Symmetry In Nature Quotes

Om (AUM) the Divine song is at the same time Symmetry, Supersymmetry, broken Symmetry, and the unbroken Symmetry of Nature.

Beauty is our weapon against nature; by it we make objects, giving them limit, symmetry, proportion. Beauty halts and freezes the melting flux of nature.

Two obsessions are the hallmarks of Nature's artistic style: Symmetry- a love of harmony, balance, and proportion Economy- satisfaction in producing an abundance of effects from very limited means

Dora found beauty in everything. She found nature’s magnificent work and incredible symmetry in a turtle’s carapace, or a stork’s egg, or an autumn reed from a swamp. How wonderful, she would often say. I understood the meaning of the word, but I could never feel the splendor it carried.

The key point to keep in mind, however, is that symmetry is one of the most important tools in deciphering nature's design.

Physics, mathematics, music, painting, my politics, my love for you, my work, the star-dust of my body, the spirit that impels it, clocks diurnal, time perpetual, the roll, rough, tender, swamping, liberating, breathing, moving, thinking nature, human nature and the cosmos are patterned together.

animals are indeed more ancient, more complex and in many ways more sophisticated than us. They are more perfect because they remain within Nature's fearful symmetry just as Nature intended. They should be respected and revered, but perhaps none more so than the elephant, the world's most emotionally human land mammal.

There’s something magical in the act of holding another’s life in your hands. A kind of symmetry found in nature, where you’re given the opportunity to bring beasts to grisly fates or heal them instead.

Supersymmetry, if correct, will be a profound new embodiment of beauty in the world. Because the transformations of supersymmetry turn substance particles into force particles, and vice versa, supersymmetry can explain, based on symmetry, why neither of those things can exist without the other: Both are the same thing, seen from different perspectives. Supersymmetry reconciles apparent opposites, in the spirit of yin-yang.

Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.

[Donald] Keene observed [in a book entitled The Pleasures of Japanese Literature, 1988] that the Japanese sense of beauty has long sharply differed from its Western counterpart: it has been dominated by a love of irregularity rather than symmetry, the impermanent rather than the eternal and the simple rather than the ornate. The reason owes nothing to climate or genetics, added Keene, but is the result of the actions of writers, painters and theorists, who had actively shaped the sense of beauty of their nation. Contrary to the Romantic belief that we each settle naturally on a fitting idea of beauty, it seems that our visual and emotional faculties in fact need constant external guidance to help them decide what they should take note of and appreciate. 'Culture' is the word we have assigned to the force that assists us in identifying which of our many sensations we should focus on and apportion value to.

Nature demands symmetry.

There’s poetry in nature. A symmetry.

On the whole, it was not the crudest, the simplest, the most animalistic and primitive aspects of the human species that were reflected in the natural phenomena. It was, rather, the more complex, the aesthetic, the intricate, and the elegant aspects of people that reflected nature. It was not my greed, my purposiveness, my so-called 'animal,' so-called 'instincts,' and so forth that I was recognizing on the other side of that mirror, over there in 'nature.' Rather, I was seeing there the roots of human symmetry, beauty and ugliness, aesthetics, the human being's very aliveness and little bit of wisdom. His wisdom, his bodily grace, and even his habit of making beautiful objects are just as 'animal' as his cruelty.

All the tension and darkness of our embodied life is held in a scaffolding of balance and symmetry, a natural order that is hard to see, like the ocean’s turbulence is held by its depths.

Gravitons are the avatars of general covariance. Photons are the avatars of gauge symmetry 1.0. Weakons are the avatars of gauge symmetry 2.0. Color gluons are the avatars of gauge symmetry 3.0.

So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why. The only thing we might suggest is something like this: There is a gate in Japan, a gate in Neiko, which is sometimes called by the Japanese the most beautiful gate in all Japan; it was built in a time when there was great influence from Chinese art. This gate is very elaborate, with lots of gables and beautiful carving and lots of columns and dragon heads and princes carved into the pillars, and so on. But when one looks closely he sees that in the elaborate and complex design along one of the pillars, one of the small design elements is carved upside down; otherwise the thing is completely symmetrical. If one asks why this is, the story is that it was carved upside down so that the gods will not be jealous of the perfection of man. So they purposely put an error in there, so that the gods would not be jealous and get angry with human beings. We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the laws only nearly symmetrical so that we should not be jealous of His perfection!

We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the laws only nearly symmetrical so that we should not be jealous of His perfection!

In other words, symmetry is the preservation of the shape of an object even after we deform or rotate it. Several kinds of symmetries occur repeatedly in nature. The first is the symmetry of rotations and reflections.

Beauty, it seemed to Amineh, did not have to be extraordinary to be cherished. Maybe that was its secret, that it lived in the most common expressions of man and nature. The artisan had discovered it in a block of wood, which he had carved into a scene of a young woman sitting at a window. The locals had created it through the colorful geraniums they placed on small protrusions covering every square meter of their adobe walls. Even the animals were not immune. Who could doubt the starlings’ ecstatic flight around the minarets of the mosque was inspired by the symmetry of that aging structure.

In a word, it was wild, and somehow beautiful and desolate at the same time, a work which could not have been contrived by Nature or by Art alone, but by their combined efforts only, with Nature's chisel going over the often senselessly elaborate work of man, relieving the heaviness, obliterating the vulgar symmetry and the crude lapses which reveal the laboriousness of the planner's efforts, and thus communicating a miraculous warmth to something created in cold, measured neatness and precision.

There were things in nature that took their beauty from delicate structure and intricate symmetry. Flowers. Seashells. Butterfly wings. And then there were things that were beautiful for their wild power and their refusal to be tamed. Snowcapped mountains. Churning thunderclouds. Shaggy, sharp-toothed lions. This man silhouetted before her? He belonged, quite solidly, in the latter category.

The Goldberg Variations is a good example of how symmetry is not just a physical property but pervades many abstract structures.

The total entropy of any system, said Dr. Hauptmann, will decrease only if the entropy of another system will increase. Nature demands symmetry. Ordnung muss sein.

total entropy of any system, said Dr. Hauptmann, will decrease only if the entropy of another system will increase. Nature demands symmetry.

With this, in a powerful sense, our Question has been answered. The world, insofar as we speak of the world of Chemistry, biology, astrophysics, engineering, and everyday life, does embody beautiful ideas. The Core, which governs those domains, is profoundly rooted in concepts of symmetry and geometry, as we have seen. And it works its will, in quantum theory, through music-like rules. Symmetry really does determine structure. A pure and perfect Music of the Spheres really does animate the soul of reality. Plato and Pythagoras: We salute you!

For us, the great conclusion is this: all the colors can be obtained from any one of them, by motion, or, as we say, by making Galilean transformations. Because Galilean transformations are symmetries of the laws of Nature, any color is fully equivalent to any other. They all emerge as different views of the same thing, seen from different but equally valid perspectives.

Stone works with you. It reveals itself. But you must strike it right. Stone does not resent the chisel. It is not being violated. Its nature is to change. Each stone has its own character. It must be understood. Handle it carefully, or it will shatter. Never let stone destroy itself. Stone gives itself to skill and to love. To kicks and curses, to hurry and dislike, it closed a hard stone veil around its soft inner nature. It could be smashed by violence but never forced to fulfill. To sympathy, it yielded: grew even more luminous and sparkling, achieved fluid forms and symmetry.

The patterns of tiles created by the Moors are of secondary interest: it is the underlying group of symmetries which preserve aspects of the patterns that defines the geometry of the [Alhambra's] murals.

At his leisure, the lieutenant allowed the unforgettable spectacle to engrave itself upon his mind. With one hand he fondled the hair, with the other he softly stroked the magnificent face, implanting kisses here and there where his eyes lingered. The quiet coldness of the high, tapering forehead, the closed eyes with their long lashes beneath faintly etched brows, the set of the finely shaped nose, the gleam of teeth glimpsed between full, regular lips, the soft cheeks and the small, wise chin… Wherever the lieutenant's eyes moved his lips faithfully followed. The high, swelling breasts, surmounted by nipples like the buds of a wild cherry, hardened as the lieutenant's lips closed about them. The arms flowed smoothly downward from each side of the breast, tapering toward the wrists, yet losing nothing of their roundness or symmetry…The natural hollow curving between the bosom and the stomach carried in its lines a suggestion not only of softness but of resilient strength, and while it gave forewarning to the rich curves spreading outward from here to the hips it had, in itself, an appearance only of restraint and proper discipline. The whiteness and richness of the stomach and hips was like milk brimming in a great bowl, and the sharply shadowed dip of the navel could have been the fresh impress of a raindrop, fallen there that very moment. Where the shadows gathered more thickly, hair clustered, gentle and sensitive, and as the agitation mounted in the now no longer passive body there hung over this region a scent like the smoldering of fragrant blossoms, growing steadily more pervasive… Passionately they held their faces close, rubbing cheek against cheek…Their breasts, moist with sweat, were tightly joined, and every inch of the young and beautiful bodies had become so much one with the other that it seemed impossible there should ever again be a separation…From the heights they plunged into the abyss, and from the abyss they took wing and soared once more to dizzying heights…As one cycle ended, almost immediately a new wave of passion would be generated, and together -with no trace of fatigue- they would climb again in a single breathless movement to the very summit.

Out here in the forests, in the mountains, in the villages, they are supposed to be pulling up disorder by the root. The total entropy of any system, said Dr. Hauptmann, will decrease only if the entropy of another system will increase. Nature demands symmetry. Ordnung muss sein. And yet what order are they making out here? The suitcases, the queues, the wailing babies, the soldiers pouring back into the cities with eternity in their eyes–in what system is order increasing? Surely not in Kiev, or Lvov, or Warsaw. It’s all Hades.

Mythic Background Describing his approach to science, Einstein said something that sounds distinctly prescientific, and hearkens back to those ancient Greeks he admired: What really interests me is whether God had any choice in the creation of the world. Einstein's suggestion that God-or a world-making Artisan-might not have choices would have scandalized Newton or Maxwell. It fits very well, however, with the Pythagorean search for universal harmony, or with Plato's concept of a changeless Ideal. If the Artisan had no choice: Why not? What might constrain a world-making Artisan? One possibility arises if the Artisan is at heart an artist. Then the constraint is desire for beauty. I'd like to (and do) infer that Einstein thought along the line of our Question-Does the world embody beautiful ideas?-and put his faith in the answer "yes!" Beauty is a vague concept. But so, to begin with, were concepts like "force" and "energy." Through dialogue with Nature, scientists learned to refine the meaning of "force" and "energy," to bring their use into line with important aspects of reality. So too, by studying the Artisan's handiwork, we evolve refined concepts of "symmetry," and ultimately of "beauty"-concepts that reflect important aspects of reality, while remaining true to the spirit of their use in common language.

Through the works of Weinberg, Glashow, and Salam on the electroweak theory and the elegant framework developed by the physicists David Gross, David Politzer, and Frank Wilczek for quantum chromodynamics, the characteristic group of the standard model has been identified with a product of three Lie groups denoted by U(1), SU(2), and SU(3). In some sense, therefore, the road toward the ultimate unification of the forces of nature has to go through the discovery of the most suitable Lie group that contains the product U(1) X SU(2) x SU(3).

I also fell in love with Borges. He is a mathematician’s writer. His short stories are like mathematical proofs, delicately constructed and with ideas laced together effortlessly. Each step is taken with precision and watertight logic, yet the narrative is full of surprising twists and turns.

Today biologists believe that during the “Cambrian explosion,” about half a billion years ago, nature experimented with a vast array of shapes and forms for tiny, emerging multicellular creatures. Some had spinal cords shaped like an X, Y, or Z. Some had radial symmetry like a starfish. By accident one had a spinal cord shaped like an I, with bilateral symmetry, and it was the ancestor of most mammals on Earth. So in principle the humanoid shape with bilateral symmetry, the same shape that Hollywood uses to depict aliens in space, does not necessarily have to apply to all intelligent life.

By a constitutional policy, working after the pattern of nature, we receive, we hold, we transmit our government and our privileges, in the same manner in which we enjoy and transmit our property and our lives. The institutions of policy, the goods of fortune, the gifts of providence are handed down to us, and from us, in the same course and order. Our political system is placed in a just correspondence and symmetry with the order of the world, and with the mode of existence decreed to a permanent body composed of transitory parts; wherein, by the disposition of a stupendous wisdom, moulding together the great mysterious incorporation of the human race, the whole, at one time, is never old, or middle-aged, or young, but, in a condition of unchangeable constancy, moves on through the varied tenor of perpetual decay, fall, renovation, and progression. Thus, by preserving the method of nature in the conduct of the state, in what we improve, we are never wholly new. . . .

In 1940, the pacifist and mathematician Andre´ Weil, brother of the French philosopher Simone Weil, found himself in prison awaiting trial for desertion. During those months in Rouen prison, Weil produced one of the greatest discoveries of the twentieth century, on solving elliptic curves. He wrote to his wife: ‘My mathematics work is proceeding beyond my wildest hopes, and I am even a bit worried – if it is only in prison that I work so well, will I have to arrange to spend two or three months locked up every year?’ On hearing of his breakthrough, fellow mathematician Henri Cartan wrote back to Weil: ‘We’re not all lucky enough to sit and work undisturbed like you...

28. It is a capital evil with respect to the question We are discussing to take for granted that the one class of society is of itself hostile to the other, as if nature had set rich and poor against each other to fight fiercely in implacable war. This is so abhorrent to reason and truth that the exact opposite is true; for just as in the human body the different members harmonize with one another, whence arises that disposition of parts and proportion in the human figure rightly called symmetry, so likewise nature has commanded in the case of the State that the two classes mentioned should agree harmoniously and should properly form equally balanced counterparts to each other.

Art is neither good nor bad, but a clairvoyant vision of the nature of both, and any attempt to align it with morality, otherwise known as bowdlerizing,is intolerably vulgar...Unimaginative realism evokes only the smug pleasure of recognition.the painter becomes popular because he assures everyone else that he sees no more than they see...Art is suggestive rather than explicit: it makes no attempt to persuade into general agreement or provide mediocre levels of explanation...the bold imagination produces great art; the timid one small art. But the healthy eye does not see more broadly and vaguely than the weak eye; it sees more clearly...a real miracle is an imaginative effort which meets with an imaginative response.

The use of spontaneous symmetry breaking in a fundamental theory was to have profound consequences, not just for the laws of nature but for the larger question of what a law of nature is. Before this, it was thought that the properties of the elementary particles are determined directly by eternally given laws of nature. But in a theory with spontaneous symmetry breaking, a new element enters, which is that the properties of the elementary particles depend in part on history and environment. The symmetry may break in different ways, depending on conditions like density and temperature. More generally, the properties of the elementary particles depend not just on the equations of the theory but on which solution to those equations applies to our universe.

Energy: vibrant color and light Abundance: lushness, multiplicity, and variety Freedom: nature, wildness, and open space Harmony: balance, symmetry, and flow Play: circles, spheres, and bubbly forms Surprise: contrast and whimsy Transcendence: elevation and lightness Magic: invisible forces and illusions Celebration: synchrony, sparkle, and bursting shapes Renewal: blossoming, expansion, and curves

At the moment of the Big Bang, an entire universe came into existence, and with it space. It all inflated, just like a balloon being blown up. So where did all this energy and space come from? How does an entire universe full of energy, the awesome vastness of space and everything in it, simply appear out of nothing? For some, this is where God comes back into the picture. It was God who created the energy and space. The Big Bang was the moment of creation. But science tells a different story. At the risk of getting myself into trouble, I think we can understand much more the natural phenomena that terrified the Vikings. We can even go beyond the beautiful symmetry of energy and matter discovered by Einstein. We can use the laws of nature to address the very origins of the universe, and discover if the existence of God is the only way to explain it.

WHY WAS A BEAUTIFUL YOUNG WOMAN SUCH A BIG DEAL? Beauty was a sign of health and reproductive capability; thus, a beautiful woman historically had wide hips (for childbearing), body symmetry (indicating no deformities), hair and teeth that weren’t falling out (indicating health). And she was young—at the beginning of her fertile years. Society needed to reinforce men’s biological dependency on female beauty for the same reasons it needed to make women dependent on male income: dependency created an incentive to marry. A man who was addicted to a woman’s beauty, youth, and sex would temporarily “lose his mind”—he would make the irrational decision to support her for the rest of his life. Female beauty, then, can be thought of as nature’s marketing tool: the way of marketing a woman for the survival of her genes.42 Which is why female beauty is the world’s most potent drug.

The swirling lines of snow were composed of separate flakes, and each flake was a cluster of separate ice crystals--scientists had counted over a hundred of them in a single flake. Under the microscope each minuscule crystal, colorless and transparent, revealed a secret symmetry: six sides, the outward expression of an inward geometry of frozen molecules of water. But the real wonder was that no two crystals were precisely alike. In one of this father's camera magazines he had seen a stunning display of photomicrographs, and what was most amazing about the enlarged crystals was that each contained in its center a whole world of intricate six-sided designs, caused by microscopic air pockets. For no conceivable reason, Nature in a kind of exuberance created an inexhaustible outpouring of variations on a single form. A snowstorm was a fall of jewels, a delirium of hexagons--clearly the work of a master animator.

No salvation comes from exhumed gods; we must penetrate deeper into substance. If I take a fossil, say, a trilobite, in my hand (marvelously preserved specimens are found in the quarries at the foot of the Casbah), I am transfixed by the impact of mathematical harmony. Purpose and beauty, as fresh as on the first day, are still seamlessly united in a medal engraved by a master's hand. The bios must have discovered the secret of tripartition in this primordial crab. Tripartition then frequently recurs, even without any natural kinship; figures, in transversal symmetry, dwell in the triptych. How many millions of years ago might this creature have animated an ocean that no longer exists? I hold its impression, a seal of imperishable beauty, in my hand. Some day, this seal, too, will decay or else burn out in cosmic conflagrations of the future. The matrix that formed it remains concealed in and operative from the law, untouched by death or fire.

But why are we attracted to symmetry? Why do we human beings delight in seeing perfectly round planets through the lens of a telescope and six-sided snowflakes on a cold winter day? The answer must be partly psychological. I would claim that symmetry represents order, and we crave order in this strange universe we find ourselves in. The search for symmetry, and the emotional pleasure we derive when we find it, must help us make sense of the the seasons and the reliability of friendships. Symmetry is also economy. Symmetry is simplicity.

I identified ten aesthetics of joy, each of which reveals a distinct connection between the feeling of joy and the tangible qualities of the world around us: Energy: vibrant color and light Abundance: lushness, multiplicity, and variety Freedom: nature, wildness, and open space Harmony: balance, symmetry, and flow Play: circles, spheres, and bubbly forms Surprise: contrast and whimsy Transcendence: elevation and lightness Magic: invisible forces and illusions Celebration: synchrony, sparkle, and bursting shapes Renewal: blossoming, expansion, and curves

The current leading candidates for dark matter are particles predicted to exist from supersymmetric theories, extensions of current particle physics that include a new symmetry of Nature. The reader may recognize the “super” in supersymmetry from superstring theory, a candidate theory for unifying general relativity and quantum mechanics. As of the winter of 2014, no evidence for supersymmetry had been found, despite decades of intense search and the enthusiastic support of many physicists. At this point, it is unclear and somewhat doubtful that supersymmetry is realized in Nature.

Even from the standpoint of the skeptic, a reasonable and candid search into the unknown, by the light of what is known, will guide the unbiased, intelligent reasoner in the direction of the truth. Yet it is evident that without a direct revelation of the plans and purposes of God, men could only approximate the truth, and arrive at indefinite conclusions. But let us for the moment lay aside the Bible, and look at things from the standpoint of reason alone. He who can look into the sky with a telescope, or even with his natural eye alone, and see the immensity of creation, its symmetry, beauty, order, harmony and diversity, and yet doubt that the Creator of these is vastly his superior both in wisdom and power, or who can suppose for a moment that such order came by chance, without a Creator, has so far lost or ignored the faculty of reason as to be properly considered what the Bible terms him, a fool (one who ignores or lacks reason): 'The fool hath said in his heart, There is no God.' However it happened, at least that much of the Bible is true, as every reasonable mind must conclude; for it is a self-evident truth that effects must be produced by competent causes.

Galois's ideas, with all their brilliance, did not appear out of thin air. They addressed a problem whose roots could be traced all the way back to ancient Babylon. Still, the revolution that Galois had started grouped together entire domains that were previously unrelated. Much like the Cambrian explosion-that stunning burst of diversification in life forms on Earth-the abstraction of group theory opened windows into an infinity of truths. Fields as far apart as the laws of nature and music suddenly became mysteriously connected. The Tower of Babel of symmetries miraculously fused into a single language.

We have posited that the fundamental theory is background independent, which means there are no symmetries. This in turn means that we cannot regard energy and momentum, and their conservation, as emergent from the properties of space. But we still have to explain why energy and momentum play the ubiquitous role they do in the structure of the equations of physics. Further, we have hypothesized that space is not present at the fundamental level in nature, but is emergent. So if we want energy and momentum to play a role in physics, there seems to be no alternative but to put them in at the beginning. What we want

the architecture of our brains was born from the same trial and error, the same energy principles, the same pure mathematics that happen in flowers and jellyfish and Higgs particles. Viewed in this way, our human aesthetic is necessarily the aesthetic of nature. Viewed in this way, it is nonsensical to ask why we find nature beautiful. Beauty and symmetry and minimum principles are not qualities we ascribe to the cosmos and then marvel at in their perfection. They are simply what is, just like the particular arrangement of atoms that make up our minds. We are not observers on the outside looking in. We are on the inside too.

Time is inexplicable because it moves – clicks away – at steady increments, while increasing the past and bringing the future into the present. Time has a necessary affinity with both heaven and the earthly reality. ‘Pythagoras, when he was asked what time was, answered that it is the soul of the world.’ Plato said that time and heaven must be coexistent. Without time nothing can be created or generated in the universe, nor is anything intelligible without eternity. Time is no accident or affection, but the cause, power, and principle of the symmetry and order that confines all created beings, by which the animated nature of the universe moves.

A good example of the archetypal ideas which the archetypes produce are natural numbers or integers. With the aid of the integers the shaping and ordering of our experiences becomes exact. Another example is mathematical group theory. ...important applications of group theory are symmetries which can be found in most different connections both in nature and among the 'artifacts' produced by human beings. Group theory also has important applications in mathematics and mathematical physics. For example, the theory of elementary particles and their interactions can in essential respects be reduced to abstract symmetries. [The Message of the Atoms: Essays on Wolfgang Pauli and the Unspeakable]

A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.

The gnarled pine, I would have said, touch it. This is China. Horticulturalists around the world have come to study it. Yet no one has ever been able to explain why it grows like a corkscrew, just as no one can adequately explain China. But like that tree, there it is, old, resilient, and oddly magnificent. Within that tree are the elements in nature that have inspired Chinese artists for centuries: gesture over geometry, subtlety over symmetry, constant flow over static form. And the temples, walk and touch them. This is China. Don't merely stare at these murals and statues. Fly up to the crossbeams, get down on your hands and knees, and press your head to the floor tiles. Hide behind that pillar and come eye to eye with its flecks of paint. Imagine that you are the interior decorator who is a thousand years in age. Start with a bit of Tibetan Buddhism, plus a dash each of animism and Taoism. A hodgepodge, you say? No, what is in those temples is an amalgam that is pure Chinese, a lovely shabby elegance, a glorious new motley that makes China infinitely intriguing. Nothing is ever completely thrown away and replaced. If one period of influence falls out of favor, it is patched over. The old views still exist, one chipped layer beneath, ready to pop through with the slightest abrasion. That is the Chinese aesthetic and also its spirit. Those are the traces that have affected all who have traveled along China's roads.

The forces of nature are color blind. Just as an infinite chessboard would look the same if we interchanged black and white, the force between a green quark and a red quark is the same as that between two blue quarks, or a blue quark and a green quark. Even if we were to use our quantum mechanical "palette" and replace each of the "pure" color states with a mixed-color state (e.g., "yellow" representing a mixture of red and green or "cyan" for a blue-green mixture), the laws of nature would still take the same form. The laws are symmetric under any color transformation. Furthermore, the color symmetry is again a gauge symmetry-the laws of nature do not care if the colors or color assortments vary from position to position or from one moment to the next.

Perhaps the heritability of IQ implies something entirely different, something that once and for all proves that Galton’s attempt to discriminate between nature and nurture is misconceived. Consider this apparently fatuous fact. People with high IQ s, on average, have more symmetrical ears than people with low IQ s. Their whole bodies seem to be more symmetrical: foot breadth, ankle breadth, finger length, wrist breadth and elbow breadth each correlates with IQ. In the early 1990s there was revived an old interest in bodily symmetry, because of what it can reveal about the body’s development during early life. Some asymmetries in the body are consistent: the heart is on the left side of the chest, for example, in most people. But other, smaller asymmetries can go randomly in either direction. In some people the left ear is larger than the right; in others, vice versa. The magnitude of this so-called fluctuating asymmetry is a sensitive measure of how much stress the body was under when developing, stress from infections, toxins or poor nutrition. The fact that people with high IQs have more symmetrical bodies suggests that they were subject to fewer developmental stresses in the womb or in childhood. Or rather, that they were more resistant to such stresses. And the resistance may well be heritable. So the heritability of IQ might not be caused by direct ‘genes for intelligence’ at all, but by indirect genes for resistance to toxins or infections – genes in other words that work by interacting with the environment. You inherit not your IQ but your ability to develop a high IQ under certain environmental circumstances. How does one parcel that one into nature and nurture? It is frankly impossible.

The realization that symmetry is the key to the understanding of the properties of subatomic particles led to an inevitable question: Is there an efficient way to characterize all of these symmetries of the laws of nature? Or, more specifically, what is the basic theory of transformations that can continuously change one mixture of particles into another and produce the observed families? By now you have probably guessed the answer. The profound truth in the phrase I have cited earlier in this book revealed itself once again: "Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos." The physicists of the 1960s were thrilled to discover that mathematicians had already paved the way. Just as fifty years earlier Einstein learned about the geometry tool-kit prepared by Riemann, Gell-Mann and Ne'eman stumbled upon the impressive group-theoretical work of Sophus Lie.

The beauty of the principle idea of string theory is that all the known elementary particles are supposed to represent merely different vibration modes of the same basic string. Just as a violin or a guitar string can be plucked to produce different harmonics, different vibrational patterns of a basic string correspond to distinct matter particles, such as electrons and quarks. The same applies to the force carriers as well. Messenger particles such as gluons or the W and Z owe their existence to yet other harmonics. Put simply, all the matter and force particles of the standard model are part of the repertoire that strings can play. Most impressively, however, a particular configuration of vibrating string was found to have properties that match precisely the graviton-the anticipated messenger of the gravitational force. This was the first time that the four basic forces of nature have been housed, if tentatively, under one roof.

The evidence of cheetah genetic monotony would only grow. Bob Wayne, a talented postdoctoral fellow in our lab, examined cranial measurements and the bilateral symmetry of cheetah skulls. Although no one is certain why, in most livestock, asymmetry in skeletal characteristics (the difference between right and left measures of a trait) increases with inbreeding. Bob measured sixteen bilateral traits in thirty-three cheetah skulls held in natural history museums in Washington, Chicago, and New York. The study was not perfect because several of the skulls were incomplete due to a bullet hole in the skull. Nonetheless, in nearly every case, cheetah skulls were more asymmetric compared to the skulls of leopards, ocelots, or margays. When I explained these skull results in a television interview, the correspondent asked, "Dr. O'Brien, are you telling me that these cheetahs are lopsided?" Not exactly, but the cheetahs certainly looked very inbred.

All our puzzles about whether or not lambda exists and, if so, what is responsible for giving it such a strange value, are like questions about the inflationary scalar field's potential landscape. Why is its final vacuum state so fantastically close to the zero line? How does it 'know' where to end up when the scalar field starts rolling downhill in its landscape? Nobody knows the answer to these questions. They are the greatest unsolved problems in gravitation physics and astronomy. The nature of their answers could take many forms. There could exist some deep new principle that links together all the different forces of Nature in a way that dictates the vacuum levels of all the fields of energy that feel their effects. This principle would be unlike any that we know because it would need to control all the possible contributions to lambda that arise at symmetry breakings during the expansion of the Universe. It would need to control physics over a vast range of energies.

But my grandmother, in all weathers, even when the rain was coming down in torrents and Françoise had rushed the precious wicker armchairs indoors so that they should not have soaked, was to be seen pacing the desert rain-lashed garden, pushing back her disordered grey locks so that her forehead might be freer to absorb the health-giving draughts of wind and rain. She would say, "At last one can breathe!" and would trot up and down the sodden paths—too straight and symmetrical for her liking, owing to the want of any feeling for nature in the new gardener, whom my father had been asking all morning if the weather were going to improve—her keen, jerky little step regulated by the various effects wrought upon her soul by the intoxication of the storm, the power of hygiene, the stupidity of my upbringing and the symmetry of gardens, rather than by any anxiety (for that was quite unknown to her) to save her plum-coloured skirt from the mudstains which it would gradually disappear to a height that was the constant bane and despair of her maid.

The German mathematician Emmy Noether proved in 1915 that each continuous symmetry of our mathematical structure leads to a so-called conservation law of physics, whereby some quantity is guaranteed to stay constant-and thereby has the sort of permanence that might make self-aware observers take note of it and give it a "baggage" name. All the conserved quantities that we discussed in Chapter 7 correspond to such symmetries: for example, energy corresponds to time-translation symmetry (that our laws of physics stay the same for all time), momentum corresponds to space-translation symmetry (that the laws are the same everywhere), angular momentum corresponds to rotation symmetry (that empty space has no special "up" direction) and electric charge corresponds to a certain symmetry of quantum mechanics. The Hungarian physicist Eugene Wigner went on to show that these symmetries also dictated all the quantum properties that particles can have, including mass and spin. In other words, between the two of them, Noether and Wigner showed that, at least in our own mathematical structure, studying the symmetries reveals what sort of "stuff" can exist in it.

The only streetlights burning were those at the top of the stairs and the light they gave fell in dingy cones that shuddered in the intermittent gusts of winds assailing them because the other neon lights positioned in the thirty or so meters between them had all been broken, leaving them squatting in darkness, yet as aware of each other, of their precise positions, as of the enormous mass of dark sky above the smashed neon, the sky which might have glimpsed the reflection of its own enormous dark mass as it trembled with stars in the vista of railway yards spreading below it, had there been some relationship between the trembling stars and the twinkling dull red lights of semaphores sprinkled among the rails, but there wasn't, there was no common denominator, no interdependence between them, the only order and relationship existing within the discrete worlds of above and below, and indeed of anywhere, for the field of stars and the forest of signals stared as blankly at each other as does each and every form of being, blind in darkness and blind in radiance, as blind on earth as it is in heaven, if only so that a long moribund symmetry among this vastness might appear in the lost glance of some higher being, at the center of which, naturally, there would be a minuscule blind spot: as with Korin . . . the footbridge . . . the seven kids.

One of the string theory pioneers, the Italian physicist Daniele Amati, characterized it as "part of the 21st century that fell by chance into the 20th century." Indeed, there is something about the very nature of the theory at present that points to the fact that we are witnessing the theory's baby steps. Recall the lesson learned from all the great ideas since Einstein's relativity-put the symmetry first. Symmetry originates the forces. The equivalence principle-the expectation that all observers, irrespective of their motions, would deduce the same laws-requires the existence of gravity. The gauge symmetries-the fact that the laws do not distinguish color, or electrons from neutrinos-dictate the existence of the messengers of the strong and electroweak forces. Yet supersymmetry is an output of string theory, a consequence of its structure rather than a source for its existence. What does this mean? Many string theorists believe that some underlying grander principle, which will necessitate the existence of string theory, is still to be found. If history is to repeat itself, then this principle may turn out to involve an all-encompassing and even more compelling symmetry, but at the moment no one has a clue what this principle might be. Since, however, we are only at the beginning of the twenty-first century, Amati's characterization may still turn out to be an astonishing prophecy.

This was undoubtedly one of symmetry's greatest success stories. Glashow, Wienberg, and Salam managed to unmask the electromagnetic and weak forces by recognizing that underneath the differences in the strengths of these two forces (the electromagnetic force is about a hundred thousand times stronger within the nucleus) and the different masses of the messenger particles lay a remarkable symmetry. The forces of nature take the same form if electrons are interchanged with neutrinos or with any mixture of the two. The same is true when photons are interchanged with the W and Z force-messengers. The symmetry persists even if the mixtures vary from place to place or from time to time. The invariance of the laws under such transformations performed locally in space and time has become known as gauge symmetry. In the professional jargon, a gauge transformation represents a freedom in formulating the theory that has no directly observable effects-in other words, a transformation to which the physical interpretation is insensitive. Just as the symmetry of the laws of nature under any change of the spacetime coordinates requires the existence of gravity, the gauge symmetry between electrons and neutrinos requires the existence of the photons and the W and Z messenger particles. Once again, when the symmetry is put first, the laws practically write themselves. A similar phenomenon, with symmetry dictating the presence of new particle fields, repeats itself with the strong nuclear force.

The world is made of fields—substances spread through all of space that we notice through their vibrations, which appear to us as particles. The electric field and the gravitational field might seem familiar, but according to quantum field theory even particles like electrons and quarks are really vibrations in certain kinds of fields. • The Higgs boson is a vibration in the Higgs field, just as a photon of light is a vibration in the electromagnetic field. • The four famous forces of nature arise from symmetries—changes we can make to a situation without changing anything important about what happens. (Yes, it makes no immediate sense that “a change that doesn’t make a difference” leads directly to “a force of nature” . . . but that was one of the startling insights of twentieth-century physics.) • Symmetries are sometimes hidden and therefore invisible to us. Physicists often say that hidden symmetries are “broken,” but they’re still there in the underlying laws of physics—they’re simply disguised in the immediately observable world. • The weak nuclear force, in particular, is based on a certain kind of symmetry. If that symmetry were unbroken, it would be impossible for elementary particles to have mass. They would all zip around at the speed of light. • But most elementary particles do have mass, and they don’t zip around at the speed of light. Therefore, the symmetry of the weak interactions must be broken. • When space is completely empty, most fields are turned off, set to zero. If a field is not zero in empty space, it can break a symmetry. In the case of the weak interactions, that’s the job of the Higgs field. Without it, the universe would be an utterly different place.   Got

The moral here is that nature and nurture should not be opposed. Pure learning, in the absence of any innate constraints, simply does not exist. Any learning algorithm contains, in one way or another, a set of assumptions about the domain to be learned. Rather than trying to learn everything from scratch, it is much more effective to rely on prior assumptions that clearly delineate the basic laws of the domain that must be explored, and integrate these laws into the very architecture of the system. The more innate assumptions there are, the faster learning is (provided, of course, that these assumptions are correct!). This is universally true. It would be wrong, for example, to think that the AlphaGo Zero software, which trained itself in Go by playing against itself, started from nothing: its initial representation included, among other things, knowledge of the topography and symmetries of the game, which divided the search space by a factor of eight. Our brain too is molded with assumptions of all kinds. Shortly, we will see that, at birth, babies' brains are already organized and knowledgeable. They know, implicitly, that the world is made of things that move only when pushed, without ever interpenetrating each other (solid objects)—and also that it contains much stranger entities that speak and move by themselves (people). No need to learn these laws: since they are true everywhere humans live, our genome hardwires them into the brain, thus constraining and speeding up learning. Babies do not have to learn everything about the world: their brains are full of innate constraints, and only the specific parameters that vary unpredictably (such as face shape, eye color, tone of voice, and individual tastes of the people around them) remain to be acquired.

Those minutes were the beginning of his abandoning himself to a very strange kind of devotion, such a reeling, intoxicated sensation that the proud and portentous word ‘love’ is not quite right for it. It was that faithful, dog-like devotion without desire that those in mid-life seldom feel, and is known only to the very young and the very old. A love devoid of any deliberation, not thinking but only dreaming. He entirely forgot the unjust yet ineradicable disdain that even the clever and considerate show to those who wear a waiter’s tailcoat, he did not look for opportunities and chance meetings, but nurtured this strange affection in his blood until its secret fervour was beyond all mockery and criticism. His love was not a matter of secret winks and lurking glances, the sudden boldness of audacious gestures, the senseless ardour of salivating lips and trembling hands; it was quiet toil, the performance of those small services that are all the more sacred and sublime in their humility because they are intended to go unnoticed. After the evening meal he smoothed out the crumpled folds of the tablecloth where she had been sitting with tender, caressing fingers, as one would stroke a beloved woman’s soft hands at rest; he adjusted everything close to her with devout symmetry, as if he were preparing it for a special occasion. He carefully carried the glasses that her lips had touched up to his own small, musty attic bedroom, and watched them sparkle like precious jewellery by night when the moonlight streamed in. He was always to be found in some corner, secretly attentive to her as she strolled and walked about. He drank in what she said as you might relish a sweet, fragrantly intoxicating wine on the tongue, and responded to every one of her words and orders as eagerly as children run to catch a ball flying through the air. So his intoxicated soul brought an ever-changing , rich glow into his dull, ordinary life. The wise folly of clothing the whole experience in the cold, destructive words of reality was an idea that never entered his mind: the poor waiter François was in love with an exotic Baroness who would be for ever unattainable. For he did not think of her as reality, but as something very distant, very high above him, sufficient in its mere reflection of life. He loved the imperious pride of her orders, the commanding arch of her black eyebrows that almost touched one another, the wilful lines around her small mouth, the confident grace of her bearing. Subservience seemed to him quite natural, and he felt the humiliating intimacy of menial labour as good fortune, because it enabled him to step so often into the magic circle that surrounded her.

Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.

As we just saw, some concepts such as symmetries retain their central status. In contrast, other concepts, such as initial conditions, complexity and randomness, get reinterpreted as mere illusions, existing only in the mind of the beholder and not in the external physical reality.

The deep question is: Why does nature embody so much symmetry? We do not know the full answer to this question. However, we have some partial answers. Symmetry leads to economy, and nature, like human beings, seems to prefer economy. If we think of nature as a vast ongoing experiment, constantly trying out different possibilities of design, then those designs that cost the least energy or that require the fewest different parts to come together at the right time will take precedence, just as the principle of natural selection says that organisms with the best ability to survive will dominate over time. One physical principle that governs nature over and over is the “energy principle”: nature evolves to minimize energy.

Music and sound have persisted, whether we have focused on them or not. They are part and parcel with the universe. The symmetry of musical composition mirrors the symmetry that exists in quantum fields, and the breaking of these symmetries in both cases lends beautiful complexity. In physics we get the distinct forces of nature with symmetry breaking, in music we get tension and resolve.

Galois did not have a clear vision of the possible shapes lurking behind an equation, or of why the language he was developing would help reveal the symmetry of those shapes. Perhaps it was just as well, because the power of the language lay in its ability to create an abstraction – a mathematical description that was independent of any underlying geometry. What Galois could see was that every equation would have its own collection of permutations of the solutions which would preserve the laws relating these solutions, and that analysing the collection of permutations together revealed the secrets of each equation. He called this collection ‘the group’ of permutations associated with the equation. Galois discovered that it was the particular way in which these permutations interacted with each other that indicated whether an equation could be solved or not.

Although the collection of known mathematical structures is large and exotic, and even more remain to be discovered, every single mathematical structure can be analyzed to determine its symmetry properties, and many have interesting symmetry. Intriguingly, one of the most important discoveries in physics has been that our physical reality also has symmetries built into it: for example, the laws of physics have rotational symmetry, which means that there's not special direction in our Universe that you can call "up." They also appear to have translation (sideways shifting) symmetry, meaning that there's no special place that we can call the center of space. Many of these spaces just mentioned have beautiful symmetries, some of which match the observed symmetries of our physical world. For example, Euclidean space has both rotational symmetry (meaning that you can't tell the difference if the space gets rotated) and translational symmetry (meaning that you can't tell the difference if the space gets shifted sideways). The four-dimensional Minkowski space has even more symmetry: you can't even tell the difference if you do a type of generalized rotation between the space and time dimensions-and Einstein showed that this explains why time appears to slow down if you travel near the speed of light, as mentioned in the last chapter. Many more subtle symmetries of nature have been discovered in the last century, and these symmetries form the foundations of Einstein's relativity theories, quantum mechanics, and the standard model of particle physics.

One of Nature's deep secrets is the fact that the outcomes of the laws of Nature do not have to possess the same symmetries as the laws themselves. The outcomes are far more complicated, and far less symmetrical, than the laws. Consequently, they are far more difficult to understand. In this way it is possible to have a Universe governed by a very small number of simple symmetrical laws (perhaps just a single law) yet manifesting a stupendous array of complex, asymmetrical states and structures that might even be able to think about themselves.

Complexity is a delicate business. Chemical and molecular bonds require a particular range of temperature in which to operate. Liquid water exists over a mere one hundred degree range on the centigrade scale. Even Earth-based life is concentrated towards particular climatic zones. The temperature at the Earth's surface keeps it tantalizingly balanced between recurrent ice ages and the roasting that results from a runaway greenhouse effect. Very slight differences in the size of our planet or its distance from the Sun would have tipped the scales irretrievably towards one or other of these fates. That such a delicate balance, which is essentially the outcome of those random symmetry-breakings that we discussed in Chapter 6, should be so crucial suggests that natural complexity may be a rather rare thing in the Universe.

Nature deals in non-uniform shapes and rough edges. Take the human form. There is a certain symmetry about it, but it is, and has always been, indescribable in terms of Euclidean geometry.

THE work of deciding cases goes on every day in hundreds of courts throughout the land. Any judge, one might suppose, would find it easy to describe the process which he had followed a thousand times and more. Nothing could be farther from the truth. Let some intelligent layman ask him to explain:  he will not go very far before taking refuge in the excuse that the language of craftsmen is unintelligible to those untutored in the craft. Such an excuse may cover with a semblance of respectability an otherwise ignominious retreat. It will hardly serve to still the pricks of curiosity and conscience. In moments of introspection, when there {10} is no longer a necessity of putting off with a show of wisdom the uninitiated interlocutor, the troublesome problem will recur, and press for a solution. What is it that I do when I decide a case? To what sources of information do I appeal for guidance? In what proportions do I permit them to contribute to the result? In what proportions ought they to contribute? If a precedent is applicable, when do I refuse to follow it? If no precedent is applicable, how do I reach the rule that will make a precedent for the future? If I am seeking logical consistency, the symmetry of the legal structure, how far shall I seek it? At what point shall the quest be halted by some discrepant custom, by some consideration of the social welfare, by my own or the common standards of justice and morals? Into that strange compound which is brewed daily in the caldron of the courts, all these ingredients enter in varying proportions. I am not concerned to inquire whether judges ought to be allowed to brew such a compound at all. I take judge-made law as one of the existing realities of life. There, before us, {11} is the brew. Not a judge on the bench but has had a hand in the making.

Animated, released from stillness by the rain, Dendroalsia begins to move, branch by delicate branch unfolding to recreate the symmetry of overlapping fronds. As each stem uncurls, its tender center is exposed and all along the midline are tiny capsules, bursting with spores. Ready for rain, they release their daughters upon the updrafts of rising mist. The oaks once more are lush and green and the air smells rich with the breath of mosses.

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst...

Even now as I look back, I marvel at the perfect pyramid of his logic, nuances that effortlessly filled the cracks, the elegantly simple foundation. His answer made a fool of Occam, had the natural symmetry of algebra.

quite match the beginning. And so we have, suddenly, because of this symmetry-breaking ‘mis-step’, something that is mobile, three-dimensional, endlessly generative, while never being wholly predictable (because always moving onward into a new realm of space, not residing always in the old one). It replaces something atemporal, two-dimensional, repetitive, and entirely regular, namely a circle. All the same, viewed down the axis of the spiral it still has the eternally unchanging quality of the circle – particle-like: though viewed from the side it has an oscillatory or vibratory movement, wave-like, changing, progressing and alive. Fractals, though quite different in nature, have this in common with spirals, that they generate difference that is also a kind of sameness.

Another significant factor in sexual attraction is scent. Th e other person’s smell— that is, his or her natural body scent mixed with the lingering smells of the day— plays a major role in drawing people together and finding optimal partners. Some people report that they know right away from his or her smell that a person is the one for them, and of course conversely some conclude that his or her body odor is a “deal-breaker.” (For a discussion of pheromones, see Chapter 3.) Psychologist Rachel Herz, author of the book Th e Scent of Desire: Discovering Our Enigmatic Sense of Smell (2007), states that “body odor is an external manifestation of the immune system and smells we think are attractive come from people who are most genetically compatible with us” (quoted in Svoboda, 2008). Interestingly, from what we discussed above about symmetry, men and women whose body odors are judged to be sexy by others are also more likely to have symmetrical faces. So, it seems that finding a person with a pleasing body odor is essential. People who want to find out their partners’ true scent can go fragrance-free for a few days. Th ey may worry about their own scent, and some people may indeed not like it, but there will always be persons who will be attracted to their natural body odor (Fisher, 2009; Herz, 2007; Martins et al. 2005; Moalem, 2009; Svoboda, 2009).

First, gravity and quantum mechanics are part and parcel of how the universe works and therefore any purported unified theory must incorporate both. String theory accomplishes this. Second, studies by physicists over the past century have revealed that there are other key ideas—many of which have been experimentally confirmed—that appear central to our understanding of the universe. These include the concepts of spin, the family structure of matter particles, messenger particles, gauge symmetry, the equivalence principle, symmetry breaking, and supersymmetry, to name a few. All of these concepts emerge naturally from string theory. Third, unlike more conventional theories such as the standard model, which has 19 free parameters that can be adjusted to ensure agreement with experimental measurements, string theory has no adjustable parameters. In principle, its implications should be thoroughly definitive—they should provide an unambiguous test of whether the theory is right or wrong.

When we pass from the fluids to their associated subatomic particles, or quanta, we realize that the existence of gravitons, photons, weakons, and color gluons-the quanta of the metric, electromagnetic, weak, and strong fluids, respectively-and their properties, are unavoidable and unique consequences of various local symmetries. The usual jargon for those local symmetries, in the physics literature, is: General covariance, for the local version of special relativity U(1) gauge symmetry, for the local version of rotation in electric charge property space SU(2) gauge symmetry, for the local version of rotation in weak charge property space SU(3) gauge symmetry, for the local version of rotation in strong charge property space

AN ANSWER TO OUR QUESTION Places of worship embody the aspirations of their architects, and the communities they represent, to ideal beauty. Their chosen means of expression feature color, geometry, and symmetry. Consider, in particular. the magnificent plate HH. Here the local geometry of the ambient surfaces and the local patterns of their color change as our gaze surveys them. It is a vibrant embodiment of anamorphy and anachromy-the very themes that our unveiling of Nature's deep design finds embodied at Nature's core. Does the world embody beautiful ideas? There is our answer, before our eyes: Yes. Color and geometry, symmetry, anachromy, and anamorphy, as ends in themselves, are only one branch of artistic beauty. Islam's injunction against representational art played an important part in bringing these forms of beauty to the fore, as did the physical constraint of structural stability (we need columns to support the weight of ceilings, and the arches and domes to distribute tension). Depictions of human faces, bodies, emotions, landscapes, historic scenes, and the like, when they are allowed, are far more common subjects for art than those austere beauties. The world does not, in its deep design, embody all forms of beauty, nor the ones that people without special study, or very unusual taste, find most appealing. But the world does, in its deep design, embody some forms of beauty that have been highly prized for their own sake, and have been intuitively associated with the divine.

In short: by imagining a space-filling fluid, and allowing for its possible effects, we are able to consider a wide variety of transformed images as representations of the same scene, viewed through different states of the fluid. In a similar way, by introducing just the right kind of material into space-time, Einstein was able to allow the distortions of physical law, which are introduced by Galilean transformations that vary in space and time, to be accomplished as modifications of a new material. That material is called the metric field or, as I prefer to say, metric fluid. The expanded system, containing the original world plus a hypothetical new material, obeys laws that remain the same even when we make variable changes in velocity, though the state of the metric fluid changes. In other words, the equations for the expanded system can support our huge, "outrageous" local symmetry. We might expect that systems of equations that support such an enormous amount of symmetry are very special, and hard to come by. The new material must have just the right properties. Equations with such enormous symmetry are the analogue of the Platonic solids-or, better, the spheres-among equations!

In fact, Einstein proceeded to turn the argument around, by showing that one could derive the complete system of four Maxwell equations from one of them, by making Galilean transformations to recover the general case. (By putting charge in motion, you get currents, and by putting electric fields in motion, you get magnetic fields. Thus the law governing how unmoving electric charges generate electric fields, after Galilean transformations, gives the general case.) That profound trick was a taste of the future. Symmetry, rather than a deduction from given laws, became a primary principle, with a life of its own. One can constrain the laws by requiring them to have symmetry.

Western science has made nature intelligible in terms of its symmetries and regularities, analyzing its most wayward forms into components of a regular and measurable shape. As a result we tend to see nature and to deal with it as an "order" from which the element of spontaneity has been "screened out." But this order is maya, and the "true suchness" of things has nothing in common with the purely conceptual aridities of perfect squares, circles, or triangles - except by spontaneous accident. Yet this is why the Western mind is dismayed when ordered conceptions of of the universe break down. and when the basic behavior of the physical world is found to be a "principle of uncertainty.

Dandy, I thought. When it gets too hot, the earth freezes over. Makes sense, though. A perfect incongruous symmetry. If life is filled with ironies, why shouldn’t nature be? Hard work leads to coronaries, love to heartbreak of another kind, life to death. As night follows day, sorrow follows joy. The affluent, many of whom labored mightily to get there, spawn indolent children. The kid from the ghetto gets an Ivy League scholarship, then is cut down in a gang fight at home. The rich get richer, the poor get poorer, and the meek shall inherit the shit.

The most general law in nature is equity-the principle of balance and symmetry which guides the growth of forms along the lines of the greatest structural efficiency.

THE TWO NEW HOUSES BY CAROLYN WELLS Once on a Time, there were Two Men, each of whom decided to build for himself a Fine, New House. One Man, being of an Arrogant and Conceited Nature, took counsel of Nobody, but declared that he would build his House to suit himself. "For," said he, "since it is My House and I am to Live in It, why should I ask the Advice of my Neighbors as to its Construction?" While the House was Building, the Neighbors came often and Looked at it, and went away, Whispering and Wagging their Heads in Derision. But the Man paid no Heed, and continued to build his House as he Would. The Result was that, when completed, his House was lacking in Symmetry and Utility, and in a Hundred ways it was Unsatisfactory, and for each Defect there was a Neighbor who said, "Had you asked Me, I would have Warned you against that Error." The Other Man, who was of a Humble and Docile Mind, went to Each of his Neighbors in Turn, and asked Advice about the Building of his House. His Friends willingly and at Great Length gave him the Benefit of their Experiences and Opinions, and the Grateful Man undertook to Follow Out all their Directions. The Result was that his House, when finished, was a Hodge-Podge of Varying Styles and Contradictory Effects, and Exceedingly Uncomfortable and Inconvenient to Live In. MORALS:

The phenomenon of symmetry breaking reveals something deeply significant about the workings of the universe. The laws of Nature are unerringly symmetrical. They do not have preferences for particular times, places and directions. Indeed, we have found that one of the most powerful guides to their forms is precisely such a requirement. Einstein was the first to recognise how this principle had been used only partially by Galileo and Newton. He elevated it to a central requirement for the laws of Nature to satisfy: that they appear the same to all observers in the Universe, no matter how they are moving or where they are located. There cannot be privileged observers for whom everything looks simpler than it does for others. To countenance such observers would be the ultimate anti-Copernican perspective on the Universe. This democratic principle is a powerful guide to arriving at the most general expression of Nature's laws.

Yet, despite the symmetry of the laws of Nature, we observe the outcomes of those symmetrical laws to be assymetrical states and structures.

Then Jerome Friedmann, Nobel prize winner of 1990, thoughtfully declares, If the Higgs is discovered, it will be a great triumph for the standard model, if the Higgs is not discovered, it is practically certain that there is something in Nature that is equally interesting, maybe even more interesting that would create the symmetry breaking required by the standard model. And why do I say it’s required? Because the standard model is so good.

Symmetry order is the disorder of grouping order, and grouping order is the disorder of symmetry order. If the order of one is the disorder of the other, then there is no room for a general disorder. All there is in nature is ordered patterns of one type or the other, and combinations thereof.

Aside from the old architecture, narrow winding roads, and driving on the left, I wondered why England looked so different from America; then I realized that the trees and fields, the buildings and barns, the small villages and narrow winding roads all fit together seamlessly, blended by time into a harmony. No one thing intruded on the other. Each fit the scene as though a natural process had ordained symmetry. Nothing jarred the eye; all was quiet beauty and neatness. There was no litter, nothing offensive to the senses. Every snug cottage had its garden, each shop a quaint window; there were no ugly signs. Even the lettering above the shop doors looked wonderfully ancient and elegant.

We've seen that the theories of the Core forces, each deeply based on symmetry, can be combined. The three separate Core symmetries can be realized as parts of a single, all-encompassing symmetry. Moreover, that encompassing symmetry brings unity and coherence to the clusters of the Core. From a motley six, we assemble the faultless Charge Account. We also discover that once we correct for the distorting effect of Grid fluctuations-and after upping the ante to include SUSY-the different powers of the Core forces derive from a common value at short distances. Even gravity, that hopelessly feeble misfit, comes into the field. To reach this clear and lofty perspective, we made some hopeful leaps of imagination. We assumed that the Grid-the entity that in everyday life we consider empty space-is a multilayered, multicolored superconductor. We assumed that the world contains the extra quantum dimensions required to support super-symmetry. And we boldly took the laws of physics, supplemented with these two "super" assumptions, up to energies and down to distances far beyond where we've tested them directly. From the intellectual success so far achieved-from the clarity and coherence of this vision of unification-we are tempted to believe that our assumptions correspond to reality. But in science, Mother Nature is the ultimate judge. After the solar expedition of 1919 confirmed his prediction for the bending of light by the Sun, a reporter asked Albert Einstein what it would have meant if the result had been otherwise. He replied, "Then God would have missed a great opportunity." Nature doesn't miss such opportunities. I anticipated that Nature's verdicts in favor of our "super" ideas will inaugurate a new golden age in fundamental physics.