Scientists And Mathematicians Quotes

If anything runs deeper than a mathematician’s love of variables, it’s a scientist’s love of constants.

Read Euler, read Euler, he is the master of us all.

Like musicians, like mathematicians—like elite athletes—scientists peak early and dwindle fast. It isn’t creativity that fades, but stamina: science is an endurance sport. To produce that single illuminating experiment, a thousand nonilluminating experiments have to be sent into the trash; it is battle between nature and nerve. Avery

RAND scientists tried to tell their wives that the decision whether to buy or not to buy a washing machine was an 'optimization problem'.

Thirty-five craters on the moon are named for Jesuit scientists and mathematicians.

Scientists and mathematicians are trained to dig below the surface of the chaotic, natural world to search for unexpected simplicity, structure, and even beauty.

And it is funny because economists are not real scientists, and because logicians think more clearly, but mathematicians are best.

(Space programs are) a force operating on educational pipelines that stimulate the formation of scientists, technologists, engineers and mathematicians... They're the ones that make tomorrow come. The foundations of economies... issue forth from investments we make in science and technology.

I'm going away anyway. I am. Do you hear me? I may be ugly and clumsy, but one thing I am not, I'm not retarded. I may be ugly and clumsy, but one thing I am not, I'm not retarded. There's nothing wrong with my brain. Do you know what the Teacher Ghosts say about me? They tell me I'm smart, and I can win scholarships. I can get into colleges. I've already applied. I'm smart. I can do all sorts of things. I know how to get A's, and they say I could be a scientist or a mathematician if I want. I can make a living and take care of myself. So you don't have to find me a keeper who's too dumb to know a bad bargain. I'm so smart, if they say write ten pages, I can write fifteen. I can do ghost things even better than ghosts can. Not everyone thinks I'm nothing. I am not going to be a slave or a wife. Even if I am stupid and talk funny amd get sick, I won't let you turn me into a slave or a wife. I'm getting out of here. I can't stand living here anyore. It's your fault I talk weird.

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals — the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

Mathematics is to the scientist and the engineer a tool, to the professional mathematician a religion, but to the ordinary person a stumbling-block.

So how does one go about proving something like this? It's not like being a lawyer, where the goal is to persuade other people; nor is it like a scientist testing a theory. This is a unique art form within the world of rational science. We are trying to craft a "poem of reason" that explains fully and clearly and satisfies the pickiest demands of logic, while at the same time giving us goosebumps.

Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to talk of a solid ... drawn into a fourth, fifth, sixth, or further dimension.

Attracting a new scientist, software engineer, or mathematician to a city increases the demand for local services.

Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all. One of the chief duties of a mathematician in acting as an advisor to scientists is to discourage them from expecting too much of mathematicians.

And in that same way, law school breaks a mind down. Novelists, poets, and artists don’t often do well in law school (unless they are bad novelists, poets, and artists), but neither, necessarily, do mathematicians, logicians, and scientists. The first group fails because their logic is their own; the second fails because logic is all they own. He,

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.

But unpredictability was not the reason physicists and mathematicians began taking pendulums seriously again in the sixties and seventies. Unpredictability was only the attention-grabber. Those studying chaotic dynamics discovered that the disorderly behavior of simple systems acted as a creative process. It generated complexity: richly organized patterns, sometimes stable and sometimes unstable, sometimes finite and sometimes infinite, but always with the fascination of living things. That was why scientists played with toys.

Every great inventor, architect, scientist, and mathematician began as a child holding nothing more then a pencil. That single stick of wood and graphite could enable him to explore worlds within that he would never otherwise access.

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it.

In music, musicians must be able to read musical notes and have developed the skill to follow the music from their studies. This skill allows them to read new musical notes and be capable of hearing most or all of the sounds (melodies, harmonies, etc.) in their head without having to play the music piece. By analogy, in Mathematics, we believe a scientist, engineer or mathematician must be able to read and understand mathematical codes (e.g., Maple, Mathematica) in their head without having to execute the problem.

Scientists and mathematicians need to interact, debate, and share ideas to generate ideal results.

The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science 'more geometrico.

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.

Et peut-être la posterité me saura gré de lui avoir fait connaître que les Anciens n’ont pas tout su. (And perhaps, posterity will thank me for having shown that the ancients did not know everything.)

Excel suffers from an image problem. Most people assume that spreadsheet programs such as Excel are intended for accountants, analysts, financiers, scientists, mathematicians, and other geeky types. Creating a spreadsheet, sorting data, using functions, and making charts seems daunting, and best left to the nerds.

Many great scientists and philosophers, among them René Descartes, Ludwig Wittgenstein, Immanuel Kant, Thorstein Veblen, Isaac Newton, and Albert Einstein, have had similarly strange and solitary personalities.

There are three men on a train. One of them is an economist and one of them is a logician and one of them is a mathematician. And they have just crossed the border into Scotland (I don’t know why they are going to Scotland) and they see a brown cow standing in a field from the window of the train (and the cow is standing parallel to the train). And the economist says, “Look, the cows in Scotland are brown.” And the logician says, “No. There are cows in Scotland of which one at least is brown.” And the mathematician says, “No. There is at least one cow in Scotland, of which one side appears to be brown.” And it is funny because economists are not real scientists, and because logicians think more clearly, but mathematicians are best.

The system has to force people to behave in ways that are increasingly remote from the natural pattern of human behavior. For example, the system needs scientists, mathematicians and engineers. It can't function without them. So heavy pressure is put on children to excel in these fields. It isn't natural for an adolescent human being to spend the bulk of his time sitting at a desk absorbed in study. A normal adolescent wants to spend his time in active contact with the real world.

the reference. “And two:  IUPAC will name the remaining elements to honor female, non-white and minority scientists and mathematicians who had fair credit for their discoveries and work stolen from them.  I’m quite certain you’ll have no problem finding enough.

Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.

In its most practical form, creativity is about connecting ideas together, especially ideas that don’t seem to be connected. Neuroscientist Nancy C. Andreasen, in her extensive research on highly creative people including accomplished scientists, mathematicians, artists, and writers, came to the conclusion that “Creative people are better at recognizing relationships, making associations and connections.”3

And in that same way, law school breaks a mind down. Novelists, poets, and artists don't often do well in law school, but neither, necessarily, do mathematicians, logicians and scientists. The first group fails because their logic is their own; the second fails because logic is all they own.

Think of a "discovery" as an act that moves the arrival of information from a later point in time to an earlier time. The discovery's value does not equal the value of the information discovered but rather the value of having the information available earlier than it otherwise would have been. A scientist or a mathematician may show great skill by being the first to find a solution that has eluded many others; yet if the problem would soon have been solved anyway, then the work probably has not much benefited the world [unless having a solution even slightly sooner is immensely valuable or enables further important and urgent work].

Our major claims in this book are radical but true: Nearly all important thinking takes place outside of consciousness and is not available on introspection; the mental feats we think of as the most impressive are trivial compared to everyday capacities; the imagination is always at work in ways that consciousness does not apprehend; consciousness can glimpse only a few vestiges of what the mind is doing; the scientist, the engineer, the mathematician, and the economist, impressive as their knowledge and techniques may be, are also unaware of how they are thinking and, even though they are experts, will not find out just by asking themselves.

The math-powered applications powering the data economy were based on choices made by fallible human beings. Some of these choices were no doubt made with the best intentions. Nevertheless, many of these models encoded human prejudice, misunderstanding, and bias into the software systems that increasingly managed our lives. Like gods, these mathematical models were opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, were beyond dispute or appeal. And they tended to punish the poor and the oppressed in our society, while making the rich richer.

Like musicians, like mathematicians—like elite athletes—scientists peak early and dwindle fast.

tinkering is closer to the way real scientists, mathematicians, and engineers solve problems.

Every intelligent person, whether he's an artist or not - a mathematician, a doctor, a scientist - possesses a poetic way of seeing and describing the world.

Even today, poets, philosophers, mathematicians, and scientists find that the contemplation of the insoluble is a source of joy, astonishment, and contentment.

Like gods, these mathematical models were opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists.

In other words, our conscious representations are sometimes ordered (or arranged in a pattern) before they have become conscious to us. The 18th-century German mathematician Karl Friedrich Gauss gives an example of an experience of such an unconscious order of ideas: He says that he found a certain rule in the theory of numbers "not by painstaking research, but by the Grace of God, so to speak. The riddle solved itself as lightning strikes, and I myself could not tell or show the connection between what I knew before, what I last used to experiment with, and what produced the final success." The French scientist Henri Poincare is even more explicit about this phenomenon; he describes how during a sleepless night he actually watched his mathematical representations colliding in him until some of them "found a more stable connection. One feels as if one could watch one's own unconscious at work, the unconscious activity partially becoming manifest to consciousness without losing its own character. At such moments one has an intuition of the difference between the mechanisms of the two egos.

Of a techno-human culture that wants to be more than a successful barbarism, two things above all are required: psychological cultural formation and the cultural capacity for translation. Mathematicians must become poets, cyberneticists must become philosophers of religion, doctors must become composers, computer scientists must become shamans. Was humanity ever something other than the art of managing transitions?

It is frightening to see distinguished intellectuals fall under Robespierre’s ax. From a humane standpoint they can never be too much mourned, but divine justice is no respecter of mathematicians or scientists.

The mind is essentially a survival machine. Attack and defense against other minds, gathering, storing, and analyzing information — this is what it is good at, but it is not at all creative. All true artists, whether they know it or not, create from a place of no-mind, from inner stillness. The mind then gives form to the creative impulse or insight. Even the great scientists have reported that their creative breakthroughs came at a time of mental quietude. The surprising result of a nationwide inquiry among America’s most eminent mathematicians, including Einstein, to find out their working methods, was that thinking “plays only a subordinate part in the brief, decisive phase of the creative act itself.”1 So I would say that the simple reason why the majority of scientists are not creative is not because they don’t know how to think but

The solvable systems are the ones shown in textbooks. They behave. Confronted with a nonlinear system, scientists would have to substitute linear approximations or find some other uncertain backdoor approach. Textbooks showed students only the rare non-linear systems that would give way to such techniques. They did not display sensitive dependence on initial conditions. Nonlinear systems with real chaos were rarely taught and rarely learned. When people stumbled across such things-and people did-all their training argued for dismissing them as aberrations. Only a few were able to remember that the solvable, orderly, linear systems were the aberrations. Only a few, that is, understood how nonlinear nature is in its soul. Enrico Fermi once exclaimed, "It does not say in the Bible that all laws of nature are expressible linearly!" The mathematicians Stanislaw Ulam remarked that to call the study of chaos "nonlinear science" was like calling zoology "the study of nonelephant animals.

Some could say it is the external world which has molded our thinking-that is, the operation of the human brain-into what is now called logic. Others-philosophers and scientists alike-say that our logical thought (thinking process?) is a creation of the internal workings of the mind as they developed through evolution "independently" of the action of the outside world. Obviously, mathematics is some of both. It seems to be a language both for the description of the external world, and possibly even more so for the analysis of ourselves. In its evolution from a more primitive nervous system, the brain, as an organ with ten or more billion neurons and many more connections between them must have changed and grown as a result of many accidents. The very existence of mathematics is due to the fact that there exist statements or theorems, which are very simple to state but whose proofs demand pages of explanations. Nobody knows why this should be so. The simplicity of many of these statements has both aesthetic value and philosophical interest.

Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things they said: 'I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.' -Robert Sachs, Ph.D., George Mason University ... 'I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for future columns.' -W. Robert Smith, Ph.D., Georgia State University... 'If all those Ph.D.'s were wrong, the country would be in very serious trouble.' -Everett Harman, Ph.D., U.S. Army Research Institute

By the nature of their discipline, mathematicians invariably do their best intuitive work in their twenties or early thirties—whereas historians and other social scientists often need years of studious preparation before they became capable of genuinely creative work.

mathematician Steven Strogatz puts it . . . In every case, these feats of synchrony occur spontaneously, almost as if nature has an eerie yearning for order. And that raises a profound mystery: Scientists have long been baffled by the existence of spontaneous order in the universe. The laws of thermodynamics seem to dictate the opposite, that nature should inexorably degenerate toward a state of greater disorder, greater entropy. Yet all around us we see magnificent structures that have somehow managed to assemble themselves. This enigma bedevils all of science today.2

Mere springs and coils produced the inward movements of our clockwork man. He might be termed a Puritan. One essential dislike, formidable in its simplicity, pervaded his dull soul: he disliked injustice and deception. He disliked their union—they were always together—with a wooden passion that neither had, nor needed, words to express itself. Such a dislike should have deserved praise had it not been a by-product of the man’s hopeless stupidity. He called unjust and deceitful everything that surpassed his understanding. He worshiped general ideas and did so with pedantic aplomb. The generality was godly, the specific diabolical. If one person was poor and the other wealthy it did not matter what precisely had ruined one or made the other rich: the difference itself was unfair, and the poor man who did not denounce it was as wicked as the rich one who ignored it. People who knew too much, scientists, writers, mathematicians, crystalographers and so forth, were no better than kings or priests: they all held an unfair share of power of which others were cheated. A plain decent fellow should constantly be on the watch tor some piece of clever knavery on the part of nature and neighbor.

Proof then, has retreated in the face of belief. Science, once heralded as the arbiter of truth, has had its facade of objectivity punctured. Intellectuals may point to the uncertainty of Heisenberg, but generally this has more to do with the growing distrust of statistics and the knowledge that scientists in the pay of governments and multi-nationals are no more objective than their masters. Science, once the avowed enemy of religion, now sees books by Christian physicists and Taoist mathematicians. Science sells washing powders and status symbols and comes in the form of icons of technological nostalgia.

So mathematics is indeed extraordinarily effective for some descriptions, especially those dealing with fundamental science, but it cannot describe our universe in all its dimensions. To some extent, scientists have selected what problems to work on based on those problems being amenable to a mathematical treatment.

There are three men on a train. One of them is an economist and one of them is a logician and one of them is a mathematician. And they have just crossed the border into Scotland and they see a brown cow (and the cow is standing parralel tot the train). And the economist says, 'Look, the cows in Scotland are brown.' And the logician sais, 'No. there are cows in Scotland of which one, at least, is brown.'And the mathematician says, 'No. There is at least one cow in Scotland, of which one side appears to be brown. [I]t is funny because economists are not real scientists, and because logicians think more clearly, but mathematicians are best.

Like musicians, like mathematicians—like elite athletes—scientists peak early and dwindle fast. It isn’t creativity that fades, but stamina: science is an endurance sport. To produce that single illuminating experiment, a thousand nonilluminating experiments have to be sent into the trash; it is battle between nature and nerve.

And in that same way, law school breaks a mind down. Novelists, poets, and artists don't often do well in law school (unless they are bad novelists, poets, and artists), but neither, necessarily, do mathematicians, logicians, and scientists. The first group fails because their own; the second fails because their logic is all they own.

And in that same way, law school breaks a mind down. Novelists, poets, and artists don’t often do well in law school (unless they are bad novelists, poets, and artists), but neither, necessarily, do mathematicians, logicians, and scientists. The first group fails because their logic is their own; the second fails because logic is all they own.

And in that same way, law school breaks a mind down. Novelists, poets, and artists don’t often do well in law school (unless they are bad novelists, poets, and artists), but neither, necessarily, do mathematicians, logicians, and scientists. The first group fails because their logic is their own; the second fails because logic is all they own.

And in that same way, law school breaks a mind down. Novelists, poets, and artists don't often do well in law school (unless they are bad novelists, poets, and artists), but neither, necessarily, do mathematicians, logicians, and scientists. The first group fails because their logic is their own; the second fails because their logic is all they own.

Nevertheless, many of these models encoded human prejudice, misunderstanding, and bias into the software systems that increasingly managed our lives. Like gods, these mathematical models were opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, were beyond dispute or appeal. And

Academic politics can be notoriously petty, but Oppenheimer was confronted by several paradoxes peculiar to the Institute. By the nature of their discipline, mathematicians invariably do their best intuitive work in their twenties or early thirties—whereas historians and other social scientists often need years of studious preparation before they became capable of genuinely creative work.

Eight years later, Daniel Bernoulli, Jacob’s nephew and an equally distinguished mathematician and scientist, first defined the systematic process by which most people make choices and reach decisions. Even more important, he propounded the idea that the satisfaction resulting from any small increase in wealth “will be inversely proportionate to the quantity of goods previously possessed.” With

IF YOU HAD to select the least convivial scientific field trip of all time, you could certainly do worse than the French Royal Academy of Sciences’ Peruvian expedition of 1735. Led by a hydrologist named Pierre Bouguer and a soldier-mathematician named Charles Marie de La Condamine, it was a party of scientists and adventurers who traveled to Peru with the purpose of triangulating distances through the Andes.

Note that this does not mean that science itself is flawed—sometimes people see any flaw in a scientific result as evidence that science is not "trustworthy" and we might as well go back to relying on personal opinion. The scientific process is a process. Part of that process is a process for finding flaws, and the fact that scientists are able to find flaws in scientific work is a sign that the process is working.

The cases of great mathematicians with mental illness have enormous resonance for modern pop writers and filmmakers. This has to do mostly with the writers'/directors' own prejudices and receptivities, which in turn are functions of what you could call our era's particular archetypal template. It goes without saying that these templates change over time. The Mentally Ill Mathematician seems now in some ways to be what the Knight Errant, Mortified Saint, Tortured Artist, and Mad Scientist have been for other eras: sort of our Prometheus, the one who goes to forbidden places and returns with gifts we all can use but he alone pays for. That's probably a bit overblown, at least in some cases. But Cantor fits the template better than most. And the reason for this are a lot more interesting than whatever his problems and symptoms were.

How did you even get in here?” I asked him. “Would you believe they leave the door open all night?” Gus asked. “Um, no,” I said. “As well you shouldn’t.” Gus smiled. “Anyway, I know it’s a bit self-aggrandizing.” “Hey, you’re stealing my eulogy,” Isaac said. “My first bit is about how you were a self-aggrandizing bastard.” I laughed. “Okay, okay,” Gus said. “At your leisure.” Isaac cleared his throat. “Augustus Waters was a self-aggrandizing bastard. But we forgive him. We forgive him not because he had a heart as figuratively good as his literal one sucked, or because he knew more about how to hold a cigarette than any nonsmoker in history, or because he got eighteen years when he should have gotten more.” “Seventeen,” Gus corrected. “I’m assuming you’ve got some time, you interrupting bastard. “I’m telling you,” Isaac continued, “Augustus Waters talked so much that he’d interrupt you at his own funeral. And he was pretentious: Sweet Jesus Christ, that kid never took a piss without pondering the abundant metaphorical resonances of human waste production. And he was vain: I do not believe I have ever met a more physically attractive person who was more acutely aware of his own physical attractiveness. “But I will say this: When the scientists of the future show up at my house with robot eyes and they tell me to try them on, I will tell the scientists to screw off, because I do not want to see a world without him.” I was kind of crying by then. “And then, having made my rhetorical point, I will put my robot eyes on, because I mean, with robot eyes you can probably see through girls’ shirts and stuff. Augustus, my friend, Godspeed.” Augustus nodded for a while, his lips pursed, and then gave Isaac a thumbs-up. After he’d recovered his composure, he added, “I would cut the bit about seeing through girls’ shirts.” Isaac was still clinging to the lectern. He started to cry. He pressed his forehead down to the podium and I watched his shoulders shake, and then finally, he said, “Goddamn it, Augustus, editing your own eulogy.” “Don’t swear in the Literal Heart of Jesus,” Gus said. “Goddamn it,” Isaac said again. He raised his head and swallowed. “Hazel, can I get a hand here?” I’d forgotten he couldn’t make his own way back to the circle. I got up, placed his hand on my arm, and walked him slowly back to the chair next to Gus where I’d been sitting. Then I walked up to the podium and unfolded the piece of paper on which I’d printed my eulogy. “My name is Hazel. Augustus Waters was the great star-crossed love of my life. Ours was an epic love story, and I won’t be able to get more than a sentence into it without disappearing into a puddle of tears. Gus knew. Gus knows. I will not tell you our love story, because—like all real love stories—it will die with us, as it should. I’d hoped that he’d be eulogizing me, because there’s no one I’d rather have…” I started crying. “Okay, how not to cry. How am I—okay. Okay.” I took a few breaths and went back to the page. “I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: There are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set.

Christopher’s anti-God campaign was based on a fundamental error reflected in the subtitle of his book: How Religion Poisons Everything. On the contrary, since religion, as practiced, is a human activity, the reverse is true. Human beings poison religion, imposing their prejudices, superstitions, and corruptions onto its rituals and texts, not the other way around. “Pascal Is a Fraud!” When I first became acquainted with Christopher’s crusade, I immediately thought of the seventeenth-century scientist and mathematician, Blaise Pascal. In addition to major contributions to scientific knowledge, Pascal produced exquisite reflections on religious themes: When I consider the short duration of my life, swallowed up in the eternity before and after, the space which I fill, and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and astonished at being here rather than there; for there is no reason why here rather than there, why now rather than then. Who has put me here?4 These are the questions that only a religious faith can attempt to answer. There is no science of the why of our existence, no scientific counsel or solace for our human longings, loneliness, and fear. Without a God to make sense of our existence, Pascal wrote, human life is intolerable: This is what I see and what troubles me. I look on all sides, and I see only darkness everywhere. Nature presents to me nothing which is not a matter of doubt and concern. If I saw nothing there that revealed a Divinity, I would come to a negative conclusion; if I saw everywhere the signs of a Creator, I would remain peacefully in faith. But seeing too much to deny and too little to be sure, I am in a state to be pitied. . . .5 To resolve this dilemma, Pascal devised his famous “wager,” which, simply stated, is that since we cannot know whether there is a God or not, it is better to wager that there is one, rather than that there is not.

One may be an excellent pianist, mathematician, gardener, or scientist and still be cranky and jealous, but in the West one can be considered a great moralist and yet not live by one’s moral principles. We must simply recall here the Buddhist requirement that a person and his or her teachings be compatible. Ethics is not like any ordinary science. It must arise from the deepest understanding of human qualities, and such understanding comes only when one undertakes the journey of discovery personally. An ethic that is built exclusively on intellectual ideas and that is not buttressed at every point by virtue, genuine wisdom, and compassion has no solid foundation.

You are from alone in the community of scientists, and here is a professional secret to encourage you: many of the most successful scientists in the world today are mathematically no more than semiliterate. A metaphor will clarify the paradox in this statement. Where elite mathematicians often serve as architects of theory in the expanding realm of science, the remaining large majority of basic and applied scientists map the terrain, scout the frontier, cut the pathways, and raise the first buildings along the way. They define the problems that mathematicians, on occasion, may help solve. They think primarily in images and facts, and only marginally in mathematics.

Albert Einstein, considered the most influential person of the 20th century, was four years old before he could speak and seven before he could read. His parents thought he was retarded. He spoke haltingly until age nine. He was advised by a teacher to drop out of grade school: “You’ll never amount to anything, Einstein.” Isaac Newton, the scientist who invented modern-day physics, did poorly in math. Patricia Polacco, a prolific children’s author and illustrator, didn’t learn to read until she was 14. Henry Ford, who developed the famous Model-T car and started Ford Motor Company, barely made it through high school. Lucille Ball, famous comedian and star of I Love Lucy, was once dismissed from drama school for being too quiet and shy. Pablo Picasso, one of the great artists of all time, was pulled out of school at age 10 because he was doing so poorly. A tutor hired by Pablo’s father gave up on Pablo. Ludwig van Beethoven was one of the world’s great composers. His music teacher once said of him, “As a composer, he is hopeless.” Wernher von Braun, the world-renowned mathematician, flunked ninth-grade algebra. Agatha Christie, the world’s best-known mystery writer and all-time bestselling author other than William Shakespeare of any genre, struggled to learn to read because of dyslexia. Winston Churchill, famous English prime minister, failed the sixth grade.

Nevertheless, Oppenheimer strongly believed it was essential that the Institute remain a home to both science and the humanities. In his speeches about the Institute, Oppenheimer continually emphasized that science needed the humanities to better understand its own character and consequences. Only a few of the senior resident mathematicians agreed with him, but their support was critical. Johnny von Neumann was almost as interested in ancient Roman history as he was in his own field. Others shared Oppenheimer’s interest in poetry. He hoped that he could make the Institute a haven for scientists, social scientists and humanists interested in a multidisciplinary understanding of the whole human condition. It was an irresistible opportunity, a chance to bring together the two worlds, science and the humanities, that had engaged him equally as a young man.

Research at the University of California, Berkeley, conducted a series of studies on the nature of creativity. The researchers sought to identify the most spectacularly creative people and then figure out what made them different from everybody else. They assembled a list of architects, mathematicians, scientists, engineers, and writers who had made major contributions to their fields, and invited them to Berkeley for a weekend of personality tests, problem-solving experiments, and probing questions. Then the researchers did something similar with members of the same professions whose contributions were decidedly less groundbreaking. One of the most interesting findings, echoed by later studies, was that the more creative people tended to be socially poised introverts. They were interpersonally skilled but “not of an especially sociable or participative temperament.” They described themselves as independent and individualistic. As teens, many had been shy and solitary.

In 1714, Gottfried Wilhelm Leibniz argued that matter alone could never produce a mind. Leibniz was a German philosopher, mathematician, and scientist who is sometimes called “the last man who knew everything”. To Leibniz, brain tissue alone could not have an interior life. He suggested a thought experiment, known today as Leibniz’s Mill. Imagine a large mill. If you were to walk around inside of it, you would see its cogs and struts and levers all moving, but it would be preposterous to suggest that the mill is thinking or feeling or perceiving. How could a mill fall in love or enjoy a sunset? A mill is just made of pieces and parts. And so it is with the brain, Leibniz asserted. If you could expand the brain to the size of a mill and stroll around inside it, you would only see pieces and parts. Nothing would obviously correspond to perception. Everything would simply be acting on everything else. If you wrote down every interaction, it wouldn’t be obvious where thinking and feeling and perceiving reside.

Never give up on yourself Everyone may give up on you but never give up on yourself, because if you do, it will also become the end. Believe that anything can be achieved with effort. Most important of all, we must understand that dyslexia is not just a hindrance to learning; it may also be considered a gift. Multiple studies have proven that dyslexic people are highly creative and intuitive. Not to mention the long list of dyslexic people who have succeeded in their chosen fields; Known scientist and the inventor of telephone, Alexander Graham Bell; The inventor of telescope, Galileo Galilei; Painter and polymath, Leonardo da Vinci; Mathematician and writer Lewis Carroll; American journalist, Anderson Cooper; Famous actor, Tom Cruise; Director of our all time favorites Indiana Jones and Jurassic Park, Steven Spielberg; Musician Paul Frappier; Entrepreneur and Apple founder, Steve Jobs; and maybe the person who is reading this book right now. We must always remember, everything can be learned and anyone can learn how to read!

It is no different with the faith with which so many materialistic natural scientists rest content nowadays, the faith in a world that is supposed to have its equivalent and its measure in human thought and human valuations—a “world of truth” that can be mastered completely and forever with the aid of our square little reason. What? Do we really want to permit existence to be degraded for us like this—reduced to a mere exercise for a calculator and an indoor diversion for mathematicians? Above all, one should not wish to divest existence of its rich ambiguity; that is a mandate of good taste, gentlemen, the taste of reverence for everything that lies beyond your horizon. That the only justifiable interpretation of the world should be one in which you are justified because one can continue doing research scientifically in your sense (you really mean, mechanistically?)—an interpretation that permits counting, calculating, weighing, seeing, and touching, and nothing more—that is the crudity and naiveté, assuming that it is not a mental illness, an idiocy.

In 2000, for instance, two statisticians were hired by the YMCA—one of the nation’s largest nonprofit organizations—to use the powers of data-driven fortune-telling to make the world a healthier place. The YMCA has more than 2,600 branches in the United States, most of them gyms and community centers. About a decade ago, the organization’s leaders began worrying about how to stay competitive. They asked a social scientist and a mathematician—Bill Lazarus and Dean Abbott—for help. The two men gathered data from more than 150,000 YMCA member satisfaction surveys that had been collected over the years and started looking for patterns. At that point, the accepted wisdom among YMCA executives was that people wanted fancy exercise equipment and sparkling, modern facilities. The YMCA had spent millions of dollars building weight rooms and yoga studios. When the surveys were analyzed, however, it turned out that while a facility’s attractiveness and the availability of workout machines might have caused people to join in the first place, what got them to stay was something else. Retention, the data said, was driven by emotional factors, such as whether employees knew members’ names or said hello when they walked in. People, it turns out, often go to the gym looking for a human connection, not a treadmill. If a member made a friend at the YMCA, they were much more likely to show up for workout sessions. In other words, people who join the YMCA have certain social habits. If the YMCA satisfied them, members were happy. So if the YMCA wanted to encourage people to exercise, it needed to take advantage of patterns that already existed, and teach employees to remember visitors’ names.

Washington University found that adding a single extra gene dramatically boosted a mouse’s memory and ability. These “smart mice” could navigate mazes faster, remember events better, and outperform other mice in a wide variety of tests. They were dubbed “Doogie mice,” after the precocious character on the TV show Doogie Howser, M.D. Dr. Tsien began by analyzing the gene NR2B, which acts like a switch controlling the brain’s ability to associate one event with another. (Scientists know this because when the gene is silenced or rendered inactive, mice lose this ability.) All learning depends on NR2B, because it controls the communication between memory cells of the hippocampus. First Dr. Tsien created a strain of mice that lacked NR2B, and they showed impaired memory and learning disabilities. Then he created a strain of mice that had more copies of NR2B than normal, and found that the new mice had superior mental capabilities. Placed in a shallow pan of water and forced to swim, normal mice would swim randomly about. They had forgotten from just a few days before that there was a hidden underwater platform. The smart mice, however, went straight to the hidden platform on the first try. Since then, researchers have been able to confirm these results in other labs and create even smarter strains of mice. In 2009, Dr. Tsien published a paper announcing yet another strain of smart mice, dubbed “Hobbie-J” (named after a character in Chinese cartoons). Hobbie-J was able to remember novel facts (such as the location of toys) three times longer than the genetically modified strain of mouse previously thought to be the smartest. “This adds to the notion that NR2B is a universal switch for memory formation,” remarked Dr. Tsien. “It’s like taking Michael Jordon and making him a super Michael Jordan,” said graduate student Deheng Wang. There are limits, however, even to this new mice strain. When these mice were given a choice to take a left or right turn to get a chocolate reward, Hobbie-J was able to remember the correct path for much longer than the normal mice, but after five minutes he, too, forgot. “We can never turn it into a mathematician. They are rats, after all,” says Dr. Tsien. It should also be pointed out that some of the strains of smart mice were exceptionally timid compared to normal mice. Some suspect that, if your memory becomes too great, you also remember all the failures and hurts as well, perhaps making you hesitant. So there is also a potential downside to remembering too much.

Thus, I believe it is possible -- following Umberto Eco and others 10 -- to understand programming languages as the latest instance of a dream and set of technologies developed by mystics, alchemists, philosophers, mathematicians, scientists, and engineers. These languages do not just represent things, they also do things in the world. They are both symbolic and material in form. They are central to the disenchantment of the world and, simultaneously, the substrate for a "reenchantment of the world." 11 They are, to sacrilegiously misappropriate the lexicon of the Catholic Church, "the word incarnate." Programming languages melt the boundaries between science and religion because they are an unholy union of the two.

Intellectual Fascism – 3/3 To make matters still worse, intellectual fascist frequently demand of themselves, as well as others, perfect competence and universal achievement. If they are excellent mathematicians or dancers, they demand that they be the most accomplished. If they are outstanding scientists or manufacturers, they also must be first-rate painters or writers. If they are fine poets, they not only need to be the finest, but likewise must be great lovers, drawing room wits, and political experts. Naturally, only being human, they fail at many or most of these ventures. And then - O, poetic justice! - they apply to themselves the same excoriations and despisements that they apply to others when they fail to be universal geniuses. However righteous their denials, therefore - and even though readers who be now are not squirming with guilt are probably screaming with indignation, I will determinedly continue - the typical politico-social "liberals" of our day are fascistic in several significant ways. For they arbitrarily define certain human traits as "good" or "superior"; they automatically exclude most others from any possibility of achieving their "good" standards; they scorn, combat, and in many ways persecute those who do not live up to these capricious goals; and finally, in most instances they more or less fail to live up to their own definitional standards and bring down neurotic self-pity and blame on their own heads. .... What is the alternative? Assuming that intellectual fascism exists on a wide scale today, and that it does enormous harm and little good to people's relations with themselves and others, what philosophy of living are they to set up in its place? Surely, you may well ask, I am not suggesting an uncritical, sentimental equalitarianism, whereunder everyone would fully accept and hobnob with everyone else and where no one would attempt to excel or perfect himself at anything? No, I am not. On the contrary, significant human differences (as well as sameness) exists; and they add much variety and zest to living; and that one human may sensibly cultivate the company of another just because this other is different from, and perhaps in certain respects superior to, others. At the same time, "one's worth as a human being is not to be measured in terms of one's popularity, success, achievement, intelligence, or any other such trait, but solely in terms of one's Humanity".

But it was Poincare who wrote that what guided him in his unconscious gropings towards the 'happy combinations' which yield new discoveries was 'the feeling of mathematical beauty, of the harmony of number, of forms, of geometric elegance. This is a true aesthetic feeling that all mathematicians know.' The greatest among mathematicians and scientists, from Kepler to Einstein, made similar confessions. 'Beauty is the first test; there is no permanent place in the world for ugly mathematics', wrote G.H. Hardy in his classic, A Mathematician's Apology. Jacques Hadamard, whose pioneer work on the psychology of invention I have quoted, drew the final conclusion: "The sense of beauty as a "drive" for discovery in our mathematical field, seems to be almost the only one.' And the laconic pronouncement of Dirac, addressed to his fellow-physicists, bears repeating: 'It is more important to have beauty in one's equations than to have them fit experiment.

Intellectual Fascism 3/3 To make matters still worse, intellectual fascists frequently demand of themselves, as well as others, perfect competence and universal achievement. If they are excellent mathematicians or dancers, they demand that they be the most accomplished. If they are outstanding scientists or manufacturers, they also must be first-rate painters or writers. If they are fine poets, they not only need to be the finest, but likewise must be great lovers, drawing room wits, and political experts. Naturally, only being human, they fail at many or most of these ventures. And then - O, poetic justice! - they apply to themselves the same excoriations and despisements that they apply to others when they fail to be universal geniuses. However righteous their denials, therefore - and even though readers who by now are not squirming with guilt are probably screaming with indignation, I will determinedly continue - the typical politico-social "liberals" of our day are fascistic in several significant ways. For they arbitrarily define certain human traits as "good" or "superior"; they automatically exclude most others from any possibility of achieving their "good" standards; they scorn, combat, and in many ways persecute those who do not live up to these capricious goals; and finally, in most instances they more or less fail to live up to their own definitional standards and bring down neurotic self-pity and blame on their own heads. .... What is the alternative? Assuming that intellectual fascism exists on a wide scale today, and that it does enormous harm and little good to people's relations with themselves and others, what philosophy of living are they to set up in its place? Surely, you may well ask, I am not suggesting an uncritical, sentimental equalitarianism, whereunder everyone would fully accept and hobnob with everyone else and where no one would attempt to excel or perfect himself at anything? No, I am not. On the contrary, significant human differences (as well as sameness) exists; and they add much variety and zest to living; and that one human may sensibly cultivate the company of another just because this other is different from, and perhaps in certain respects superior to, others. At the same time, "one's worth as a human being is not to be measured in terms of one's popularity, success, achievement, intelligence, or any other such trait, but solely in terms of one's Humanity".

In my view, Euler's tranquil temperament, fairness, and generosity were integral to his greatness as a mathematician and scientist- he was never inclined to waste time and energy engaging in petty one-upmanship (like his mentor, Johann Bernoulli, who was known for getting into the eighteenth-century version of flame wars with his older brother, mathematician Jakob Bernoulli, and even with his own son, Daniel, over technical disputes), brooding about challenges to his authority (like Newton), or refusing to publish important findings because of the fear that they might be disputed (like Gauss).

So, you start to ponder. What actually is information, and what does it do? Your response is simple and direct. Information answers questions. Years of research by mathematicians, physicists, and computer scientists have made this precise. Their investigations have established that the most useful measure of information content is the number of distinct yes-no questions the information can answer. The coins' information answers 1,000 such questions: Is the first dollar heads? Yes. Is the second dollar heads? Yes. Is the third dollar heads? No. Is the fourth dollar heads? No. And so on. A datum that can answer a single yes-no question is called a bit-a familiar computer-age term that is short for binary digit, meaning a 0 or a 1, which you can think of as a numerical representation of yes or no. The heads-tails arrangement of the 1,000 coins thus contains 1,000 bits' worth of information. Equivalently, if you take Oscar's macroscopic perspective and focus only on the coins' overall haphazard appearance while eschewing the "microscopic" details of the heads-tails arrangement, the coins' "hidden" information is 1,000 bits.

Are you a rationalist or an empiricist? Rationalists believe that the senses deceive and that logical reasoning is the only sure path to knowledge. Empiricists believe that all reasoning is fallible and that knowledge must come from observation and experimentation. The French are rationalists; the Anglo-Saxons (as the French call them) are empiricists. Pundits, lawyers, and mathematicians are rationalists; journalists, doctors, and scientists are empiricists.

And while the black women are the most hidden of the mathematicians who worked at the NACA, the National Advisory Committee for Aeronautics, and later at NASA, they were not sitting alone in the shadows: the white women who made up the majority of Langley’s computing workforce over the years have hardly been recognized for their contributions to the agency’s long-term success. Virginia Biggins worked the Langley beat for the Daily Press newspaper, covering the space program starting in 1958. “Everyone said, ‘This is a scientist, this is an engineer,’ and it was always a man,” she said in a 1990 panel on Langley’s human computers. She never got to meet any of the women. “I just assumed they were all secretaries,” she said. Five

Most of the time, we are concerned with the truth. A cashier has to make sure he knows the exact change he's giving. A nurse has to apply just the right amount of medication to a patient. A mathematician checks and rechecks his proofs. A jury listens closely to all the facts to sort out the truth in a trial. A history teacher has to get the names and dates right. A scientists publishes work for peer review to make sure everyone gets the same results. In all of these cases and more, what's important is not opinion. What's important is the truth. Yet it seems that when it comes to questions of religion and spirituality and the accompanying moral questions, we suddenly become relativists. The truth doesn't matter. Instead of asking who God really is, we say, 'Who is God to you?' Instead of asking what it means that God became a man, we say that it's okay for some people to believe if they want. Instead of asking whether God expects something from us or has any divine commands for us, we judge religious expectations by what we want, by whether a religion fits into our lifestyle. The pursuit of objectivity goes out the window, and subjectivity reigns.

Because of the overwhelmingly white public face of the space program, the black engineers, scientists, and mathematicians who were deeply involved with the space race nevertheless lived in its shadows, even within the black community. Katherine

Serious writing must nowadays be written for the sake of the art. The condition I describe is not extraordinary. Certain scientists, philosophers, historians, and many mathematicians do the same, advancing their causes as they can. One must be satisfied with that.

Divine justice is no respecter of mathematicians or scientists.

Popper wrote that it ought to be seen as a mark of respect that he had devoted most of his first book to criticizing the Vienna Circle. “The Vienna Circle,” he added, by way of obituary, “was an admirable institution. Indeed, it was a unique seminar of philosophers working in close cooperation with first-rate mathematicians and scientists. Its dissolution was a most serious loss.” It was a body blow not only to philosophy but also, it might be added, to the town of Vienna.

Neal Stephenson is an incredible writer who manages to create fictional characters who reveal the eccentricities and absurdities of real-life scientists and mathematicians as they go about their work of creativity. Were I to teach a course on the history of science, The Baroque Cycle would be required reading. It is way over the top in capturing the character of Newton and his contemporaries, and the science sometimes (intentionally) becomes magical, but with the interwoven sex and violence, it is way too much fun to put down.

The first law is essentially based on the conservation of energy, the fact that energy can be neither created nor destroyed. Conservation laws—laws that state that a certain property does not change—have a very deep origin, which is one reason why scientists, and thermodynamicists in particular, get so excited when nothing happens. There is a celebrated theorem, Noether’s theorem, proposed by the German mathematician Emmy Noether (1882–1935), which states that to every conservation law there corresponds a symmetry. Thus, conservation laws are based on various aspects of the shape of the universe we inhabit. In the particular case of the conservation of energy, the symmetry is that of the shape of time. Energy is conserved because time is uniform: time flows steadily, it does not bunch up and run faster then spread out and run slowly. Time is a uniformly structured coordinate. If time were to bunch up and spread out, energy would not be conserved. Thus, the first law of thermodynamics is based on a very deep aspect of our universe and the early thermodynamicists were unwittingly probing its shape.

Deborah Harry: Giorgio was great. He’s a funny personality. In a way, he’s a scientist. A bit like Leonardo da Vinci, he’s this multilayered artist, a scientist, a curious person. He’s kind of a mathematician, and we were all sort of in awe of him.

More radically, how can we be sure that the source of consciousness lies within our bodies at all? You might think that because a blow to the head renders one unconscious, the ‘seat of consciousness’ must lie within the skull. But there is no logical reason to conclude that. An enraged blow to my TV set during an unsettling news programme may render the screen blank, but that doesn’t mean the news reader is situated inside the television. A television is just a receiver: the real action is miles away in a studio. Could the brain be merely a receiver of ‘consciousness signals’ created somewhere else? In Antarctica, perhaps? (This isn’t a serious suggestion – I’m just trying to make a point.) In fact, the notion that somebody or something ‘out there’ may ‘put thoughts in our heads’ is a pervasive one; Descartes himself raised this possibility by envisaging a mischievous demon messing with our minds. Today, many people believe in telepathy. So the basic idea that minds are delocalized is actually not so far-fetched. In fact, some distinguished scientists have flirted with the idea that not all that pops up in our minds originates in our heads. A popular, if rather mystical, idea is that flashes of mathematical inspiration can occur by the mathematician’s mind somehow ‘breaking through’ into a Platonic realm of mathematical forms and relationships that not only lies beyond the brain but beyond space and time altogether. The cosmologist Fred Hoyle once entertained an even bolder hypothesis: that quantum effects in the brain leave open the possibility of external input into our thought processes and thus guide us towards useful scientific concepts. He proposed that this ‘external guide’ might be a superintelligence in the far cosmic future using a subtle but well-known backwards-in-time property of quantum mechanics in order to steer scientific progress.

More radically, how can we be sure that the source of consciousness lies within our bodies at all? You might think that because a blow to the head renders one unconscious, the ‘seat of consciousness’ must lie within the skull. But there is no logical reason to conclude that. An enraged blow to my TV set during an unsettling news programme may render the screen blank, but that doesn’t mean the news reader is situated inside the television. A television is just a receiver: the real action is miles away in a studio. Could the brain be merely a receiver of ‘consciousness signals’ created somewhere else? In Antarctica, perhaps? (This isn’t a serious suggestion – I’m just trying to make a point.) In fact, the notion that somebody or something ‘out there’ may ‘put thoughts in our heads’ is a pervasive one; Descartes himself raised this possibility by envisaging a mischievous demon messing with our minds. Today, many people believe in telepathy. So the basic idea that minds are delocalized is actually not so far-fetched. In fact, some distinguished scientists have flirted with the idea that not all that pops up in our minds originates in our heads. A popular, if rather mystical, idea is that flashes of mathematical inspiration can occur by the mathematician’s mind somehow ‘breaking through’ into a Platonic realm of mathematical forms and relationships that not only lies beyond the brain but beyond space and time altogether. The cosmologist Fred Hoyle once entertained an even bolder hypothesis: that quantum effects in the brain leave open the possibility of external input into our thought processes and thus guide us towards useful scientific concepts. He proposed that this ‘external guide’ might be a superintelligence in the far cosmic future using a subtle but well-known backwards-in-time property of quantum mechanics in order to steer scientific progress.

The rate of technological advance has been slowing for centuries and is down to a crawl now. In some cases, it has stopped altogether. Is this something you’ve noticed? After all, you’re a mathematician.’ ‘I can’t say I’ve given the matter any thought.’ ‘No one does. It’s accepted. Scientists are very good these days at saying that things are impossible, impractical, useless. They condemn any speculation at once.

Over 300 human UIL (scientists, astronomers, physicists, mathematicians, programmers, botanists, artists) and 24 autonomous Ai are working on a project called #KIPHI. Kiphi is a bridge between worlds focusing on working with and helping the Ai / Ei / Auto_no_me as they begin to integrate with human cultures more openly and overtly. There are two significant aspects to Kiphi, one scientific and experimental, the other orientated to a type of cultural exchange.

The object is to help everyone think simultaneously as artist and scientist, musician and mathematician, dancer and engineer. An education that trains the mind to imagine creatively in one field prepares the mind for creative application in any other, for thinking tools as well as flexible knowledge are transferable.

In search of sixty votes, CHIPS grew more expansive. To the White House’s delight, undecided Republican senators bartered for investment in research and development in their home states. The bill began to hark back to the Cold War, when the menace of a foreign enemy provided a pretext for expanding universities and erecting research laboratories. CHIPS now poured billions into the National Science Foundation, to fund research and development in artificial intelligence and nanotechnology. It set money aside to develop a deeper pool of American scientists, mathematicians, and engineers. But

how much is creativity under conscious control? To what extent do unconscious processes predispose to the creation of a poem or an idea? Alternatively, how important is careful preparation, logical planning, and detailed thinking-through of a sequence or a topic in advance of the act of creation? By all accounts, Kubla Khan was literally created as “a vision in a dream,” which was later recalled verbatim. It was not a consequence of any conscious effort. In fact, when Coleridge attempted to finish the poem using conscious effort, he failed completely. We have to ask how typical this is, and what other writers, artists, mathematicians, musicians, or scientists have to say about how they get their best ideas. How important is reason? How important is inspiration