Calculus Quotes

In the calculus of feelings, you never really know how one person's absence will affect you more than another's.

Dude, you're such a geek. And that's coming from an overweight Star Trek fan who scored a 5 on the AP Calculus test. So you know your condition is grave

You can't teach calculus to a chimpanzee. So just share your banana.

I don't want just a night or a week or a month with you. I want you all the time. I like you better than calculus, and math is the only thing that unites the universe.

We liked to be known as the clever girls. When we decorated our hands with henna for holidays and weddings, we drew calculus and chemical formulae instead of flowers and butterflies.

Well, I live a double life. Tonight, I'll escort you to dinner. Then I have to rush home and finish my calculus homework.' 'You're not joking, are you?' 'I never joke about calculus homework.

Calculus was not math. It was a fucking science experiment gone wrong.

She gave me the same smile I'd seen on Saturday night. That type of smile caused men to write those pussy-ass songs that Isaiah and I made fun of. I'd sit in Mrs. Collins's office for hours and wake my ass up early to go to calculus in order to see that smile again.

...magic was ugly—-a hard bargain with the universe, a calculus of pain.

Everyone has their weak spot. The one thing that despite your best efforts, will always bring you to your knees, regardless of how strong you are otherwise. For some people, it's love. Others, money or alcohol. Mine was even worse: calculus.

In the horrifying calculus of self-deception, the greater the pain we inflict on others, the greater the need to justify it to maintain our feelings of decency and self-worth.

Cam was so much clearer, easier to figure out. Like he was algebra and Daniel was calculus.

As you will find in multivariable calculus, there is often a number of solutions for any given problem.

History was easy, but I don't know about the Calculus. It seemed like it was making sense, so that probably means I failed.

Nothing takes place in the world whose meaning is not that of some maximum or minimum.

Tell them you came, and saw, and looked into my eyes and saw the shadow of the guard receding. Thoughts in time and out of season, the hitchinker stood by the side of the road and levelled his thumb in the calm calculus of reason. [...] Why does my mind circle around you? Why do planets wonder what it would be like to be you? All your soft wild promises were words, birds, endlessly in flight.

Justice is the first virtue of social institutions, as truth is of systems of thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust. Each person possesses an inviolability founded on justice that even the welfare of society as a whole cannot override. For this reason justice denies that the loss of freedom for some is made right by a greater good shared by others. It does not allow that the sacrifices imposed on a few are outweighed by the larger sum of advantages enjoyed by many. Therefore in a just society the liberties of equal citizenship are taken as settled; the rights secured by justice are not subject to political bargaining or to the calculus of social interests.

Normal. She wanted normal and so did I. "You know what's normal?" "What?" She wiped away her remaining tears. "Calculus.

Of course, I couldn’t explain this vector calculus concept and so, slightly embarrassed in front of Rahul and the other Bengali students, I told Sanjit just that; he had cornered me, and honesty emerged as my only option. Simultaneous to my humiliating disclosure of the truth, Sanjit gradually inched toward where I was sitting. After hearing my reply, he slowly returned to his teacher stool and whiteboard, his back turned away from the class, the suspense building and his words impending, before turning around and breaking into speech, “Don’t trust your interior monologue. If you are asked something and you know it, then express or demonstrate it. Don’t just nod or say yes because then you are lying to yourself. Any ass can say yes, but not all asses can express it.” I modified my first impression: Sanjit was full of explicit aphorisms. Humbled, those words encouragingly rang between my ears for quite some time.

I don’t believe in statistics. I believe in calculus.

I think I quit reading at the word stochastic, which actually sort of reminded me of Reid, if what it means is a combination of stoic and sarcastic. But I’m pretty sure it has to do with calculus.

I like you better than calculus, and maths is the only thing that unites the universe.

Hey, Tate. Do you just screw in the locker room or do you do blowjobs as well?” Hannah Forrest, queen bee of the mean girls, shouted to my back while I walked to Calculus. Her drones laughed with her. I spun around to face them and held my hand to my heart. “And steal all of your business?” I took the time to enjoy their dumbstruck looks before I twisted on my heel and headed to class.

Non- Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of Gothic tales and the wild whispers of the chimney-corner, one can hardly expect to be wholly free from mental tension. (Dreams In The Witch-House)

In the calculus of good deeds you have the most to gain.

Don’t Drink and DERIVE, Alcohol and Calculus Don’t Mix

Okay, so I may use basic math for doing my checking account, the percent-off sales on my favorite shoes, and other mundane things, but Calculus? When the hell would I ever use this?

No matter how significant or life-changing your greatest hit or miss might be, neither even begins to define who you are. Each of us is a product of all our experiences and all our interactions with other people. To cite calculus, we are the area under the curve.

If slavery persists as an issue in the political life of black America, it is not because of an antiquarian obsession with bygone days or the burden of a too-long memory, but because black lives are still imperiled and devalued by a racial calculus and a political arithmetic that were entrenched centuries ago. This is the afterlife of slavery--skewed life chances, limited access to health and education, premature death, incarceration, and impoverishment.

She used to leave chewed pencils on her desk every single day in calculus class. I may have picked them up. I may have saved them. They may still be in a drawer somewhere in my old room.

...love knows not of death nor calculus above the simple sum of heart plus heart.

This room was worse than she thought. Dark. Remote. Practically in the trees. Practically Enchanted. A calculus test would feel intimate in here.

Part of my job is to help other kids find books, because not everyone has a keenly organized mind. Some kids could wander the library for hours and still have no idea how to find anything. For them, the Dewey Decimal System might as well be advanced calculus.

That girl's visible collarbone is distracting me from calculus." - No Person Ever

Imagine a life-form whose brainpower is to ours as ours is to a chimpanzee’s. To such a species, our highest mental achievements would be trivial. Their toddlers, instead of learning their ABCs on Sesame Street, would learn multivariable calculus on Boolean Boulevard. Our most complex theorems, our deepest philosophies, the cherished works of our most creative artists, would be projects their schoolkids bring home for Mom and Dad to display on the refrigerator door.

Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy -- it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.

Each person possesses and inviolability founded on justice that even the welfare of society as a whole cannot override. For this reason, justice denies that the loss of freedom for some is made right by a greater good shared by others. It does not allow that the sacrifices imposed on a few are outweighed by the larger sum of advantages enjoyed by many. Therefore in a just society the liberties of equal citizenship are taken as settled; the rights secured by justice are not subject to political bargaining or to the calculus of social interests. The only thing that permits us to acquiesce in an erroneous theory is the lack of a better one; analogously, an injustice is tolerable only when it is necessary to avoid an even greater injustice. Being first virtues of human activities, truth and justice are uncompromising.

I think scientists have a valid point when they bemoan the fact that it's socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate.

This book is for all of us who looked up at the sky in wonder, and then cried when we learned how much calculus separated us from the stars

...film and calculus, both pornographies of flight.

And how many Daeva children died when your people invaded? Far more than the Geziri children who will be lost tonight." Muntadhir stared at him in shock. "Do you hear yourself? What sort of man plots that calculus?" Hate filled his gray eyes. "God, I hope it's her in the end. I hope Nahri puts a goddamned knife through whatever passes for your heart.

What music is to the heart, mathematics is to the mind.

What would you attempt to do if you knew you couldn't fail?" "Calculus, prolly. Why?

As a student, frustrated by the limitations of conventional mathematics, he invented an entirely new form, the calculus, but then told no-one about it for twenty-seven years5.

An uncredited study she read once said, quote, “Girls become really stupid in science after they get their period, so you’d better learn as much as possible before that happens.” I had such anxiety about this “clearly proven” biological fact that I was studying calculus by the age of twelve. When I finally got my period, I cried, not because I was growing up, but because I had just learned derivatives and really enjoyed doing them. I was scared that estrogen would wipe the ability to do them from my brain.

Abuse of the military metaphor may be inevitable in a capitalist society, a society that increasingly restricts the scope and credibility of appeals to ethical principle, in which it is thought foolish not to subject one's actions to the calculus of self-interest and profitability. War-making is one of the few activities that people are not supposed to view 'realistically'; that is, with an eye to expense and practical outcome. In all-out war, expenditure is all-out, unprudent--war being defined as as an emergency in which no sacrifice is excessive.

From my point of view, any outstanding work of art is a fantasy insofar as it reflects the unique world of a unique individual. Art is not just simple arithmetic, it's a delicate calculus. Keep in mind the passion of the scientist and the precision of the artist.

Why did they all think alike? Typical bourgeois brainwashed homogeneity? How else could this unvarying calculus abouth the worth of one's own kind measured against the lives of others have come about?

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus.

For remember that in general we don't use language according to strict rules-- it hasn't been taught to us by means of strict rules, either. We, in our discussions on the other hand, constantly compare language with a calculus preceding to exact rules.

I never joke about calculus homework." - Sam al-Abbas

She marvels again at how the planet’s supreme intelligence could discover calculus and the universal laws of gravitation before anyone knew what a flower was for.

Pratap Mehta wrote: The targeting of enemies—minorities, liberals, secularists, leftists, urban naxals, intellectuals, assorted protestors—is not driven by a calculus of ordinary politics….When you legitimize yourself entirely by inventing enemies, the truth ceases to matter, normal restraints of civilization and decency cease to matter, the checks and balances of normal politics cease to matter.*2

It was in this man's class that I first began to wonder if people who wrote fiction were not suffering from some kind of disorder--from what I've since come to think of, remembering the wild nocturnal rocking of Albert Vetch, as the midnight disease. The midnight disease is a kind of emotional insomnia; at every conscious moment its victim--even if he or she writes at dawn, or in the middle of the afternoon--feels like a person lying in a sweltering bedroom, with the window thrown open, looking up at a sky filled with stars and airplanes, listening to the narrative of a rattling blind, an ambulance, a fly trapped in a Coke bottle, while all around him the neighbors soundly sleep. this is in my opinion why writers--like insomniacs--are so accident-prone, so obsessed with the calculus of bad luck and missed opportunities, so liable to rumination and a concomitant inability to let go of a subject, even when urged repeatedly to do so.

Marriage is like calculus. Complicated and inexplicably remote. People think it's about loving one another and riding off into the sunset, but no one tells you the horse is lame or that it's an eclipse, and there won't be a sunset that day.

Empathy is not only a personal feeling; it can be a potent force for political and social change. And thus the suppression or denial of empathy is a deliberate part of a cynical political calculus. Dividing people and stoking animosity can pave a path to power (and in many recent elections, it has). This has been well known since the time of the ancients. But these divisions inevitably come at the expense of the long-term health and welfare of the nation as a whole.

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.

Yet in another way, calculus is fundamentally naive, almost childish in its optimism. Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus draws its power by refusing to see that. It insists on a world without accidents, where one thing leads logically to another. Give me the initial conditions and the law of motion, and with calculus I can predict the future -- or better yet, reconstruct the past. I wish I could do that now.

The world of the known and the not yet known is bridged by wonderment. But wonderment happens largely in a situation where the child’s world is separate from the adult world, where children must seek entry, through their questions, into the adult world. As media merge the two worlds, as the tension created by secrets to be unraveled is diminished, the calculus of wonderment changes. Curiosity is replaced by cynicism or, even worse, arrogance. We are left with children who rely not on authoritative adults but on news from nowhere. We are left with children who are given answers to questions they never asked. We are left, in short, without children.

That is what is marvelous about school, she realized: when you are in school, your talents are without number, and your promise is boundless. You ace a math test: you will one day work for NASA. The choir director asks you to sing a solo at the holiday concert: you are the next Mariah Carey. You score a goal, you win a poetry contest, you act in a play. And you are everything at once: actor, astronomer, gymnast, star. But at a certain point, you begin to feel your talents dropping away, like feathers from a molting bird. Cello lessons conflict with soccer practice. There aren't enough spots on the debating team. Calculus remains elusive. Until the day you realize that you cannot think of a single thing you are wonderful at.

And then he was there, staring at me from behind the screen door. I'd like to say he no longer affected me, that seeing him was a disappointment. But it wasn't true. I felt as strongly about him as I had on that first day I'd seen him in calculus class.

To grasp how different a million is from a billion, think about it like this: A million seconds is a little under two weeks; a billion seconds is about thirty-two years.

We've developed algorithms for orgasms, broken it down to a science, I spell out equations on the small of your back, your kisses, the most beautiful calculus I've ever studied. You do fractions and long handed division up my thighs, balance equations between my legs...even my sharp clefts and C-notes can't match our depths...

[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.

Everyone hated Calculus. Quadratic equations, parabolas, logarithms, trigonometry - you name it. It was like floating in an endless, frictionless void traveling at x miles per hour at a descension rate of one half the speed of gravity. Solve for x.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

That was the danger of being old and a politician. Habits outlived the situations that created them. Policies remained in place after the situations that inspired them had changed. The calculus of all human power was changing, and the models she used to make sense of it shifted with them, and she had to keep reminding herself that the past was a different place. She didn’t live there anymore.

It was an admission of defeat. ... He knew he needed to do a better job of navigating the world, but he didn't know how. He couldn't even talk to his calculus teacher, for goodness' sake. These were things that others, with lesser minds, could master easily. But that's because those others had had help along the way, and Chris Langan never had. It wasn't an excuse. It was a fact. He'd had to make his way alone, and no one--not even rock stars, not professional athletes, not software billionaires, and not even geniuses--ever makes it alone.

But here, Ms. Pelletier, is the thing. Without infinitesimals, the calculus as we know and love it simply wouldn't exist. It is these nearly-zero, sort-of-zero, sometimes-zero quantities that allow us to understand the world. Something which seems to be nearly nothing turns out to be crucial to everything. So though I, or for you that matter, or any of us, may be, as a collection of atoms, practically indistinguishable from zero, this does not necessarily mean we are insignificant. Indeed, it may be that we are actually crucially important.

It is not easy to become an educated person.

Then he smiled into her eyes and asked, in the dry academic tones of an astronomer discussing a theoretical point with a colleague, 'How long do you suppose I can go on loving you more every day?' And he devised for her a calculus of love, which approached infinity as a limit, and made her smile again.

The intentions of the cybernetic totalist tribe are good. They are simply following a path that was blazed in earlier times by well-meaning Freudians and Marxists - and I don't mean that in a pejorative way. I'm thinking of the earliest incarnations of Marxism, for instance, before Stalinism and Maoism killed millions. Movements associated with Freud and Marx both claimed foundations in rationality and the scientific understanding of the world. Both perceived themselves to be at war with the weird, manipulative fantasies of religions. And yet both invented their own fantasies that were just as weird. The same thing is happening again. A self-proclaimed materialist movement that attempts to base itself on science starts to look like a religion rather quickly. It soon presents its own eschatology and its own revelations about what is really going on - portentous events that no one but the initiated can appreciate. The Singularity and the noosphere, the idea that a collective consciousness emerges from all the users on the web, echo Marxist social determinism and Freud's calculus of perversions. We rush ahead of skeptical, scientific inquiry at our peril, just like the Marxists and Freudians.

Cooking, I found, gives us the opportunity, so rare in modern life, to work directly in our own support, and in the support of the people we feed. If this is not “making a living,” I don’t know what is. In the calculus of economics, doing so may not always be the most efficient use of an amateur cook’s time, but in the calculus of human emotion, it is beautiful even so. For is there any practice less selfish, any labor less alienated, any time less wasted, than preparing something delicious and nourishing for people you love?

If you put it as 'complex nervous systems' it sounds pretty deflationary. What's so special about a complex nervous system? But of course, that complex nervous system allows you to do calculus. It allows you to do astrophysics… to write poetry... to fall in love. Put under that description, when asked 'What’s so special about humans...?', I’m at a loss to know how to answer that question. If you don’t see why we’d be special… because we can do poetry [and] think philosophical thoughts [and] we can think about the morality of our behavior, I’m not sure what kind of answer could possibly satisfy you at that point. ...I could pose the same kinds of questions of you... So God says, 'You are guys are really, really special.' How does his saying it make us special? 'But you see, he gave us a soul.' How does our having a soul make us special? Whatever answer you give, you could always say… 'What’s so special about that?

Alongside the liberating relief of the veteran who tells us his story, I now felt in the writing a complex, intense, and new pleasure, similar to that I felt as a student when penetrating the solemn order of differentials calculus. It was exalting to search and find, or create, the right word, that is, commensurate, concise, and strong; to dredge up events from my memory and describe them with the greatest rigor and the least clutter.

Though blessed with the enviable properties of a mink coat—graceful, unreasonable, and impractical no matter what she was draped over—she was nevertheless one of those people whose personality proved to be the bane of modern mathematicians. She was neither a flat nor solid shape. She showed no symmetry at all. Trigonometry, Calculus and Statistics all proved useless. Her Pie Chart was a muddle of arbitrary wedges, her Line Graph, the silhouette of the Alps. And just when one listed her under Chaos Theory—Butterfly Effects, Weather Predictions, Fractals, Bifurcation diagrams and whatnot—she showed up as an equilateral triangle, sometimes even a square.

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!

As Brother Francis readily admitted, his mastery of pre-Deluge English was far from masterful yet. The way nouns could sometimes modify other nouns in that tongue had always been one of his weak points. In Latin, as in most simple dialects of the region, a construction like servus puer meant about the same thing as puer servus, and even in English slave boy meant boy slave. But there the similarity ended. He had finally learned that house cat did not mean cat house, and that a dative of purpose or possession, as in mihi amicus, was somehow conveyed by dog food or sentry box even without inflection. But what of a triple appositive like fallout survival shelter? Brother Francis shook his head. The Warning on Inner Hatch mentioned food, water, and air; and yet surely these were not necessities for the fiends of Hell. At times, the novice found pre-Deluge English more perplexing than either Intermediate Angelology or Saint Leslie's theological calculus.

Have you ever wanted to learn Geometry, Calculus, Physics, German, and the mystical teachings of Orafoura? Well, now you can! Just not with this book. Well, except for the mystical bit. This book is guaranteed to cost you, or your money back. If there is ever a book that deserves to be burned, this is it. And while you are lighting a fire, why don't you also set your imagination ablaze? You can start by taking a gasoline shower and sprinting naked through Flint, Michigan. Or Phoenix. After all, the only way you'll ever be able to reach your true potential is with a stepladder and a stretch.

Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel’s Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country’s greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome".

Critics often say that DDLJ, with its emphasis on patriarchal permission for young love, discourages dissent. This argument narrows the space for dissent by legitimizing it only in its most blatant, combative form, demanding that dissent always be obvious and 'out there' in full view of TV cameras and Twitter. So, no act of protest short of elopement, short of the most radical rejection of family, would suffice. Demanding such all-or-nothing actions doesn't account for the costs that eloping and actively abandoning their families would impose on women from any economic strata. The way we express resistance is subject to our own personal calculus of risk and reward.

The midnight disease is a kind of emotional insomnia; at every conscious moment its victim—even if he or she writes at dawn, or in the middle of the afternoon—feels like a person lying in a sweltering bedroom, with the window thrown open, looking up at a sky filled with stars and airplanes, listening to the narrative of a rattling blind, an ambulance, a fly trapped in a Coke bottle, while all around him the neighbors soundly sleep. This is in my opinion why writers—like insomniacs—are so accident-prone, so obsessed with the calculus of bad luck and missed opportunities, so liable to rumination and a concomitant inability to let go of a subject, even when urged repeatedly to do so.

Right. I don't believe in the idea that there are a few peculiar people capable of understanding math, and the rest of the world is normal. Math is a human discovery, and it's no more complicated than humans can understand. I had a calculus book once that said, 'What one fool can do, another can.' What we've been able to work out about nature may look abstract and threatening to someone who hasn't studied it, but it was fools who did it, and in the next generation, all the fools will understand it. There's a tendency to pomposity in all this, to make it deep and profound.

Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

As to the 'Left' I'll say briefly why this was the finish for me. Here is American society, attacked under open skies in broad daylight by the most reactionary and vicious force in the contemporary world, a force which treats Afghans and Algerians and Egyptians far worse than it has yet been able to treat us. The vaunted CIA and FBI are asleep, at best. The working-class heroes move, without orders and at risk to their lives, to fill the moral and political vacuum. The moral idiots, meanwhile, like Falwell and Robertson and Rabbi Lapin, announce that this clerical aggression is a punishment for our secularism. And the governments of Pakistan and Saudi Arabia, hitherto considered allies on our 'national security' calculus, prove to be the most friendly to the Taliban and Al Qaeda. Here was a time for the Left to demand a top-to-bottom house-cleaning of the state and of our covert alliances, a full inquiry into the origins of the defeat, and a resolute declaration in favor of a fight to the end for secular and humanist values: a fight which would make friends of the democratic and secular forces in the Muslim world. And instead, the near-majority of 'Left' intellectuals started sounding like Falwell, and bleating that the main problem was Bush's legitimacy. So I don't even muster a hollow laugh when this pathetic faction says that I, and not they, are in bed with the forces of reaction.

In such a wild, uncharted place the book of God was vital, for it nourished their spirit and laid boundaries for their conduct. Other subjects simply had no relevance. Trigonometry and calculus would not help them find their way among the mountain trails. Adam Smith's economics were of no consequence in the matter of planting corn and breeding cattle. Nor did they need the essays of Plato or the plays of Shakespeare to teach them how to shoot a rifle, or to make clothes from animal skins, or to clear away the wilderness with their own bare hands.

In the Blue Room, Cora Cash was trying to concentrate on her book. Cora found most novels hard to sympathise with -- all those plain governesses -- but this one had much to recommend it. The heroine was 'handsome, clever, and rich', rather like Cora herself. Cora knew she was handsome -- wasn't she always referred to in the papers as 'the divine Miss Cash'? She was clever -- she could speak three languages and could handle calculus. And as to rich, well, she was undoubtedly that. Emma Woodhouse was not rich in the way that she, Cora Cash, was rich. Emma Woodhouse did not lie on a lit à la polonaise once owned by Madame du Barry in a room which was, but for the lingering smell of paint, an exact replica of Marie Antoinette's bedchamber at le petit Trianon. Emma Woodhouse went to dances at the Assembly Rooms, not fancy dress spectaculars in specially built ballrooms. But Emma Woodhouse was motherless which meant, thought Cora, that she was handsome, clever, rich and free.

If you wrestle an angel, you will grow muscle. There’s no doubt of that. You will also hurt in places that you didn’t know you had. There’s no doubt of that either. And you will lose, by the normal calculus of trying to engineer the life that you’re sure you deserve. It will not come out as you planned, wrestling angels. Your plans our usually the first casualty of the match. But here is that great secret of it: you will be able to boast of your defeat. You will be able to stand in the wreckage of what used to be your certainty, your creed, your way of doing life’s business, and you can tell wild, true stories about how it all came to ruin. Whatever is left standing - and there is always something left standing when you wrestle angels - is the thing that was true about you and your life all along, as faithful a companion as the Earth that will one day cradle you again.

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer...

The semanticists maintained that everything depends on how you interpret the words “potato,” “is” and “moving.” Since the key here is the operational copula “is,” one must examine “is” rigorously. Whereupon they set to work on an Encyclopedia of Cosmic Semasiology, devoting the first four volumes to a discussion of the operational referents of “is.” The neopositivists maintained that it is not clusters of potatoes one directly perceives, but clusters of sensory impressions. Then, employing symbolic logic, they created terms for “cluster of impressions” and “cluster of potatoes,” devised a special calculus of propositions all in algebraic signs and after using up several seas of ink reached the mathematically precise and absolutely undeniable conclusion that 0=0.

Tinkerers built America. Benjamin Franklin, Thomas Edison, Henry Ford, all were tinkerers in their childhood. Everything from the airplane to the computer started in somebody's garage. Go back even further: the Industrial Revolution was a revolution of tinkerers. The great scientific thinkers of eighteenth-century England couldn't have been less interested in cotton spinning and weaving. Why would you be? It was left to a bloke on the shop floor who happened to glance at a one-thread wheel that had toppled over and noticed that both the wheel and the spindle were still turning. So James Hargreaves invented the spinning jenny, and there followed other artful gins and mules and frames and looms, and Britain and the world were transformed. By tinkerers rather than thinkerers. "Technological change came from tinkerers," wrote Professor J.R. McNeill of Georgetown, "people with little or no scientific education but with plenty of hands-on experience." John Ratzenberger likes to paraphrase a Stanford University study: "Engineers who are great in physics and calculus but can't think in new ways about old objects are doomed to think in old ways about new objects." That's the lesson of the spinning jenny: an old object fell over and someone looked at it in a new way.

To me, it is entirely clear that the relation between the rhythmics of verse and prose is the same as that between arithmetic and integral calculus. In arithmetic we sum up individual items; in integral calculus we deal with sums, series. The prose foot is measured, not by the distance between stressed syllables, but by the distance between (logically) stressed words . And in prose, just as in integral calculus, we deal not with constant quantities (as in verse and arithmetic) but with variable ones. In prose, the foot is always a variable quantity, it is always being either slowed or accelerated. This, of course, is not fortuitous: it is determined by the emotional and semantic accelerations and retardations in the text.22

In mathematical modeling, as in all of science, we always have to make choices about what to stress and what to ignore. The art of abstraction lies in knowing what is essential and what is minutia, what is signal and what is noise, what is trend and what is wiggle. It's an art because such choices always involve an element of danger; they come close to wishful thinking and intellectual dishonesty.

It was as if she had just discovered the irreversible process. It astonished her to think that so much could be lost, even the quantity of hallucination belonging just to the sailor that the world would bear no further trace of. She knew, because she had held him, that he suffered DT’s. Behind the initials was a metaphor, a delirium tremens, a trembling unfurrowing of the mind’s plowshare. The saint whose water can light lamps, the clairvoyant whose lapse in recall is the breath of God, the true paranoid for whom all is organized in spheres joyful or threatening about the central pulse of himself, the dreamer whose puns probe ancient fetid shafts and tunnels of truth all act in the same special relevance to the word, or whatever it is the word is there, buffering, to protect us from. The act of metaphor then was a thrust at truth and a lie, depending where you were: inside, safe, or outside, lost. Oedipa did not know where she was. Trembling, unfurrowed, she slipped sidewise, screeching back across grooves of years, to hear again the earnest, high voice of her second or third collegiate love Ray Glozing bitching among “uhs” and the syncopated tonguing of a cavity, about his freshman calculus; “dt,” God help this old tattooed man, meant also a time differential, a vanishingly small instant in which change had to be confronted at last for what it was, where it could no longer disguise itself as something innocuous like an average rate; where velocity dwelled in the projectile though the projectile be frozen in midflight, where death dwelled in the cell though the cell be looked in on at its most quick. She knew that the sailor had seen worlds no other man had seen if only because there was that high magic to low puns, because DT’s must give access to dt’s of spectra beyond the known sun, music made purely of Antarctic loneliness and fright. But nothing she knew of would preserve them, or him.

The list of correlations to that night is as long as the Jersey coast. And so is the list of reasons I shouldn't be looking forward to seeing him at school. But I can't help it. He's already texted me three times this morning: Can I pick you up for school? and Do u want 2 have breakfast? and R u getting my texts? My thumbs want to answer "yes" to all of the above, but my dignity demands that I don't answer at all. He called my his student. He stood there alone with me on the beach and told me he thinks of me as a pupil. That our relationship is platonic. And everyone knows what platonic means-rejected. Well, I might be his student, but I'm about to school, him on a few things. The first lesson of the day is Silent Treatment 101. So when I see him in the hall, I give him a polite nod and brush right by him. The zap from the slight contact never quite fades, which mean he's following me. I make it to my locker before his hand is on my arm. "Emma." The way he whispers my name sends goose bumps all the way to my baby toes. But I'm still in control. I nod to him, dial the combination to my locker, then open it in his face. He moves back before contact. Stepping around me, he leans his hand against the locker door and turns me around to face him. "That's not very nice." I raise my best you-started-this brow. He sighs. "I guess that means you didn't miss me." There are so many things I could pop off right now. Things like, "But at least I had Toraf to keep my company" or "You were gone?" Or "Don't feel bad, I didn't miss my calculus teacher either." But the goal is to say nothing. So I turn around. I transfer books and papers between my locker and backpack. As I stab a pencil into my updo, his breath pushes against my earlobe when he chuckles. "So your phone's not broken; you just didn't respond to my texts." Since rolling my eyes doesn't make a sound, it's still within the boundaries of Silent Treatment 101. So I do this while I shut my locker. As I push past him, he grabs my arm. And I figure if stomping on his toe doesn't make a sound... "My grandmother's dying," he blurts. Commence with the catching-Emma-off-guard crap. How can I continue Silent Treatment 101 after that? He never mentioned his grandmother before, but then again, I never mentioned mine either. "I'm sorry, Galen." I put my hand on his, give it a gentle squeeze. He laughs. Complete jackass. "Conveniently, she lives in a condo in Destin and her dying request is to meet you. Rachel called your mom. We're flying out Saturday afternoon, coming back Sunday night. I already called Dr. Milligan." "Un-freaking-believable.

Loftus grew up with a cold father who taught her nothing about love but everything about angles. A mathematician, he showed her the beauty of the triangle's strong tip, the circumference of the circle, the rigorous mission of calculus. Her mother was softer, more dramatic, prone to deep depressions. Loftus tells all this to me with little feeling "I have no feelings about this right now," she says, "but when I'm in the right space I could cry." I somehow don't believe her; she seems so far from real tears, from the original griefs, so immersed in the immersed in the operas of others. Loftus recalls her father asking her out to see a play, and in the car, coming home at night, the moon hanging above them like a stopwatch, tick tick, her father saying to her, "You know, there's something wrong with your mother. She'll never be well again. Her father was right. When Loftus was fourteen, her mother drowned in the family swimming pool. She was found floating face down in the deep end, in the summer. The sun was just coming up, the sky a mess of reds and bruise. Loftus recalls the shock, the siren, an oxygen mask clamped over her mouth as she screamed, "Mother mother mother," hysteria. That is a kind of drowning. "I loved her," Loftus says. "Was it suicide?" I ask. She says, "My father thinks so. Every year when I go home for Christmas, my brothers and I think about it, but we'll never know," she says. Then she says, "It doesn't matter." "What doesn't matter?" I ask. "Whether it was or it wasn't," she says. "It doesn't matter because it's all going to be okay." Then I hear nothing on the line but some static. on the line but some static. "You there?" I say. "Oh I'm here," she says. "Tomorrow I'm going to Chicago, some guy on death row, I'm gonna save him. I gotta go testify. Thank God I have my work," she says. "You've always had your work," I say. "Without it," she says, "Where would I be?

We know, however, that the mind is capable of understanding these matters in all their complexity and in all their simplicity. A ball flying through the air is responding to the force and direction with which it was thrown, the action of gravity, the friction of the air which it must expend its energy on overcoming, the turbulence of the air around its surface, and the rate and direction of the ball's spin. And yet, someone who might have difficulty consciously trying to work out what 3 x 4 x 5 comes to would have no trouble in doing differential calculus and a whole host of related calculations so astoundingly fast that they can actually catch a flying ball. People who call this "instinct" are merely giving the phenomenon a name, not explaining anything. I think that the closest that human beings come to expressing our understanding of these natural complexities is in music. It is the most abstract of the arts - it has no meaning or purpose other than to be itself. Every single aspect of a piece of music can be represented by numbers. From the organization of movements in a whole symphony, down through the patterns of pitch and rhythm that make up the melodies and harmonies, the dynamics that shape the performance, all the way down to the timbres of the notes themselves, their harmonics, the way they change over time, in short, all the elements of a noise that distinguish between the sound of one person piping on a piccolo and another one thumping a drum - all of these things can be expressed by patterns and hierarchies of numbers. And in my experience the more internal relationships there are between the patterns of numbers at different levels of the hierarchy, however complex and subtle those relationships may be, the more satisfying and, well, whole, the music will seem to be. In fact the more subtle and complex those relationships, and the further they are beyond the grasp of the conscious mind, the more the instinctive part of your mind - by which I mean that part of your mind that can do differential calculus so astoundingly fast that it will put your hand in the right place to catch a flying ball- the more that part of your brain revels in it. Music of any complexity (and even "Three Blind Mice" is complex in its way by the time someone has actually performed it on an instrument with its own individual timbre and articulation) passes beyond your conscious mind into the arms of your own private mathematical genius who dwells in your unconscious responding to all the inner complexities and relationships and proportions that we think we know nothing about. Some people object to such a view of music, saying that if you reduce music to mathematics, where does the emotion come into it? I would say that it's never been out of it.

As soon as she releases me, Galen grabs my hand and I don’t even have time to gasp before he snatches me to the surface and pulls me toward shore, only pausing to dislodge his pair of swimming trunks from under his favorite rock, where he had just moments before taken the time to hide them. I know the routine and turn away so he can change, but it seems like no time before he hauls me onto the beach and drags me to the sand dunes in front of my house. “What are we doing?” I ask. His legs are longer than mine so for every two of his strides I have to take three, which feels a lot like running. He stops us in between the dunes. “I’m doing something that is none of anyone else’s business.” Then he jerks me up against him and crushes his mouth on mine. And I see why he didn’t want an audience for this kiss. I wouldn’t want an audience for this kiss, either, especially if the audience included my mother. This is our first kiss after he announced that he wanted me for his mate. This kiss holds promises of things to come. When he pulls away I feel drunk and excited and nervous and filled with a craving that I’m not sure can ever be satisfied. And Galen looks startled. “Maybe I shouldn’t have done that,” he says. “That makes it about fifty times harder to leave, I think.” He tucks my head under his chin and I wrap my arms around him until both our breathing returns to normal. I take the time to soak in his scent, his warmth, the hard contours of his-well, his everything. It’s really not fair that he has to leave when he’s only just gotten back. We didn’t have much time to talk on the way back home. We haven’t had much time for anything. “Emma,” he murmurs. “The water isn’t safe for you right now. Please don’t get in it. Please.” “I won’t.” I really won’t. He said please, after all. He lifts my chin with the crook of his finger. His eyes hold all the gentleness and love in the world, with a pinch of mischief. “And take good notes in calculus, or I’ll be forced to cheat off you and for some weird reason that makes me feel guilty.” I wonder what Grom the Triton king would think of that. That Galen basically just stated his intention to keep doing human things. Galen pushes his lips against my forehead, then disentangles himself from me and leads me back toward the water. My body feels ten degrees cooler when his arms fall, and it’s got nothing to do with the temperature outside. We reach the others just in time to see Rayna all but throw herself at Toraf. I can’t help but smile as they kiss. It’s like watching Beauty and the Beast. And Toraf’s not the Beast.

The three thousand miles in distance he put between himself and Emma tonight is nothing compared with the enormous chasm separating them when they sit next to each other in calculus. Emma's ability to overlook his existence is a gift-but not one that Poseidon handed down. Rachel insists this gift is uniquely a female trait, regardless of the species. Since their breakup, Emma seems to be the only female utilizing this particular gift. Even Rayna could learn a few lessons from Emma in the art of torturing a smitten male. Smitten? More like fanatical. He shakes his head in disgust. Why couldn't I just sift when I turned of age? Why couldn't I find a suitable mild-tempered female to mate with? Live a peaceful life, produce offspring, grow old, and watch my own fingerlings have fingerlings someday? He searches through his mind for someone he might have missed in the past. For a face he overlooked before but could now look forward to every day. For a docile female who would be honored to mate with a Triton prince-instead of a temperamental siren who mocks his title at every opportunity. He scours his memory for a sweet-natured Syrena who would take care of him, who would do whatever he asked, who would never argue with him. Not some human-raised snippet who stomps her foot when she doesn't get her way, listens to him only when it suits some secret purpose she has, or shoves a handful of chocolate mints down his throat if he lets his guard down. Not some white-haired angelfish whose eyes melt him into a puddle, whose blush is more beautiful than sunrise, and whose lips send heat ripping through him like a mine explosion. He sighs as Emma's face eclipses hundreds of mate-worthy Syrena. That's just one more quality I'll have to add to the list: someone who won't mind being second best. His just locks as he catches a glimpse of his shadow beneath him, cast by slithers of sterling moonlight. Since it's close to three a.m. here, he's comfortable walking around without the inconvenience of clothes, but sitting on the rocky shore in the raw is less than appealing. And it doesn't matter which Jersey shore he sits on, he can't escape the moon that connects them both-and reminds him of Emma's hair. Hovering in the shallows, he stares up at it in resentment, knowing the moon reminds him of something else he can' escape-his conscience. If only he could shirk his responsibilities, his loyalty to his family, his loyalty to his people. If only he could change everything about himself, he could steal Emma away and never look back-that is, if she'll ever talk to him again.