Mathematical Equation Quotes

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

The ‘Muse’ is not an artistic mystery, but a mathematical equation. The gift are those ideas you think of as you drift to sleep. The giver is that one you think of when you first awake.

Once upon a time, there was a girl who talked to the moon. And she was mysterious and she was perfect, in that way that girls who talk to moons are. In the house next door, there lived a boy. And the boy watched the girl grow more and more perfect, more and more beautiful with each passing year. He watched her watch the moon. And he began to wonder if the moon would help him unravel the mystery of the beautiful girl. So the boy looked into the sky. But he couldn't concentrate on the moon. He was too distracted by the stars. And it didn't matter how many songs or poems had already been written about them, because whenever he thought about the girl, the stars shone brighter. As if she were the one keeping them illuminated. One day, the boy had to move away. He couldn't bring the girl with him, so he brought the stars. When he'd look out his window at night, he would start with one. One star. And the boy would make a wish on it, and the wish would be her name. At the sound of her name, a second star would appear. And then he'd wish her name again, and the stars would double into four. And four became eight, and eight became sixteen, and so on, in the greatest mathematical equation the universe had ever seen. And by the time an hour had passed, the sky would be filled with so many stars that it would wake the neighbors. People wondered who'd turned on the floodlights. The boy did. By thinking about the girl.

Today’s scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.

The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are the words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality––Dr. Li had once called it coy and twee, a fan dance of an axiom––but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. It was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life. But now he knows for certain how true the axiom is, because he himself––his very life––has proven it. The person I was will always be the person I am, he realizes. The context may have changed: he may be in this apartment, and he may have a job that he enjoys and that pays him well, and he may have parents and friends he loves. He may be respected; in court, he may even be feared. But fundamentally, he is the same person, a person who inspires disgust, a person meant to be hated.

You have a roommate." "Yeah." He sounds confused. "The, um, picture on your door surprised me." "NO. No. I prefer my women with...fewer carnivorous beasts and less weaponry." He pauses and smiles. "Naked is okay. What she needs are a golden retriever and a telescope. Maybe then it would do it for me." I laugh. "A squirrel and a laboratory beaker?" "A bunny rabbit and a flip chart," I say. "Only if the flip chart has mathematical equations on it." I fake swoon onto his bed. "Too much, too much!

We are mathematical equations where your life is the sum of all choices you've made until now. The good news is you can change the equation so that you start making a difference in your life.

Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, squares, and the like, but for the human emotions. If one has a mind which inclines to magic rather than science, one will prefer to speak of these equations as spells or incantations; it sounds more arcane, mysterious, recondite.

Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.

There is a secret bond between slowness and memory, between speed and forgetting. A man is walking down the street. At a certain moment, he tries to recall something, but the recollection escapes him. Automatically, he slows down. Meanwhile, a person who wants to forget a disagreeable incident he has just lived through starts unconsciously to speed up his pace, as if he were trying to distance himself from a thing still too close to him in time. In existential mathematics that experience takes the form of two basic equations: The degree of slowness is directly proportional to the intensity of memory; the degree of speed is directly proportional to the intensity of forgetting.

…Our sunsets have been reduced to wavelengths and frequencies. The complexities of the universe have been shredded into mathematical equations. Even our self-worth as human beings has been destroyed.

If one is working from the point of view of getting beauty into one's equation, ... one is on a sure line of progress.

One must divide one's time between politics and equations. But our equations are much more important to me, because politics is for the present, while our equations are for eternity.

For existential mathematics, which does not exist, would probably propose this equation: the value of coincidence equals the degree of its improbability.

How did you know?” “I…” Thomas swallowed hard, his attention fixed on the painting. “The truth?” “Please.” “You’ve got a dress with orchid blossoms embroidered on it. Ribbons in the deepest purple. You favor the color, but not nearly as much as I find myself favoring you.” He took a deep breath. “As to the stars? Those are what I prefer. More than medical practices and deductions. The universe is vast. A mathematical equation even I have no hope of solving. For there are no limits to the stars; their numbers are infinite. Which is precisely why I measure my love for you by them. An amount too boundless to count.

As to the stars? Those are what I prefer. More than medical practices and deductions. The universe is vast. A mathematical equation even I have no hope of solving. For there are no limits to the stars; their numbers are infinite. Which is precisely why i measure my love for you by them An amount too boundless to count.

Codes and patterns are very different from each other,” Langdon said. “And a lot of people confuse the two. In my field, it’s crucial to understand their fundamental difference.” “That being?” Langdon stopped walking and turned to her. “A pattern is any distinctly organized sequence. Patterns occur everywhere in nature—the spiraling seeds of a sunflower, the hexagonal cells of a honeycomb, the circular ripples on a pond when a fish jumps, et cetera.” “Okay. And codes?” “Codes are special,” Langdon said, his tone rising. “Codes, by definition, must carry information. They must do more than simply form a pattern—codes must transmit data and convey meaning. Examples of codes include written language, musical notation, mathematical equations, computer language, and even simple symbols like the crucifix. All of these examples can transmit meaning or information in a way that spiraling sunflowers cannot.

If he loved you guys, he wouldn’t hurt you.” He made it sound so simple, as if it were a mathematical equation. But the connection between pain and love wasn’t linear. It was a web.

The complexity of economics can be calculated mathematically. Write out the algebraic equation that is the human heart and multiply each unknown by the population of the world.

We love men because they can never fake orgasms, even if they wanted to. Because they write poems, songs, and books in our honor. Because they never understand us, but they never give up. Because they can see beauty in women when women have long ceased to see any beauty in themselves. Because they come from little boys. Because they can churn out long, intricate, Machiavellian, or incredibly complex mathematics and physics equations, but they can be comparably clueless when it comes to women. Because they are incredible lovers and never rest until we’re happy. Because they elevate sports to religion. Because they’re never afraid of the dark. Because they don’t care how they look or if they age. Because they persevere in making and repairing things beyond their abilities, with the naïve self-assurance of the teenage boy who knew everything. Because they never wear or dream of wearing high heels. Because they’re always ready for sex. Because they’re like pomegranates: lots of inedible parts, but the juicy seeds are incredibly tasty and succulent and usually exceed your expectations. Because they’re afraid to go bald. Because you always know what they think and they always mean what they say. Because they love machines, tools, and implements with the same ferocity women love jewelry. Because they go to great lengths to hide, unsuccessfully, that they are frail and human. Because they either speak too much or not at all to that end. Because they always finish the food on their plate. Because they are brave in front of insects and mice. Because a well-spoken four-year old girl can reduce them to silence, and a beautiful 25-year old can reduce them to slobbering idiots. Because they want to be either omnivorous or ascetic, warriors or lovers, artists or generals, but nothing in-between. Because for them there’s no such thing as too much adrenaline. Because when all is said and done, they can’t live without us, no matter how hard they try. Because they’re truly as simple as they claim to be. Because they love extremes and when they go to extremes, we’re there to catch them. Because they are tender they when they cry, and how seldom they do it. Because what they lack in talk, they tend to make up for in action. Because they make excellent companions when driving through rough neighborhoods or walking past dark alleys. Because they really love their moms, and they remind us of our dads. Because they never care what their horoscope, their mother-in-law, nor the neighbors say. Because they don’t lie about their age, their weight, or their clothing size. Because they have an uncanny ability to look deeply into our eyes and connect with our heart, even when we don’t want them to. Because when we say “I love you” they ask for an explanation.

Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal.

Everything can be summed up into an equation.

Nutrition is not a mathematical equation in which two plus two is four. The food we put in our mouths doesn’t control our nutrition—not entirely. What our bodies do with that food does.

Life is a linear equation in which you can't cross multiply! If you think you can do it, you can do it. If you think you can't do it, you can't do it. It's a simple formula!

The staunchest conservatives advocate a range of changes which differ in specifics, rather than in number or magnitude, from the changes advocated by those considered liberal…change, as such, is simply not a controversial issue. Yet a common practice among the anointed is to declare themselves emphatically, piously, and defiantly in favor of 'change.' Thus those who oppose their particular changes are depicted as being against change in general. It is as if opponents of the equation 2+2=7 were depicted as being against mathematics. Such a tactic might, however, be more politically effective than trying to defend the equation on its own merits.

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

She is like a mathematical equation, always there and impossible to disprove.

The further on we go, the more meaning there is, but the less articulable. You live your life and the older you get- the more specifically you harvest- the more precious becomes every ounce and spasm. Your life and times don’t drain of meaning because they become more contradictory, ornamented by paradox, inexplicable. The less explicable, the more meaning. The less like a mathematics equation (a sum game); the more like music (significant secret).

He walked straight out of college into the waiting arms of the Navy. They gave him an intelligence test. The first question on the math part had to do with boats on a river: Port Smith is 100 miles upstream of Port Jones. The river flows at 5 miles per hour. The boat goes through water at 10 miles per hour. How long does it take to go from Port Smith to Port Jones? How long to come back? Lawrence immediately saw that it was a trick question. You would have to be some kind of idiot to make the facile assumption that the current would add or subtract 5 miles per hour to or from the speed of the boat. Clearly, 5 miles per hour was nothing more than the average speed. The current would be faster in the middle of the river and slower at the banks. More complicated variations could be expected at bends in the river. Basically it was a question of hydrodynamics, which could be tackled using certain well-known systems of differential equations. Lawrence dove into the problem, rapidly (or so he thought) covering both sides of ten sheets of paper with calculations. Along the way, he realized that one of his assumptions, in combination with the simplified Navier Stokes equations, had led him into an exploration of a particularly interesting family of partial differential equations. Before he knew it, he had proved a new theorem. If that didn't prove his intelligence, what would? Then the time bell rang and the papers were collected. Lawrence managed to hang onto his scratch paper. He took it back to his dorm, typed it up, and mailed it to one of the more approachable math professors at Princeton, who promptly arranged for it to be published in a Parisian mathematics journal. Lawrence received two free, freshly printed copies of the journal a few months later, in San Diego, California, during mail call on board a large ship called the U.S.S. Nevada. The ship had a band, and the Navy had given Lawrence the job of playing the glockenspiel in it, because their testing procedures had proven that he was not intelligent enough to do anything else.

Psychohistory was the quintessence of sociology; it was the science of human behavior reduced to mathematical equations. The individual human being is unpredictable, but the reactions of human mobs, Seldon found, could be treated statistically.

Your blood for mine. If not these, then those. War is the supreme mathematics problem. It strains our skulls, yet we work out the sums, believing we have pressed the most monstrous quantities into a balanced equation.

There are other reasons we use math in physics. Besides keeping us honest, math is also the most economical and unambiguous terminology that we know of. Language is malleable; it depends on context and interpretation. But math doesn’t care about culture or history. If a thousand people read a book, they read a thousand different books. But if a thousand people read an equation, they read the same equation.

Although in principle we know the equations that govern the whole of biology, we have not been able to reduce the study of human behavior to a branch of applied mathematics.

She was his comet, his shooting star. She sparkled like the heavens, and when she smiled it felt like mathematical equations sliding into place. The world in balance, each side properly weighted. She was everything that was beauty, and everything that was brilliant, and he was – He was not well.

As he soars, he thinks, suddenly, of Dr. Kashen. Or not of Dr. Kashen, necessarily, but the question he had asked him when he was applying to be his advisee: What's your favorite axiom? (The nerd pickup line, CM had once called it.) "The axiom of equality," he'd said, and Kashen had nodded, approvingly. "That's a good one," he'd said. The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are the words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality––Dr. Li had once called it coy and twee, a fan dance of an axiom––but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. I was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life. But now he knows for certain how true the axiom is, because he himself––his very life––has proven it. The person I was will always be the person I am, he realizes. The context may have changed: he may be in this apartment, and he may have a job that he enjoys and that pays him well, and he may have parents and friends he loves. He may be respected; in court, he may even be feared. But fundamentally, he is the same person, a person who inspires disgust, a person meant to be hated. And in that microsecond that he finds himself suspended in the air, between ecstasy of being aloft and the anticipation of his landing, which he knows will be terrible, he knows that x will always equal x, no matter what he does, or how many years he moves away from the monastery, from Brother Luke, no matter how much he earns or how hard he tries to forget. It is the last thing he thinks as his shoulder cracks down upon the concrete, and the world, for an instant, jerks blessedly away from beneath him: x = x, he thinks. x = x, x = x.

In existential mathematics that experience takes the form of two basic equations: The degree of slowness is directly proportional to the intensity of memory; the degree of speed is directly proportional to the intensity of forgetting.

My sub doesn't pay for me,” he says, pulling me to my feet. “That just doesn't happen.” “But we ordered so much,” I say helplessly. “It made you happy,” he says simply. “Now I get to play with you. And that makes me happy.” “I don't think it's that simple an equation.” “Maybe not,” he concedes. “But then, if if sex were the same thing as math, a lot more people would be lining up to take calculus.

You can't apply mathematical formulas to people, Cresswell. There's no equation for human emotion, there are too many variables.

between a Lanvin show and a coffee with Anna Dello Russo, then go for it. GETTING INVITED: A complex mathematical equation.

Music, like the visual arts, is rooted in our experience of the natural world," said Schwartz. "It emulates our sound environment in the way that visual arts emulate the visual environment." In music we hear the echo of our basic sound making instrument-the vocal tract. This explanation for human music is simpler still than Pythagoras's mathematical equations: we like the sounds that are familiar to us-specifically, we like sounds that remind us of us.

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.

Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works.

THE BOTTOM LINE •  Parallel universes are not a theory, but a prediction of certain theories. •  Eternal inflation predicts that our Universe (the spherical region of space from which light has had time to reach us during the 14 billion years since our Big Bang) is just one of infinitely many universes in a Level I multiverse where everything that can happen does happen somewhere. •  For a theory to be scientific, we need not be able to observe and test all its predictions, merely at least one of them. Inflation is the leading theory for our cosmic origins because it’s passed observational tests, and parallel universes seem to be a non-optional part of the package. •  Inflation converts potentiality into reality: if the mathematical equations governing

The aim of Mathematical Physics is not only to facilitate for the physicist the numerical calculation of certain constants or the integration of certain differential equations. It is besides, it is above all, to reveal to him the hidden harmony of things in making him see them in a new way.

I don't mind nothing happening in a book, but nothing happening in a phony way--characters saying things people never say, doing jobs that don't fit, the whole works--is simply asking too much of a reader. Something happening in a phony way must beat nothing happening in a phony way every time, right? I mean, you could prove that, mathematically, in an equation, and you can't often apply science to literature.

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding

Did your mathematical studies ever reach to the quadratic equation, Stephen?' 'They did not reach to the far end of the multiplication table.

A mathematician is an individual who proves his beliefs with equations.

War is the supreme mathematics problem. It strains our skulls, yet we work out the sums, believing we have pressed the most monstrous quantities into a balanced equation

Certainly one of the most important things I learned is that numbers can be deceiving. There is a logic to mathematics, but there is also the underlying human element that must be considered. Numbers can't lie, but the people who create those numbers can and do. As so many people have learned, forgetting to include human nature in an equation can be devastating.

There is no such thing as beauty, especially in the human face… what we call the physiognomy. It’s all a mathematical and imagined alignment of features. Like, if the nose doesn’t stick out too much, the sides are in fashion, if the earlobes aren’t too large, if the hair is long… It’s kind of a mirage of generalization. People think of certain faces as beautiful, but, truly, in the final measure, they are not. It’s a mathematical equation of zero. “True beauty” comes, of course, of character. Not through how the eyebrows are shaped. So many women that I’m told are beautiful… hell, it’s like looking into a soup bowl.

It's not for nothing that advanced mathematics tend to be invented in hot countries. It's because of the morphic resonance of all the camels who have that disdainful expression and famous curled lip as a natural result of an ability to do quadratic equations.

IQ is a statistical method for quantifying specific kinds of problem-solving ability, mathematically convenient but not necessarily corresponding to a real attribute of the human brain, and not necessarily representing whatever it is that we mean by ‘intelligence’.

They were very upset when I said that the thing of greatest importance to mathematics in Europe was the discovery by Tartaglia that you can solve a cubic equation-which, altho it is very little used, must have been psychologically wonderful because it showed a modern man could do something no ancient Greek could do, and therefore helped in the renaissance which was the freeing of man from the intimidation of the ancients-what they are learning in school is to be intimidated into thinking they have fallen so far below their super ancestors.

Her husband once said that he believed some sort of mathematical equation could be applied to life - since the longer you lived, the greater its seeming velocity. She always attributed this to familiarity. If you kept the same habits - and if you lived in the same place, worked in the same place - then you no longer spent a lot of time noticing. Noticing things - and trying to make sense of them - is what makes time remarkable. Otherwise, life blurs by, as it does now, so that she has difficulty keeping track of time at all, one day evaporating into the next.

Even there, something inside me (and, I suspect, inside many other computer scientists!) is suspicious of those parts of mathematics that bear the obvious imprint of physics, such as partial differential equations, differential geometry, Lie groups, or anything else that's “too continuous.

The association of multiplication with vector rotation was one of the geometric interpretation's most important elements because it decisively connected the imaginaries with rotary motion. As we'll see, that was a big deal.

You think you have it all figured out—you’ve timed your commute, you’ve fit in your weekend run or you haven’t, you’ve got life down to a science, a mathematical equation of time, interest, and energy. But one day something stands up to you, surprises you in a place where you’ve determined never to be surprised. And that’s when you run. You move fast the wrong way through traffic. You think it’s working. But something deep inside, driving the rhythm of your steps, tells you that it isn’t. So you try again. You search for that tiny space hidden in you, untouched by everything that you’ve experienced or survived.

The problem is that we don’t really know what we want until we find it. Unlike with Amazon or Netflix, where we truly know our tastes in films and other products, a questionnaire about our personal preferences just isn’t enough to predict who will make us happy. Ultimately, finding a partner is just a lot more complicated than buying a DVD box set.

When I described Madame de T's night, I recalled the well-known equation from one of the first chapters of the textbook of existential mathematics: the degree of speed is directly proportional to the intensity of forgetting. From that equation we can deduce various corrollaries, for instance this one: our period is given over to the demon of speed, and that is the reason it so easily forgets its own self. Now I would reverse that statement and say: our period is obsessed by the desire to forget, and it is to fulfill that desire that it gives over to the demon of speed; it picks up the pace to show us that it no longer wishes to be remembered; that it is tired of itself; sick of itself; that it wants to blow out the tiny trembling flame of memory.

The combination of Bayes and Markov Chain Monte Carlo has been called "arguably the most powerful mechanism ever created for processing data and knowledge." Almost instantaneously MCMC and Gibbs sampling changed statisticians' entire method of attacking problems. In the words of Thomas Kuhn, it was a paradigm shift. MCMC solved real problems, used computer algorithms instead of theorems, and led statisticians and scientists into a worked where "exact" meant "simulated" and repetitive computer operations replaced mathematical equations. It was a quantum leap in statistics.

But Einstein refused to be mathematics’ pawn. He bucked the equations in favor of his intuition about how the cosmos should be, his deep-seated belief that the universe was eternal and, on the largest of scales, fixed and unchanging. The universe, Einstein admonished Lemaître, is not now expanding and never was.

This is known in economics as the “decoy effect.” What it demonstrates is that the presence of an irrelevant alternative can change how you view your choices. It has been exploited by marketing experts for decades.

According to Plato, a hierarchy of being and a hierarchy of knowledge exist, knowledge of ideas rests at the top, while at the bottom lies knowledge of trickery, illusions, shadows dancing on cave walls. By the way, mathematical knowledge is not in the highest position; philosophical knowledge is. Mathematics can’t describe the whole truth—even if we were to describe the entire world in precise mathematical equations, we would not have full knowledge.

Science may have alleviated the miseries of disease and drudgery and provided an array of gadgetry for our entertainment and convenience, but it has left us in a world without wonder. Our sunsets have been reduced to wavelengths and frequencies. The complexities of the universe have been shredded into mathematical equations. Even our self-worth as human beings has been destroyed. Science proclaims that Planet Earth and its inhabitants are a meaningless speck in the grand scheme. A cosmic accident.” He paused. “Even the technology that promises to unite us, divides us. Each of us is now electronically connected to the globe, and yet we feel utterly alone. We are bombarded with violence, division, fracture, and betrayal. Skepticism has become a virtue. Cynicism and demand for proof has become enlightened thought. Is it any wonder that humans now feel more depressed and defeated than they have at any point in human history? Does science hold anything sacred? Science looks for answers by probing our unborn fetuses. Science even presumes to rearrange our own DNA. It shatters God’s world into smaller and smaller pieces in quest of meaning . . . and all it finds is more questions.

Unlike the laws of reality that scientist describe in complex mathematical equations, the laws that govern human behavior are imprecise and in constant flux. We are complex organisms because we possess the capacity to experience, recall, and imagine. We are self-constructed. How we think becomes our reality. The highest act of human intelligence is not building bombs and inventing poisons that can destroy the world, but engaging in acts of contemplation that expands human consciousness.

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.

As girls go through puberty, their hormones will have a direct impact on how their facial features develop. Women with high levels of estrogen will end up with full lips and a large waist-to-hip ratio, while women with lower levels of androgen, the steroid hormones, will keep their short and narrow jaws from childhood, along with their flatter brows—giving them much larger eyes. And—surprise, surprise—this balance of female hormones is also positively linked to fertility.

I’m trying to justify it somehow, he thought, meaning it not in the moral sense but rather in the mathematical one. Buildings are built by observing certain natural laws; natural laws may be expressed by equations; equations must be justified. Where was the justification in what had happened less than half an hour ago?

In the West, there was an old debate as to whether mathematical reality was made by mathematicians or, existing independently, was merely discovered by them. Ramanujan was squarely in the latter camp; for him, numbers and their mathematical relationships fairly threw off clues to how the universe fit together. Each new theorem was one more piece of the Infinite unfathomed. So he wasn’t being silly, or sly, or cute when later he told a friend, “An equation for me has no meaning unless it expresses a thought of God.

There are many ways to generate numerical falsehoods from data, many ways to create proofiness from even valid meaurements. Causuistry distorts the relationships between two sets of numbers. Randumbness creates patterns where none are to be found. Regression to the moon disguises nonsense in mathematical-looking lines or equations or formulae, making even the silliest ideas seem respectable. Such as the one described by this formula: Callipygianness=(S+C)x(B+F)/T-V) Where S is shape, C is circularity, B is bounciness, F ir firmness, T is texture, and V is waist-to-hip ratio. This formula was devised by a team of academic psychologists after many hours of serious research into the female derriere. Yes, indeed. This is supposed to be the formula for the perfect butt. It fact, it's merely a formula for a perfect ass

Even today, I am in total awe of the following wondrous chain of ideas and interconnections. Guided throughout by principles of symmetry, Einstein first showed that acceleration and gravity are really two sides of the same coin. He then expanded the concept to demonstrate that gravity merely reflects the geometry of spacetime. The instruments he used to develop the theory were Riemann's non-Euclidean geometries-precisely the same geometries used by Felix Klein to show that geometry is in fact a manifestation of group theory (because every geometry is defined by its symmetries-the objects it leaves unchanged). Isn't this amazing?

Evidence in support of general relativity came quickly. Astronomers had long known that Mercury’s orbital motion around the sun deviated slightly from what Newton’s mathematics predicted. In 1915, Einstein used his new equations to recalculate Mercury’s trajectory and was able to explain the discrepancy, a realization he later described to his colleague Adrian Fokker as so thrilling that for some hours it gave him heart palpitations.

The axiom of equality states that x always equals x: it assumes that if you have a conceptual thing named x, that it must always be equivalent to itself, that it has a uniqueness about it, that it is in possession of something so irreducible that we must assume it is absolutely, unchangeably equivalent to itself for all time, that its very elementalness can never be altered. But it is impossible to prove. Always, absolutes, nevers: these are words, as much as numbers, that make up the world of mathematics. Not everyone liked the axiom of equality - Dr. Li had once called it coy and twee, a fan dance of an axiom - but he had always appreciated how elusive it was, how the beauty of the equation itself would always be frustrated by the attempts to prove it. It was the kind of axiom that could drive you mad, that could consume you, that could easily become an entire life.

It is one of the fundamental mysteries of nature, this dichotomy between what is given and what we, with our minds, create. We owe our very existence as a species to our ability to delineate patterns. We can even see patterns where none exist – the faces in a sun-lit curtain, the Greek heroes and monsters among the stars. What else might the human mind be recognizing that is not really there? And what, in any case, do we mean by "real"?

No physicist started out impatient with common-sense notions, eager to replace them with some mathematical abstraction that could be understood only by rarified theoretical physics. Instead, they began, as we all do, with comfortable, standard, common-sense notions. The trouble is that Nature does not comply. If we no longer insist on our notions of how Nature ought to behave, but instead stand before Nature with an open and receptive mind, we find that common sense often doesn't work. Why not? Because our notions, both hereditary and learned, of how Nature works were forged in the millions of years our ancestors were hunters and gatherers. In this case common sense is a faithless guide because no hunter-gatherer's life ever depended on understanding time-variable electric and magnetic fields. There were no evolutionary penalties for ignorance of Maxwell's equations. In our time it's different.

But Miss Ferguson preferred science over penmanship. Philosophy over etiquette. And, dear heavens preserve them all, mathematics over everything. Not simply numbering that could see a wife through her household accounts. Algebra. Geometry. Indecipherable equations made up of unrecognizable symbols that meant nothing to anyone but the chit herself. It was enough to give Miss Chase hives. The girl wasn’t even saved by having any proper feminine skills. She could not tat or sing or draw. Her needlework was execrable, and her Italian worse. In fact, her only skills were completely unacceptable, as no one wanted a wife who could speak German, discuss physics, or bring down more pheasant than her husband.

The shadows on the flat screen of a shadow play are projections from more complex objects. Our three-dimensional hands can cast a variety of two-dimensional shadows to delight the audience. In the same way there are fabulous beasts that swim in the seas of mathematics. Multidimensional behemoths of incredible beauty that even the best of minds struggle to glimpse. The equations we battle with, the proofs that we use to nibble at the edges of such wonders: these are the shadows cast by those we hunt.

“Mathematics isn’t just science, it is poetry—our efforts to crystallize the unglimpsed connections between things. Poetry that bridges and magnifies the mysteries of the galaxy. But the signs and symbols and equations sentients employ to express these connections are not discoveries but the teasing out of secrets that have always existed. All our theories belong to nature, not to us. As in music, every combination of notes and chords, every melody has already been played and sung, somewhere, by someone—”

Euler’s Formula encapsulates the whole of existence. It contains 0, the number of the monad (ontological zero); the number e that determines exponentiation; the number i that determines the imaginary domain (time); the number 1 that determines the domain of counting numbers (and with 0 creates the binary system of computing), and real numbers (space); -1, the number of the negative domain (antimatter); and the number π that determines the world of the circle and geometry. Euler’s Formula is the unquestionable God Equation.

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).

Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonlinear web of incentives and constraints and connections. The slightest change in one place causes tremors everywhere else. We can't help but disturb the universe, as T.S. Eliot almost said. The whole is almost always equal to a good deal more than the sum of its parts. And the mathematical expression of that property-to the extent that such systems can be described by mathematics at all-is a nonlinear equation: one whose graph is curvy.

The human mind is an incredible thing. It can conceive of the magnificence of the heavens and the intricacies of the basic components of matter. Yet for each mind to achieve its full potential, it needs a spark. The spark of enquiry and wonder. Often that spark comes from a teacher. Allow me to explain. I wasn’t the easiest person to teach, I was slow to learn to read and my handwriting was untidy. But when I was fourteen my teacher at my school in St Albans, Dikran Tahta, showed me how to harness my energy and encouraged me to think creatively about mathematics. He opened my eyes to maths as the blueprint of the universe itself. If you look behind every exceptional person there is an exceptional teacher. When each of us thinks about what we can do in life, chances are we can do it because of a teacher. [...] The basis for the future of education must lie in schools and inspiring teachers. But schools can only offer an elementary framework where sometimes rote-learning, equations and examinations can alienate children from science. Most people respond to a qualitative, rather than a quantitative, understanding, without the need for complicated equations. Popular science books and articles can also put across ideas about the way we live. However, only a small percentage of the population read even the most successful books. Science documentaries and films reach a mass audience, but it is only one-way communication.

Simply put, within AS, there is a wide range of function. In truth, many AS people will never receive a diagnosis. They will continue to live with other labels or no label at all. At their best, they will be the eccentrics who wow us with their unusual habits and stream-of-consciousness creativity, the inventors who give us wonderfully unique gadgets that whiz and whirl and make our life surprisingly more manageable, the geniuses who discover new mathematical equations, the great musicians and writers and artists who enliven our lives. At their most neutral, they will be the loners who never now quite how to greet us, the aloof who aren't sure they want to greet us, the collectors who know everyone at the flea market by name and date of birth, the non-conformists who cover their cars in bumper stickers, a few of the professors everyone has in college. At their most noticeable, they will be the lost souls who invade our personal space, the regulars at every diner who carry on complete conversations with the group ten tables away, the people who sound suspiciously like robots, the characters who insist they wear the same socks and eat the same breakfast day in and day out, the people who never quite find their way but never quite lose it either.

I’ll be honest with you. The variables that construct my existence are confusing. Like handwritten math equations jammed together on a sloppy page of homework. They don’t make any sense. One math problem leads to another, and then another and so it goes. One day you realize that your life is one whole page of problems and nothing ever gets solved. One ongoing equation with no equal sign at the end. But it occurred to me, beneath the canopy of a starlight heaven, that I’d been looking at my life all wrong. It wasn’t a math equation. Things weren’t supposed to add up. There was no solution. In fact, there was no problem. Life’s variables and numbers and pages of chicken scratch weren’t mathematical marks. They were art. A drawing. An abstract painting. It was meant to be beautiful, not sensical. And embedded within the mess of it all were miracles. Small ones. I’d never paid attention to them because I was too busy, but it didn’t make them less real.

There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory. For most physics students, this might occupy them from, say, third grade to early graduate school—roughly 15 years. Such a course of study does not actually involve learning any quantum mechanics, but merely establishing the mathematical framework required to approach it deeply.

5.4 The question of accumulation. If life is a wager, what form does it take? At the racetrack, an accumulator is a bet which rolls on profits from the success of one of the horse to engross the stake on the next one. 5.5 So a) To what extent might human relationships be expressed in a mathematical or logical formula? And b) If so, what signs might be placed between the integers?Plus and minus, self-evidently; sometimes multiplication, and yes, division. But these sings are limited. Thus an entirely failed relationship might be expressed in terms of both loss/minus and division/ reduction, showing a total of zero; whereas an entirely successful one can be represented by both addition and multiplication. But what of most relationships? Do they not require to be expressed in notations which are logically improbable and mathematically insoluble? 5.6 Thus how might you express an accumulation containing the integers b, b, a (to the first), a (to the second), s, v? B = s - v (*/+) a (to the first) Or a (to the second) + v + a (to the first) x s = b 5.7 Or is that the wrong way to put the question and express the accumulation? Is the application of logic to the human condition in and of itself self-defeating? What becomes of a chain of argument when the links are made of different metals, each with a separate frangibility? 5.8 Or is "link" a false metaphor? 5.9 But allowing that is not, if a link breaks, wherein lies the responsibility for such breaking? On the links immediately on the other side, or on the whole chain? But what do you mean by "the whole chain"? How far do the limits of responsibility extend? 6.0 Or we might try to draw the responsibility more narrowly and apportion it more exactly. And not use equations and integers but instead express matters in the traditional narrative terminology. So, for instance, if...." - Adrian Finn

In summary, the rather obscure laws of the weather are easy to understand once we view the earth from space. Thus the solution to the problem is to go up into space, into the third dimension. Facts that were impossible to understand in a flat world suddenly become obvious when viewing a three-dimensional earth. Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then the equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained as vibrations in the fifth dimension. In this way, we see that the laws of light and gravity become simpler in five dimensions.

As a civilization progresses, it goes through wars, pandemics, catastrophes. those that survive grow more astute, more perceptive, more advanced. Diseases are conquered, infirmity eliminated. Life spans increase. Suffering becomes largely a memory. "Meanwhile, their explorers and historians find evidence of past cultures, and cultures before that. At first it is exciting. But all they keep finding are ruins. And slowly, either through science or history, every advanced civilizations becomes aware of a disturbing possibility -- that their futures may end in ruin too. "The civilization then rushes to probe other stars, even other galaxies; it increases its research, attempting to manipulate space, time, in the hope that somewhere, someone might have found an escape, a loophole. "But eventually, the find, and solve, the mathematical equation that explains the entire universe." "I think our scientists are working on something like that too," Shizuka said. Lan shook her head. "They'll need to find the Grand Unified Theory a few more times before they can even begin to understand what 'everything' is -- sorry, I didn't mean to offend your civilization." Shizuka shrugged. "No offense taken." "Still, should your civilization survive, it will eventually find the same equation. And that will be your death sentence. For in that equation, there will be no forever, no eternity. Nothing. "And this collapse, and all its attendant despair, is the Endplague." Shizuka was puzzled. Space aliens, she could understand. Purple skin? Cute. Two elbows? Weird, but fine. Galactic warfare? Frankly, expected. Being a refugee? Of course. But how could the mere concept of mortality be enough to topple advanced civilizations? People live, people die, and so what?

Many other physicists get a little blasé about the vastness of the cosmos and forces too powerful to comprehend. You can reduce it all to mathematics, tweak some equations, and get on with your day. But the shock and vertigo of the recognition of the fragility of everything, and my own powerlessness in it, has left its mark on me. There’s something about taking the opportunity to wade into that cosmic perspective that is both terrifying and hopeful, like holding a newborn infant and feeling the delicate balance of the tenuousness of life and the potential for not-yet-imagined greatness. It is said that astronauts returning from space carry with them a changed perspective on the world, the “overview effect,” in which, having seen the Earth from above, they can fully perceive how fragile our little oasis is and how unified we ought to be as a species, as perhaps the only thinking beings in the cosmos.

Science in its everyday practice is much closer to art than to philosophy. When I look at Godel's proof of his undecidability theorem, I do not see a philosophical argument. The proof is a soaring piece of architecture, as unique and as lovely as Chartres Cathedral. Godel took Hilbert's formalized axioms of mathematics as his building blocks and built out of them a lofty structure of ideas into which he could finally insert his undecidable arithmetical statement as the keystone of the arch. The proof is a great work of art. It is a construction, not a reduction. It destroyed Hilbert's dream of reducing all mathematics to a few equations, and replaced it with a greater dream of mathematics as an endlessly growing realm of ideas. Godel proved that in mathematics the whole is always greater than the sum of the parts. Every formalization of mathematics raises questions that reach beyond the limits of the formalism into unexplored territory.

Olo, Remi, Kwuga, Nur, Anajama, Rhoden. Only Olo and Remi were in my group. Everyone else I met in the dining area or the learning room where various lectures were held by professors onboard the ship. They were all girls who grew up in sprawling houses, who’d never walked through the desert, who’d never stepped on a snake in the dry grass. They were girls who could not stand the rays of Earth’s sun unless it was shining through a tinted window. Yet they were girls who knew what I meant when I spoke of “treeing.” We sat in my room (because, having so few travel items, mine was the emptiest) and challenged each other to look out at the stars and imagine the most complex equation and then split it in half and then in half again and again. When you do math fractals long enough, you kick yourself into treeing just enough to get lost in the shallows of the mathematical sea. None of us would have made it into the university if we couldn’t tree, but it’s not easy. We were the best and we pushed each other to get closer to “God.

We have already seen that gauge symmetry that characterizes the electroweak force-the freedom to interchange electrons and neturinos-dictates the existence of the messenger electroweak fields (photon, W, and Z). Similarly, the gauge color symmetry requires the presence of eight gluon fields. The gluons are the messengers of the strong force that binds quarks together to form composite particles such as the proton. Incidentally, the color "charges" of the three quarks that make up a proton or a neutron are all different (red, blue, green), and they add up to give zero color charge or "white" (equivalent to being electrically neutral in electromagnetism). Since color symmetry is at the base of the gluon-mediated force between quarks, the theory of these forces has become known as quantum chromodynamics. The marriage of the electroweak theory (which describes the electromagnetic and weak forces) with quantum chromodynamics (which describes the strong force) produced the standard model-the basic theory of elementary particles and the physical laws that govern them.

Feynman said, “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied” Our sentence would be: “The Monadology asserts that the fundamental units of existence are INFINITE, dimensionless, living, thinking points – monads, ZEROS, souls – each of which has INFINITE energy content, all controlled by a single equation – Euler’s Formula – and the collective energy of this universe of mathematical points creates a physical universe of which every objective value is ZERO, but, through a self-solving, self-optimizing, dialectical, evolving process, the universe generates a final, subjective value of INFINITY – divinity, perfection, the ABSOLUTE.” For ours is the religion of zero and infinity, the two numbers that define the soul and the whole of existence. As above, so below.

Surprisingly, palindromes appear not just in witty word games but also in the structure of the male-defining Y chromosome. The Y's full genome sequencing was completed only in 2003. This was the crowning achievement of a heroic effort, and it revealed that the powers of preservation of this sex chromosome have been grossly underestimated. Other human chromosome pairs fight damaging mutations by swapping genes. Because the Y lacks a partner, genome biologists had previously estimated that its cargo was about to dwindle away in perhaps as little as five million years. To their amazement, however, the researchers on the sequencing team discovered that the chromosome fights withering with palindromes. About six million of its fifty million DNA letters form palindromic sequences-sequences that read the same forward and backward on the two strands of the double helix. These copies not only provide backups in case of bad mutations, but also allow the chromosome, to some extent, to have sex with itself-arms can swap position and genes are shuffled. As team leader David Page of MIT has put it, "The Y chromosome is a hall of mirrors.

There are some mysteries in this world," Yukawa said suddenly, "that cannot be unraveled with modern science. However, as science develops, we will one day be able to understand them. The question is, is there a limit to what science can know? If so, what creates that limit?" Kyohei looked at Yukawa. He couldn't figure out why the professor was telling him this, except he had a feeling it was very important. Yukawa pointed a finger at Kyohei's forehead. "People do." he said. "People's brains, to be more precise. For example, in mathematics, when somebody discovers a new theorem, they may have other mathematicians verify it to see if it's correct. The problem is, the theorems getting discovered are becoming more and more complex. That limits the number of mathematicians who can properly verify them. What happens when someone comes up with a theorem so hard to understand that there isn't anyone else who can understand it? In order for that theorem to be accepted as fact, they have to wait until another genius comes along. That's the limit the human brain imposes on the progress of scientific knowledge. You understand?" Kyohei nodded, still having no idea where he was going with this. "Every problem has a solution," Yukawa said, staring straight at Kyohei through his glasses. "But there's no guarantee that the solution will be found immediately. The same holds true in our lives. We encounter several problems to which the solutions are not immediately apparent in life. There is value to be had in worrying about those problems when you get to them. But never feel rushed. Often, in order to find the answer, you need time to grow first. That's why we apply ourselves, and learn as we go." Kyohei chewed on that for a moment, then his mouth opened a little and he looked up with sudden understanding. "You have questions now, I know, and until you find your answers, I'll be working on those questions too, and worrying with you. So don't forget, you're never alone.

In 1994 another bombshell was dropped. Edward Witten of Princeton's Institute for Advanced Study and Paul Townsend of Cambridge University speculated that all five string theories were in fact the same theory-but only if we add an eleventh dimension. From the vantage point of the eleventh dimension, all five different theories collapsed into one! The theory was unique after all, but only if we ascended to the mountaintop of the eleventh dimension. In the eleventh dimension a new mathematical object can exist, called the membrane (e.g., like the surface of a sphere). Here was the amazing observation: if one dropped from eleven dimensions down to ten dimensions, all five string theories would emerge, starting from a single membrane. Hence all five string theories were just different ways of moving a membrane down from eleven to ten dimensions. (To visualize this, imagine a beach ball with a rubber band stretched around the equator. Imagine taking a pair of scissors and cutting the beach ball twice, once above and once below the rubber band, thereby lopping off the top and bottom of the beach ball. All that is left is the rubber band, a string. In the same way, if we curl up the eleventh dimension, all that is left of a membrane is its equator, which is the string. In fact, mathematically there are five ways in which this slicing can occur, leaving us with five different string theories in ten dimensions.)

I took care to replace the Compendium in its correct pamphlet, and in doing so dislodged a slim pamphlet by Grastrom, one of the most eccentric authors in Solarist literature. I had read the pamphlet, which was dictated by the urge to understand what lies beyond the individual, man, and the human species. It was the abstract, acidulous work of an autodidact who had previously made a series of unusual contributions to various marginal and rarefied branches of quantum physics. In this fifteen-page booklet (his magnum opus!), Grastrom set out to demonstrate that the most abstract achievements of science, the most advanced theories and victories of mathematics represented nothing more than a stumbling, one or two-step progression from our rude, prehistoric, anthropomorphic understanding of the universe around us. He pointed out correspondences with the human body-the projections of our sense, the structure of our physical organization, and the physiological limitations of man-in the equations of the theory of relativity, the theorem of magnetic fields and the various unified field theories. Grastrom’s conclusion was that there neither was, nor could be any question of ‘contact’ between mankind and any nonhuman civilization. This broadside against humanity made no specific mention of the living ocean, but its constant presence and scornful, victorious silence could be felt between every line, at any rate such had been my own impression. It was Gibarian who drew it to my attention, and it must have been Giarian who had added it to the Station’s collection, on his own authority, since Grastrom’s pamphlet was regarded more as a curiosity than a true contribution to Solarist literature

If we shuffle three colored quarks and the equations remain the same, then we say that the equations possess something called SU(3) symmetry. The 3 represents the fact that we have three types of colors, and the SU stands for a specific mathematical property of the symmetry. We say that there are three quarks in a multiplet. The quarks in a multiplet can be shuffled among one another without changing the physics of the theory. Similarly, the weak force governs the properties of two particles, the electron and the neutrino. The symmetry that interchanges these particles, yet leaves the equation the same, is called SU(2). This means that a multiplet of the weak force contains an electron and a neutrino, which can be rotated into each other. Finally, the electromagnetic force has U(1) symmetry, which rotates the components of the Maxwell field into itself. Each of these symmetries is simple and elegant. However, the most controversial aspect of the Standard Model is that it "unifies" the three fundamental forces by simply splicing all three theories into one large symmetry. SU(3) X SU(2) X U(1), which is just the product of the symmetries of the individual forces. (This can be compared to assembling a jigsaw puzzle. If we have three jigsaw pieces that don't quite fit, we can always take Scotch tape and splice them together by hand. This is how the Standard Model is formed, by taping three distinct multiplets together. This may not be aesthetically pleasing, but at least the three jigsaw puzzles now hang together by tape.) Ideally, one might have expected that "the ultimate theory" would have all the particles inside just a single multiplet. Unfortunately, the Standard Model has three distinct multiplets, which cannot be rotated among one another.

So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!