundamentals, A Beautiful Question, The Lightness of Being, Fantastic Realities, Longing for the Harmonies, and hundreds of articles in leading scientific journals. His "Wilczek's Universe" column appears regularly in the Wall Street Journal. Wilczek is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology, founding director of the T. D. Lee Institute and chief scientist at the Wilczek Quantum Center in Shanghai, China, and a distinguished professor at Arizona State University and Stockholm University.
This work was prepared especially for A Beautiful Question by He Shuifa,a modern master of traditional Chinese art and calligraphy. He is renownedfor the vigor and subtlety of his brushwork and for the spiritual depth of hisdepictions of flowers, birds, and nature. A simple translation of the inscriptionis this: “Taiji double fish is the essence of Chinese culture. This imagewas painted by He Shuifa on a lake in early winter.” The playful “doublefish” aspect of Taiji comes to life in He Shuifa’s image. The yin and yangresemble two carp playing together, and there are hints of their eyes and fins.In Henan, on the Yellow River, there is a waterfall called Dragon’s Gate.Yulong carp attempt to jump the cataract, although it is very difficult forthem. Those that succeed transform into lucky dragons. With a sense ofhumor, we may associate this event with the transformation of virtual intoreal particles, an essential quantum process that is now thought to underliethe origin of structure in the Universe (see plates XX and AAA). Alternativelywe may identify ourselves with the carp, and their strivings with ourquest for understanding. USER’S MANUAL There’s also a “User’s Manual”—but you knew that. THE QUESTION This book is a long meditation on a single question: Does the world embody beautiful ideas? Our Question may seem like a strange thing to ask. Ideas are one thing, physical bodies are quite another. What does it mean to “embody” an “idea”? Embodying ideas is what artists do. Starting from visionary conceptions, artists produce physical objects (or quasi-physical products, like musical scores that unfold into sound). Our Beautiful Question, then, is close to this one: Is the world a work of art? Posed this way, our Question leads us to others. If it makes sense to consider the world as a work of art, is it a successful work of art? Is the physical world, considered as a work of art, beautiful? For knowledge of the physical world we call on the work of scientists, but to do justice to our questions we must also bring in the insights and contributions of sympathetic artists. SPIRITUAL COSMOLOGY Our Question is a most natural one, in the context of spiritual cosmology. If an energetic and powerful Creator made the world, it could be that what moved Him—or Her, or Them, or It—to create was precisely an impulse to make something beautiful. Natural though it may be, this is assuredly not an orthodox idea, according to most religious traditions. Many motivations have been ascribed to the Creator, but artistic ambition is rarely prominent among them. In Abrahamic religions, conventional doctrine holds that the Creator set out to embody some combination of goodness and righteousness, and to create a monument to His glory. Animistic and polytheistic religions have envisaged beings and gods who create and govern different parts of the world with many kinds of motives, running the gamut from benevolence to lust to carefree exuberance. On a higher theological plane, the Creator’s motivations are sometimes said to be so awesome that finite human intellects can’t hope to comprehend them. Instead we are given partial revelations, which are to be believed, not analyzed. Or, alternatively, God is Love. None of those contradictory orthodoxies offers compelling reasons to expect that the world embodies beautiful ideas; nor do they suggest that we should strive to find such ideas. Beauty can form part of their cosmic story, but it is generally regarded as a side issue, not the heart of the matter. Yet many creative spirits have found inspiration in the idea that the Creator might be, among other things, an artist whose esthetic motivations we can appreciate and share—or even, in daring speculation, that the Creator is primarily a creative artist. Such spirits have engaged our Question, in varied and evolving forms, across many centuries. Thus inspired, they have produced deep philosophy, great science, compelling literature, and striking imagery. Some have produced works that combine several, or all, of those features. These works are a vein of gold running back through our civilization. Galileo Galilei made the beauty of the physical world central to his own deep faith, and recommended it to all: The greatness and the glory of God shine forth marvelously in all His works, and is to be read above all in the open book of the heavens. . . . as did Johannes Kepler, Isaac Newton, and James Clerk Maxwell. For all these searchers, finding beauty embodied in the physical world, reflecting God’s glory, was the goal of their search. It inspired their work, and sanctified their curiosity. And with their discoveries, their faith was rewarded. While our Question finds support in spiritual cosmology, it can also stand on its own. And though its positive answer may inspire a spiritual interpretation, it does not require one. We will return to these thoughts toward the end of our meditation, by which point we will be much better prepared to appraise them. Between now and then, the world can speak for itself. HEROIC VENTURES Just as art has a history, with developing standards, so does the concept of the world as a work of art. In art history, we are accustomed to the idea that old styles are not simply obsolete, but can continue to be enjoyed on their own terms, and also offer important context for later developments. Though that idea is much less familiar in science, and in science it is subject to important limitations, the historical approach to our Question offers many advantages. It allows us—indeed, forces us—to proceed from simpler to more complex ideas. At the same time, by exploring how great thinkers struggled and often went astray, we gain perspective on the initial strangeness of ideas that have become, through familiarity, too “obvious” and comfortable. Last but by no means least, we humans are especially adapted to think in story and narrative, to associate ideas with names and faces, and to find tales of conflicts and their resolution compelling, even when they are conflicts of ideas, and no blood gets spilled. (Actually, a little does . . .) For these reasons we will sing, to begin, songs of heroes: Pythagoras, Plato, Filippo Brunelleschi, Newton, Maxwell. (Later a major heroine, Emmy Noether, will enter too.) Real people went by those names—very interesting ones! But for us they are not merely people, but also legends and symbols. I’ve portrayed them, as I think of them, in that style, emphasizing clarity and simplicity over scholarly nuance. Here biography is a means, not an end. Each hero advances our meditation several steps: When thus stated broadly, Analysis and Synthesis may not seem terribly impressive. It is, after all, closely related to common rules of thumb, e.g., “to solve a complex problem, divide and conquer”—hardly an electrifying revelation. But Newton demanded precision and completeness of understanding, saying, ’Tis much better to do a little with certainty & leave the rest for others that come after than to explain all things by conjecture without making sure of any thing. And in these impressive examples, he achieved his ambitions. Newton showed, convincingly, that Nature herself proceeds by Analysis and Synthesis. There really is simplicity in the “atoms,” and Nature really does operate by letting them do their thing. Newton also, in his work on motion and mechanics, enriched our concept of what physical laws are. His laws of motion and of gravity are dynamical laws. In other words, they are laws of change. Laws of this kind embody a different concept of beauty than the static perfection beloved of Pythagoras and (especially) Plato. Dynamical beauty transcends specific objects and phenomena, and invites us to imagine the expanse of possibilities. For example, the sizes and shapes of actual planetary orbits are not simple. They are neither the (compounded) circles of Aristotle, Ptolemy, and Nicolaus Copernicus, nor even the more nearly accurate ellipses of Kepler, but rather curves that must be calculated numerically, as functions of time, evolving in complicated ways that depend on the positions and masses of the Sun and the other planets. There is great beauty and simplicity here, but it is only fully evident when we understand the deep design. The appearance of particular objects does not exhaust the beauty of the laws. Maxwell also, in his work on color perception, discovered that Plato’s metaphorical Cave reflects something quite real and specific: the paltriness of our sensory experience, relative to available reality. And his work, by clarifying the limits of perception, allows us to transcend those limits. For the ultimate sense-enhancing device is a searching mind. QUANTUM FULFILLMENT The definitive answer “yes” to our Question came only in the twentieth century, with the development of quantum theory. The quantum revolution gave this revelation: we’ve finally learned what Matter is. The necessary equations are part of the theoretical structure often called the Standard Model. That yawn-inducing name hardly does the achievement justice, and I’m going to continue my campaign, begun in The Lightness of Being, to replace it with something more appropriately awesome: Standard Model Core Theory This change is more than justified, because 1. “Model” connotes a disposable makeshift, awaiting replacement by the “real thing.” But the Core Theory is already an accurate representation of physical reality, which any future, hypothetical “real thing” must take into account. 2. “Standard” connotes “conventional,” and hints at superior wisdom. But no such superior wisdom is available. In fact, I think—and mountains of evidence attest—that while the Core Theory will be supplemented, its core will persist. The Core Theory embodies beautiful ideas. The equations for atoms and light are, almost literally, the same equations that govern musical instruments and sound. A handful of elegant designs support Nature’s exuberant construction, from simple building blocks, of the material world. Our Core Theories of the four forces of Nature—gravity, electromagnetism, and the strong and weak forces—embody, at their heart, a common principle: local symmetry. As you will read, this principle both fulfills and transcends the yearnings of Pythagoras and Plato for harmony and conceptual purity. As you will see, this principle both builds upon and transcends the artistic geometry of Brunelleschi and the brilliant insights of Newton and Maxwell into the nature of color. The Core Theory completes, for practical purposes, the analysis of matter. Using it, we can deduce what sorts of atomic nuclei, atoms, molecules—and stars—exist. And we can reliably orchestrate the behavior of larger assemblies of these elements, to make transistors, lasers, or Large Hadron Colliders. The equations of the Core Theory have been tested with far greater accuracy, and under far more extreme conditions, than are required for applications in chemistry, biology, engineering, or astrophysics. While there certainly are many things we don’t understand—I’ll mention some important ones momentarily!—we do understand the Matter we’re made from and that we encounter in normal life (even if we’re chemists, engineers, or astrophysicists). Despite its overwhelming virtues, the Core Theory is imperfect. Indeed, precisely because it is such a faithful description of reality, we must, in pursuit of our Question, hold it to the highest esthetic standards. So scrutinized, the Core Theory reveals flaws. Its equations are lopsided, and they contain several loosely connected pieces. Furthermore, the Core Theory does not account for so-called dark matter and dark energy. Although those tenuous forms of matter are negligible in our immediate neighborhood, they persist in the interstellar and intergalactic voids, and thereby come to dominate the overall mass of the Universe. For those and other reasons, we cannot remain satisfied. Having tasted beauty at the heart of the world, we hunger for more. In this quest there is, I think, no more promising guide than beauty itself. I shall show you some hints that suggest concrete possibilities for improving our description of Nature. As I aspire to inspired guesswork, beauty is my inspiration. Several times it’s worked well for me, as you’ll see. VARIETIES OF BEAUTY Different artists have different styles. We don’t expect to find Renoir’s shimmering color in Rembrandt’s mystic shadows, or the elegance of Raphael in either. Mozart’s music comes from a different world entirely, the Beatles’ from another, and Louis Armstrong’s from yet another. Likewise, the beauty embodied in the physical world is a particular kind of beauty. Nature, as an artist, has a distinctive style. To appreciate Nature’s art, we must enter her style with sympathy. Galileo, ever eloquent, expressed it this way: Philosophy [Nature] is written in that great book which ever is before our eyes—I mean the universe—but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth. Today we’ve penetrated much further into the great book, and discovered that its later chapters use a more imaginative, less familiar language than the Euclidean geometry Galileo knew. To become a fluent speaker in it is the work of a lifetime (or at least of several years in graduate school). But just as a graduate degree in art history is not a prerequisite for engaging with the world’s best art and finding that a deeply rewarding experience, so I hope, in this book, to help you engage with Nature’s art, by making her style accessible. Your effort will be rewarded, for as Einstein might have said, Subtle is the Lord, but malicious She is not. Two obsessions are the hallmarks of Nature’s artistic style: Now, a disclaimer. Many varieties of beauty are underrepresented in Nature’s style, as expressed in her fundamental operating system. Our delight in the human body and our interest in expressive portraits, our love of animals and of natural landscapes, and many other sources of artistic beauty are not brought into play. Science isn’t everything, thank goodness. CONCEPTS AND REALITIES; MIND AND MATTER Our Question can be read in two directions. Most obviously, it is a question about the world. That is the direction we’ve emphasized so far. But the other direction is likewise fascinating. When we find that our sense of beauty is realized in the physical world, we are discovering something about the world, but also something about ourselves. Human appreciation of the fundamental laws of Nature is a recent development on evolutionary or even historical time scales. Moreover, those laws reveal themselves only after elaborate operations—looking through sophisticated microscopes and telescopes, tearing atoms and nuclei apart, and processing long chains of mathematical reasoning—that do not come naturally. Our sense of beauty is not in any very direct way adapted to Nature’s fundamental workings. Yet just as surely, our sense of beauty is excited by what we find there. What explains that miraculous harmony of Mind and Matter? Without an explanation of that miracle, our Question remains mysterious. It is an issue our meditation will touch upon repeatedly. For now, two brief anticipations: 1. We human beings are, above all, visual creatures. Our sense of vision, of course, and in a host of less obvious ways our deepest modes of thought, are conditioned by our interaction with light. Each of us, for example, is born to become an accomplished, if unconscious, practitioner of projective geometry. That ability is hardwired into our brain. It is what allows us to interpret the two-dimensional image that arrives on our retinas as representing a world of objects in three-dimensional space. Our brains contain specialized modules that allow us to construct, very quickly and without conscious effort, a dynamic worldview based on three-dimensional objects located in three-dimensional space. We do this beginning from two two-dimensional images on the retinas of our eyes (which, in turn, are the product of light rays emitted or reflected from the surfaces of external objects, which propagate to us in straight lines). To work back from the images we receive to the objects that cause them is a tricky problem in inverse projective geometry. In fact, as stated, it is an impossible problem, because there’s not nearly enough information in the projections to do an unambiguous reconstruction. A basic problem is that even to get started we need to separate objects from their background (or foreground). We exploit all kinds of tricks based on typical properties of objects we encounter, such as their color or texture contrast and distinctive boundaries, to do that job. But even after that step is accomplished, we are left with a difficult geometrical problem, for which Nature has helpfully provided us, in our visual cortex, an excellent specialized processor. Another important feature of vision is that light arrives to us from very far away, and gives us a window into astronomy. The regular apparent motion of stars and the slightly less regular apparent motion of planets gave early hints of a lawful Universe, and provided an early inspiration and testing ground for the mathematical description of Nature. Like a good textbook, it contains problems with varying degrees of difficulty. In the more advanced, modern parts of physics we learn that light itself is a form of matter, and indeed that matter in general, when understood deeply, is remarkably light-like. So again, our interest in and experience with light, which is deeply rooted in our essential nature, proves fortunate. Creatures that, like most mammals, perceive the world primarily through the sense of smell would have a much harder time getting to physics as we know it, even if they were highly intelligent in other ways. One can imagine dogs, say, evolving into extremely intelligent social creatures, developing language, and experiencing rich lives full of interest and joy, but devoid of the specific kinds of curiosity and outlook, based on visual experience, that lead to our kind of deep understanding of the physical world. Their world would be rich in reactions and decays—they’d have great chemistry sets, elaborate cuisines, aphrodisiacs, and, à la Proust, echoing memories. Projective geometry and astronomy, maybe not so much. We understand that smell is a chemical sense, and we are beginning to understand its foundation in molecular events. But the “inverse” problem of working from smell back to molecules and their laws, and eventually to physics as we know it, seems to me hopelessly difficult. Birds, on the other hand, are visual creatures, like us. Beyond that, their way of life would give them an extra advantage over humans, in getting started on physics. For birds, with their freedom of flight, experience the essential symmetry of three-dimensional space in an intimate way that we do not. They also experience the basic regularities of motion, and especially the role of inertia, in their everyday lives, as they operate in a nearly frictionless environment. Birds are born, one might say, with intuitive knowledge of classical mechanics and Galilean relativity, as well as of geometry. If some species of bird evolved high abstract intelligence—that is, if they ceased being birdbrains—their physics would develop rapidly. Humans, on the other hand, have to unlearn the friction-laden Aristotelean mechanics they use in everyday life, in order to achieve deeper understanding. Historically that involved quite a struggle! Dolphins, in their watery environment, and bats, with their echolocation, give us other interesting variations on these themes. But I will not develop those here. A general philosophical point, which these considerations illustrate, is that the world does not provide its own unique interpretation. The world offers many possibilities for different sensory universes, which support very different interpretations of the world’s significance. In this way our so-called Universe is already very much a multiverse. 2. Successful perception involves sophisticated inference, because the information we sample about the world is both very partial and very noisy. For all our innate powers, we must also learn how to see by interacting with the world, forming expectations, and comparing our predictions with reality. When we form expectations that turn out to be correct, we experience pleasure and satisfaction. Those reward mechanisms encourage successful learning. They also stimulate—indeed, at base they are—our sense of beauty. Putting those observations together, we discover an explanation of why we find interesting phenomena (phenomena we can learn from!) in physics beautiful. An important consequence is that we especially value experience that is surprising, but not too surprising. Routine, superficial recognition will not challenge us, and may not be rewarded as active learning. On the other hand, patterns whose meaning we cannot make sense of at all will not offer rewarding experience either; they are noise. And here we are lucky too, in that Nature employs, in her basic workings, symmetry and economy of means. For these principles, like our intuitive understanding of light, promote successful prediction and learning. From the appearance of part of a symmetric object we can predict (successfully!) the appearance of the rest; from the behavior of parts of natural objects we can predict (sometimes successfully!) the behavior of wholes. Symmetry and economy of means, therefore, are exactly the sorts of things we are apt to experience as beautiful. NEW IDEAS AND INTERPRETATIONS Together with new appreciations of some very old and some less old ideas, you will find in this book several essentially new ones. Here I’d like to mention some of the most important. My presentation of the Core Theory as geometry, and my speculations about the next steps beyond it, are adaptations of my technical work in fundamental physics. That work builds, of course, on the work of many others. My use of color fields as an example of extra dimensions, and my exploitation of the possibilities they open up for illustrating local symmetry, are (as far as I know) new. My theory that promotion of learning underlies, and is the evolutionary cause of, our sense of beauty in important cases, and the application of that theory to musical harmony, which offers a rational explanation for Pythagoras’s discoveries in music, form a constellation of ideas I’ve entertained privately for a long time but present here for the first time publicly. Caveat emptor. My discussion of the expansion of color perception draws on an ongoing program of practical research that I hope will lead to commercial products. Patents have been applied for. I’d like to think that Niels Bohr would approve of my broad interpretation of complementarity, and might even acknowledge his paternity—but I’m not sure he would. PYTHAGORAS I: THOUGHT AND OBJECT THE SHADOW PYTHAGORAS There was a person named Pythagoras who lived and died around 570–495 BCE, but very little is known about him. Or rather a lot is “known” about him, but most of it is surely wrong, because the documentary trail is littered with contradictions. It combines the sublime, the ridiculous, the unbelievable, and the just plain weird. Pythagoras was said to be the son of Apollo, to have a golden thigh, and to glow. He may or may not have advocated vegetarianism. Among his most notorious sayings is an injunction not to eat beans, because “beans have a soul.” Yet several early sources explicitly deny that Pythagoras said or believed anything of the sort. More reliably, Pythagoras believed in, and taught, the transmigration of souls. There are several stories—each, to be sure, dubious—that corroborate this. According to Aulus Gellius, Pythagoras remembered four of his own past lives, including one as a beautiful courtesan named Alco. Xenophanes recounts that Pythagoras, upon hearing the cries of a dog who was being beaten, rushed to halt the beating, claiming to recognize the voice of a departed friend. Pythagoras also, like Saint Francis centuries later, preached to animals. The Stanford Encyclopedia of Philosophy—a free and extremely valuable online resource, by the way—sums it up as follows: The popular modern image of Pythagoras is that of a master mathematician and scientist. The early evidence shows, however, that, while Pythagoras was famous in his own day and even 150 years later in the time of Plato and Aristotle, it was not mathematics or science upon which his fame rested. Pythagoras was famous 1. As an expert on the fate of the soul after death, who thought that the soul was immortal and went through a series of reincarnations 2. As an expert on religious ritual 3. As a wonder-worker who had a thigh of gold and who could be two places at the same time 4. As the founder of a strict way of life that emphasized dietary restrictions, religious ritual and rigorous self discipline A few things do seem clear. The historical Pythagoras was born on the Greek island of Samos, traveled widely, and became the inspiration for and founder of an unusual religious movement. His cult flourished briefly in Crotone, in southern Italy, and developed chapters in several other places before being everywhere suppressed. The Pythagoreans formed secretive societies, on which the initiates’ lives centered. These communities, which included both men and women, promoted a kind of intellectual mysticism that seemed marvelous, yet strange and threatening, to most of their contemporaries. Their worldview centered on worshipful admiration of numbers and musical harmony, which they saw as reflecting the deep structure of reality. (As we’ll see, they were on to something.) THE REAL PYTHAGORAS Here again is the Stanford Encyclopedia: The picture ofRead an Excerpt
I hope you’ve already enjoyed the cover art and the frontispiece, which set the tone for our meditation beautifully.
Pythagoras also discovered, in the laws of stringed instruments, simple and surprising relationships between numbers and musical harmony. That discovery completes a trinity, Mind-Matter-Beauty, with Number as the linking thread. Heady stuff! It led Pythagoras to surmise that All Things Are Number. With these discoveries and speculations, our Question comes to life.
Plato was also a great literary artist. His metaphor of the Cave captures important emotional and philosophical aspects of our relationship, as human inquirers, with reality. At its core is the belief that everyday life offers us a mere shadow of reality, but that through adventures of mind, and sensory expansion, we can get to its essence—and that the essence is clearer and more beautiful than its shadow. He imagined a mediating demiurge, which can be translated as Artisan, who rendered the realm of perfect, eternal Ideas into its imperfect copy, the world we experience. Here the concept of the world as a work of art is explicit.
A common theme pervades Newton’s titanic work on light, the mathematics of calculus, motion, and mechanics. It is the method he called Analysis and Synthesis. The method of Analysis and Synthesis suggests a two-stage strategy to achieve understanding. In the analysis stage, we consider the smallest parts of what we are studying their “atoms,” using the word figuratively. In a successful analysis, we identify small parts that have simple properties that we can summarize in precise laws. For example:
(We’ll discuss these in more depth later.) In the synthesis stage we build up, by logical and mathematical reasoning, from the behavior of individual atoms to the description of systems that contain many atoms.
By what is the physicist’s “inspired guesswork” inspired? Logical consistency is necessary, but hardly sufficient. Rather it was beauty and symmetry that guided Maxwell and his followers—that is, all modern physicists—closer to truth, as we shall see.
Watch for these themes as they recur, grow, and develop throughout our narrative and give it unity. Our appreciation of them has evolved from intuition and wishful thinking into precise, powerful, and fruitful methods.