Mathematical Thinking Quotes

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

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

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.

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

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!

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.

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.

Knowing mathematics is like wearing a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world.

I think we need more math majors who don't become mathematicians. More math major doctors, more math major high school teachers, more math major CEOs, more math major senators. But we won't get there unless we dump the stereotype that math is only worthwhile for kid geniuses.

Improbable things happen a lot.

Dividing one number by another is mere computation ; knowing what to divide by what is mathematics.

if gambling is exciting, you’re doing it wrong.

Although personally, I think cyberspace means the end of our species.

I think that consciousness is the way information feels when being processed in certain complex ways.

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.

Genius is a thing that happens, not a kind of person.

To enjoy life, we might have to stop thinking about what we will never be able to read and watch and say and do, and start to think of how to enjoy the world within our boundaries. To live on a human scale. To focus on the few things we can do, rather than the millions of things we can't. To not crave parallel lives. To find a smaller mathematics. To be a proud and singular one. An indivisible prime.

he presented me with a mathematical conundrum,” he said. “It’s a famous one, the P = NP problem. Basically, it asks whether it’s more difficult to think of the solution to a problem yourself or to ascertain if someone else’s answer to the same problem is correct.

I guess I think of lotteries as a tax on the mathematically challenged.

Nonlinear thinking means which way you should go depends on where you already are.

Mathematics is the extension of common sense by other means.

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.

It was all so very businesslike that one watched it fascinated. It was pork-making by machinery, pork-making by applied mathematics. And yet somehow the most matter-of-fact person could not help thinking of the hogs; they were so innocent, they came so very trustingly; and they were so very human in their protests - and so perfectly within their rights! They had done nothing to deserve it; and it was adding insult to injury, as the thing was done here, swinging them up in this cold-blooded, impersonal way, without pretence at apology, without the homage of a tear.

Let's face it, the universe is messy. It is nonlinear, turbulent, and chaotic. It is dynamic. It spends its time in transient behavior on its way to somewhere else, not in mathematically neat equilibria. It self-organizes and evolves. It creates diversity, not uniformity. That's what makes the world interesting, that's what makes it beautiful, and that's what makes it work.

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.

Its a mathematical fact that two negatives make a positive so even under adverse circumstances think positively.

Scientists and inventors of the USA (especially in the so-called "blue state" that voted overwhelmingly against Trump) have to think long and hard whether they want to continue research that will help their government remain the world's superpower. All the scientists who worked in and for Germany in the 1930s lived to regret that they directly helped a sociopath like Hitler harm millions of people. Let us not repeat the same mistakes over and over again.

It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbable, must be the truth, unless the truth is a hypothesis it didn’t occur to you to consider.

If nature leads us to mathematical forms of great simplicity and beauty—by forms, I am referring to coherent systems of hypotheses, axioms, etc.—to forms that no one has previously encountered, we cannot help thinking that they are “true,” that they reveal a genuine feature of nature…. You must have felt this too: the almost frightening simplicity and wholeness of the relationships which nature suddenly spreads out before us and for which none of us was in the least prepared.

A math teacher’s least favorite thing to hear from a student is “I get the concept, but I couldn’t do the problems.” Though the student doesn’t know it, this is shorthand for “I don’t get the concept.

The only definition of rationality that I’ve found that is practically, empirically, and mathematically rigorous is the following: what is rational is that which allows for survival. Unlike modern theories by psychosophasters, it maps to the classical way of thinking. Anything that hinders one’s survival at an individual, collective, tribal, or general level is, to me, irrational.

Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense—or deciding whether the method is the right one to use in the first place—requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel.

What I'm thinking is: here I am, lying under a haystack ... The tiny little place I occupy is so small in relation to the rest of space where I am not and where it's none of my business; and the amount of time which I'll succeed in living is so insignificant by comparison with the eternity where I haven't been and never will be ... And yet in this atom, in this mathematical point, the blood circulates, the brain works and even desires something as well .. What sheer ugliness! What sheer nonsense!

These are lives, Lada,” Radu said. “How can you speak of them like they are matters of simple mathematics, a problem to be solved?” “Because thinking like that is the only way to keep from losing our minds.” “What about our souls?” Mehmed whispered. “Souls and thrones are irreconcilable.

You know, people think mathematics is complicated. Mathematics is the simple bit. It's the stuff we can understand. It's cats that are complicated. I mean, what is it in those little molecules and stuff that make one cat behave differently than another, or that make a cat? And how do you define a cat? I have no idea.

Physicists believe that the Gaussian law has been proved in mathematics while mathematicians think that it was experimentally established in physics.

A man may possess a profound knowledge of history and mathematics; he may be an authority in psychology, biology, or astronomy; he may know all the discovered truths pertaining to geology and natural science; but if he has not with this knowledge that nobility of soul which prompts him to deal justly with his fellow men, to practice virtue and holiness in his personal life, he is not truly an educated man. Character is the aim of true education; and science, history, and literature are but means used to accomplish the desired end. Character is not the result of chance work but of continuous right thinking and right acting.

...it's really more intelligent to be able to simplify things than to complicate them. Even if some people think it makes you look stupid.

A reasonable person believes, in short, that each of his beliefs is true and that some of them are false.

In the Bayesian framework, how much you believe something after you see the evidence depends not just on what the evidence shows, but on how much you believed it to begin with.

In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy, and that is just what mathematics can provide -- a relief from daily life, an anodyne to the practical workaday world.

Why don't we want our children to learn to do mathematics? Is it that we don't trust them, that we think it's too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon. Why not about triangles?

You know,” he said, “this design begins to appeal to me after all. Sea slugs aren’t the least bit arousing, but logarithms . . . I’ve always thought that word sounded splendidly naughty.” He let it roll off his tongue with ribald inflection. “Logarithm.” He gave an exaggerated shiver. “Ooh. Yes and thank you and may I have some more.” “Lots of mathematical terms sound that way. I think it’s because they were all coined by men. ‘Hypotenuse’ is downright lewd.” “ ‘Quadrilateral’ brings rather carnal images to mind.” She was silent for a long time. Then one of her dark eyebrows arched. “Not so many as ‘rhombus.’ ” Good Lord. That word was wicked. Her pronunciation of it did rather wicked things to him. He had to admire the way she didn’t shrink from a challenge, but came back with a new and surprising retort. One day, she’d make some fortunate man a very creative lover.

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.

What drove me? I think most creative people want to express appreciation for being able to take advantage of the work that's been done by others before us. I didn't invent the language or mathematics I use. I make little of my own food, none of my own clothes. Everything I do depends on other members of our species and the shoulders that we stand on. And a lot of us want to contribute something back to our species and to add something to the flow. It's about trying to express something in the only way that most of us know how-because we can't write Bob Dylan songs or Tom Stoppard plays. We try to use the talents we do have to express our deep feelings, to show our appreciation of all the contributions that came before us, and to add something to that flow. That's what has driven me.

Overstimulation has been the real drawback. I need to find ways to stop thinking about analysis of algorithms, in order to do various other things that human beings ought to do.

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

Safety warning: never divide by zero unless a licensed mathematician is present.

317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.

If you can't test it, it's not theorics -- it's metatheorics. A branch of philosophy. So, if you want to think of it this way, our test equipment is what defines the boundary separating theorics from philosophy.

The aspirations of democracy are based on the notion of an informed citizenry, capable of making wise decisions. The choices we are asked to make become increasingly complex. They require the longer-term thinking and greater tolerance for ambiguity that science fosters. The new economy is predicated on a continuous pipeline of scientific and technological innovation. It can not exist without workers and consumers who are mathematically and scientifically literate.

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.

A man craves ultimate truths. Every mortal mind, I think, is that way. But what is ultimate truth? It's the end of the road, where there is no more mystery, no more hope. And no more questions to ask, since all the answers have been given. But there is no such place. The Universe is a labyrinth made of labyrinths. Each leads to another. And wherever we cannot go ourselves, we reach with mathematics. Out of mathematics we build wagons to carry us into the nonhuman realms of the world.

One of the great joys of mathematics is the incontrovertible feeling that you've understood something the right way, all the way down to the bottom; it's a feeling I haven't experienced in any other sphere of mental life. And when you know how to do something the right way, it's hard-for some stubborn people, impossible-to make yourself explain it the wrong way.

A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile in the math SAT, there were 11 boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking and giving adults testosterone enhances their math skills. Oh, okay, it's biological. But consider a paper published in science in 2008. The authors examined the relationship between math scores and sexual equality in 40 countries based on economic, educational and political indices of gender equality. The worst was Turkey, United States was middling, and naturally, the Scandinavians were tops. Low and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries it's statistically insignificant. And by the time you examine the most gender equal country on earth at the time, Iceland, girls are better at math than boys. Footnote, note that the other reliable sex difference in cognition, namely better reading performance by girls than by boys doesn't disappear in more gender equal societies. It gets bigger. In other words, culture matters. We carry it with us wherever we go.

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.

People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.

The afflicted are almost upon them. The air is a din of hypersonic bursts, snarls and empty shell casings. But still I hear him. As his people start to fall. As his pistol clicks empty. As he rises with only his knuckles left between him and the sheer brutality of mathematics. As the music swells above the carnage, still I hear him breathe the words. "Tell them I was thinking of them. At the end." They pile onto him. All snarls and teeth and fists. But as he falls, I am holding his hand. Easing him into his long good night. "I will tell them, David." The last words he will ever hear. 'I promise.

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 concern for content.

One of the most painful parts of teaching mathematics is seeing students damaged by the cult of the genius. The genius cult tells students it’s not worth doing mathematics unless you’re the best at mathematics, because those special few are the only ones whose contributions matter. We don’t treat any other subject that way! I’ve never heard a student say, “I like Hamlet, but I don’t really belong in AP English—that kid who sits in the front row knows all the plays, and he started reading Shakespeare when he was nine!” Athletes don’t quit their sport just because one of their teammates outshines them. And yet I see promising young mathematicians quit every year, even though they love mathematics, because someone in their range of vision was “ahead” of them.

Physics, mathematics, music, painting, my politics, my love for you, my work, the star-dust of my body, the spirit that impels it, clocks diurnal, time perpetual, the roll, rough, tender, swamping, liberating, breathing, moving, thinking nature, human nature and the cosmos are patterned together.

And I think that if God did exist, he had many children. I think Jesus proves this. Jesus must be the seventh son of God. A-sus, B-sus, C-sus, D-sus, E-sus, F-sus, G-sus. That's just logic. That's just mathematical. And T-sus would always be fucking about. And P-sus does deliveries. C-sus started the Roman Empire. Cae-sus. F-sus, City in Turkey. B-sus was covered in something. Some people applauding there; other people going, "What?" ... B-sus was covered in bees.

You call a tree a tree, he said, and you think nothing more of the word. But it was not a 'tree' until someone gave it that name. You call a star a star, and say it is just a ball of matter moving on a mathematical course. But that is merely how you see it. By so naming things and describing them you are only inventing your own terms about them. And just as speech is invention about objects and ideas, so myth is invention about truth. We have come from God (continued Tolkien), and inevitably the myths woven by us, though they contain error, will also reflect a splintered fragment of the true light, the eternal truth that is with God. Indeed only by myth-making, only by becoming a 'sub-creator' and inventing stories, can Man aspire to the state of perfection that he knew before the Fall. Out myths may be misguided, but they steer however shakily towards the true harbor, while materialistic 'progress' leads only to a yawning abyss and the Iron Crown of evil.

...whatever we do whatever way we move forward there will be damage carried from all previous rows and columns in this mathematical computation we make, all the multi-configured additions and subtractions in language America, in all bases, particularly I'm thinking about at the moment 1492, 1776, 1861, 1867, 1980, 2016, 2020.

So, I convinced myself that, because the statistical likelihood of something happening in real life exactly the way I imagined it was so low, if I imagined the worst possible things in vivid detail, I could mathematically reduce the odds of them happening. I convinced myself that my brain had power over the probability projections of the universe. I’d lie awake at night thinking about all the worst stuff that could happen like it was my job, and I don’t know if I ever really broke the habit.

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

Before the work of Georg Cantor in the nineteenth century, the study of the infinite was as much theology as science; now, we understand Cantor’s theory of multiple infinities, each one infinitely larger than the last, well enough to teach it to first-year math majors. (To be fair, it does kind of blow their minds.)

People who don't like math always accuse mathematicians of trying to make math complicated. (...) But anyone who does love math knows it's really the opposite: math rewards simplicity, and mathematicians value it above all else. So it's no surprise that Walter's favourite axiom was also the most simple in the realm of mathematics: the axiom of the empty set. The axiom of the empty set is the axiom of zero. it states that there must be a concept of nothingness, that there must be the concept of zero: zero value, zero items. Math assumes there's a concept of nothingness, but is it proven? No. But it must exist. And if we're being philosophical—which we today are—we can say that life itself is the axiom of the empty set. It begins in zero and ends in zero. We know that both states exist, but we will not be conscious of either experience: they are states that are necessary parts of life, even as they cannot be experienced as life. We assume the concept of nothingness, but we cannot prove it. But it must exist. So I prefer to think that Walter has not died but has instead proven for himself the axiom of the empty set, that he has proven the concept of zero. I know nothing else would have made him happier. An elegant mind wants elegant endings, and Walter had the most elegant mind. So I wish him goodbye; I wish him the answer to the axiom he so loved.

People enjoy inventing slogans which violate basic arithmetic but which illustrate “deeper” truths, such as “1 and 1 make 1” (for lovers), or “1 plus 1 plus 1 equals 1” (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds -more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called “addition”, and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, “There are 17 languages in India, and 462 dialects.” There is something strange about the precise statements like that, when the concepts “language” and “dialect” are themselves fuzzy.

What is remarkable is that there are no traces of evolution from simple to sophisticated, and the same is true of mathematics, medicine, astronomy and architecture and of Egypt's amazingly rich and convoluted religio-mythological system (even the central content of such refined works as the Book of the Dead existed right at the start of the dynastic period). 7 The majority of Egyptologists will not consider the implications of Egypt's early sophistication. These implications are startling, according to a number of more daring thinkers. John Anthony West, an expert on the early dynastic period, asks: How does a complex civilization spring full-blown into being? Look at a 1905 automobile and compare it to a modern one. There is no mistaking the process of `development'. But in Egypt there are no parallels. Everything is right there at the start. The answer to the mystery is of course obvious but, because it is repellent to the prevailing cast of modern thinking, it is seldom considered. Egyptian civilization was not a `development', it was a legacy.

I'm angry because you think everything happened by chance but there are billions of people on this planet and I found you so if you're saying I could just as well have found someone else then I can't bear your bloody mathematics!" Her fists had been clenched. He stood there looking at her for several minutes. Then he said that he loved her. It was the first time. They never stopped arguing and they never slept apart; he spent an entire working life calculating probabilities and she was the most improbable person he ever met. She turned him upside-down.

Listen, Ducklescence, he whispered. You will never know what the world is made of. The only thing that’s certain is that it’s not made of the world. As you close upon some mathematical description of reality you cant help but lose what is being described. Every inquiry displaces what is addressed. A moment in time is a fact, not a possibility. The world will take your life. But above all and lastly the world does not know that you are here. You think that you understand this. But you dont. Not in your heart you dont. If you did you would be terrified. And you’re not. Not yet. And now, good night.

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.

How can I number the worlds to which the eye gives me entry? - the world of light, of colour, of shape, of shadow: of mathematical precision in the snowflake, the ice formation, the quartz crystal, the patterns of stamen and petal: of rhythm in the fluid curve and plunging line of the mountain faces. Why some blocks of stone, hacked into violent and tortured shapes, should so profoundly tranquillise the mind I do not know. Perhaps the eye imposes its own rhythm on what is only a confusion: one has to look creatively to see this mass of rock as more than jag and pinnacle - as beauty. Else why did men for so many centuries think mountains repulsive? A certain kind of consciousness interacts with the mountain-forms to create this sense of beauty. Yet the forms must be there for the eye to see. And forms of a certain distinction: mere dollops won't do it. It is, as with all creation, matter impregnated with mind: but the resultant issue is a living spirit, a glow in the consciousness, that perishes when the glow is dead. It is something snatched from non-being, that shadow which creeps in on us continuously and can be held off by continuous creative act. So, simply to look on anything, such as a mountain, with the love that penetrates to its essence, is to widen the domain of being in the vastness of non-being. Man has no other reason for his existence.

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

You ask me if an ordinary person—by studying hard—would get to be able to imagine these things like I imagine. Of course. I was an ordinary person who studied hard. There's no miracle people. It just happens they got interested in this thing, and they learned all this stuff. They're just people. There's no talent or special miracle ability to understand quantum mechanics or a miracle ability to imagine electromagnetic fields that comes without practice and reading and learning and study. So if you take an ordinary person who's willing to devote a great deal of time and study and work and thinking and mathematics, then he's become a scientist.

And why are you so firmly, so triumphantly, convinced that only the normal and the positive—in other words, only what is conducive to welfare—is for the advantage of man? Is not reason in error as regards advantage? Does not man, perhaps, love something besides well-being? Perhaps he is just as fond of suffering? Perhaps suffering is just as great a benefit to him as well-being? Man is sometimes extraordinarily, passionately, in love with suffering, and that is a fact. [. . .] And yet I think man will never renounce real suffering, that is, destruction and chaos. Why, suffering is the sole origin of consciousness. Though I did lay it down at the beginning that consciousness is the greatest misfortune for man, yet I know man prizes it and would not give it up for any satisfaction. Consciousness, for instance, is infinitely superior to twice two makes four. Once you have mathematical certainty there is nothing left to do or to understand. There will be nothing left but to bottle up your five senses and plunge into contemplation.

They had chains which they fastened about the leg of the nearest hog, and the other end of the chain they hooked into one of the rings upon the wheel. So, as the wheel turned, a hog was suddenly jerked off his feet and borne aloft. At the same instant the ear was assailed by a most terrifying shriek; the visitors started in alarm, the women turned pale and shrank back. The shriek was followed by another, louder and yet more agonizing--for once started upon that journey, the hog never came back; at the top of the wheel he was shunted off upon a trolley and went sailing down the room. And meantime another was swung up, and then another, and another, until there was a double line of them, each dangling by a foot and kicking in frenzy--and squealing. The uproar was appalling, perilous to the ear-drums; one feared there was too much sound for the room to hold--that the walls must give way or the ceiling crack. There were high squeals and low squeals, grunts, and wails of agony; there would come a momentary lull, and then a fresh outburst, louder than ever, surging up to a deafening climax. It was too much for some of the visitors--the men would look at each other, laughing nervously, and the women would stand with hands clenched, and the blood rushing to their faces, and the tears starting in their eyes. Meantime, heedless of all these things, the men upon the floor were going about their work. Neither squeals of hogs nor tears of visitors made any difference to them; one by one they hooked up the hogs, and one by one with a swift stroke they slit their throats. There was a long line of hogs, with squeals and life-blood ebbing away together; until at last each started again, and vanished with a splash into a huge vat of boiling water. It was all so very businesslike that one watched it fascinated. It was pork-making by machinery, pork-making by applied mathematics. And yet somehow the most matter-of-fact person could not help thinking of the hogs; they were so innocent, they came so very trustingly; and they were so very human in their protests--and so perfectly within their rights! They had done nothing to deserve it; and it was adding insult to injury, as the thing was done here, swinging them up in this cold-blooded, impersonal way, without a pretence at apology, without the homage of a tear. Now and then a visitor wept, to be sure; but this slaughtering-machine ran on, visitors or no visitors. It was like some horrible crime committed in a dungeon, all unseen and unheeded, buried out of sight and of memory.

The hoodlum-occultist is “sociopathic” enough to, see through the conventional charade, the social mythology of his species. “They’re all sheep,” he thinks. “Marks. Suckers. Waiting to be fleeced.” He has enough contact with some more-or-less genuine occult tradition to know a few of the gimmicks by which “social consciousness,” normally conditioned consciousness, can be suspended. He is thus able to utilize mental brutality in place of the simple physical brutality of the ordinary hooligan. He is quite powerless against those who realize that he is actually a stupid liar. He is stupid because spending your life terrorizing and exploiting your inferiors is a dumb and boring existence for anyone with more than five billion brain cells. Can you imagine Beethoven ignoring the heavenly choirs his right lobe could hear just to pound on the wall and annoy the neighbors? Gödel pushing aside his sublime mathematics to go out and cheat at cards? Van Gogh deserting his easel to scrawl nasty caricatures in the men’s toilet? Mental evil is always the stupidest evil because the mind itself is not a weapon but a potential paradise. Every kind of malice is a stupidity, but occult malice is stupidest of all. To the extent that the mindwarper is not 100 percent charlatan through-and-through (and most of them are), to the extent that he has picked up some real occult lore somewhere, his use of it for malicious purposes is like using Shakespeare’s sonnets for toilet tissue or picking up a Picasso miniature to drive nails. Everybody who has advanced beyond the barbarian stage of evolution can see how pre-human such acts are, except the person doing them. Genuine occult initiation confers “the philosopher’s stone,” “the gold of the wise” and “the elixir of life,” all of which are metaphors for the capacity to greet life with the bravery and love and gusto that it deserves. By throwing this away to indulge in spite, malice and the small pleasure of bullying the credulous, the mindwarper proves himself a fool and a dolt. And the psychic terrorist, besides being a jerk, is always a liar and a fraud. Healing is easier (and more fun) than cursing, to begin with, and cursing usually backfires or misfires. The mindwarper doesn’t want you to know that. He wants you to think he’s omnipotent.

There is no great religion without a great schism. All of them have it. And that's because you're dealing with something called faith. And faith is not something you can prove; faith is personal opinion. Uh, when you're dealing with something with certainty, like, y'know, science or logic, you don't have the--there's no wiggle room; that's why history is not filled with warring math cults, y'know, because you can settle the issue; you can prove something to be right or wrong, and that's the end of the argument: next case. Whereas, when you're dealing with faith, you can forever argue your point, or another point, because you're dealing with intangibles. Personally, I think, faith is what you ask of somebody when you don't have the goods to prove your point.

But that would mean it was originally a sideways number eight. That makes no sense at all. Unless..." She paused as understanding dawned. "You think it was the symbol for infinity?" "Yes, but not the usual one. A special variant. Do you see how one line doesn't fully connect in the middle? That's Euler's infinity symbol. Absolutus infinitus." "How is it different from the usual one?" "Back in the eighteenth century, there were certain mathematical calculations no one could perform because they involved series of infinite numbers. The problem with infinity, of course, is that you can't come up with a final answer when the numbers keep increasing forever. But a mathematician named Leonhard Euler found a way to treat infinity as if it were a finite number- and that allowed him to do things in mathematical analysis that had never been done before." Tom inclined his head toward the date stone. "My guess is whoever chiseled that symbol was a mathematician or scientist." "If it were my date stone," Cassandra said dryly, "I'd prefer the entwined hearts. At least I would understand what it means." "No, this is much better than hearts," Tom exclaimed, his expression more earnest than any she'd seen from him before. "Linking their names with Euler's infinity symbol means..." He paused, considering how best to explain it. "The two of them formed a complete unit... a togetherness... that contained infinity. Their marriage had a beginning and end, but every day of it was filled with forever. It's a beautiful concept." He paused before adding awkwardly, "Mathematically speaking.

Don't be scared by the word authority. Believing things on authority only means believing them because you've been told them by someone you think trustworthy. Ninety-nine per cent of the things you believe are believed on authority. I believe there is such a place as New York. I haven't seen it myself. I couldn't prove by abstract reasoning that there must be such a place. I believe it because reliable people have told me so. The ordinary man believes in the Solar System, atoms, evolution, and the circulation of the blood on authority -because the scientists say so. Every historical statement in the world is believed on authority. None of us has seen the Norman Conquest or the defeat of the Armada. None of us could prove them by pure logic as you prove a thing in mathematics. We believe them simply because people who did see them have left writings that tell us about them: in fact, on authority. A man who jibbed at authority in other things as some people do in religion would have to be content to know nothing all his life.

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.

A man may possess a profound knowledge of history and mathematics; he may be an authority in psychology, biology, or astronomy; he may know all the discovered truths pertaining to geology and natural science; but if he has not with this knowledge that nobility of soul which prompts him to deal justly with his fellow men, to practice virtue and holiness in personal life, he is not a truly educated man. "Character is the aim of true education; and science, history, and literature are but means used to accomplish the desired end. Character is not the result of chance work but of continuous right thinking and right acting. "True education seeks, then, to make men and women not only good mathematicians, proficient linguists, profound scientists, or brilliant literary lights, but also honest men, combined with virtue, temperance, and brotherly love-men and women who prize truth, justice, wisdom, benevolence, and self-control as the choicest acquisitions of a successful life.

When will you ask for your post back?” he whispered in her ear. “I miss the smell of industrial-strength solvents.” She laughed softly. “Soon. And when will you have papers read at the mathematical society again? I rather like having my husband called a genius for reasons that are not clear to me.” My husband. The words rolled off her tongue, easy and beautiful. He kissed her fervently. “Soon. My brilliance quite overflowed on the way home. I have four notebooks to show for it.” “Good. We don’t want people to think I love you for your looks alone.” “In that case we should also put you in some rather revealing gowns once in a while, so that people don’t think I married you for your accomplishments alone.

Doing a geographic” is a term alcoholics often use for acting on the impulse to start over by moving to a new town, or state, instead of making any internal changes. It’s the anywhere-but-here part of the disease that says, “Remove yourself from this, go someplace new, and everything will be better.” Two years into our Florida stint, my mother pulled a geographic as radical as the move from Rochester. The new plan was to head for California. She enrolled in the mathematics graduate program at the University of California’s shiny new campus in San Diego, and as soon as our elementary school let out for the summer, she put us into a new Buick station wagon – a gift from her parents – and drove us across the country. You’d think we’d have protested at yet another move. After all, having been duped before, we were in no position to believe that the next move would be any different. But I have no memory of being unhappy about the news. Because that’s what often happens when an alcoholic parent is doing a geographic. She pulls you in and, before you know it, you, too, believe in the promise of the new place.

What is the proper justification of a mathematician’s life? My answers will be, for the most part, such as are expected from a mathematician: I think that it is worthwhile, that there is ample justification. But I should say at once that my defense of mathematics will be a defense of myself, and that my apology is bound to be to some extent egotistical. I should not think it worth while to apologize for my subject if I regarded myself as one of its failures. Some egotism of this sort is inevitable, and I do not feel that it really needs justification. Good work is no done by "humble" men. It is one of the first duties of a professor, for example, in any subject, to exaggerate a little both the importance of his subject and his own importance in it. A man who is always asking "Is what I do worth while?" and "Am I the right person to do it?" will always be ineffective himself and a discouragement to others. He must shut his eyes a little and think a little more of his subject and himself than they deserve. This is not too difficult: it is harder not to make his subject and himself ridiculous by shutting his eyes too tightly.

Quantum mechanics. What a repository, a dump, of human aspiration it was, the borderland where mathematical rigor defeated common sense, and reason and fantasy irrationally merged. Here the mystically inclined could find whatever they required and claim science as their proof. And for these ingenious men in their spare time, what ghostly and beautiful music it must be--spectral asymmetry, resonances, entanglement, quantum harmonic oscillators--beguiling ancient airs, the harmony of the spheres that might transmute a lead wall into gold and bring into being the engine that ran on virtually nothing, on virtual particles, that emitted no harm and would power the human enterprise as well as save it. Beard was stirred by the yearnings of these lonely men. And why should he think they were lonely? It was not, or not only, condescension that made him think them so. They did not know enough, but they knew too much to have anyone to talk to. What mate waiting down the pub or in the British Legion, what hard-pressed wife with job and kids and housework, was going to follow them down these warped funnels in the space-time continuum, into the wormhole, the shortcut to a single, final answer to the global problem of energy?

Do reflections also travel at the speed of light? What does your buddy Albert think? When the light hits the glass and starts back in the opposite direction doesnt it have to come to a full stop first? And so everything is supposed to hang on the speed of light but nobody wants to talk about the speed of dark. What’s in a shadow? Do they move along at the speed of the light that casts them? How deep do they get? How far down can you clamp your calipers? You scribbled somewhere in the margins that when you lose a dimension you’ve given up all claims to reality. Save for the mathematical. Is there a route here from the tangible to the numerical that hasnt been explored? I dont know. Me either. Photons are quantum particles. They’re not little tennisballs. Yeah, said the Kid. He dredged up his watch and checked the time. Maybe you’d better go eat. You need to keep your strength up if you aim to wrest the secrets of creation from the gods. They’re a testy lot by all accounts.

Another time somebody gave a talk about poetry. He talked about the structure of the poem and the emotions that come with it; he divided everything up into certain kinds of classes. In the discussion that came afterwards, he said, “Isn’t that the same as in mathematics, Dr. Eisenhart?” Dr. Eisenhart was the dean of the graduate school and a great professor of mathematics. He was also very clever. He said, “I’d like to know what Dick Feynman thinks about it in reference to theoretical physics.” He was always putting me on in this kind of situation. I got up and said, “Yes, it’s very closely related. In theoretical physics, the analog of the word is the mathematical formula, the analog of the structure of the poem is the interrelationship of the theoretical bling-bling with the so-andso”–and I went through the whole thing, making a perfect analogy. The speaker’s eyes were _beaming_ with happiness. Then I said, “It seems to me that no matter _what_ you say about poetry, I could find a way of making up an analog with _any_ subject, just as I did for theoretical physics. I don’t consider such analogs meaningful.

A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the science: 'The probability of an event is the reason we have to believe that it has taken place, or that it will take place.' 'The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible' (equally like to happen). From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary. Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave neither room nor demand for a theory of probabilities.

The only gain of civilisation for mankind is the greater capacity for variety of sensations--and absolutely nothing more. And through the development of this many-sidedness man may come to finding enjoyment in bloodshed. In fact, this has already happened to him. Have you noticed that it is the most civilised gentlemen who have been the subtlest slaughterers, to whom the Attilas and Stenka Razins could not hold a candle, and if they are not so conspicuous as the Attilas and Stenka Razins it is simply because they are so often met with, are so ordinary and have become so familiar to us. In any case civilisation has made mankind if not more bloodthirsty, at least more vilely, more loathsomely bloodthirsty. In old days he saw justice in bloodshed and with his conscience at peace exterminated those he thought proper. Now we do think bloodshed abominable and yet we engage in this abomination, and with more energy than ever. Which is worse? Decide that for yourselves. They say that Cleopatra (excuse an instance from Roman history) was fond of sticking gold pins into her slave-girls' breasts and derived gratification from their screams and writhings. You will say that that was in the comparatively barbarous times; that these are barbarous times too, because also, comparatively speaking, pins are stuck in even now; that though man has now learned to see more clearly than in barbarous ages, he is still far from having learnt to act as reason and science would dictate. But yet you are fully convinced that he will be sure to learn when he gets rid of certain old bad habits, and when common sense and science have completely re-educated human nature and turned it in a normal direction. You are confident that then man will cease from INTENTIONAL error and will, so to say, be compelled not to want to set his will against his normal interests. That is not all; then, you say, science itself will teach man (though to my mind it's a superfluous luxury) that he never has really had any caprice or will of his own, and that he himself is something of the nature of a piano-key or the stop of an organ, and that there are, besides, things called the laws of nature; so that everything he does is not done by his willing it, but is done of itself, by the laws of nature. Consequently we have only to discover these laws of nature, and man will no longer have to answer for his actions and life will become exceedingly easy for him. All human actions will then, of course, be tabulated according to these laws, mathematically, like tables of logarithms up to 108,000, and entered in an index; or, better still, there would be published certain edifying works of the nature of encyclopaedic lexicons, in which everything will be so clearly calculated and explained that there will be no more incidents or adventures in the world.

I don't know which is worse—to have a bad teacher or no teacher at all. In any case, I believe the teacher's work should be largely negative. He can't put the gift into you, but if he finds it there, he can try to keep it from going in an obviously wrong direction. We can learn how not to write, but this is a discipline that does not simply concern writing itself but concerns the whole intellectual life. A mind cleared of false emotion and false sentiment and egocentricity is going to have at least those roadblocks removed from its path. If you don't think cheaply, then there at least won't be the quality of cheapness in your writing, even though you may not be able to write well. The teacher can try to weed out what is positively bad, and this should be the aim of the whole college. Any discipline can help your writing: logic, mathematics, theology, and of course and particularly drawing. Anything that helps you to see, anything that makes you look. The writer should never be ashamed of staring. There is nothing that doesn't require his attention.

In the beginning of the year 1665 I found the Method of approximating series & the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of Tangents of Gregory & Slusius, & in November had the direct method of fluxions & the next year in January had the Theory of Colours & in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon & (having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere) from Kepler's rule of the periodic times of the Planets being in sesquialterate proportion of their distances from the center of their Orbs, I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: & thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, & found them answer pretty nearly. All this was in the two plague years of 1665-1666. For in those days I was in the prime of my age for invention & minded Mathematicks & Philosophy more then than at any time since.

Questioner: I am full of hate. Will you please teach me how to love? KRISHNAMURTI: No one can teach you how to love. If people could be taught how to love, the world problem would be very simple, would it not? If we could learn how to love from a book as we learn mathematics, this would be a marvellous world; there would be no hate, no exploitation, no wars, no division of rich and poor, and we would all be really friendly with each other. But love is not so easily come by. It is easy to hate, and hate brings people together after a fashion; it creates all kinds of fantasies, it brings about various types of cooperation as in war. But love is much more difficult. You cannot learn how to love, but what you can do is to observe hate and put it gently aside. Don’t battle against hate, don’t say how terrible it is to hate people, but see hate for what it is and let it drop away; brush it aside, it is not important. What is important is not to let hate take root in your mind. Do you understand? Your mind is like rich soil, and if given sufficient time any problem that comes along takes root like a weed, and then you have the trouble of pulling it out; but if you do not give the problem sufficient time to take root, then it has no place to grow and it will wither away. If you encourage hate, give it time to take root, to grow, to mature, it becomes an enormous problem. But if each time hate arises you let it go by, then you will find that your mind becomes very sensitive without being sentimental; therefore it will know love. The mind can pursue sensations, desires, but it cannot pursue love. Love must come to the mind. And, when once love is there, it has no division as sensuous and divine: it is love. That is the extraordinary thing about love: it is the only quality that brings a total comprehension of the whole of existence.

Sometimes it's hard because I don't like to hurt people's feelings. So there have been times when a friend will get a haircut and I will see it and my initial reaction is "Oh my God, you look like a streetwalker who got caught in a wind tunnel." But I obviously can't say that because that would be an insult to streetwalkers. So I have to say, "I love it! It looks great!" But when I say it my voice goes up about three octaves. "It looks greee-aaattt!" So I'm certain they know I'm lying. How come when we lie our voices go up so many octaves? It's a dead giveaway. It happens when we dole out compliments we don't mean and it happens when we say things like "You didn't have to get my anything!" or "What do you mean you weren't invited to my party? You're always invited!" Everyone knows what those mean. "You definitely had to get me something" and "You haven't been invited back to the house since the urn incident of '04." And it's a mathematical fact: the higher the octave, the bigger the lie. "I didn't even hear my phone ring!" is usually like a four on the scale. "You think I'm sleeping with someone else?" is off the charts. I can tell when people are lying to me when they start their sentence with "I have to be honest with you." They may as well say, "Listen, I'm about to lie straight to your face." Why do people need to clarify when they're being honest? Does that mean everything else they've ever said has been a lie? Yesterday they said they liked my sweater but they didn't say they were being honest. Does that mean they hated it? It's so strange to me. It almost feels like they're giving me the option to not hear the truth. As if when they say, "I have to be honest with you," I might say, "No, no. Please. Only lies right now.

He was beautiful when he sat alone, he was like me, he had wide lapels, he was holding the mug in the hardest possible way so that his fingers were all twisted but still long and beautiful, he didn’t like to sit alone all the time, but this time, I swear, he didn’t care on way or the other. I’ll tell you why I like to sit alone, because I’m a sadist, that’s why we like to sit alone, because we’re the sadists who like to sit alone. He sat alone because he was beautifully dressed for the occasion and because he was not a civilian. We are the sadists you don’t have to worry about, you think, and we have no opinion on the matter of whether you have to worry about us, and we don’t even like to think about the matter because it baffles us. Maybe he doesn’t mean a thing to me any more but I think he was like me. You didn’t expect to fall in love, I said to myself and at the same time I answered gently, Do you think so? I heard you humming beautifully, your hum said that I can’t ignore you, that I’d finally come around for a number of delicious reasons that only you knew about, and here I am, Miss Blood. And you won’t come back, you won’t come back to where you left me, and that’s why you keep my number, so you don’t dial it by mistake when you’re fooling with the dial not even dialing numbers. You begin to bore us with your pain and we have decided to change your pain. You said you were happiest when you danced, you said you were happiest when you danced with me, now which do you mean? And so we changed his pain, we threw the idea of a body at him and we told him a joke, and then he thought a great deal about laughing and about the code. And he thought that she thought that he thought that she thought the worst thing a woman could do was to take a man away from his work because that made her what, ugly or beautiful? And now you’ve entered the mathematical section of your soul which you claimed you never had. I suppose that this, plus the broken heart, makes you believe that now you have a perfect right to go out and tame the sadists. He had the last line of each verse of the song but he didn’t have any of the other lines, the last line was always the same, Don’t call yourself a secret unless you mean to keep it. He thought he knew, or he actually did know too much about singing to be a singer; and if there is actually such a condition, is anybody in it, and are sadists born there? It is not a question mark, it is not an exclamation point, it is a full stop by the man who wrote Parasites of Heaven. Even if we stated our case very clearly and all those who held as we do came to our side, all of them, we would still be very few.

I always felt that someone, a long time ago, organized the affairs of the world into areas that made sense-catagories of stuff that is perfectible, things that fit neatly in perfect bundles. The world of business, for example, is this way-line items, spreadsheets, things that add up, that can be perfected. The legal system-not always perfect, but nonetheless a mind-numbing effort to actually write down all kinds of laws and instructions that cover all aspects of being human, a kind of umbrella code of conduct we should all follow. Perfection is crucial in building an aircraft, a bridge, or a high-speed train. The code and mathematics residing just below the surface of the Internet is also this way. Things are either perfectly right or they will not work. So much of the world we work and live in is based upon being correct, being perfect. But after this someone got through organizing everything just perfectly, he (or probably a she) was left with a bunch of stuff that didn't fit anywhere-things in a shoe box that had to go somewhere. So in desperation this person threw up her arms and said, 'OK! Fine. All the rest of this stuff that isn't perfectible, that doesn't seem to fit anywhere else, will just have to be piled into this last, rather large, tattered box that we can sort of push behind the couch. Maybe later we can come back and figure where it all is supposed to fit in. Let's label the box ART.' The problem was thankfully never fixed, and in time the box overflowed as more and more art piled up. I think the dilemma exists because art, among all the other tidy categories, most closely resembles what it is like to be human. To be alive. It is our nature to be imperfect. The have uncategorized feelings and emotions. To make or do things that don't sometimes necessarily make sense. Art is all just perfectly imperfect. Once the word ART enters the description of what you're up to , it is almost getting a hall pass from perfection. It thankfully releases us from any expectation of perfection. In relation to my own work not being perfect, I just always point to the tattered box behind the couch and mention the word ART, and people seem to understand and let you off the hook about being perfect a go back to their business.

All this attempt to control... We are talking about Western attitudes that are five hundred years old... The basic idea of science - that there was a new way to look at reality, that it was objective, that it did not depend on your beliefs or your nationality, that it was rational - that idea was fresh and exciting back then. It offered promise and hope for the future, and it swept away the old medieval system, which was hundreds of years old. The medieval world of feudal politics and religious dogma and hateful superstitions fell before science. But, in truth, this was because the medieval world didn't really work any more. It didn't work economically, it didn't work intellectually, and it didn't fit the new world that was emerging... But now... science is the belief system that is hundreds of years old. And, like the medieval system before it, science is starting to not fit the world any more. Science has attained so much power that its practical limits begin to be apparent. Largely through science, billions of us live in one small world, densely packed and intercommunicating. But science cannot help us decide what to do with that world, or how to live. Science can make a nuclear reactor, but it can not tell us not to build it. Science can make pesticide, but cannot tell us not to use it. And our world starts to seem polluted in fundamental ways - air, and water, and land - because of ungovernable science... At the same time, the great intellectual justification of science has vanished. Ever since Newton and Descartes, science has explicitly offered us the vision of total control. Science has claimed the power to eventually control everything, through its understanding of natural laws. But in the twentieth century, that claim has been shattered beyond repair. First, Heisenberg's uncertainty principle set limits on what we could know about the subatomic world. Oh well, we say. None of us lives in a subatomic world. It doesn't make any practical difference as we go through our lives. Then Godel's theorem set similar limits to mathematics, the formal language of science. Mathematicians used to think that their language had some inherent trueness that derived from the laws of logic. Now we know what we call 'reason' is just an arbitrary game. It's not special, in the way we thought it was. And now chaos theory proves that unpredictability is built into our daily lives. It is as mundane as the rain storms we cannot predict. And so the grand vision of science, hundreds of years old - the dream of total control - has died, in our century. And with it much of the justification, the rationale for science to do what it does. And for us to listen to it. Science has always said that it may not know everything now but it will know, eventually. But now we see that isn't true. It is an idle boast. As foolish, and misguided, as the child who jumps off a building because he believes he can fly... We are witnessing the end of the scientific era. Science, like other outmoded systems, is destroying itself. As it gains in power, it proves itself incapable of handling the power. Because things are going very fast now... it will be in everyone's hands. It will be in kits for backyard gardeners. Experiments for schoolchildren. Cheap labs for terrorists and dictators. And that will force everyone to ask the same question - What should I do with my power? - which is the very question science says it cannot answer.