Symmetry Of The World Quotes

There are several ways to react to being lost. One is to panic: this was usually Valentina's first impulse. Another is to abandon yourself to lostness, to allow the fact that you've misplaced yourself to change the way you experience the world.

My dear, In the midst of hate, I found there was, within me, an invincible love. In the midst of tears, I found there was, within me, an invincible smile. In the midst of chaos, I found there was, within me, an invincible calm. I realized, through it all, that… In the midst of winter, I found there was, within me, an invincible summer. And that makes me happy. For it says that no matter how hard the world pushes against me, within me, there’s something stronger – something better, pushing right back. Truly yours, Albert Camus” I like this because only one part is usually quoted but the full quote has such symmetry.

Occupied in observing Mr. Bingley’s attentions to her sister, Elizabeth was far from suspecting that she was herself becoming an object of some interest in the eyes of his friend. Mr. Darcy had at first scarcely allowed her to be pretty: he had looked at her without admiration at the ball; and when they next met, he looked at her only to criticise. But no sooner had he made it clear to himself and his friends that she had hardly a good feature in her face, than he began to find it was rendered uncommonly intelligent by the beautiful expression of her dark eyes. To this discovery succeeded some others equally mortifying. Though he had detected with a critical eye more than one failure of perfect symmetry in her form, he was forced to acknowledge her figure to be light and pleasing; and in spite of his asserting that her manners were not those of the fashionable world, he was caught by their easy playfulness. Of this she was perfectly unaware: to her he was only the man who made himself agreeable nowhere, and who had not thought her handsome enough to dance with.

She saw it in a flash of utter clarity. She knew what she had to do. The only path, the only way forward. And what a familiar path it was. It was so obvious now. The world was a dream of the gods, and the gods dreamed in sequences, in symmetry, in patterns. History repeated itself, and she was only the latest iteration of the same scene in a tapestry that had been spun long before her birth.

I cannot assume you will understand me. It is just as likely that as I invent what I want to say, you will invent what you want to hear. Some story we must have. Stray words on crumpled paper. A weak signal into the outer space of each other. The probability of seperate worlds meeting is very small. The lure is immense. We send starships. We fall in love

Plato defined good as threefold in character: good in the soul, expressed through the virtues; good in the body, expressed through the symmetry and endurance of the parts; and good in the external world, expressed through social position and companionship.

Walk with me, hand in hand through the neon and styrofoam. Walk the razor blades and the broken hearts. Walk the fortune and the fortune hunted. Walk the chop suey bars and the tract of stars. I know I am a fool, hoping dirt and glory are both a kind of luminous paint; the humiliations and exaltations that light us up. I see like a bug, everything too large, the pressure of infinity hammering at my head. But how else to live, vertical that I am, pressed down and pressing up simultaneously? I cannot assume you will understand me. It is just as likely that as I invent what I want to say, you will invent what you want to hear. Some story we must have. Stray words on crumpled paper. A weak signal into the outer space of each other. The probability of separate worlds meeting is very small. The lure of it is immense. We send starships. We fall in love.

She was fragile, gentle, wide awake in a sleeping world.

The human heart is my territory. I write about love because it’s the most important thing in the world. I write about sex because often it feels like the most important thing in the world.

Now that physics is proving the intelligence of the universe what are we to do about the stupidity of mankind? I include myself. I know that the earth is not flat but my feet are. I know that space is curved but my brain has been condoned by habit to grow in a straight line. What I call light is my own blend of darkness. What I call a view is my hand-painted trompe-l'oeil. I run after knowledge like a ferret down a ferret hole. My limitations, I call the boundaries of what can be known. I interpret the world by confusing other people's psychology with my own.

When we were that young we invented the world, no one could tell us a thing.

The world is paralyzed, and humanity is in quarantine. It is a strange symmetry that I was born in one pandemic and will die during another.

Jessica put out her hand and braced herself against the door jamb. She experienced one of those rare moments when understanding of the world alters and a previously impossible thing is admitted, if not understood.

You didn’t answer my question. I asked you about being in love. You said what it was like when your wife went away.” Martin sat down again. How young she is. When we were that young we invented the world, no one could tell us a thing. Julia stood with her hands clenched, as though she wanted to pound an answer out of him. “Being in love is…anxious,” he said. “Wanting to please, worrying that she will see me as I really am. But wanting to be known. That is…you’re naked, moaning in the dark, no dignity at all…I wanted her to see me and to love me even though she knew everything I am, and I knew her. Now she’s gone, and my knowledge is incomplete. So all day I imagine what she is doing, what she says and who she talks to, how she looks. I try to supply the missing hours, and it gets harder as they pile up, all the time she’s been gone. I have to imagine. I don’t know, really. I don’t know any more.

It is good you have each other, the artist had said, regarding them seriously as she worked. You never have to explain yourself to sisters. It was true. Being one of four sisters always felt like being part of something magic. Once Bonnie noticed it, she saw the world was made up of fours. The seasons. The elements. The points on a compass. Four suits in a pack of cards. Four chambers of a human heart. Bonnie loved being a part of this mystical number, this perfect symmetry of two sets of two.

The Roman genius, and perhaps the Roman flaw was an obsession with order. One sees it in their architecture, their literature, their laws—this fierce denial of darkness, unreason, chaos. Easy to see why the Romans, usually so tolerant of foreign religions, persecuted the Christians mercilessly—how absurd to think a common criminal had risen from the dead, how appalling that his followers celebrated him by drinking his blood. The illogic of it frightened them and they did everything they could to crush it. In fact, I think the reason they took such drastic steps was because they were not only frightened but also terribly attracted to it. Pragmatists are often strangely superstitious. For all their logic, who lived in more abject terror of the supernatural than the Romans? The Greeks were different. They had a passion for order and symmetry, much like the Romans, but they knew how foolish it was to deny the unseen world, the old gods. Emotion, darkness, barbarism.

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.

And so the twins had remained virgins. Julia and Valentina watched all of their high school and college friends disappear one by one into the adult world of sex, until they were the only people they knew who lingered in the world of the uninitiated. "What was it like?" they asked each friend. The answers were vague. Sex was a private joke: you had to be there.

Wisdom is the central form which gives meaning and position to all the facts which are acquired by knowledge, the digestion and assimilation of whatever in the material world the man comes in contact with.

But science has given us new eyes that allow us to see down to the deeper roots of the world’s structure, and there all we see is order and symmetry of pristine mathematical purity.

Many years later when I began training as a plastic surgeon, I understood something that I had not that day in the kitchen arguing for Thalia to leave Tinos for the boarding school. I learned that the world didn't see the inside of you, that it didn't care a whit about the hopes and dreams, and sorrows, that lay masked by skin and bone. It was as simple, as absurd, and as cruel as that. My patients knew this. They saw that much of what they were, would be, or could be hinged on the symmetry of their bone structure, the space between their eyes, their chin length, the tip projection of their nose, whether they had an ideal nasofrontal angle or not. Beauty is an enormous unmerited gift given randomly, stupidly.

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.

Be consoled in the secret symmetry of your soul.

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 world around us, just as we find satisfaction in the repetition of the seasons and the reliability of friendships. Symmetry is also economy. Symmetry is simplicity. Symmetry is elegance.

But when the light cleared I had new eyes, and I could see my own words in new ways—and the words from which they were derived—the stories, columns, speeches, and talks presented by “willing intellectuals.” So much seemed obvious. I now noted a symmetry in the bromides—that those who claimed Israel as the only democracy in the Middle East were just as likely to claim that America was the oldest democracy in the world.

Out of the quiet emerges the sheer incarnational presence of the world, a presence that seems to demand a moving internal symmetry in the one breathing and listening equal to its own breathing, listening elemental powers.

It turns out that this new numerical system has a hidden property that the rational numbers didn’t have. This property will be our portal into the magical world of numbers. Namely, it turns out that this numerical system has symmetries.

Hold in, hold in, one crack and the wall is breached. I need now to be finite, self-contained, to stop this bacterial grief dividing and multiplying till its weight is the weight of the world. Bacteria: agents of putrefaction. My father's decay lodged in me.

mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics.” And that beauty is symmetry.

I now noted a symmetry in the bromides—that those who claimed Israel as the only democracy in the Middle East were just as likely to claim that America was the oldest democracy in the world. And both claims relied on excluding whole swaths of the population living under the rule of the state.

To a physicist, beauty means symmetry and simplicity. If a theory is beautiful, this means it has a powerful symmetry that can explain a large body of data in the most compact, economical manner. More precisely, and equation is considered to be beautiful if it remains the same when we interchange its components among themselves.

I learned that the world didn’t see the inside of you, that it didn’t care a whit about the hopes and dreams, and sorrows, that lay masked by skin and bone. It was as simple, as absurd, and as cruel as that. My patients knew this. They saw that much of what they were, would be, or could be hinged on the symmetry of their bone structure, the space between their eyes, their chin length, the tip projection of their nose, whether they had an ideal nasofrontal angle or not. Beauty is an enormous, unmerited gift given randomly, stupidly.

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!

When your conscious and subconscious are at symmetry with each other, intuition plays little to no role in your decisions. Everything becomes blurry, because you are finally starting to drift away from the picture that the world wants you to see.

There is incredible symmetry in a tree, between its inner life and its outer life,between its rooted memory and its external active presence. A tree grows up and down at once and produces enough branches too incarnate it’s wild divinity. It doesn’t limit itself- it reaches for the sky and it reaches for the source, all in one kind of seamless movement. So I think landscape is an incredible, mystical teacher, and when you begin to tune into its sacred presence, something shifts inside you.

The peregrine’s view of the land is like the yachtsman’s view of the shore as he sails into the long estuaries. A wake of water recedes behind him, the wake of the pierced horizon glides back on either side. Like the seafarer, the peregrine lives in a pouring-away world of no attachment, a world of wakes and tilting, of sinking planes of land and water. We who are anchored and earthbound cannot envisage this freedom of the eye. The peregrine sees and remembers patterns we do not know exist: the neat squares of orchard and woodland, the endlessly varying quadrilateral shapes of fields. He finds his way across the land by a succession of remembered symmetries. But what does he understand? Does he really ‘know’ that an object that increases in size is moving towards him? Or is it that he believes in the size he sees, so that a distant man is too small to be frightening but a man near is a man huge and therefore terrifying? He may live in a world of endless pulsations, of objects forever contracting or dilating in size. Aimed at a distant bird, a flutter of white wings, he may feel – as it spreads out beneath him like a stain of white – that he can never fail to strike. Everything he is has been evolved to link the targeting eye to the striking talon.

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.

David Whyte offers a beautiful poem on the ways we are invited to welcome back the outcast parts of our being. This stanza from “Coleman’s Bed” is filled with self-compassion. Be taught now, among the trees and rocks, how the discarded is woven into shelter, learn the way things hidden and unspoken slowly proclaim their voice in the world. Find that inward symmetry to all outward appearances, apprentice yourself to yourself, begin to welcome back all you sent away, be a new annunciation, make yourself a door through which to be hospitable, even to the stranger in you.

Though he had detected with a critical eye more than one failure of perfect symmetry in her form, he was forced to acknowledge her figure to be light and pleasing; and in spite of his asserting that her manners were not those of the fashionable world, he was caught by their easy playfulness.

Even if a particle could travel backward in time, information could not. Retrocausality will be replaced by something more sophisticated. There are no perfect symmetries, there is no pure randomness everything is an approximation of something else. Information may appear in a digital form but meaning never does. Spacetime is built up from approximations, not discrete ones and zeros, and the only constant may be ratios. Quantum entanglement and geometry; if we think of a particle as being at one pole of an expanding sphere that is not perfectly symmetrical, this surface would be "rippling" like the surface of the ocean (in the audio world this is called dithering), at the other pole is the entangled particle's pair and it is a property of the sphere that gives the illusion of connectivity. This is not a physical geometry, it is a computational geometry. Is spacetime a product of entanglement? Renate Loll believes that time is not perfectly symmetrical. Her computer models require causality. Possibly some form of quantum random walk in state space. If a photon is emitted by an electron inside of a clock on Earth and it travels to a clock four light years away, time stops for the clock on Earth and time jumps forward eight years for the distant clock also, the electron that will capture the photon becomes infinitely large relative to the photon but the electron that emitted it does not become infinitely small therefore, time is not perfectly symmetrical.

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.

The Greeks were different. They had a passion for order and symmetry, much like the Romans, but they knew how foolish it was to deny the unseen world, the old gods. Emotion, darkness, barbarism.' He looked at the ceiling for a moment, his face almost troubled. 'Do you remember what we were speaking of earlier, of how bloody, terrible things are sometimes the most beautiful?' he said. 'It´s a very Greek idea, and a very profound one. Beauty is terror. Whatever we call beautiful, we quiver before it. And what could be more terrifying and beautiful, to souls like the Greeks or our own, than to lose control completly?

I could not immunize myself against the germ warfare of object and dream. There seemed to be no bridge between mind and matter, between myself and the world, no point of reference that was not a handy deception…I tried to copy other children but lacked their tough skin. I was a glove turned inside-out, softness showing.

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. . . .

If we know an object has symmetry, we can deduce some of its properties. If we know a set of objects has symmetry, we can infer from our knowledge of one object the existence and properties of others. And if we know that the laws of the world have symmetry, we can infer from one object the existence, properties, and behavior of new objects.

Like nothing else, words organized my world, put order to chaos, divided things neatly into black and white. Words even helped me organize my parents. My mother was the printed word—tangible, present, real—while my father was the spoken word—invisible, ephemeral, instantly part of memory. There was something comforting about this rigid symmetry.

MY FATHER If I have to write a poem about my father it has to be about integrity and kindness — the selfless kind of kindness that is so very rare I am sure there will be many people living somewhere who must be as kind as him but what I mean to say is I have not met one yet and when it comes to helping others he always helps too much and as the saying goes — help someone, you earn a friend. help someone too much, you make an enemy. — so you know the gist of what I’m trying to say here anyways I was talking about the poem about my father it has to be about passion and hard work because you see you cannot separate these things from him they are part of him as his two eyes and two hands and his heart and his soul and his whole being and you cannot separate wind and waves or living and the universe or earth and heavens and although he never got any award from bureaucracy the students he taught ages ago still touch his feet and some of them are the people you have to make an appointment to meet even if it is for two minutes of their time and that’s a reward for him bigger than any other that some of his colleagues got for their flattery and also I have to write about reliability as well because you see as the sun always rises and the snowflakes are always six-folds and the spring always comes and the petals of a sunflower and every flower follows the golden ratio of symmetry my father never fails to keep his promise I have to mention the rage as well that he always carries inside him like a burning fire for wrongdoings for injustice and now he carries a bitterness too for people who used him good and discarded as it always happens with every good man in our world of humans and you must be thinking he has learned his lessons well you go to him — it does not matter who you are if he knows you or you are a stranger from other side of the world — and ask for his help he will be happy to do so as you must know people never change not their soul in any case.

What a mercy, I thought, that the crippled, the maimed, those whom Fate has cheated, at least in sleep have no knowledge of the shapeliness or unshapeliness of their bodies, that there at least that kindly deceiver, the dream, reveals their form to them as a thing of beauty and symmetry, that at least in the nebulous world of slumber the sufferer can escape the curse to which he is physically chained!

I was transfixed by the possibility of imagination within this home, no matter how strange it appeared to be. This wasn't the quiet symmetry of my everyday, the rows of terraced houses with their rectangular gardens and the routines as reliable as sturdy hairs. This wasn't the world in which things matched, or even went with. This was a world devoid of harmony. This was a world of drama, where comedy and tragedy fought for space.

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.

The train reached Ogden at two o’clock, where it rested for six hours, Mr. Fogg and his party had time to pay a visit to Salt Lake City, connected with Ogden by a branch road; and they spent two hours in this strikingly American town, built on the pattern of other cities of the Union, like a checker-board, “with the sombre sadness of right-angles,” as Victor Hugo expresses it. The founder of the City of the Saints could not escape from the taste for symmetry which distinguishes the Anglo-Saxons.

The nations of the earth through the centuries of time have waged war to gain territory. I think ours is the only nation on the face of the earth which has not claimed territory gained out of conflict. I have stood in the American Military Cemetery in Suresnes, France, where are buried some who died in the First World War. Among those was my eldest brother. It is a quiet and hallowed place, a remembrance of great sacrifice 'to make the world safe for democracy.' No territory was claimed by America as recompense for the sacrifices of those buried there. I have stood in reverence in the beautiful American military cemetery on the outskirts of Manila in the Philippines. There marble crosses and the Star of David stand in perfect symmetry marking the burial places of some 17,000 Americans who lost their lives in the Second World War. Surrounding that sacred ground are marble colonnades on which are incised the names of another 35,000 who were lost in the battles of the Pacific during that terrible conflict. After so great a sacrifice there was victory, but there was never a claim for territory except for some small islands over which we have had guardianship. I have been up and down South Korea from the 38th parallel in the North to Pusan in the South, and I have seen the ridges and the valleys where Americans fought and died, not to save their own land but to preserve freedom for people who were strangers to them but whom they acknowledged to be brothers under the fatherhood of God. Not an inch of territory was sought for nor added to the area of the United States out of that conflict. I have been from one end of South Vietnam to the other in the days of war. More than 55,000 Americans died in the sultry, suffocating heat of that strange and foreign place fighting in the cause of human liberty without ambition for territory. In no instance--not in the First World War or the Second, not in the Korean War or in Vietnam--did our nation seize and hold territory for itself as a prize of war.

Much of the structure of the world, both social and physical, is a consequence of the requirement that the world, in its actuality, break symmetries present in the space of possibilities. An important feature of this requirement is the trade-off between symmetry and stability. The symmetric situation, in which we are all potentially friends and romantic partners, is unstable. In reality, we must make choices, and this leads to more stability. We trade the unstable freedom of potentiality for the stable experience of actuality.

We must let go of any fantasy concerning the church as a stable, predictable, well-regulated organization. If the church is truly the place in the world where the existence of God is brought to the level of narrative discernment, the the church will always be disorderly. …We must let go of the desire for theology to be a finished product of complete conceptual symmetry. If theology is in fact the attempt to understand living faith, then it must always be an unfinished process, for the data continues to come in, as the Living God persists in working through the lives of people and being revealed in their stories. …We must let go of any pretense of closing the New Testament within some comprehensive, all-purpose, singular reading which reduces its complexity to simplicity. We must recognize our attempts to reduce multiplicity to unity. We must recognize our tendency to seek a stable package of meaning that we can then apply to other situations or fit within our systematic theological constructs, so that, ideally, we need never really read the texts again.

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

Passion for science derives from an aesthetic sensibility, not a practical one. We discover something new about the world, and that lets us better appreciate its beauty. On the surface, the weak interactions are a mess: The force-carrying bosons have different masses and charges, and different interaction strengths for different particles. Then we dig deeper, and an elegant mechanism emerges: a broken symmetry, hidden from our view by a field pervading space. It’s like being able to read poetry in the original language, instead of being stuck with mediocre translations.

The ten-dimensional universe was a world of light. The entire universe was constructed upon energy exchange between photons. All particles and antiparticles were formed from photons, and their mutual annihilation resulted in yet more photons. Thus, everything occurred at the speed of light, which was infinite. Even more marvelously, because particles and antiparticles balanced each other out, the total energy level of the universe was zero. This was an incredible state of symmetry, and the foundation of the emergence of intelligence in the ten-dimensional universe.” Matter, life, sentience, civilization … in this Edenic universe, everything was part of the same whole. All matter possessed life, and all life possessed sentience, and all sentience existed in a state of harmonious civilization. Unlike the three-dimensional universe, in which lonely stars hung in the vast emptiness of space, the entire universe was a living being. All life was but a part of this one grand Life, and all intelligence but a component of the highest Intelligence. The dark forest state was an impossibility for this transcendent being of unified matter and spirit. Tianming felt awe at the root of his soul. This was the original form of the Master. The ten-dimensional universe was itself alive. Sophon offered more explanations. “The Master is not an individual like a human being; rather, it is the sum of an infinite number of self-aware consciousnesses. Every consciousness shares the awareness of every other consciousness as well as the presence of the universe itself, and yet each possesses an independent will. This is a state of existence simply unimaginable by humans: individual presence absolutely, seamlessly harmonized with the universe, akin to the geometric construction of the Spirit you saw.

A common example from physics is of a pencil balanced on its point. It is symmetric, in that while it is balanced on its point, one direction is as good as another. But it is unstable. When the pencil falls, as it inevitably must, it will fall randomly, in one direction or another, breaking the symmetry. Once it has fallen, it is stable, but it no longer manifests the symmetry- although the symmetry is still there in the underlying laws. The laws describe only the space of what possibly may happen, the actual world governed by those laws involves a choice of one realization from many possibilities.

He’d been at college less than two months but had already stepped directly into the world he wanted, analyzing the stunning symmetry of the DNA molecule as if he’d crawled inside a glistening cathedral of coiling atoms and climbed the winding, acidic rungs of the helix. Seeing that all life depends on this precise and intricate code transcribed on fragile, organic slivers, which would perish instantly in a slightly warmer or colder world. At last, surrounded by enormous questions and people as curious as he to find the answers, drawing him toward his goal of research biologist in his own lab, interacting with other scientists

Branes also opened up a whole new way of thinking about how our three-dimensional world might relate to the extra spatial dimensions of string theory. Some of the branes that Polchinsky discovered are three-dimensional. By piling up three-dimensional branes, you get a three-dimensional world with whatever symmetries you like, floating in a higher-dimensional world. Could our three-dimensional universe be such a surface in a higher-dimensional world? This is a big idea, and it makes a possible connection to a field of research called brane worlds, in which our universe is seen as a surface floating in a higher-dimensional universe.

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 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.

emotion. It was all absurd—she had been a silly, romantic, inexperienced goose. Well, she would be wiser in the future—very wise—and very discreet—and very contemptuous of men and their ways. "I suppose I'd better go with Una and take up Household Science too," she thought, as she stood by her window and looked down through a delicate emerald tangle of young vines on Rainbow Valley, lying in a wonderful lilac light of sunset. There did not seem anything very attractive just then about Household Science, but, with a whole new world waiting to be built, a girl must do something. The door bell rang, Rilla turned reluctantly stairwards. She must answer it—there was no one else in the house; but she hated the idea of callers just then. She went downstairs slowly, and opened the front door. A man in khaki was standing on the steps—a tall fellow, with dark eyes and hair, and a narrow white scar running across his brown cheek. Rilla stared at him foolishly for a moment. Who was it? She ought to know him—there was certainly something very familiar about him—"Rilla-my-Rilla," he said. "Ken," gasped Rilla. Of course, it was Ken—but he looked so much older—he was so much changed—that scar—the lines about his eyes and lips—her thoughts went whirling helplessly. Ken took the uncertain hand she held out, and looked at her. The slim Rilla of four years ago had rounded out into symmetry. He had left a school girl, and he found a woman—a

She ran her hand through a shell bowl absently, letting the trinkets slide through her fingers. Mostly they weren't cut or polished the way a human jeweler would treat them: they sparkled here and there out of a chunk of brownish rock. A single crystal might shine like the weapon of a god- but be topped by the lumpy bit where it had been prized out of a geode. Ariel regarded the stones with fascination. Of course they were beautiful. Yet she still found the bits and baubles from the human world, made by humans, far more alluring. Why? Why couldn't she be content with the treasures of the sea the way the ocean had made them? What was wrong with them that they had to be altered, or put on something else, or framed, or forced in a bunch onto a necklace, in perfect, unnatural symmetry?

Mr. Darcy had at first scarcely allowed her to be pretty; he had looked at her without admiration at the ball; and when they next met, he looked at her only to criticise. But no sooner had he made it clear to himself and his friends that she hardly had a good feature in her face, than he began to find it was rendered uncommonly intelligent by the beautiful expression of her dark eyes. To this discovery succeeded some others equally mortifying. Though he had detected with a critical eye more than one failure of perfect symmetry in her form, he was forced to acknowledge her figure to be light and pleasing; and in spite of his asserting that her manners were not those of the fashionable world, he was caught by their easy playfulness. Of this she was perfectly unaware; to her he was only the man who made himself agreeable nowhere, and who had not thought her handsome enough to dance with.

Supersymmetry was (and is) a beautiful mathematical idea. The problem with applying supersymmetry is that it is too good for this world. We simply do not find particles of the sort it predicts. We do not, for example, see particles with the same charge and mass as electrons, but a different amount of spin. However, symmetry principles that might help to unify fundamental physics are hard to come by, so theoretical physicists do not give up on them easily. Based on previous experience with other forms of symmetry, we have developed a fallback strategy, called spontaneous symmetry breaking. In this approach, we postulate that the fundamental equations of physics have the symmetry, but the stable solutions of these equations do not. The classic example of this phenomenon occurs in an ordinary magnet. In the basic equations that describe the physics of a lump of iron, any direction is equivalent to any other, but the lump becomes a magnet with some definite north-seeking pole.

Elizabeth was far from suspecting that she was herself becoming an object of some interest in the eyes of his friend. Mr. Darcy had at first scarcely allowed her to be pretty; he had looked at her without admiration at the ball; and when they next met, he looked at her only to criticise. But no sooner had he made it clear to himself and his friends that she had hardly a good feature in her face, than he began to find it was rendered uncommonly intelligent by the beautiful expression of her dark eyes. To this discovery succeeded some others equally mortifying. Though he had detected with a critical eye more than one failure of perfect symmetry in her form, he was forced to acknowledge her figure to be light and pleasing; and in spite of his asserting that her manners were not those of the fashionable world, he was caught by their easy playfulness. Of this she was perfectly unaware;—to her he was only the man who made himself agreeable no where, and who had not thought her handsome enough to dance with.

When we have to pay a lot for something nice, we appreciate it to the full. Yet as its price in the market falls, passion has a habit of fading away. Why, then, do we associate a cheap price with lack of value? Our response is a hangover from our long preindustrial past. For most of human history, there truly was a strong correlation between cost and value: The higher the price, the better things tended to be, because there was simply no way both for prices to be low and for quality to be high. It is not that we refuse to buy inexpensive or cheap things. It's just that getting excited over cheap things has come to seem a little bizarre. How do we reverse this? The answer lies in a slightly unexpected area: the mind of a four-year-old. Children have two advantages: They don't know what they're supposed to like and they don't understand money, so price is never a guide to value for them. We buy them a costly wooden toy made by Swedish artisans who hope to teach lessons in symmetry and find that they prefer the cardboard box that it came in. If asked to put a price on things, children tend to answer by the utility and charm of an object, not its manufacturing costs. We have been looking at prices the wrong way. We have fetishised them as tokens of intrinsic value; we have allowed them to set how much excitement we are allowed to have in given areas, how much joy is to be mined in particular places. But prices were never meant to be like this: We are breathing too much life into them and thereby dulling too many of our responses to the inexpensive world. At a certain age, something very debilitating happens to children. They start to learn about "expensive" and "cheap" and absorb the view that the more expensive something is, the better it may be. They are encouraged to think well of saving up pocket money and to see the "big" toy they are given as much better than the "cheaper" one. We can't directly go backwards; we can't forget what we know of prices. However, we can pay less attention to what things cost and more to our own responses. We need to rethink our relationship to prices. The price of something is principally determined by what it cost to make, not how much human value is potentially to be derived from 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.

The properties that define a group are: 1. Closure. The offspring of any two members combined by the operation must itself be a member. In the group of integers, the sum of any two integers is also an integer (e.g., 3 + 5 = 8). 2. Associativity. The operation must be associative-when combining (by the operation) three ordered members, you may combine any two of them first, and the result is the same, unaffected by the way they are bracketed. Addition, for instance, is associative: (5 + 7) + 13 = 25 and 5 + (7 + 13) = 25, where the parentheses, the "punctuation marks" of mathematics, indicate which pair you add first. 3. Identity element. The group has to contain an identity element such that when combined with any member, it leaves the member unchanged. In the group of integers, the identity element is the number zero. For example, 0 + 3 = 3 + 0 = 3. 4. Inverse. For every member in the group there must exist an inverse. When a member is combined with its inverse, it gives the identity element. For the integers, the inverse of any number is the number of the same absolute value, but with the opposite sign: e.g., the inverse of 4 is -4 and the inverse of -4 is 4; 4 + (-4) = 0 and (-4) + 4 = 0. The fact that this simple definition can lead to a theory that embraces and unifies all the symmetries of our world continues to amaze even mathematicians.

We are all gastropods, soft, sticky creatures pulling ourselves along the earth from which we came and leaving a trail of silvery drool behind. But the snail, a worm that eternally slides along the horizon, lifts into the air, from its soft bivalve back, the geometrical wonder of its spiral shell, seemingly unrelated to the body that produced it in fear and loneliness. We secrete our shell in the sweat and mucous of our skin, in the transparent, scaly flesh of the foot we use to drag ourselves along. Through an alchemical transmutation, our drool turns to ivory and the spasms of our flesh into an undisturbed stillness. We curl around our central pilaster of rose-colored kaolin, we add, in our desperate drive to persist, spiral after spiral, each one wider, asymptotic, and translucid, until the miracle comes to pass: the revolting worm—existing in the life it lives, fermenting in its sins, irrigated by hormones and blood and sperm and lymph—rots and dies, leaving behind the ceramic filigree of its shell, a triumph of symmetry, the deathless icon in the platonic world of the mind. We all secrete, as we live, poems and pictures, ideas and hope, glistening palaces of music and faith, shells which begin by protecting our soft abdomen but after our disappearance live in the golden air of pure forms. Geometry always appears out of the amorphous, serenity out of pain and torture, just as dry tears leave behind the most wondrous crystals of salt.

Or think of the tale of the blind men who encounter an elephant for the first time. One wise man, touching the ear of the elephant, declares the elephant is flat and two-dimensional like a fan. Another wise man touches the tail and assumes the elephant is like rope or a one-dimensional string. Another, touching a leg, concludes the elephant is a three-dimensional drum or a cylinder. But actually, if we step back and rise into the third dimension, we can see the elephant as a three-dimensional animal. In the same way, the five different string theories are like the ear, tail, and leg, but we still have yet to reveal the full elephant, M-theory. Holographic Universe As we mentioned, with time new layers have been uncovered in string theory. Soon after M-theory was proposed in 1995, another astonishing discovery was made by Juan Maldacena in 1997. He jolted the entire physics community by showing something that was once considered impossible: that a supersymmetric Yang-Mills theory, which describes the behavior of subatomic particles in four dimensions, was dual, or mathematically equivalent, to a certain string theory in ten dimensions. This sent the physics world into a tizzy. By 2015, there were ten thousand papers that referred to this paper, making it by far the most influential paper in high-energy physics. (Symmetry and duality are related but different. Symmetry arises when we rearrange the components of a single equation and it remains the same. Duality arises when we show that two entirely different theories are actually mathematically equivalent. Remarkably, string theory has both of these highly nontrivial features.)

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.

MY FATHER If I have to write a poem about my father it has to be about integrity and kindness — the selfless kind of kindness that is so very rare I am sure there will be many people living somewhere who must be as kind as him but what I mean to say is I have not met one yet and when it comes to helping others he always helps too much and as the saying goes — help someone, you earn a friend. help someone too much, you make an enemy. — so you know the gist of what I’m trying to say here anyways I was talking about the poem about my father it has to be about passion and hard work because you see you cannot separate these things from him they are part of him as his two eyes and two hands and his heart and his soul and his whole being and you cannot separate wind and waves or living and the universe or earth and heavens and although he never got any award from bureaucracy the students he taught ages ago still touch his feet and some of them are the people you have to make an appointment to meet even if it is for two minutes of their time and that’s a reward for him bigger than any other that some of his colleagues got for their flattery and also I have to write about reliability as well because you see as the sun always rises and the snowflakes are always six-folds and the spring always comes and the petals of a sunflower and every flower follows the golden ratio of symmetry my father never fails to keep his promise I have to mention the rage as well that he always carries inside him like a burning fire for wrongdoings for injustice and now he carries a bitterness too for people who used him good and discarded as it always happens with every good man in our world of humans and you must be thinking he has learned his lessons well you go to him — it does not matter who you are if he knows you or you are a stranger from other side of the world — and ask for his help he will be happy to do so as you must know people never change not their soul in any case.

Hitherto I have used the words imperfect and perfect merely to distinguish between work grossly unskilful, and work executed with average precision and science; and I have been pleading that any degree of unskilfulness should be admitted, so only that the labourer’s mind had room for expression. But, accurately speaking, no good work whatever can be perfect, and the demand for perfection is always a sign of a misunderstanding of the ends of art. This for two reasons, both based on everlasting laws. The first, that no great man ever stops working till he has reached his point of failure: that is to say, his mind is always far in advance of his powers of execution, and the latter will now and then give way in trying to follow it;... And therefore, if we are to have great men working at all, or less men doing their best, the work will be imperfect, however beautiful. Of human work none but what is bad can be perfect, in its own bad way. The second reason is, that imperfection is in some sort essential to all that we know of life. It is the sign of life in a mortal body, that is to say, of a state of progress and change. Nothing that lives is, or can be, rigidly perfect; part of it is decaying, part nascent. The foxglove blossom—a third part bud, a third part past, a third part in full bloom—is a type of the life of this world. And in all things that live there are certain irregularities and deficiencies which are not only signs of life, but sources of beauty. No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry. All admit irregularity as they imply change; and to banish imperfection is to destroy expression, to check exertion, to paralyze vitality. All things are literally better, lovelier, and more beloved for the imperfections which have been divinely appointed, that the law of human life may be Effort, and the law of human judgment, Mercy. Accept this then for a universal law, that neither architecture nor any other noble work of man can be good unless it be imperfect; and let us be prepared for the otherwise strange fact, which we shall discern clearly as we approach the period of the Renaissance, that the first cause of the fall of the arts of Europe was a relentless requirement of perfection, incapable alike either of being silenced by veneration for greatness, or softened into forgiveness of simplicity.

Hitherto I have used the words imperfect and perfect merely to distinguish between work grossly unskilful, and work executed with average precision and science; and I have been pleading that any degree of unskilfulness should be admitted, so only that the labourer’s mind had room for expression. But, accurately speaking, no good work whatever can be perfect, and the demand for perfection is always a sign of a misunderstanding of the ends of art. This for two reasons, both based on everlasting laws. The first, that no great man ever stops working till he has reached his point of failure: that is to say, his mind is always far in advance of his powers of execution, and the latter will now and then give way in trying to follow it;... And therefore, if we are to have great men working at all, or less men doing their best, the work will be imperfect, however beautiful. Of human work none but what is bad can be perfect, in its own bad way. The second reason is, that imperfection is in some sort essential to all that we know of life. It is the sign of life in a mortal body, that is to say, of a state of progress and change. Nothing that lives is, or can be, rigidly perfect; part of it is decaying, part nascent. The foxglove blossom—a third part bud, a third part past, a third part in full bloom—is a type of the life of this world. And in all things that live there are certain irregularities and deficiencies which are not only signs of life, but sources of beauty. No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry. All admit irregularity as they imply change; and to banish imperfection is to destroy expression, to check exertion, to paralyze vitality. All things are literally better, lovelier, and more beloved for the imperfections which have been divinely appointed, that the law of human life may be Effort, and the law of human judgment, Mercy. Accept this then for a universal law, that neither architecture nor any other noble work of man can be good unless it be imperfect; and let us be prepared for the otherwise strange fact, which we shall discern clearly as we approach the period of the Renaissance, that the first cause of the fall of the arts of Europe was a relentless requirement of perfection, incapable alike either of being silenced by veneration for greatness, or softened into forgiveness of simplicity.

But so far, we have only discussed applying quantum mechanics to the matter that moves within the gravity fields of Einstein’s theory. We have not discussed a much more difficult question: applying quantum mechanics to gravity itself in the form of gravitons. And this is where we encounter the biggest question of all: finding a quantum theory of gravity, which has frustrated the world’s great physicists for decades. So let us review what we have learned so far. We recall that when we apply the quantum theory to light, we introduce the photon, a particle of light. As this photon moves, it is surrounded by electric and magnetic fields that oscillate and permeate space and obey Maxwell’s equations. This is the reason why light has both particle-like and wavelike properties. The power of Maxwell’s equations lies in their symmetries—that is, the ability to turn electric and magnetic fields into each other. When the photon bumps into electrons, the equation that describes this interaction yields results that are infinite. However, using the bag of tricks devised by Feynman, Schwinger, Tomonaga, and many others, we are able to hide all the infinities. The resulting theory is called QED. Next, we applied this method to the nuclear force. We replaced the original Maxwell field with the Yang-Mills field, and replaced the electron with a series of quarks, neutrinos, etc. Then we introduced a new bag of tricks devised by ’t Hooft and his colleagues to eliminate all the infinities once again. So three of the four forces of the universe could now be unified into a single theory, the Standard Model. The resulting theory was not very pretty, since it was created by cobbling together the symmetries of the strong, weak, and electromagnetic forces, but it worked. But when we apply this tried-and-true method to gravity, we have problems. In theory, a particle of gravity should be called the graviton. Similar to the photon, it is a point particle, and as it moves at the speed of light, it is surrounded by waves of gravity that obey Einstein’s equations. So far, so good. The problem occurs when the graviton bumps into other gravitons and also atoms. The resulting collision creates infinite answers. When one tries to apply the bag of tricks painfully formulated over the last seventy years, we find that they all fail. The greatest minds of the century have tried to solve this problem, but no one has been successful. Clearly, an entirely new approach must be used, since all the easy ideas have been investigated and discarded. We need something truly fresh and original. And that leads us to perhaps the most controversial theory in physics, string theory, which might just be crazy enough to be the theory of everything.

Or think of the tale of the blind men who encounter an elephant for the first time. One wise man, touching the ear of the elephant, declares the elephant is flat and two-dimensional like a fan. Another wise man touches the tail and assumes the elephant is like rope or a one-dimensional string. Another, touching a leg, concludes the elephant is a three-dimensional drum or a cylinder. But actually, if we step back and rise into the third dimension, we can see the elephant as a three-dimensional animal. In the same way, the five different string theories are like the ear, tail, and leg, but we still have yet to reveal the full elephant, M-theory. Holographic Universe As we mentioned, with time new layers have been uncovered in string theory. Soon after M-theory was proposed in 1995, another astonishing discovery was made by Juan Maldacena in 1997. He jolted the entire physics community by showing something that was once considered impossible: that a supersymmetric Yang-Mills theory, which describes the behavior of subatomic particles in four dimensions, was dual, or mathematically equivalent, to a certain string theory in ten dimensions. This sent the physics world into a tizzy. By 2015, there were ten thousand papers that referred to this paper, making it by far the most influential paper in high-energy physics. (Symmetry and duality are related but different. Symmetry arises when we rearrange the components of a single equation and it remains the same. Duality arises when we show that two entirely different theories are actually mathematically equivalent. Remarkably, string theory has both of these highly nontrivial features.) As we saw, Maxwell’s equations have a duality between electric and magnetic fields—that is, the equations remain the same if we reverse the two fields, turning electric fields into magnetic fields. (We can see this mathematically, because the EM equations often contain terms like E2 + B2, which remain the same when we rotate the two fields into each other, like in the Pythagorean theorem). Similarly, there are five distinct string theories in ten dimensions, which can be proven to be dual to each other, so they are really a single eleven-dimensional M-theory in disguise. So remarkably, duality shows that two different theories are actually two aspects of the same theory. Maldacena, however, showed that there was yet another duality between strings in ten dimensions and Yang-Mills theory in four dimensions. This was a totally unexpected development but one that has profound implications. It meant that there were deep, unexpected connections between the gravitational force and the nuclear force defined in totally different dimensions. Usually, dualities can be found between strings in the same dimension. By rearranging the terms describing those strings, for example, we can often change one string theory into another. This creates a web of dualities between different string theories, all defined in the same dimension. But a duality between two objects defined in different dimensions was unheard of.

understand what part they played. Symmetry. And because I understood that, I understood that a single painting or composition or poem might change the future. Where its influence might end—if it ever did—was a mystery. I had spent lifetimes watching the effects of my choices, and so I knew that Joseph Hannigan was meant to be the very best of them. The world had put him into my hands; I could only guess at its design. But I knew he

In Fantasia, the physics is different. It’s not the property of mass that’s causing people to throw themselves into the Nothing, to let themselves be devoured into suicide. It’s imagination and feeling and inspiration that’s the basic currency of this world. The expectation of wonder is what holds Fantasia together—wonder and creative currents, fantasy and inventiveness. These are the things that give meaning and purpose to Fantasia and its citizens. So when the Nothing comes along, devouring all these things indiscriminately, undermining their importance in a fundamental way, its very lack calls to the part of the Fantasian people that is the very opposite of imagination… the angst and nihilism inherent in each individual. The part that says What if we’ve been wrong all along? It doesn’t take much doubt (just a little chunk) but the resulting horror feeds on every positive thought, every creative impulse, until the symmetry of lack between the Nothing and the despairing individual acts as gravity, drawing them closer and closer to the Nothing until the only alternative is to become part of it. It really is like a black hole.

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.

The pleasure of this kind of narrative is not that we think we are reading about the real world (although the story usually does map onto our world fairly closely), but rather that the wings of symmetry are unfolding around us; briefly we are on a planet where, as E.M. Forster says, there are no secrets and human behavior makes sense. I call this 'fiction.

What was the Big Bang? It was where a perfect set of monads – all perfectly in phase with each other (thus producing a Singularity of perfect light) – suffered a break of symmetry, leading to a tidal wave of out of phase relations, and thus the production of the material world.

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.

But gradually through the tumultuous talk of the days and the nightlong wonderings when I sat groping for hope through the darkness, there began to form in me one deep belief, that if there were no God there was no meaning in life. Like a child with a foot rule trying to measure a mountain, I demanded of this Mystery what its attributes were, asking assurance, trying to frame a pattern for the Ultimate. Every time I turned back baffled from that hidden face I was brought up again by the beautiful symmetry of the world or by the strangeness of some everyday organism. The delicate beauty of leaves and of bare branches, the perfection with which the tiniest creatures were designed, the constant recurrence of the seasons were phenomena which tugged at my senses, saying, “Somewhere there is a Cause for us.” I grew thin with tension, straining beyond my strength. The more I tried to probe this Mystery the greater it became; the closer I attempted to approach Him to test Him the vaster and more impenetrable He appeared, until I saw I had no measure huge enough to encompass Him and began to sense why faith must accept Him without questioning.

The pain and exhaustion of her body dropped away from her mind as she gathered the energy of the world and let it fuel her body. She forgot Seawind’s enmity, the Hunter in the forest, the Coven’s need to lock her away, and the possibility of her own death. It was just her, her two short sticks, the boy in front of her, and the dance between them. Serenity filled her, the motions of the sparring match an art form of perfect symmetry.

But perhaps most of us all, magnetism has aroused humanity’s basic curiosity. The image in Figure 1 of the pattern produced in iron filings from a magnet shows an experiment that can be done by a child. But that experiment illustrates relativity (magnetic fields are a relativistic correction of moving charges), quantum mechanics (the Bohr–van Leeuwen theorem forbids magnetism in classical systems), the mystery of spin (it is electron spin which produces the magnetism), exchange symmetry (which keeps the spins aligned), and emergent phenomena (many spins doing what a single spin cannot). With this in mind, one cannot escape the conclusion that magnetism itself is emblematic of the mystery, the wonder and the richness of the physical world.

Be taught now, among the trees and rocks, how the discarded is woven into shelter, learn the way things hidden and unspoken slowly proclaim their voice in the world. Find that far inward symmetry to all outward appearances, apprentice yourself to yourself, begin to welcome back all you sent away, be a new annunciation, make yourself a door through which to be hospitable, even to the stranger in you.

But the nineteenth-century idea of beauty can also be regarded as an attempt to grapple with the deeper implications of the new sciences, primarily the idea that the world was held together not by structural symmetries, but by universal rules that from a religious point of view could be interpreted as evidence of the wisdom and power of God.

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...

People can be incredibly resistant to considering facts that don't fit with their world view and the belief that women are as violent and abusive as men is one that too many seem to be unwilling to let go of. Sex differences in intimate partner homicide rates (homicide includes killings sentenced as both murders and manslaughters) show that so-called 'sex symmetry' is a myth.

Furthermore, every sacred building was laid out according to a specific rite. A team of oxen opened furrows at the four points of a square starting at the southern side and working their way around it in a carefully defined order and direction. Moreover, the priests who read the auspices and auguries, after having divided up the celestial region (regions caeli) with the help of a curved staff, “freed and declared empty” the future building site. “What is then inaugurated is put in communication, in an effective symmetry, with the heavens . . . ; what is not inaugurated remains essentially earthbound,” notes Georges Dumézil.3 “The Italic temple,” says Eliade, “was the zone where the upper (divine), terrestrial, and subterranean worlds intersected.

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.

Many years later, when I began training as a plastic surgeon, I understood something that I had not that day in the kitchen arguing for Thalia to leave Tinos for the boarding school. I learned that the world didn’t see the inside of you, that it didn’t care a whit about the hopes and dreams, and sorrows, that lay masked by skin and bone. It was as simple, as absurd, and as cruel as that. My patients knew this. They saw that much of what they were, would be, or could be hinged on the symmetry of their bone structure, the space between their eyes, their chin length, the tip projection of their nose, whether they had an ideal nasofrontal angle or not. Beauty is an enormous, unmerited gift given randomly, stupidly. And so I chose my specialty to even out the odds for people like Thalia, to rectify, with each slice of my scalpel, an arbitrary injustice, to make a small stand against a world order I found disgraceful, one in which a dog bite could rob a little girl of her future, make her an outcast, an object of scorn.

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!