Mathematical Quotes

Don’t try to make life a mathematics problem with yourself in the center and everything coming out equal. When you’re good, bad things can still happen. And if you’re bad, you can still be lucky.

It's not because I want to make out with her." Hold on." He grabbed a pencil and scrawled excitedly at the paper as if he'd just made a mathematical breakthrough and then looked back up at me. "I just did some calculations, and I've been able to determine that you're full of shit

Life is not so idiotically mathematical that only the big eat the small; it is just as common for a bee to kill a lion or at least to drive it mad.

A mathematical formula for happiness:Reality divided by Expectations.There were two ways to be happy:improve your reality or lower your expectations.

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

In real life, I assure you, there is no such thing as algebra.

What do we call visible light? We call it color. But the electromagnetic spectrum runs to zero in one direction and infinity in the other, so really, children, mathematically, all of light is invisible.

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?

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

Cats can work out mathematically the exact place to sit that will cause most inconvenience.

You’re perfect,” I tell him, so overcome I forget myself. “All of you. Your entire body. Proportionally. Symmetrically. You’re absurdly, mathematically perfect. It doesn’t even make sense that a person could look like you,

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.

Hold on." He grabbed a pencil and scrawled excitedly at the paper as if he'd just made a mathematical breakthrough and then looked back up at me. "I just did some calculations, and I've been able to determine that you're full of shit.

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 science of government it is my duty to study, more than all other sciences; the arts of legislation and administration and negotiation ought to take the place of, indeed exclude, in a manner, all other arts. I must study politics and war, that our sons may have liberty to study mathematics and philosophy. Our sons ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry and porcelain.

Dull minds are never either intuitive or mathematical.

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.

Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts... A graphic representation of data abstracted from banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, receding...

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.

Anyone who cannot cope with mathematics is not fully human. At best, he is a tolerable subhuman who has learned to wear his shoes, bathe, and not make messes in the house.

I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody's easiest course at school and our species would not have taken several millennia to figure out the scientific method.

I'm sorry to say that the subject I most disliked was mathematics. I have thought about it. I think the reason was that mathematics leaves no room for argument. If you made a mistake, that was all there was to it.

Our species is the only creative species, and it has only one creative instrument, the individual mind and spirit of man. Nothing was ever created by two men. There are no good collaborations, whether in music, in art, in poetry, in mathematics, in philosophy. Once the miracle of creation has taken place, the group can build and extend it, but the group never invents anything. The preciousness lies in the lonely mind of a man.

Young man, in mathematics you don't understand things. You just get used to them.

But in my opinion, all things in nature occur mathematically.

The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.

Pure mathematics is in its way the poetry of logical ideas.

Since the mathematicians have invaded the theory of relativity I do not understand it myself any more.

It has become almost a cliché to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics.

I had a polynomial once. My doctor removed it.

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.

Eternity is said not to be an extension of time but an absence of time, and sometimes it seemed to me that her abandonment touched that strange mathematical point of endlessness, a point with no width, occupying no space.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

Mathematics is the language in which God has written the universe

Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.

Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning.

Do you know what the mathematical expression is for longing? ... The negative numbers. The formalization of the feeling that you are missing something.

Whereas I think: I’m lying here in a haystack... The tiny space I occupy is so infinitesimal in comparison with the rest of space, which I don’t occupy and which has no relation to me. And the period of time in which I’m fated to live is so insignificant beside the eternity in which I haven’t existed and won’t exist... And yet in this atom, this mathematical point, blood is circulating, a brain is working, desiring something... What chaos! What a farce!

Maybe that is what beauty was, for humans. Accidents, imperfections, placed inside a pretty pattern. Asymmetry. The defiance of mathematics.

Solving a problem for which you know there’s an answer is like climbing a mountain with a guide, along a trail someone else has laid. In mathematics, the truth is somewhere out there in a place no one knows, beyond all the beaten paths. And it’s not always at the top of the mountain. It might be in a crack on the smoothest cliff or somewhere deep in the valley.

My first feeling was that there was no way to continue. Writing isn't like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything.

I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.

Give me but a firm spot on which to stand, and I shall move the earth.

All I know, all I can comprehend of the mathematics of a life, are the times your hand is inside my hand, and the times it is not.

Sex is mathematics. Individuality no longer an issue. What does intelligence signify? Define reason. Desire - meaningless. Intellect is not a cure. Justice is dead.

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

I couldn't claim that I was smarter than sixty-five other guys--but the average of sixty-five other guys, certainly!

With me, everything turns into mathematics.

There was a footpath leading across fields to New Southgate, and I used to go there alone to watch the sunset and contemplate suicide. I did not, however, commit suicide, because I wished to know more of mathematics.

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.

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend.

What comes, is called.

Mathematics rightly viewed possesses not only truth but supreme beauty.

I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you.

Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty.

It is the story that matters not just the ending.

As a purely mathematical fact, people who sleep less live more.

I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.

There are worlds built on rainbows and worlds built on rain. There are worlds of pure mathematics, where every number chimes like crystal as it rolls into reality. There are worlds of light and worlds of darkness, worlds of rhyme and worlds of reason, and worlds where the only thing that matters is the goodness in a hero's heart.

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.

This most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being... This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont, to be called Lord God παντοκρατωρ or Universal Ruler.

The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.

As an orangutan cannot embrace higher mathematics or comprehend the architecture and operation of a computer, we humans __ so good at loudly proclaiming our intelligence and applauding our own doltish displays of cerebral gymnastics __ cannot begin to understand the true structure and functioning of the Universe.

[When asked why are numbers beautiful?] It’s like asking why is Ludwig van Beethoven’s Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is.

This is the world we live in, a world of safety and happiness and order, a world without love. A world where children crack their heads on stone fireplaces and nearly gnaw off their tongues and the parents are concerned. Not heartbroken, frantic, desperate. Concerned, as they are when you fail mathematics, as they are when they are late to pay their taxes.

Ideas that require people to reorganize their picture of the world provoke hostility.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

You put together two people who have not been put together before. Sometimes it is like that first attempt to harness a hydrogen balloon to a fire balloon: do you prefer crash and burn, or burn and crash? But sometimes it works, and something new is made, and the world is changed. Then, at some point, sooner or later, for this reason or that, one of them is taken away. and what is taken away is greater than the sum of what was there. this may not be mathematically possible; but it is emotionally possible.

We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew?

You’re probably better at math than I am, because pretty much everyone’s better at math than I am, but it’s okay, I’m fine with it. See, I excel at other, more important things—guitar, sex, and consistently disappointing my dad, to name a few.

Rohan, one of us is an unmarried man with superior mathematical abilities and no prospects for the evening. The other is a confirmed lecher in an amorous mood, with a willing and nubile young wife waiting at home. Who do you think should do the damned account books?" And, with a nonchalant wave, St. Vincent had left the office.

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!

And silence. She liked the silence most of all. The silence in which the body, senses, the instincts, are more alert, more powerful, more sensitized, live a more richly perfumed and intoxication life, instead of transmuting into thoughts, words, into exquisite abstractions, mathematics of emotion in place of violent impact, the volcanic eruptions of fever, lust and delight.

Having solved all the major mathematical, physical, chemical, biological, sociological, philosophical, etymological, meteorological and psychological problems of the Universe except for his own, three times over, [Marvin] was severely stuck for something to do, and had taken up composing short dolorous ditties of no tone, or indeed tune. The latest one was a lullaby. Marvin droned, Now the world has gone to bed, Darkness won't engulf my head, I can see in infrared, How I hate the night. He paused to gather the artistic and emotional strength to tackle the next verse. Now I lay me down to sleep, Try to count electric sheep, Sweet dream wishes you can keep, How I hate the night.

To my wife Marganit and my children Ella Rose and Daniel Adam without whom this book would have been completed two years earlier.

No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a "mixed number " while 5/2 is an "improper fraction." They're EQUAL for crying out loud. They are the exact same numbers and have the exact same properties. Who uses such words outside of fourth grade?

Physics depends on a universe infinitely centred on an equals sign.

There are 10 kinds of people in the world: those who understand binary numerals, and those who don't.

Satan, on the contrary, is thin, ascetic and a fanatical devotee of logic. He reads Machiavelli, Ignatius of Loyola, Marx and Hegel; he is cold and unmerciful to mankind, out of a kind of mathematical mercifulness. He is damned always to do that which is most repugnant to him: to become a slaughterer, in order to abolish slaughtering, to sacrifice lambs so that no more lambs may be slaughtered, to whip people with knouts so that they may learn not to let themselves be whipped, to strip himself of every scruple in the name of a higher scrupulousness, and to challenge the hatred of mankind because of his love for it--an abstract and geometric love.

They shouldn't be allowed to teach math so early in the morning.

You only learn when you give your whole being to something. When you give your whole being to mathematics,you learn; but when you are in a state of contradiction, when you do not want to learn but are forced to learn, then it becomes merely a process of accumulation. To learn is like reading a novel with innumerable characters; it requires your full attention, not contradictory attention.

The law of gravity and gravity itself did not exist before Isaac Newton." ...and what that means is that that law of gravity exists nowhere except in people's heads! It 's a ghost!" Mind has no matter or energy but they can't escape its predominance over everything they do. Logic exists in the mind. numbers exist only in the mind. I don't get upset when scientists say that ghosts exist in the mind. it's that only that gets me. science is only in your mind too, it's just that that doesn't make it bad. or ghosts either." Laws of nature are human inventions, like ghosts. Law of logic, of mathematics are also human inventions, like ghosts." ...we see what we see because these ghosts show it to us, ghosts of Moses and Christ and the Buddha, and Plato, and Descartes, and Rousseau and Jefferson and Lincoln, on and on and on. Isaac Newton is a very good ghost. One of the best. Your common sense is nothing more than the voices of thousands and thousands of these ghosts from the past.

Reading list (1972 edition)[edit] 1. Homer – Iliad, Odyssey 2. The Old Testament 3. Aeschylus – Tragedies 4. Sophocles – Tragedies 5. Herodotus – Histories 6. Euripides – Tragedies 7. Thucydides – History of the Peloponnesian War 8. Hippocrates – Medical Writings 9. Aristophanes – Comedies 10. Plato – Dialogues 11. Aristotle – Works 12. Epicurus – Letter to Herodotus; Letter to Menoecus 13. Euclid – Elements 14. Archimedes – Works 15. Apollonius of Perga – Conic Sections 16. Cicero – Works 17. Lucretius – On the Nature of Things 18. Virgil – Works 19. Horace – Works 20. Livy – History of Rome 21. Ovid – Works 22. Plutarch – Parallel Lives; Moralia 23. Tacitus – Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa – Introduction to Arithmetic 25. Epictetus – Discourses; Encheiridion 26. Ptolemy – Almagest 27. Lucian – Works 28. Marcus Aurelius – Meditations 29. Galen – On the Natural Faculties 30. The New Testament 31. Plotinus – The Enneads 32. St. Augustine – On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Njál 36. St. Thomas Aquinas – Summa Theologica 37. Dante Alighieri – The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer – Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci – Notebooks 40. Niccolò Machiavelli – The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus – The Praise of Folly 42. Nicolaus Copernicus – On the Revolutions of the Heavenly Spheres 43. Thomas More – Utopia 44. Martin Luther – Table Talk; Three Treatises 45. François Rabelais – Gargantua and Pantagruel 46. John Calvin – Institutes of the Christian Religion 47. Michel de Montaigne – Essays 48. William Gilbert – On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes – Don Quixote 50. Edmund Spenser – Prothalamion; The Faerie Queene 51. Francis Bacon – Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare – Poetry and Plays 53. Galileo Galilei – Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler – Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey – On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes – Leviathan 57. René Descartes – Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton – Works 59. Molière – Comedies 60. Blaise Pascal – The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens – Treatise on Light 62. Benedict de Spinoza – Ethics 63. John Locke – Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine – Tragedies 65. Isaac Newton – Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz – Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe – Robinson Crusoe 68. Jonathan Swift – A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve – The Way of the World 70. George Berkeley – Principles of Human Knowledge 71. Alexander Pope – Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu – Persian Letters; Spirit of Laws 73. Voltaire – Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding – Joseph Andrews; Tom Jones 75. Samuel Johnson – The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets

Where there was nature and earth, life and water, I saw a desert landscape that was unending, resembling some sort of crater, so devoid of reason and light and spirit that the mind could not grasp it on any sort of conscious level and if you came close the mind would reel backward, unable to take it in. It was a vision so clear and real and vital to me that in its purity it was almost abstract. This was what I could understand, this was how I lived my life, what I constructed my movement around, how I dealt with the tangible. This was the geography around which my reality revolved: it did not occur to me, ever, that people were good or that a man was capable of change or that the world could be a better place through one’s own taking pleasure in a feeling or a look or a gesture, of receiving another person’s love or kindness. Nothing was affirmative, the term “generosity of spirit” applied to nothing, was a cliche, was some kind of bad joke. Sex is mathematics. Individuality no longer an issue. What does intelligence signify? Define reason. Desire- meaningless. Intellect is not a cure. Justice is dead. Fear, recrimination, innocence, sympathy, guilt, waste, failure, grief, were things, emotions, that no one really felt anymore. Reflection is useless, the world is senseless. Evil is its only permanence. God is not alive. Love cannot be trusted. Surface, surface, surface, was all that anyone found meaning in…this was civilization as I saw it, colossal and jagged…

Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too try, philosophy too difficult, geology too petroleum-oriented, and math too mathematical - because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

The Hitchhiker's Guide to the Galaxy's definition of "Universe": The Universe is a very big thing that contains a great number of planets and a great number of beings. It is Everything. What we live in. All around us. The lot. Not nothing. It is quite difficult to actually define what the Universe means, but fortunately the Guide doesn't worry about that and just gives us some useful information to live in it. Area: The area of the Universe is infinite. Imports: None. This is a by product of infinity; it is impossible to import things into something that has infinite volume because by definition there is no outside to import things from. Exports: None, for similar reasons as imports. Population: None. Although you might see people from time to time, they are most likely products of your imagination. Simple mathematics tells us that the population of the Universe must be zero. Why? Well given that the volume of the universe is infinite there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is zero, therefore the average population of the Universe is zero, and so the total population must be zero. Art: None. Because the function of art is to hold a mirror up to nature there can be no art because the Universe is infinite which means there simply isn't a mirror big enough. Sex: None. Although in fact there is quite a lot, given the zero population of the Universe there can in fact be no beings to have sex, and therefore no sex happens in the Universe.

Logic, n. The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. The basic of logic is the syllogism, consisting of a major and a minor premise and a conclusion - thus: Major Premise: Sixty men can do a piece of work sixty times as quickly as one man. Minor Premise: One man can dig a post-hole in sixty seconds; Therefore- Conclusion: Sixty men can dig a post-hole in one second. This may be called syllogism arithmetical, in which, by combining logic and mathematics, we obtain a double certainty and are twice blessed.

We find that at present the human race is divided into one wise man, nine knaves, and ninety fools out of every hundred. That is, by an optimistic observer. The nine knaves assemble themselves under the banner of the most knavish among them, and become 'politicians'; the wise man stands out, because he knows himself to be hopelessly outnumbered, and devotes himself to poetry, mathematics, or philosophy; while the ninety fools plod off under the banners of the nine villains, according to fancy, into the labyrinths of chicanery, malice and warfare. It is pleasant to have command, observes Sancho Panza, even over a flock of sheep, and that is why the politicians raise their banners. It is, moreover, the same thing for the sheep whatever the banner. If it is democracy, then the nine knaves will become members of parliament; if fascism, they will become party leaders; if communism, commissars. Nothing will be different, except the name. The fools will be still fools, the knaves still leaders, the results still exploitation. As for the wise man, his lot will be much the same under any ideology. Under democracy he will be encouraged to starve to death in a garret, under fascism he will be put in a concentration camp, under communism he will be liquidated.

Me, and thousands of others in this country like me, are half-baked, because we were never allowed to complete our schooling. Open our skulls, look in with a penlight, and you'll find an odd museum of ideas: sentences of history or mathematics remembered from school textbooks (no boy remembers his schooling like the one who was taken out of school, let me assure you), sentences about politics read in a newspaper while waiting for someone to come to an office, triangles and pyramids seen on the torn pages of the old geometry textbooks which every tea shop in this country uses to wrap its snacks in, bits of All India Radio news bulletins, things that drop into your mind, like lizards from the ceiling, in the half hour before falling asleep--all these ideas, half formed and half digested and half correct, mix up with other half-cooked ideas in your head, and I guess these half-formed ideas bugger one another, and make more half-formed ideas, and this is what you act on and live with.

[The Old Astronomer to His Pupil] Reach me down my Tycho Brahe, I would know him when we meet, When I share my later science, sitting humbly at his feet; He may know the law of all things, yet be ignorant of how We are working to completion, working on from then to now. Pray remember that I leave you all my theory complete, Lacking only certain data for your adding, as is meet, And remember men will scorn it, 'tis original and true, And the obloquy of newness may fall bitterly on you. But, my pupil, as my pupil you have learned the worth of scorn, You have laughed with me at pity, we have joyed to be forlorn, What for us are all distractions of men's fellowship and smiles; What for us the Goddess Pleasure with her meretricious smiles. You may tell that German College that their honor comes too late, But they must not waste repentance on the grizzly savant's fate. Though my soul may set in darkness, it will rise in perfect light; I have loved the stars too fondly to be fearful of the night. What, my boy, you are not weeping? You should save your eyes for sight; You will need them, mine observer, yet for many another night. I leave none but you, my pupil, unto whom my plans are known. You 'have none but me,' you murmur, and I 'leave you quite alone'? Well then, kiss me, -- since my mother left her blessing on my brow, There has been a something wanting in my nature until now; I can dimly comprehend it, -- that I might have been more kind, Might have cherished you more wisely, as the one I leave behind. I 'have never failed in kindness'? No, we lived too high for strife,-- Calmest coldness was the error which has crept into our life; But your spirit is untainted, I can dedicate you still To the service of our science: you will further it? you will! There are certain calculations I should like to make with you, To be sure that your deductions will be logical and true; And remember, 'Patience, Patience,' is the watchword of a sage, Not to-day nor yet to-morrow can complete a perfect age. I have sown, like Tycho Brahe, that a greater man may reap; But if none should do my reaping, 'twill disturb me in my sleep So be careful and be faithful, though, like me, you leave no name; See, my boy, that nothing turn you to the mere pursuit of fame. I must say Good-bye, my pupil, for I cannot longer speak; Draw the curtain back for Venus, ere my vision grows too weak: It is strange the pearly planet should look red as fiery Mars,-- God will mercifully guide me on my way amongst the stars.

I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It's difficult to describe because it's an emotion. It's analogous to the feeling one has in religion that has to do with a god that controls everything in the whole universe: there's a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run "behind the scenes" by the same organization, the same physical laws. It's an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It's a feeling of awe — of scientific awe — which I felt could be communicated through a drawing to someone who had also had this emotion. It could remind him, for a moment, of this feeling about the glories of the universe.

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.

Some of the owner men were kind because they hated what they had to do, and some of them were angry because they hated to be cruel, and some of them were cold because they had long ago found that one could not be an owner unless one were cold. And all of them were caught in something larger than themselves. Some of them hated the mathematics that drove them, and some were afraid, and some worshiped the mathematics because it provided a refuge from thought and from feeling. If a bank or a finance company owned the land, the owner man said, The Bank - or the Company - needs - wants - insists - must have - as though the Bank or the Company were a monster, with thought and feeling, which had ensnared them. These last would take no responsibility for the banks or the companies because they were men and slaves, while the banks were machines and masters all at the same time. Some of the owner men were a little proud to be slaves to such cold and powerful masters. The owner men sat in the cars and explained. You know the land is poor. You've scrabbled at it long enough, God knows.

In my own professional work I have touched on a variety of different fields. I’ve done work in mathematical linguistics, for example, without any professional credentials in mathematics; in this subject I am completely self-taught, and not very well taught. But I’ve often been invited by universities to speak on mathematical linguistics at mathematics seminars and colloquia. No one has ever asked me whether I have the appropriate credentials to speak on these subjects; the mathematicians couldn’t care less. What they want to know is what I have to say. No one has ever objected to my right to speak, asking whether I have a doctor’s degree in mathematics, or whether I have taken advanced courses in the subject. That would never have entered their minds. They want to know whether I am right or wrong, whether the subject is interesting or not, whether better approaches are possible… the discussion dealt with the subject, not with my right to discuss it. But on the other hand, in discussion or debate concerning social issues or American foreign policy…. The issue is constantly raised, often with considerable venom. I’ve repeatedly been challenged on grounds of credentials, or asked, what special training do I have that entitles you to speak on these matters. The assumption is that people like me, who are outsiders from a professional viewpoint, are not entitled to speak on such things. Compare mathematics and the political sciences… it’s quite striking. In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is the concern for content.

The Couple Overfloweth We sometimes go on as though people can’t express themselves. In fact they’re always expressing themselves. The sorriest couples are those where the woman can’t be preoccupied or tired without the man saying “What’s wrong? Say something…,” or the man, without the woman saying … and so on. Radio and television have spread this spirit everywhere, and we’re riddled with pointless talk, insane quantities of words and images. Stupidity’s never blind or mute. So it’s not a problem of getting people to express themselves but of providing little gaps of solitude and silence in which they might eventually find something to say. Repressive forces don’t stop people expressing themselves but rather force them to express themselves; What a relief to have nothing to say, the right to say nothing, because only then is there a chance of framing the rare, and ever rarer, thing that might be worth saying. What we’re plagued by these days isn’t any blocking of communication, but pointless statements. But what we call the meaning of a statement is its point. That’s the only definition of meaning, and it comes to the same thing as a statement’s novelty. You can listen to people for hours, but what’s the point? . . . That’s why arguments are such a strain, why there’s never any point arguing. You can’t just tell someone what they’re saying is pointless. So you tell them it’s wrong. But what someone says is never wrong, the problem isn’t that some things are wrong, but that they’re stupid or irrelevant. That they’ve already been said a thousand times. The notions of relevance, necessity, the point of something, are a thousand times more significant than the notion of truth. Not as substitutes for truth, but as the measure of the truth of what I’m saying. It’s the same in mathematics: Poincaré used to say that many mathematical theories are completely irrelevant, pointless; He didn’t say they were wrong – that wouldn’t have been so bad. (Negotiations)

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.

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.

Saint Bartleby's School for Young Gentlemen Annual Report Student: Artemis Fowl II Year: First Fees: Paid Tutor: Dr Po Language Arts As far as I can tell, Artemis has made absolutely no progress since the beginning of the year. This is because his abilities are beyond the scope of my experience. He memorizes and understands Shakespeare after a single reading. He finds mistakes in every exercise I administer, and has taken to chuckling gently when I attempt to explain some of the more complex texts. Next year I intend to grant his request and give him a library pass during my class. Mathematics Artemis is an infuriating boy. One day he answers all my questions correctly, and the next every answer is wrong. He calls this an example of the chaos theory, and says that he is only trying to prepare me for the real world. He says the notion of infinity is ridiculous. Frankly, I am not trained to deal with a boy like Artemis. Most of my pupils have trouble counting without the aid of their fingers. I am sorry to say, there is nothing I can teach Artemis about mathematics, but someone should teach him some manners. Social Studies Artemis distrusts all history texts, because he says history was written by the victors. He prefers living history, where survivors of certain events can actually be interviewed. Obviously this makes studying the Middle Ages somewhat difficult. Artemis has asked for permission to build a time machine next year during double periods so that the entire class may view Medieval Ireland for ourselves. I have granted his wish and would not be at all surprised if he succeeded in his goal. Science Artemis does not see himself as a student, rather as a foil for the theories of science. He insists that the periodic table is a few elements short and that the theory of relativity is all very well on paper but would not hold up in the real world, because space will disintegrate before lime. I made the mistake of arguing once, and young Artemis reduced me to near tears in seconds. Artemis has asked for permission to conduct failure analysis tests on the school next term. I must grant his request, as I fear there is nothing he can learn from me. Social & Personal Development Artemis is quite perceptive and extremely intellectual. He can answer the questions on any psychological profile perfectly, but this is only because he knows the perfect answer. I fear that Artemis feels that the other boys are too childish. He refuses to socialize, preferring to work on his various projects during free periods. The more he works alone, the more isolated he becomes, and if he does not change his habits soon, he may isolate himself completely from anyone wishing to be his friend, and, ultimately, his family. Must try harder.