Life Is An Arithmetic Quotes

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

You are a name, not a number. Never forget that name, whatever they tell you here. You will always be Chaya—life—to me.

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

Part of her revolted against the insanity of the rules. Part of her was grateful. In a world of chaos, any guidelines helped. And she knew that each day she remained alive, she remained alive. One plus one plus one. The Devil's arithmetic...

I do know the sorrow of being ordinary, and that much of our life is spent doing the crazy mental arithmetic of how, at any given moment, we might improve, or at least disguise or present our defects and screw-ups in either more charming or more intimidating ways.

I would say that the five most important skills are of course, reading, writing, arithmetic, and then as you’re adding in, persuasion, which is talking. And then finally, I would add computer programming just because it’s an applied form of arithmetic that just gets you so much leverage for free in any domain that you operate in. If you’re good with computers, if you’re good at basic mathematics, if you’re good at writing, if you’re good at speaking, and if you like reading, you’re set for life.

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.

We say to the confused, Know thyself, as if knowing yourself was not the fifth and most difficult of human arithmetical operations, we say to the apathetic, Where there's a will, there's a way, as if the brute realities of the world did not amuse themselves each day by turning that phrase on its head, we say to the indecisive, Begin at the beginning, as if beginning were the clearly visible point of a loosely wound thread and all we had to do was to keep pulling until we reached the other end, and as if, between the former and the latter, we had held in our hands a smooth, continuous thread with no knots to untie, no snarls to untangle, a complete impossibility in the life of a skein, or indeed, if we may be permitted one more stock phrase, in the skein of life.

I'd often wished I could work out people as easily as I did arithmetic: simply break them down to their common denominators and solve. Numbers didn't' lie; there was always an answer, and the answer was either right or it was wrong. Simple. But nothing in life was simple, and there was no answer to solve for.

Thomas Edison said in all seriousness: "There is no expedient to which a man will not resort to avoid the labour of thinking"-if we bother with facts at all, we hunt like bird dogs after the facts that bolster up what we already think-and ignore all the others! We want only the facts that justify our acts-the facts that fit in conveniently with our wishful thinking and justify our preconceived prejudices! As Andre Maurois put it: "Everything that is in agreement with our personal desires seems true. Everything that is not puts us into a rage." Is it any wonder, then, that we find it so hard to get at the answers to our problems? Wouldn't we have the same trouble trying to solve a second-grade arithmetic problem, if we went ahead on the assumption that two plus two equals five? Yet there are a lot of people in this world who make life a hell for themselves and others by insisting that two plus two equals five-or maybe five hundred!

I have been taking stock of my 50 years since I left Wichita in 1922 at the age of 15 to become a dancer with Ruth St. Denis and Ted Shawn. How I have existed fills me with horror. For I have failed in everything -- spelling, arithmetic, riding, tennis, golf; dancing, singing, acting; wife, mistress, whore, friend. Even cooking. And I do not excuse myself with the usual escape of 'not trying.' I tried with all my heart.

Life is not a math problem, Charlotte.” If it was, I’d have been a lot better at it. I’d often wished I could work out people as easily as I did arithmetic: simply break them down to their common denominators and solve. Numbers didn’t lie; there was always an answer, and the answer was either right or it was wrong. Simple. But nothing in life was simple, and there was no answer here to solve for.

I felt there was a lot I needed to teach her. I wanted to give her an early grounding in the basics of arithmetic and reading, but even more important, I wanted to get across the idea that the world was a dangerous place and life was unpredictable and you had to be smart, focused, and determined to make it through. You had to be willing to work hard and persevere in the face of misfortune. A lot of people, even those born with brains and beauty, didn't have what it took to knuckle down and get the thing done.

Tuna fish demonstrate a sophisticated understanding of astronomy: when the winter solstice arrives, the whole school stops precisely where it is in the water, and stays there until the following spring equinox. They know geometry and arithmetic too, for they have been observed to form themselves into a perfect cube of which all six sides are equal.

May our lives be like arithmetic: friends added, enemies subtracted, sorrows divided, joys multiplied.

Apparently, in the realm of higher animals, it takes 2 to make 1. The arithmetic of this mystery seems to suggest 1 + 1 = 1.

Seven Rules Formulated for Teaching Arithmetic: 1) Consider the situation the pupils faces. 2) Consider the response you wish to connect with. 3) Form the bond; do not expect it to come by miracle. 4) Other things being equal, form no bond that will have to be broken. 5) Other things being equal, do not form two or three bonds when one will serve. 6) Other things being equal, form bonds in the way that they are required later to act. 7) Favor, therefore, the situations which life itself will offer, and the responses which life itself will demand. (p. 101)

Let us remember that, despite the tasteless fables in the Holy Writ -- Sodom and Gomorrah, for example -- Nature does not have two voices; She does not create the appetite for buggery, then proscribe its practice. This fallacious proscription is the work of those imbeciles who seem unable to view sex as anything but an instrumentality for the multiplication of their own imbecilic kind. But I put it to you thusly: would it not be unreasonable for Nature, if she opposed buggery, to reward its practitioners with consummate pleasure at the very moment when they, by buggering, heap insults upon Her "natural" order? Furthermore, if procreation were the primary purpose of sex, would woman be created capable of conceiving during only sixteen to eighteen hours of each month -- and thus, all arithmetic being performed, during only four to six years of her total life span? No, child, let us not ascribe to Nature those prohibitions which we acquire through fear or prejudice; all things which are possible are natural; let no one ever persuade you otherwise.

Cards and boards, [Johnny] thought. And the dead. That's not dark forces. Making a fuss about cards and heavy metal and going on about Dungeons and Dragons stuff because it's got demon gods in it is like guarding to door when it is really coming up through the floorboards. Real dark forces... aren't dark. They're sort of gray, like Mr. Grimm. They take all the color out of life; they take a town like Blackbury and turn it into frightened streets and plastic signs and Bright New Futures and towers where no one wants to live and no one really does live. The dead seem more alive than us. And everyone becomes gray and turns into numbers and then, somewhere, someone starts to do arithmetic...

Here we come to the central question of this book: What, precisely, does it mean to say that our sense of morality and justice is reduced to the language of a business deal? What does it mean when we reduce moral obligations to debts? What changes when the one turns into the other? And how do we speak about them when our language has been so shaped by the market? On one level the difference between an obligation and a debt is simple and obvious. A debt is the obligation to pay a certain sum of money. As a result, a debt, unlike any other form of obligation, can be precisely quantified. This allows debts to become simple, cold, and impersonal-which, in turn, allows them to be transferable. If one owes a favor, or one’s life, to another human being-it is owed to that person specifically. But if one owes forty thousand dollars at 12-percent interest, it doesn’t really matter who the creditor is; neither does either of the two parties have to think much about what the other party needs, wants, is capable of doing-as they certainly would if what was owed was a favor, or respect, or gratitude. One does not need to calculate the human effects; one need only calculate principal, balances, penalties, and rates of interest. If you end up having to abandon your home and wander in other provinces, if your daughter ends up in a mining camp working as a prostitute, well, that’s unfortunate, but incidental to the creditor. Money is money, and a deal’s a deal. From this perspective, the crucial factor, and a topic that will be explored at length in these pages, is money’s capacity to turn morality into a matter of impersonal arithmetic-and by doing so, to justify things that would otherwise seem outrageous or obscene. The factor of violence, which I have been emphasizing up until now, may appear secondary. The difference between a “debt” and a mere moral obligation is not the presence or absence of men with weapons who can enforce that obligation by seizing the debtor’s possessions or threatening to break his legs. It is simply that a creditor has the means to specify, numerically, exactly how much the debtor owes.

What will that mean to each of you? “It will mean that those of you who might have lived to be seventy-one must die at seventy. Some of you who might have lived to be eighty-six must cough up your ghost at eighty-five. That’s a great age. A year more or less doesn’t sound like much. When the time comes, boys, you may regret. But, you will be able to say, this year I spent well, I gave for Pip, I made a loan of life for sweet Pipkin, the fairest apple that ever almost fell too early off the harvest tree. Some of you at forty-nine must cross life off at forty-eight. Some at fifty-five must lay them down to Forever’s Sleep at fifty-four. Do you catch the whole thing intact now, boys? Do you add the figures? Is the arithmetic plain? A year! Who will bid three hundred and sixty-five entire days from out his own soul, to get old Pipkin back? Think, boys. Silence. Then, speak.

Gottfried Leibniz wrote that music’s pleasure consisted of “unconscious counting” or an “arithmetical exercise of which we are unaware.

I was about to graduate, and what I’d learned most in four years besides biology and arithmetic was just how much people can hate you because of the color of your skin.

For the rest, all that rises out of the sea of arithmetic is a jungle of dates, battles, exports, imports and the like, forgotten as soon as learned and perfectly useless had they been remembered.

The rock I'd seen in my life looked dull because in all ignorance I'd never thought to knock it open. People have cracked ordinary New England pegmatite - big, coarse granite - and laid bare clusters of red garnets, or topaz crystals, chrysoberyl, spodumene, emerald. They held in their hands crystals that had hung in a hole in the dark for a billion years unseen. I was all for it. I would lay about me right and left with a hammer, and bash the landscape to bits. I would crack the earth's crust like a piñata and spread to the light the vivid prizes in chunks within. Rock collecting was opening the mountains. It was like diving through my own interior blank blackness to remember the startling pieces of a dream: there was a blue lake, a witch, a lighthouse, a yellow path. It was like poking about in a grimy alley and finding an old, old coin. Nothing was at it seemed. The earth was like a shut eye. Mother's not dead, dear - she's only sleeping. Pry open the thin lid and find a crystalline intelligence inside, a rayed and sidereal beauty. Crystals grew inside rock like arithmetical flowers. They lengthened and spread, adding plane to plane in awed and perfect obedience to an absolute geometry that even the stones - maybe only the stones - understood.

She liked numbers and sums. She devised a game in which each number was a family member and the “answer” made a family grouping with a story to it. Naught was a babe in arms. He gave no trouble. Whenever he appeared you just “carried” him. The figure 1 was a pretty baby girl just learning to walk, and easy to handle; 2 was a baby boy who could walk and talk a little. He went into family life (into sums, etc.) with very little trouble. And 3 was an older boy in kindergarten, who had to be watched a little. Then there was 4, a girl of Francie’s age. She was almost as easy to “mind” as 2. The mother was 5, gentle and kind. In large sums, she came along and made everything easy the way a mother should. The father, 6, was harder than the others but very just. But 7 was mean. He was a crotchety old grandfather and not at all accountable for how he came out. The grandmother, 8, was hard too, but easier to understand than 7. Hardest of all was 9. He was company and what a hard time fitting him into family life! When Francie added a sum, she would fix a little story to go with the result. If the answer was 924, it meant that the little boy and girl were being minded by company while the rest of the family went out. When a number such as 1024 appeared, it meant that all the little children were playing together in the yard. The number 62 meant that papa was taking the little boy for a walk; 50 meant that mama had the baby out in the buggy for an airing and 78 meant grandfather and grandmother sitting home by the fire of a winter’s evening. Each single combination of numbers was a new set-up for the family and no two stories were ever the same. Francie took the game with her up into algebra. X was the boy’s sweetheart who came into the family life and complicated it. Y was the boy friend who caused trouble. So arithmetic was a warm and human thing to Francie and occupied many lonely hours of her time.

Well, listen then. On the other side, fresh young lives thrown away for want of help and by thousands, on every side! A hundred thousand good deeds could be done and helped, on that old woman's money which will be buried in a monastery! Hundreds, thousands perhaps, might be set on the right path; dozens of families saved from destitution, from ruin, from vice, from the Lock hospitals—and all with her money. Kill her, take her money and with the help of it devote oneself to the service of humanity and the good of all. What do you think, would not one tiny crime be wiped out by thousands of good deeds? For one life thousands would be saved from corruption and decay. One death, and a hundred lives in exchange—it's simple arithmetic! Besides, what value has the life of that sickly, stupid, ill-natured old woman in the balance of existence! No more than the life of a louse, of a black-beetle, less in fact because the old woman is doing harm. She is wearing out the lives of others; the other day she bit Lizaveta's finger out of spite; it almost had to be amputated.

After a heated dispute, we each undertook an assignment for the next class: to engage in one pleasurable activity and one philanthropic activity, and write about both. The results were life-changing. The afterglow of the “pleasurable” activity (hanging out with friends, or watching a movie, or eating a hot fudge sundae) paled in comparison with the effects of the kind action. When our philanthropic acts were spontaneous and called upon personal strengths, the whole day went better. One junior told about her nephew phoning for help with his third-grade arithmetic. After an hour of tutoring him, she was astonished to discover that “for the rest of the day, I could listen better, I was mellower, and people liked me much more than usual.” The exercise of kindness is a gratification, in contrast to a pleasure. As a gratification, it calls on your strengths to rise to an occasion and meet a challenge. Kindness is not accompanied by a separable stream of positive emotion like joy; rather, it consists in total engagement and in the loss of self-consciousness. Time stops.

I remember one teacher there -- I can't recall her name now. She was short and spare, and I remember her eager jutting chin. Quite unexpectedly one day (in the middle, I think, of an arithmetic lesson) she suddenly launched forth on a speech on life and religion. "All of you," she said, "every one of you -- will pass through a time when you will face despair. If you never face despair, you will never have faced, or become, a Christian, or known a Christian life. To be a Christian you must face and accept the life that Christ faced and lived; you must enjoy things as he enjoyed things; be as happy as he was at the marriage at Canaan, know the peace and happiness that it means to be in harmony with God and with God's will. But you must also know, as he did, what it means to be alone in the Garden of Gethsemane, to feel that all your friends have forsaken you, that those you love and trust have turned away from you, and that God Himself has forsaken you. Hold on then to the belief that that is not the end. If you love, you will suffer, and if you do not love, you do not know the meaning of a Christian life." She then returned to the problems of compound interest ...

Still, through a complex combination of optimism and longing and bravado, you would round it up. While a cruder name for this process is lying , one could make a case that delusion is a variant of generosity. After all, you practiced rounding up on Kevin from the day he was born. Me, I’m a stickler. I prefer my photographs in focus. At the risk of tautology, I like people only as much as I like them. I lead an emotional life of such arithmetic precision, carried to two or three digits after the decimal, that I am even willing to allow for degrees of agreeableness in my own son. In other words, Franklin: I leave the $17.

I’d often wished I could work out people as easily as I did arithmetic: simply break them down to their common denominators and solve. Numbers didn’t lie; there was always an answer, and the answer was either right or it was wrong. Simple. But nothing in life was simple, and there was no answer here to solve for.

We had better want the consequences of what we believe or disbelieve, because the consequences will come! . . . But how can a society set priorities if there are no basic standards? Are we to make our calculations using only the arithmetic of appetite? . . . The basic strands which have bound us together socially have begun to fray, and some of them have snapped. Even more pressure is then placed upon the remaining strands. The fact that the giving way is gradual will not prevent it from becoming total. . . . Given the tremendous asset that the family is, we must do all we can within constitutional constraints to protect it from predatory things like homosexuality and pornography. . . . Our whole republic rests upon the notion of “obedience to the unenforceable,” upon a tremendous emphasis on inner controls through self-discipline. . . . Different beliefs do make for different behaviors; what we think does affect our actions; concepts do have consequences. . . . Once society loses its capacity to declare that some things are wrong per se, then it finds itself forever building temporary defenses, revising rationales, drawing new lines—but forever falling back and losing its nerve. A society which permits anything will eventually lose everything! Take away a consciousness of eternity and see how differently time is spent. Take away an acknowledgement of divine design in the structure of life and then watch the mindless scurrying to redesign human systems to make life pain-free and pleasure-filled. Take away regard for the divinity in one’s neighbor, and watch the drop in our regard for his property. Take away basic moral standards and observe how quickly tolerance changes into permissiveness. Take away the sacred sense of belonging to a family or community, and observe how quickly citizens cease to care for big cities. Those of us who are business-oriented are quick to look for the bottom line in our endeavors. In the case of a value-free society, the bottom line is clear—the costs are prohibitive! A value-free society eventually imprisons its inhabitants. It also ends up doing indirectly what most of its inhabitants would never have agreed to do directly—at least initially. Can we turn such trends around? There is still a wealth of wisdom in the people of this good land, even though such wisdom is often mute and in search of leadership. People can often feel in their bones the wrongness of things, long before pollsters pick up such attitudes or before such attitudes are expressed in the ballot box. But it will take leadership and articulate assertion of basic values in all places and in personal behavior to back up such assertions. Even then, time and the tides are against us, so that courage will be a key ingredient. It will take the same kind of spunk the Spartans displayed at Thermopylae when they tenaciously held a small mountain pass against overwhelming numbers of Persians. The Persians could not dislodge the Spartans and sent emissaries forward to threaten what would happen if the Spartans did not surrender. The Spartans were told that if they did not give up, the Persians had so many archers in their army that they would darken the skies with their arrows. The Spartans said simply: “So much the better, we will fight in the shade!

I know perfectly well that it is impossible, according to arithmetic and scholarly books, to live in a far valley off a handful of ewes and two low yield cows. But we live, I say. You children all lived; your sisters now have sturdy children in far-off districts. And what you are now carrying under your heart will also live and be welcome, little one, despite arithmetic and scholarly books.

The fundamental reason for the superiority of totalitarian propaganda over the propaganda of other parties and movements is that its content, for the members of the movement at any rate, is no longer an objective issue about which people may have opinions, but has become as real and untouchable an element in their lives as the rules of arithmetic. The organization of the entire texture of life according to an ideology can be fully carried out only under a totalitarian regime. In Nazi Germany, questioning the validity of racism and antisemitism when nothing mattered but race origin, when a career depended upon an “Aryan” physiognomy (Himmler used to select the applicants for the SS from photographs) and the amount of food upon the number of one’s Jewish grandparents, was like questioning the existence of the world.

In the morning I walked to the bank. I went to the automated teller machine to check my balance. I inserted my card, entered my secret code, tapped out my request. The figure on the screen roughly corresponded to my independent estimate, feebly arrived at after long searches through documents, tormented arithmetic. Waves of relief and gratitude flowed over me. The system had blessed my life. I felt its support and approval. The system hardware, the mainframe sitting in a locked room in some distant city. What a pleasing interaction. I sensed that something of deep personal value, but not money, not that at all, had been authenticated and confirmed. A deranged person was escorted from the bank by two armed guards. The system was invisible, which made it all the more impressive, all the more disquieting to deal with. But we were in accord, at least for now.

The fairy tale belongs to the child and ought always to be within his reach, not only because it is his special literary form and his nature craves it, but because it is one of the most vital of the textbooks offered to him in the school of life. In ultimate importance it outranks the arithmetic, the grammar, the geography, the manuals of science; for without the aid of the imagination none of these books is really comprehensible.

It is almost as if ideas set in mathematical form melt and become liquid and just as rivers can, from the most humble beginnings, flow for thousands of miles, through the most varied topography bringing nourishment and life with them wherever they go, so too can ideas cast in mathematical form flow far from their original sources, along well-defined paths, electrifying and dramatically affecting much of what they touch. pp. xii - xiii.

the 1950s, the top skills employers wanted were: 1) the ability to work rapidly and for long periods of time, 2) memory for details and directions, and 3) arithmetic computation.2 But according to Forbes, the employees of 2020 need: 1) complex problem solving, 2) critical thinking, 3) creativity, 4) people management, 5) coordinating with others, and 6) emotional intelligence. Employers want innovative thinking, independence, initiative.

Turning captives into commodities was a thoroughly scientific enterprise. It turned on perfecting the practices required to commodify people and determining where those practices reached their outer limits (that is, the point at which they extinguished the lives they were meant to sustain in commodified form). Traders reduced people to the sum of their biological parts, thereby scaling life down to an arithmetical equation and finding the lowest common denominator.

There's no end to this tunnel', said Phyllis - and indeed it did seem very, very long. 'Stick to it', said Peter; 'everything has an end, and you get to it if you only keep on.' Which is quite true, if you come to think of it, and a useful thing to remember in seasons of trouble - such as measles, arithmetic, impositions, and those times when you are in disgrace , and feel as though no one would ever love you again, and you could never - never again - love anybody.

And this is apparently not without merit. Because in our countries for some time now a great hurricane of subversion has arisen, pushed forward by I do not know what vicious demons—and doubtless in accord with the life-style that we have made our own, unfortunately. This hurricane tries to reverse our traditional order of values, to throw out all that we put forward as being unselfish, gracious and open to the world, open to things and to others, all that is active in dilating our minds and our hearts. It wants to replace it by the single, brutal, arithmetic, and inhuman motivation of profit. Henceforth, all that counts, all that is to be considered and preserved, is what brings profit. The truly ideal aspects of knowledge will not be more valuable than those of interest rates and of financial laws. The only sciences that are to be encouraged are those that teach us how to exploit the earth and the people. Besides that, everything is useless.

In the 1950s, the top skills employers wanted were: 1) the ability to work rapidly and for long periods of time, 2) memory for details and directions, and 3) arithmetic computation.2 But according to Forbes, the employees of 2020 need: 1) complex problem solving, 2) critical thinking, 3) creativity, 4) people management, 5) coordinating with others, and 6) emotional intelligence. Employers want innovative thinking, independence, initiative.3 These were not coveted skills in our grandparents’ time.

You have no idea how long I’ve wanted to do this,” he pants as I drag my fingers down his back, admiring each muscly ridge along the way. I peer at him and contemplate requesting specifics. How many months, weeks, days, hours, seconds, exactly? I’m a woman of detail and precision, after all. But bringing arithmetic into this seems like a surefire way to kill the vibe and sabotage the hottest moment of my entire life. So I keep kissing him. And kissing him. Absorbing every bit of him as if making up for lost time.

When we're all so terribly alone. The least we can do in this life is love one another... just a hug and a kiss...' He was right, of course; but how could you love everyone? If only enough of us loved enough--perhaps by some arithmetical progression, everyone would be given this gift. But that was useless. Speculation for those of us left behind, who were not going to hurl ourselves off a building in the pressure of a summer heat wave, a lover's quarrel, a drug, I thought as we sat there now. There was no such end for the rest of us, or glorious legacy of love

Arithmetic Matilda longed for her parents to be good and loving and understanding and honourable and intelligent. The fact that they were none of these things was something she had to put up with. It was not easy to do so. But the new game she had invented of punishing one or both of them each time they were beastly to her made her life more or less bearable. Being very small and very young, the only power Matilda had over anyone in her family was brain-power. For sheer cleverness she could run rings around them all. But the fact remained that any five-year-old girl in any family was always obliged to do as she was told, however asinine the orders might be. Thus she was always forced to eat her evening meals out of TV-dinner-trays in front of the dreaded box. She always had to stay alone on weekday afternoons, and whenever she was told to shut up, she had to shut up. Her safety-valve, the thing that prevented her from going round the bend, was the fun of devising and dishing out these splendid punishments, and the lovely thing was that they seemed to work, at any rate for short periods. The father in particular became less cocky

Life goes on, probably too long if we’re being honest about it. In a long life there are thirty or thirty-five thousand days to be got through, but only a few dozen that really matter, Big Days when Something Momentous Happens. The rest—the vast majority, tens of thousands of days—are unremarkable, repetitive, even monotonous. We glide through them then instantly forget them. We tend not to think about this arithmetic when we look back on our lives. We remember the handful of Big Days and throw away the rest. We organize our long, shapeless lives into tidy little stories, as I am doing here. But our lives are mostly made up of junk, of ordinary, forgettable days, and “The End” is never the end.

the aging and grumpy Plato, in Book VII of the Laws, gave his definition of scientific illiteracy: Who is unable to count one, two, three, or to distinguish odd from even numbers, or is unable to count at all, or reckon night and day, and who is totally unacquainted with the revolution of the Sun and Moon, and the other stars … All freemen, I conceive, should learn as much of these branches of knowledge as every child in Egypt is taught when he learns the alphabet. In that country arithmetical games have been invented for the use of mere children, which they learn as pleasure and amusement … I … have late in life heard with amazement of our ignorance in these matters; to me we appear to be more like pigs than men, and I am quite ashamed, not only of myself, but of all Greeks.

For example, all three partners cooperate to make nutrients. To create the amino acid phenylalanine, they need nine enzymes. Tremblaya can build 1,2,5,6,7, and 8; Moranella can make 3,4, and 5; and the mealybug alone makes the 9th. Neither mealybug nor the two bacteria can make phenylalanine on their own; they depend on each other to fill the gaps in their repertoires. This reminds me of the Graeae of Greek mythology: the three sisters who share one ee and one tooth between them. Anything more would be redundant: their arrangement, though odd, still allows them to see and chew. So it is with the mealybug and its symbionts. They ended up with a single metabolic network, distributed between their three complementary genomes. In the arithmetic of symbionts, one plus one plus one can equal one.

Many, perhaps even most, of the adults who abuse children were abused themselves as children. However, the majority of people who were abused as children do not abuse their own children. This is a well-established fact, which can be demonstrated, simply, arithmetically, in this way: if one parent abused three children, and each of those children had three children, and so on, then there would be three abusers the first generation, nine the second, twenty-seven the third, eighty-one the fourth—and so on exponentially. After twenty generations, more than ten billion would have suffered childhood abuse: more people than currently inhabit the planet. But instead, abuse disappears across generations. People constrain its spread. That’s a testament to the genuine dominance of good over evil in the human heart.

There has been an enduring misunderstanding that needs to be cleared up. Turing’s core message was never “If a machine can imitate a man, the machine must be intelligent.” Rather, it was “Inability to imitate does not rule out intelligence.” In his classic essay on the Turing test, Turing encouraged his readers to take a broader perspective on intelligence and conceive of it more universally and indeed more ethically. He was concerned with the possibility of unusual forms of intelligence, our inability to recognize those intelligences, and the limitations of the concept of indistinguishability as a standard for defining what is intelligence and what is not. In section two of the paper, Turing asks directly whether imitation should be the standard of intelligence. He considers whether a man can imitate a machine rather than vice versa. Of course the answer is no, especially in matters of arithmetic, yet obviously a man thinks and can think computationally (in terms of chess problems, for example). We are warned that imitation cannot be the fundamental standard or marker of intelligence. Reflecting on Turing’s life can change one’s perspective on what the Turing test really means. Turing was gay. He was persecuted for this difference in a manner that included chemical castration and led to his suicide. In the mainstream British society of that time, he proved unable to consistently “pass” for straight. Interestingly, the second paragraph of Turing’s famous paper starts with the question of whether a male or female can pass for a member of the other gender in a typed conversation. The notion of “passing” was of direct personal concern to Turing and in more personal settings Turing probably did not view “passing” as synonymous with actually being a particular way.

The emotions, I have observed, are but slightly influenced by arithmetical considerations: the mother, when her sweet lisping little ones have all been taken from her one after another, and she is hanging over her last dead babe, finds small consolation in the fact that the tiny dimpled corpse is but one of a necessary average, and that a thousand other babes brought into the world at the same time are doing well, and are likely to live; and if you stood beside that mother—if you knew her pang and shared it—it is probable you would be equally unable to see a ground of complacency in statistics. Doubtless a complacency resting on that basis is highly rational; but emotion, I fear, is obstinately irrational: it insists on caring for individuals; it absolutely refuses to adopt the quantitative view of human anguish, and to admit that thirteen happy lives are a set-off against twelve miserable lives, which leaves a clear balance on the side of satisfaction.

Our Earth is 4,600 million years old,’ he told his audience. ‘Now let us imagine that those 4,600 million years are like the life of a forty-six-year-old woman. Each year of this woman’s life represents 100 million years of Earth’s existence.’ Some members of the audience tittered. No one had ever explained it like that to them before. ‘By that arithmetic, animals appeared only during the last six years of this woman’s life,’ said the monk. ‘And it was only a week ago that some apes began to take on human qualities. And taking it from there, it was just four hours ago that our own species, we homo sapiens, learned to hunt, gather and cultivate.’ He smiled at the range of gob-smacked expressions. ‘Isn’t that amazing? But the one fact that should shock you is—’ The audience waited to hear more startling facts from Brahmananda. ‘—that we started maintaining some semblance of historical records only during the last ten minutes,’ he said. ‘In that sense, our written record of history is pathetic and we only have scattered records for the last ten minutes of the forty-six years that Earth has been around.’ A

As he got to know her better, he learned more of her childhood; and he came to realize that it was typical of that of most girls of her time and circumstance. She was educated upon the premise that she would be protected from the gross events that life might thrust in her way, and upon the premise that she had no other duty than to be a graceful and accomplished accessory to that protection, since she belonged to a social and economic class to which protection was an almost sacred obligation. She attended private schools for girls where she learned to read, to write, and to do simple arithmetic; in her leisure she was encouraged to do needlepoint, to play the piano, to paint water colors, and to discuss some of the more gentle works of literature. She was also instructed in matters of dress, carriage, ladylike diction, and morality. Her moral training, both at the schools she attended and at home, was negative in nature, prohibitive in intent, and almost entirely sexual. The sexuality, however, was indirect and unacknowledged; therefore it suffused every other part of her education, which received most of its energy from that recessive and unspoken moral force. She learned that she would have duties toward her husband and family and that she must fulfill them.

The Renaissance deepened the influence of medieval development with its striving towards capitalistic economic and social system only in so far as it confirms the rationalism which now dominates the whole intellectual and material life of the time. [...] They are arecreation of the same spirit which makes its way in the organization of labour, in trading methods, the credit system and double-entry book keeping, in methods of government, in diplomacy and warfare. The whole development of art becomes part of the total process of rationalization. The irrational ceases to make any deeper impression. The things that are now felt as 'beautiful' are the logical conformity of the individual parts of a whole, the arithmetically definable harmony of the relationships and the calculable rhythm of a composition, the exclusion of discords in the relation of the figures to the space they occupy and in the mutual relationship of the various parts of the space itself. And just a central perspective is space seen from a mathematical standpoint, and right proportions are only equivalent to the systematic organization of the individual forms in a picture, so in the course of time call criteria of artistic quality are subjected to rational scrutiny and all the laws of art are rationalized.

In vain did Ransom try to remember that he had been in ‘space’ and found it Heaven, tingling with a fulness of life for which infinity itself was not one cubic inch too large. All that seemed like a dream. That opposite mode of thought which he had often mocked and called in mockery The Empirical Bogey, came surging into his mind–the great myth of our century with its gases and galaxies, its light years and evolutions, its nightmare perspectives of simple arithmetic in which everything that can possibly hold significance for the mind becomes the mere by-product of essential disorder. Always till now he had belittled it, had treated with a certain disdain its flat superlatives, its clownish amazement that different things should be of different sizes, its glib munificence of ciphers. Even now, his reason was not quite subdued, though his heart would not listen to his reason. Part of him still knew that the size of a thing is the least important characteristic, that the material universe derived from the comparing and mythopoeic power within him that very majesty before which he was now asked to abase himself, and that mere numbers could not overawe us unless we lent them, from our own resources, that awfulness which they themselves could no more supply than a banker’s ledger. But this knowledge remained an abstraction. Mere bigness and loneliness overbore him.

It is the postscript to the war that offers the most revelatory and startling commentary on Dutugemunu's life. Despite his newfound wealth and his peactime luxuries, Dutugemunu wanders gloomily about his palace, too often remembering the carnage he wrought on the battlefield and worried over the deep karmic deficits he has incurred. The elders of the Sangha, the Buddhist clergy, notice this and send a delegation of eight monks to minister to his anguish. 'In truth, venerable sirs,' Dutugemunu tells the monks when they arrive, 'how can there be comfort to me in that I caused the destruction of a great army of myriads of men?' 'There is no hindrance on the way to heaven because of your acts,' one of the monks assures his king. Slaughtering Tamils is no moral mistake. Only the equivalent of one and a half men died at Dutugemunu's hands, according to the Sangha's official arithmetic, because the Tamils 'were heretical and evil and dies as though they were animals. You will make the Buddha's faith shine in many ways. Therefore, Lord of Men, cast away your mental confusion.' Being thus exhorted, the great king was comforted; his kill rate would never disturb him again. He does, however, recall that, once upon a breakfast, he ate a red-pepper pod without consciously setting aside a portion of it for the Sangha, as was the royal practice. 'For this,' he decides, 'penance must be done by me.' A hierarchy of sin springs into being, in which dishonouring the Sangha by denying it a due share of a red-pepper pod counts as a graver transgression, worthier of penance, than massacring thousands of Tamils on the battlefield.

Schools, gymnasiums, arithmetic, geometry, history, rhetoric, physics, biology, anatomy, hygiene, therapy, cosmetics, poetry, music, tragedy, comedy, philosophy, theology, agnosticism, skepticism, stoicism, epicureanism, ethics, politics, idealism, philanthropy, cynicism, tyranny, plutocracy, democracy: these are all Greek words for cultural forms seldom originated, but in many cases first matured for good or evil by the abounding energy of the Greeks. All the problems that disturb us today—the cutting down of forests and the erosion of the soil; the emancipation of woman and the limitation of the family; the conservatism of the established, and the experimentalism of the unplaced, in morals, music, and government; the corruptions of politics and the perversions of conduct; the conflict of religion and science, and the weakening of the supernatural supports of morality; the war of the classes, the nations, and the continents; the revolutions of the poor against the economically powerful rich, and of the rich against the politically powerful poor; the struggle between democracy and dictatorship, between individualism and communism, between the East and the West—all these agitated, as if for our instruction, the brilliant and turbulent life of ancient Hellas. There is nothing in Greek civilization that does not illuminate our own. We shall try to see the life of Greece both in the mutual interplay of its cultural elements, and in the immense five-act drama of its rise and fall. We shall begin with Crete and its lately resurrected civilization, because apparently from Crete, as well as from Asia, came that prehistoric culture of Mycenae

this I say,—we must never forget that all the education a man's head can receive, will not save his soul from hell, unless he knows the truths of the Bible. A man may have prodigious learning, and yet never be saved. He may be master of half the languages spoken round the globe. He may be acquainted with the highest and deepest things in heaven and earth. He may have read books till he is like a walking cyclopædia. He may be familiar with the stars of heaven,—the birds of the air,—the beasts of the earth, and the fishes of the sea. He may be able, like Solomon, to "speak of trees, from the cedar of Lebanon to the hyssop that grows on the wall, of beasts also, and fowls, and creeping things, and fishes." (1 King iv. 33.) He may be able to discourse of all the secrets of fire, air, earth, and water. And yet, if he dies ignorant of Bible truths, he dies a miserable man! Chemistry never silenced a guilty conscience. Mathematics never healed a broken heart. All the sciences in the world never smoothed down a dying pillow. No earthly philosophy ever supplied hope in death. No natural theology ever gave peace in the prospect of meeting a holy God. All these things are of the earth, earthy, and can never raise a man above the earth's level. They may enable a man to strut and fret his little season here below with a more dignified gait than his fellow-mortals, but they can never give him wings, and enable him to soar towards heaven. He that has the largest share of them, will find at length that without Bible knowledge he has got no lasting possession. Death will make an end of all his attainments, and after death they will do him no good at all. A man may be a very ignorant man, and yet be saved. He may be unable to read a word, or write a letter. He may know nothing of geography beyond the bounds of his own parish, and be utterly unable to say which is nearest to England, Paris or New York. He may know nothing of arithmetic, and not see any difference between a million and a thousand. He may know nothing of history, not even of his own land, and be quite ignorant whether his country owes most to Semiramis, Boadicea, or Queen Elizabeth. He may know nothing of the affairs of his own times, and be incapable of telling you whether the Chancellor of the Exchequer, or the Commander-in-Chief, or the Archbishop of Canterbury is managing the national finances. He may know nothing of science, and its discoveries,—and whether Julius Cæsar won his victories with gunpowder, or the apostles had a printing press, or the sun goes round the earth, may be matters about which he has not an idea. And yet if that very man has heard Bible truth with his ears, and believed it with his heart, he knows enough to save his soul. He will be found at last with Lazarus in Abraham's bosom, while his scientific fellow-creature, who has died unconverted, is lost for ever. There is much talk in these days about science and "useful knowledge." But after all a knowledge of the Bible is the one knowledge that is needful and eternally useful. A man may get to heaven without money, learning, health, or friends,—but without Bible knowledge he will never get there at all. A man may have the mightiest of minds, and a memory stored with all that mighty mind can grasp,—and yet, if he does not know the things of the Bible, he will make shipwreck of his soul for ever. Woe! woe! woe to the man who dies in ignorance of the Bible! This is the Book about which I am addressing the readers of these pages to-day. It is no light matter what you do with such a book. It concerns the life of your soul. I summon you,—I charge you to give an honest answer to my question. What are you doing with the Bible? Do you read it? HOW READEST THOU?

She liked numbers and sums. She devised a game in which each number was a family member and the “answer” made a family grouping with a story to it. Naught was a babe in arms. He gave no trouble. Whenever he appeared you just “carried” him. The figure 1 was a pretty baby girl just learning to walk, and easy to handle; 2 was a baby boy who could walk and talk a little. He went into family life (into sums, etc.) with very little trouble. And 3 was an older boy in kindergarten, who had to be watched a little. Then there was 4, a girl of Francie’s age. She was almost as easy to “mind” as 2. The mother was 5, gentle and kind. In large sums, she came along and made everything easy the way a mother should. The father, 6, was harder than the others but very just. But 7 was mean. He was a crotchety old grandfather and not at all accountable for how he came out. The grandmother, 8, was hard too, but easier to understand than 7. Hardest of all was 9. He was company and what a hard time fitting him into family life! When Francie added a sum, she would fix a little story to go with the result. If the answer was 924, it meant that the little boy and girl were being minded by company while the rest of the family went out. When a number such as 1024 appeared, it meant that all the little children were playing together in the yard. The number 62 meant that papa was taking the little boy out for a walk; 50 meant that mama had the baby out in the buggy for an airing and 78 meant grandfather and grandmother sitting home by the fire of a winter’s evening. Each single combination of numbers was a new set-up for the family and no two stories were ever the same. Francie took the game with her up into algebra. X was the boy’s sweetheart who came into the family life and complicated it. Y was the boy friend who caused trouble. So arithmetic was a warm and human thing to Francie and occupied many lonely hours of her time.

I turned fifty and decided to take a break. After twenty-five years of working, it seemed like a good idea. Honestly, I was feeling depleted. I still cared about my career and realized, amid a worsening economic climate, that I was lucky to have one. But that appreciation felt more lodged in my head than my heart. One day, United Airlines sent me a card, along with some new luggage tags, offering congratulations on having flown 2 million miles. Quick arithmetic translated all those zeroes into the equivalent of flying from one side of the country to the other every single day—Sundays, holidays, birthdays, sick or well—for more than two years. Maybe the card from United should have offered condolences. It all added up to an abiding fatigue. And a question: Did I want to fly 2 million more miles over the next twenty-five years of my life? Was I having a low-grade midlife crisis? I had no red sports car, reckless affair,

Less than one percent. That’s how many we saved. But the arithmetic, though severe, is important. During the liquidation of the ghetto, 5,000 to 8,000 Jews were taken every day to Treblinka and murdered. During the entire war – more than five years – we saved only 2,500 children. The mathematics of rescue was also severe. To save one Jewish child, ten Poles and two Jews had to risk death. To betray that same child and the family that hid him required only one informer or, worse still, one blackmailer. The risk of being caught by the SS was not prison, but death – death for the entire family. “We all have to ask ourselves, ‘What would I have done?’ But understanding does not erase the regret I feel for my own insufficient efforts. Less than one percent. I agree with Wladyslaw Bartoszewski, one of the organizers of ZEGOTA, who said, ‘Only the dead have done enough.

by 2008 the arithmetic of climate change presented an almost unimaginable challenge. If the world were to stay within the range of carbon emissions that scientists deemed reasonable in order for atmospheric temperatures to remain tolerable through the mid-century, 80 percent of the fossil fuel industry’s reserves would have to stay unused in the ground. In other words, scientists estimated that the fossil fuel industry owned roughly five times more oil, gas, and coal than the planet could safely burn. If the government interfered with the “free market” in order to protect the planet, the potential losses for these companies were catastrophic. If, however, the carbon from these reserves were burned wantonly without the government applying any brakes, scientists predicted an intolerable rise in atmospheric temperatures, triggering potentially irreversible global damage to life on earth.

Interesting-sounding, supposed applications of the incompleteness theorem [here earlier taken explicitly to refer to the incompleteness theorems as a whole] outside mathematics, therefore, often ignore the essential condition of encompassing some basic arithmetic, and formulate the theorem incorrectly as a theorem about formal systems in general. When they do take this condition into account, authors may resort to formulations such as 'Our hypothesis is that the universe is at least as big as arithmetic, so that it is affected by incompleteness' or 'The philosophy should incorporate arithmetic, or else it is already limited'. The first of these makes no apparent sense, while the second amounts to feeble criticism of a system of philosophy that it cannot be a complete guide to life or the universe since it fails to decide every arithmetical statement. Such implications of the incompleteness theorem will be further commented on in Chapter 4.

Skipping Breakfast Eating Breakfast ↓Problem-solving ability ↑Problem-solving ability ↓Short-term memory ↑Arithmetic skills ↓Attention and episodic memory ↑Vigilant attention

Twenty-four hundred years ago, the ageing and grumpy Plato, in Book VII of the Laws, gave his definition of scientific illiteracy: Who is unable to count one, two, three, or to distinguish odd from even numbers, or is unable to count at all, or reckon night and day, and who is totally unacquainted with the revolution of the Sun and Moon, and the other stars . . . All freemen, I conceive, should learn as much of these branches of knowledge as every child in Egypt is taught when he learns the alphabet. In that country arithmetical games have been invented for the use of mere children, which they learn as pleasure and amusement ... I ... have late in life heard with amazement of our ignorance in these matters; to me we appear to be more like pigs than men, and I am quite ashamed, not only of myself, but of all Greeks.

The tragedy of polytheism and idolatry is not the arithmetic (many gods instead of one), but that they exchange the only true source of salvation for lifeless and powerless substitutes, and in doing so, introduce injustice, bondage, and cruelty into human life (cf. Rom. 1:21–32).

Real dark forces…aren’t dark. They’re sort of gray, like Mr. Grimm. They take all the color out of life; they take a town like Blackbury and turn it into frightened streets and plastic signs and Bright New Futures and towers where no one wants to live and no one really does live. The dead seem more alive than us. And everyone becomes gray and turns into numbers and then, somewhere, someone starts to do arithmetic…. The

There’s no simple arithmetic for life’s distribution of happiness and sorrow, no such thing as a standard share.

But life is not a simple arithmetic equation. Life is algorithmic in its complications.

The way they introduced rigor into intellectual life is by declaring that a statement could fall only into two categories: deductive, like “2 +2 =4,” i.e., incontrovertibly flowing from a precisely defined axiomatic framework (here the rules of arithmetic), or inductive, i.e., verifiable in some manner (experience, statistics, etc.),

The proof of Euclidean geometry’s consistency eluded mathematicians. By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

in 1900, David Hilbert listed what he considered to be the twenty-three most important unsolved problems of mathematics. The second item on his list was a request for a proof of the consistency of arithmetic. Such a proof would ensure the consistency of a great deal of higher mathematics. What this proof had to guarantee was, in essence, that one could never prove one equals two. Few mathematicians regarded this as a matter of much import.

In 1931, Kurt Gödel demonstrated two theorems. The first one shows, in effect, that mathematics contains statements that may be true, but are inherently unprovable. Even a formal system as simple as arithmetic permits statements that are precise, meaningful, and seem certainly true, and yet cannot be proven true by formal means. His second theorem shows that a claim of the consistency of arithmetic is just such a statement; it cannot be proven true by any means using the axioms of arithmetic. That is, arithmetic as a formal system cannot guarantee that it will not produce results such as “1 = 2”; such contradictions may never have been encountered, but it is impossible to prove that they never will be.

That’s right. Arithmetic as a formal system is inconsistent.

Among socialists only Saint Simon realized to some extent the position of the entrepreneurs in the capitalistic economy. As a result he is often denied the name of Socialist. The others completely fail to realize that the functions of entrepreneurs in the capitalist order must be performed in a socialist community also. This is reflected most clearly in the writings of Lenin. According to him the work performed in a capitalist order by those whom he refused to designate as ‘working’ can be boiled down to ‘Auditing of Production and Distribution’ and ‘keeping the records of labour and products’. This could easily be attended to by the armed workers, ‘by the whole of the armed people’.1 Lenin quite rightly separates these functions of the ‘capitalists and clerks’ from the work of the technically trained higher personnel, not however missing the opportunity to take a side thrust at scientifically trained people by giving expression to that contempt for all highly skilled work which is characteristic of Marxian proletarian snobbishness. ‘This recording, this exercise of audit,’ he says, ‘Capitalism has simplified to the utmost and has reduced to extremely simple operations of superintendence and book-entry within the grasp of anyone able to read and write. To control these operations a knowledge of elementary arithmetic and the drawing of correct receipts is sufficient.’2 It is therefore possible straisrhtwav to enable all members of society to do these things for themselves.3 This is all, absolutely all that Lenin had to say on this problem; and no socialist has a word more to say. They have no greater perception of the essentials of economic life than the errand boy, whose only idea of the work of the entrepreneur is that he covers pieces of paper with letters and figures.

As he spoke and she listened, the sounds of people talking, of children playing, became faint. The girl and he were alone under the great sailing moon. . . He told a story he was amazed to hear. What he had to say about horses seemed to have meanings pertinent to the whole world. He was clearing up mysteries for himself as he went along. If you got to the bottom of one subject, did the truth about all other subjects lie there, too? If you knew one thing fully, did you, in a way, know all? Was that the reason old farmers and coon hunters were so wise? Once before in his life he had been drunk. At the age of sixteen, he had sampled a jug of raw corn whisky. He had felt a kind of power at the time: as if he had transcended himself, were suspended above himself. This enabled him to see a lot of the world ordinarily not visible; he saw also his own smallness in this world. Now he was drunk again, but in an entirely different way. He was more himself than he had ever been before; and this was happening at the very minute when he was also more aware of another person than he had ever been before. How could this be? It contradicted all the rules of arithmetic. To give himself away and to have more left. He felt like saying his own name over and over again. . .that was who he had been, but might never be again; for this girl was making him over by listening to him. . . .it was not a one-sided conversation. . .he could never have done it without her. She taught him all his powers, showed him all his meanings. Until she asked her questions, he didn't know his answers. He had never in his life felt so radiant. She looked at him, she asked. He spoke. Something towered upward out of the interchange; together they opened up meaning he had never glimpsed before. . .

All these civilizations, some of which we are still unable to decipher many of their codes, such as the Pharaonic civilization that refused to deal with zero! We see them as smart enough to build the pyramids with their miraculous geometry and to calculate the orbits of stars and planets with extreme accuracy, but they are very stupid for not defining zero in a way that they can deal with, and use it in arithmetic operations, how strange this really is! But in fact, they did not ignore it, but gave it its true value, and refused to build their civilizations on an unknown and unknown illusion, and on a wrong arithmetical frame of reference. Throughout their history, humans have looked at zero as the unknown, they refused to define it and include it in their calculations and equations, not because it has no effect, but because its true effect is unknown, and remaining unknown is better than giving it a false effect.

The fact of zero He added nonstop: Did you know that zero was not used throughout human history! Until 781 A.D, when it was first embodied and used in arithmetic equations by the Arab scholar Al-Khwarizmi, the founder of algebra. Algorithms took their name from him, and they are algorithmic arithmetic equations that you have to follow as they are and you will inevitably get the result, the inevitable result. And before that, across tens and perhaps hundreds of thousands of years, humans refused to deal with zero. While the first reference to it was in the Sumerian civilization, where inscriptions were found three thousand years ago in Iraq, in which the Sumerians indicated the existence of something before the one, they refused to deal with it, define it and give it any value or effect, they refused to consider it a number. All these civilizations, some of which we are still unable to decipher many of their codes, such as the Pharaonic civilization that refused to deal with zero! We see them as smart enough to build the pyramids with their miraculous geometry and to calculate the orbits of stars and planets with extreme accuracy, but they are very stupid for not defining zero in a way that they can deal with, and use it in arithmetic operations, how strange this really is! But in fact, they did not ignore it, but gave it its true value, and refused to build their civilizations on an unknown and unknown illusion, and on a wrong arithmetical frame of reference. Throughout their history, humans have looked at zero as the unknown, they refused to define it and include it in their calculations and equations, not because it has no effect, but because its true effect is unknown, and remaining unknown is better than giving it a false effect. Like the wrong frame of reference, if you rely on it, you will inevitably get a wrong result, and you will fall into the inevitability of error, and if you ignore it, your chance of getting it right remains. Throughout their history, humans have preferred to ignore zero, not knowing its true impact, while we simply decided to deal with it, and even rely on it. Today we build all our ideas, our civilization, our software, mathematics, physics, everything, on the basis that 1 + 0 equals one, because we need to find the effect of zero so that our equations succeed, and our lives succeed with, but what if 1 + 0 equals infinity?! Why did we ignore the zero in summation, and did not ignore it in multiplication?! 1×0 equals zero, why not one? What is the reason? He answered himself: There is no inevitable reason, we are not forced. Humans have lived throughout their ages without zero, and it did not mean anything to them. Even when we were unable to devise any result that fits our theorems for the quotient of one by zero, then we admitted and said unknown, and ignored it, but we ignored the logic that a thousand pieces of evidence may not prove me right, and one proof that proves me wrong. Not doing our math tables in the case of division, blowing them up completely, and with that, we decided to go ahead and built everything on that foundation. We have separated the arithmetic tables in detail at our will, to fit our calculations, and somehow separate the whole universe around us to fit these tables, despite their obvious flaws. And if we decide that the result of one multiplied by zero is one instead of zero, and we reconstruct the whole world on this basis, what will happen? He answered himself: Nothing, we will also succeed, the world, our software, our thoughts, our dealings, and everything around us will be reset according to the new arithmetic tables. After a few hundred years, humans will no longer be able to understand that one multiplied by zero equals zero, but that it must be one because everything is built on this basis.

What the poor as well as the rich require is not to be indoctrinated, is not to be taught other people’s opinions, but to be induced and enabled to think for themselves. It is not physical science that will do this, even if they could learn it much more thoroughly than they are able to do. After reading, writing, and arithmetic (the last a most important discipline in habits of accuracy and precision, in which they are extremely deficient), the desirable thing for them seems to be the most miscellaneous information, and the most varied exercise of their faculties. They cannot read too much. Quantity is of more importance than quality, especially all reading which relates to human life and the ways of mankind; geography, voyages and travels, manners and customs, and romances, which must tend to awaken their imagination and give them some of the meaning of self-devotion and heroism, in short, to unbrutalise them.

I have confirmed from my many years of teaching abstract mathematics to art students that I am not the only one who prefers to use abstract ideas to illuminate concrete examples rather than the other way round. Many of these art students consider that they’re bad at math because they were bad at memorizing times tables, because they’re bad at mental arithmetic, and they can’t solve equations. But this doesn’t mean they’re bad at math—it just means they’re not very good at times tables, mental arithmetic and equations, an absolutely tiny part of mathematics that hardly counts as abstract at all. It turns out that they do not struggle nearly as much when we get to abstract things such as higher dimensional spaces, subtle notions of equivalence, and category theory structures. Their blockage on mental arithmetic becomes irrelevant.

You have to be more than an interpreter. You have to be a creator as well. Music is a dream, as life is a dream. It is never finished. It is always becoming. It is not your task to play every note with arithmetical precision. It is your task to allow the music to flow through you and become what it wants to become.

Motivation can be a good building block or serve as basic learning, just like you learn basic math and arithmetic when you are really young, but if counting numbers is all you know even when you are old, and refuse to see the truth in anything beyond what was taught when you were young, you my friend have failed to grow in life.

Well, listen then. On the other side, fresh young lives thrown away for want of help and by thousands, on every side! A hundred thousand good deeds could be done and helped, on that old woman’s money which will be buried in a monastery! Hundreds, thousands perhaps, might be set on the right path; dozens of families saved from destitution, from ruin, from vice, from the Lock hospitals—and all with her money. Kill her, take her money and with the help of it devote oneself to the service of humanity and the good of all. What do you think, would not one tiny crime be wiped out by thousands of good deeds? For one life thousands would be saved from corruption and decay. One death, and a hundred lives in exchange—it’s simple arithmetic!

A hundred thousand good deeds could be done and helped, on that old woman’s money which will be buried in a monastery! Hundreds, thousands perhaps, might be set on the right path; dozens of families saved from destitution, from ruin, from vice, from the Lock hospitals—and all with her money. Kill her, take her money and with the help of it devote oneself to the service of humanity and the good of all. What do you think, would not one tiny crime be wiped out by thousands of good deeds? For one life thousands would be saved from corruption and decay. One death, and a hundred lives in exchange—it’s simple arithmetic! Besides, what value has the life of that sickly, stupid, ill-natured old woman in the balance of existence! No more than the life of a louse, of a black-beetle, less in fact because the old woman is doing harm. She is wearing out the lives of others;

Excepting machinery, there is hardly anything secular in our culture that does not come from Greece. Schools, gymnasiums, arithmetic, geometry, history, rhetoric, physics, biology, anatomy, hygiene, therapy, cosmetics, poetry, music, tragedy, comedy, philosophy, theology, agnosticism, skepticism, stoicism, epicureanism, ethics, politics, idealism, philanthropy, cynicism, tyranny, plutocracy, democracy: these are all Greek words

The proof of existence of arithmetic is the reality in the partialization of the barter trade. The proof of existence of mathematical logic is the arithmetic. Therefore mathematical logic can only serve as a centralization of arithmetic. It derives its life from arithmetic.

Thus Plato offers one version of a philosophical poverty, by which wisdom alienates one from conventional ideals and makes one indifferent to worldly concerns. The Cynics philosophized in the same general rubric, though obviously details differ significantly. One notable difference between the two is the value placed upon learning and science. Unlike his Platonic counterpart, the Cynic rejects arithmetic, geometry, dialectic, and the rest as superfluous distractions from the "one big" requirement of self-knowledge. So in the famous anecdote, when Plato and his followers have defined man as the "featherless biped," Diogenes rushes into the Academy with a plucked chicken, crying, "Here is Plato's human being!" For the Cynic, logical exercises, definitionmaking, and the like are not preparatory to the vision of some Good or intuition of eternity. All such talk is a form of pride, a strategy to overawe others, and contributes less to the good life than does a healthy skepticism. Yet, like Plato, the Cynics also travel along the Eleatic Way of Truth and shun what they ridicule as the Way of Seeming. For what can be said truly? In short, the Cynics are profoundly skeptical about the possibility of almost all knowledge.

But King James I hated learned ladies. they were ridiculed at court, and soon the normal Stuart education for girls went little beyond the most basic skills of reading and writing, and the elementary arithmetic they would need in their household management.

Computers are universal machines, their potential extends uniformly over a boundless expanse of tasks. Human potentials, on the other hand, are strong in areas long important for survival, but weak in things far removed. Imagine a “landscape of human competence,” having lowlands with labels like “arithmetic” and “rote memorization,” foothills like “theorem proving” and “chess playing,” and high mountain peaks labeled “locomotion,” “hand-eye coordination” and “social interaction.” Advancing computer performance is like water slowly flooding the landscape. A half century ago it began to drown the lowlands, driving out human calculators and record clerks, but leaving most of us dry. Now the flood has reached the foothills, and our outposts there are contemplating retreat. We feel safe on our peaks, but, at the present rate, those too will be submerged within another half century. I propose that we build Arks as that day nears, and adopt a seafaring life!2

Consider the power of love. I remember a mother I met once as I made a professional house call. This woman was confined in an iron lung. The ravages of polio had effectively destroyed all the breathing muscles so that her life was completely dependent upon the large metal tank and the electrical motor that powered its noisy bellows. While there, I watched her three children as they related to their mother. The oldest interrupted our work to ask permission to go to a friend's house for an hour. Later the second child asked her mother for help with arithmetic. Finally the youngest child, so small that she couldn't see her mother's face directly, looked up at the mother's image in a mirror that had been placed over her head and asked, "Mommy, may I have a cookie?" I've never forgotten that lesson on the power of love. This woman, virtually disabled and certainly incapable of any degree of physical enforcement of parental authority, sweetly influenced that home solely with the power to love.

I was transformed...because I caught a glimpse of a revolutionary use for computers. We seized the opportunity to the computer as a general processor for symbols (hence thoughts) rather than just a speedy engine for arithmetic.

...he will accompany us on a hike in the hills, leaping and whizzing back and forth, and coming when called as well as a dog. It is just that the organism, the whole pattern of nerve and muscle, is more complex and intelligent than logical systems of arithmetic, geometry and grammar - which are in fact nothing but inferior ritual. Life itself dances, for what else are trees, ferns, butterflies, and snakes but elaborate forms of dancing? Even wood and bones show, in their structure, the characteristic patterns of flowing water, which (as Lao-tzu pointed out in 400 B.C.) derives its incredible power by following gravity and seeking that "lowest level which all men abhor." When dance I do not think-count my steps, and some women say I have no sense of rhythm, but I have a daughter who (without ever having taken lessons in dancing) can follow me as if she were my shadow or I were hers. The whole secret of life and of creative energy consists in flowing with gravity. Even when he leaps and bounces our cat is going with it. This is the way the whole earth and everything in the universe beehives.* But man is making a mess of the earth be- *Harrumph! Excuse the pun, but it is important, because bees live in hexagonal as distinct from quadrilateral structures, and this is the natural way in which all things, such as bubbles and pebbles, congregate, nestling into each other by gravity. It will follow, because 2 x 6 is 12, that - as Buckminster Fuller has pointed out - as number-system to the base 12 (duodecimal) is closer to nature than one to the base of 10 (decimal). For 12 is divisible by both 2 and 3, whereas 10 is not. After all, we use the base 12 for measuring circles and spheres and time, and so can "think circles" around people who use only meters. The world is better duodecimal than decimated.

2,000–3,000 PEOPLE, NOT GENERAL FAME This is one of the messages Eric burned into my brain last year, and it’s guided many decisions since. We were sitting in a large soaking tub talking about the world (as mathematicians and human guinea pigs do in San Francisco), and he said: “General fame is overrated. You want to be famous to 2,000 to 3,000 people you handpick.” I’m paraphrasing, but the gist is that you don’t need or want mainstream fame. It brings more liabilities than benefits. However, if you’re known and respected by 2–3K high-caliber people (e.g., the live TED audience), you can do anything and everything you want in life. It provides maximal upside and minimal downside. GOOD QUESTION TO ASK YOURSELF WHEN TACKLING INCUMBENT COMPANIES (OR IDEAS) “How is their bread buttered?” “What is it that they can’t afford to say or think?” “CONSENSUS” SHOULD SET OFF YOUR SPIDEY SENSE “Somehow, people have to learn that consensus is a huge problem. There’s no ‘arithmetic consensus’ because it doesn’t require a consensus. But there is a Washington consensus. There is a climate consensus. In general, consensus is how we bully people into pretending that there’s nothing to see. ‘Move along, everyone.’ I think that, in part, you should learn that people don’t naturally come to high levels of agreement unless something is either absolutely clear, in which case consensus isn’t present, or there’s an implied threat of violence to livelihood or self.” TF: I start nearly every public presentation I give with a slide that contains one quote: “Whenever you find yourself on the side of the majority, it’s time to pause and reflect.” —Mark Twain. This isn’t just for my audience. It’s also a reminder for me.

A key ingredient in appreciating what mathematics is about is to realize that it is concerned with ideas, understanding, and communication more than it is with any specific brand of symbols....It is almost as if ideas set in mathematical form melt and become liquid and just as rivers can, from the most humble beginnings, flow for thousands of miles, through the most varied topography bringing nourishment and life with them wherever they go, so too can ideas cast in mathematical form flow far from their original sources, along well-defined paths, electrifying and dramatically affecting much of what they touch. pp. xii - xiii.

Oh, guns! In seconds, great holes you can bore; used for justice, how you the world adore! But as wickedness gets immensely more, used for crime, how you the world so abhor! I’m so confused the world can’t see logic in that very simple arithmetic— that tolls on gun deaths can be wholly stripped by simple banning of gun ownership!

A popular misconception is that decision analysis is unemotional, dehumanizing, and obsessive because it uses numbers and arithmetic in order to guide important life decisions. Isn’t this turning over important human decisions “to a machine,” sometimes literally a computer — which now picks our quarterbacks, our chief executive officers, and even our lovers? Aren’t the “mathematicizers” of life, who admittedly have done well in the basic sciences, moving into a context where such uses of numbers are irrelevant and irreverent? Don’t we suffer enough from the tyranny of numbers when our opportunities in life are controlled by numerical scores on aptitude tests and numbers entered on rating forms by interviewers and supervisors? In short, isn’t the human spirit better expressed by intuitive choices than by analytic number crunching? Our answer to all these concerns is an unqualified “no.” There is absolutely nothing in the von Neumann and Morgenstern theory — or in this book — that requires the adoption of “inhumanly” stable or easily accessed values. In fact, the whole idea of utility is that it provides a measure of what is truly personally important to individuals reaching decisions. As presented here, the aim of analyzing expected utility is to help us achieve what is really important to us. As James March (1978) points out, one goal in life may be to discover what our values are. That goal might require action that is playful, or even arbitrary. Does such action violate the dictates of either rationality or expected utility theory? No. Upon examination, an individual valuing such an approach will be found to have a utility associated with the existential experimentation that follows from it. All that the decision analyst does is help to make this value explicit so that the individual can understand it and incorporate it into action in a noncontradictory manner.

As André Maurois put it: “Everything that is in agreement with our personal desires seems true. Everything that is not puts us into a rage.” Is it any wonder, then, that we find it so hard to get at the answers to our problems? Wouldn’t we have the same trouble trying to solve a second-grade arithmetic problem, if we went ahead on the assumption that two plus two equals five? Yet there are a lot of people in this world who make life a hell for themselves and others by insisting that two plus two equals five—or maybe five hundred!

Peter announced that Paul do Mar was not a surf spot, that it was just a picturesque, kamikaze close-out. I disagreed. I found it a mesmerizing wave. But absurdly dangerous. Besides the raw power, there was the shoreline. The rocks were round, mostly, but the shorebreak borderland you had to cross to enter the water was simply too wide, particularly when the surf was big. Even after timing it carefully, waiting for a lull, letting a shorebreak wave expend itself, then running recklessly with your board over wet boulders, you sometimes didn’t make it to water deep enough to paddle on before the next wave slammed you, banging you backward across the rocks—board, body, dignity all battered, sometimes severely. This was not a normal ocean problem. It felt like bad arithmetic—the time and distance did not, for some Madeira-only reason, compute. I had never seen a surf spot with an entrance so daunting. And the exit, getting back onto dry land, could be even worse. The wave we were there to ride was at most only thirty yards offshore, but I sometimes resorted to a very long paddle, around a seawall at the far east end of the village, rather than face that shorebreak.

By the end of the nineteenth century, the best that was achieved was a proof that Euclidean geometry was consistent as long as arithmetic was consistent.

I was sitting in a bar one night, talking rather loudly about a person I hated - and a man with a beard sat down beside me, and he said amiably, "Why don't you have him killed?" "I've thought of it," I said. "Don't think I haven't." "Let me help you to think about it clearly," he said. His voice was deep. His beak was large. He wore a black mohair suit and a black string tie. His little red mouth was obscene. "You're looking at the situation through a red haze of hate," he said. "What you need are the calm, wise services of a murder counsellor, who can plan the job for you, and save you an unnecessary trip to the hot squat." "Where do I find one?" I said. "You've found one, " he said. "You're crazy," I said. "That's right," he said. "I've been in and out mental institutions all my life. That makes my services all the more appealing. If I were to testify against you, your lawyer would have no trouble establishing that I was a well-known nut, and a convicted felon besides." "What was the felony?" I said. "A little thing - practising medicine without a license," he said. "Not murder then?" I said. "No," he said, "but that doesn't mean I haven't murdered. As a matter of fact, I murdered almost everyone who had anything to do with convicting me of practising medicine without a license." He looked at the ceiling, did some arithmetic. "Twenty-two, twenty-three - maybe more," he said. "Maybe more. I've killed them over a period of years, and I haven't read the paper every single day.