Number Theory Quotes

The Hindu religion is the only one of the world’s great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang.

The amount of violations of human rights in a country is always an inverse function of the amount of complaints about human rights violations heard from there. The greater the number of complaints being aired, the better protected are human rights in that country.

I'll tell you once, and I'll tell you again. There's always a prime between n and 2n.

I dug the untraceable phone Patch had given me out of my handbag and dialled his number. "I have a free couple of hours," I told him, walking toward my car, which was parked on the next block. "There's a very dark, very secluded barn in Lookout Hill Park behind the carousel. I could be there in fifteen minutes." I heard the smile in his voice."You want me bad." "I need and an endorphin boost." "And making out in an abandoned barn with me will give you one?" "No, it will probably put me in an endorphin coma, and I'm more than happy to test the theory.

We tend to think human knowledge as progressive; because we know more and more, our parents and grandparents are back numbers. But a contrary theory is possible - that we simply recognize different things at different times and in different ways.

Shepherd Book: What are we up to, sweetheart? River: Fixing your Bible. Book: I, um... What? River: Bible's broken. Contradictions, false logistics - doesn't make sense. Shepherd Book: No, no. You-you-you can't... River: So we'll integrate non-progressional evolution theory with God's creation of Eden. Eleven inherent metaphoric parallels already there. Eleven. Important number. Prime number. One goes into the house of eleven eleven times, but always comes out one. Noah's ark is a problem. Shepherd Book: Really? River: We'll have to call it early quantum state phenomenon. Only way to fit 5000 species of mammal on the same boat. Shepherd Book: River, you don't fix the Bible. River: It's broken. It doesn't make sense. Book: It's not about making sense. It's about believing in something, and letting that belief be real enough to change your life. It's about faith. You don't fix faith, River. It fixes you.

Don't let numbers tell you what to do. You are blood and earth, not theory and chalk.

At this point I think we need to embrace the weird. High-five it. Give it our phone number.

Do you know about the spoons? Because you should. The Spoon Theory was created by a friend of mine, Christine Miserandino, to explain the limits you have when you live with chronic illness. Most healthy people have a seemingly infinite number of spoons at their disposal, each one representing the energy needed to do a task. You get up in the morning. That’s a spoon. You take a shower. That’s a spoon. You work, and play, and clean, and love, and hate, and that’s lots of damn spoons … but if you are young and healthy you still have spoons left over as you fall asleep and wait for the new supply of spoons to be delivered in the morning. But if you are sick or in pain, your exhaustion changes you and the number of spoons you have. Autoimmune disease or chronic pain like I have with my arthritis cuts down on your spoons. Depression or anxiety takes away even more. Maybe you only have six spoons to use that day. Sometimes you have even fewer. And you look at the things you need to do and realize that you don’t have enough spoons to do them all. If you clean the house you won’t have any spoons left to exercise. You can visit a friend but you won’t have enough spoons to drive yourself back home. You can accomplish everything a normal person does for hours but then you hit a wall and fall into bed thinking, “I wish I could stop breathing for an hour because it’s exhausting, all this inhaling and exhaling.” And then your husband sees you lying on the bed and raises his eyebrow seductively and you say, “No. I can’t have sex with you today because there aren’t enough spoons,” and he looks at you strangely because that sounds kinky, and not in a good way. And you know you should explain the Spoon Theory so he won’t get mad but you don’t have the energy to explain properly because you used your last spoon of the morning picking up his dry cleaning so instead you just defensively yell: “I SPENT ALL MY SPOONS ON YOUR LAUNDRY,” and he says, “What the … You can’t pay for dry cleaning with spoons. What is wrong with you?” Now you’re mad because this is his fault too but you’re too tired to fight out loud and so you have the argument in your mind, but it doesn’t go well because you’re too tired to defend yourself even in your head, and the critical internal voices take over and you’re too tired not to believe them. Then you get more depressed and the next day you wake up with even fewer spoons and so you try to make spoons out of caffeine and willpower but that never really works. The only thing that does work is realizing that your lack of spoons is not your fault, and to remind yourself of that fact over and over as you compare your fucked-up life to everyone else’s just-as-fucked-up-but-not-as-noticeably-to-outsiders lives. Really, the only people you should be comparing yourself to would be people who make you feel better by comparison. For instance, people who are in comas, because those people have no spoons at all and you don’t see anyone judging them. Personally, I always compare myself to Galileo because everyone knows he’s fantastic, but he has no spoons at all because he’s dead. So technically I’m better than Galileo because all I’ve done is take a shower and already I’ve accomplished more than him today. If we were having a competition I’d have beaten him in daily accomplishments every damn day of my life. But I’m not gloating because Galileo can’t control his current spoon supply any more than I can, and if Galileo couldn’t figure out how to keep his dwindling spoon supply I think it’s pretty unfair of me to judge myself for mine. I’ve learned to use my spoons wisely. To say no. To push myself, but not too hard. To try to enjoy the amazingness of life while teetering at the edge of terror and fatigue.

The history of atomism is one of reductionism – the effort to reduce all the operations of nature to a small number of laws governing a small number of primordial objects.

The damp floor of the Internet sprouted Lecter theories like toadstools and sightings of the doctor rivaled those of Elvis in number.

Gödel saw beyond the surface level of number theory, realizing that numbers could represent any kind of structure.

Sitting there on the heather, on our planetary grain, I shrank from the abysses that opened up on every side, and in the future. The silent darkness, the featureless unknown, were more dread than all the terrors that imagination had mustered. Peering, the mind could see nothing sure, nothing in all human experience to be grasped as certain, except uncertainty itself; nothing but obscurity gendered by a thick haze of theories. Man's science was a mere mist of numbers; his philosophy but a fog of words. His very perception of this rocky grain and all its wonders was but a shifting and a lying apparition. Even oneself, that seeming-central fact, was a mere phantom, so deceptive, that the most honest of men must question his own honesty, so insubstantial that he must even doubt his very existence.

In the business people with expertise, experience and evidence will make more profitable decisions than people with instinct, intuition and imagination.

How many people ruin themselves by laying out money on trinkets of frivolous utility? What pleases these lovers of toys is not so much the utility, as the aptness of the machines which are fitted to promote it. All their pockets are stuffed with little conveniences. They contrive new pockets, unknown in the clothes of other people, in order to carry a greater number. They walk about loaded with a multitude of baubles, in weight and sometimes in value not inferior to an ordinary Jew's-box, some of which may sometimes be of some little use, but all of which might at all times be very well spared, and of which the whole utility is certainly not worth the fatigue of bearing the burden.

The special knowledge you are about to learn will reveal a “letter theory” that was set into motion from the very first verse in your Bible. It is as though the divine author is telling the reader to expect Hebrew letters and numbers to weave messages, in the sub-text, through the rest of the Bible—starting with verse one.

Der Zweck der Philosophie ist die logische Klärung der Gedanken. Die Philosophie ist keine Lehre, sondern eine Tätigkeit. Ein philosophisches Werk besteht wesentlich aus Erläuterungen. Das Resultat der Philosophie sind nicht »philosophische Sätze«, sondern das Klarwerden von Sätzen. Die Philosophie soll die Gedanken, die sonst, gleichsam, trübe und verschwommen sind, klar machen und scharf abgrenzen. 4.112 The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of "philosophical propositions", but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred.

Yangi, a philosopher, art historian and poet, had evolved a theory of why some objects - pots, baskets, cloth made by unknown craftsmen - were so beautiful. In his view, they expressed unconscious beauty because they had been made in such numbers that the craftsman had been liberated from his ego.

The universe is math on fire.

I was reading a book about the cosmos recently,” he says, and then he looks around and goes, “Hold on, trust me, this relates.” The crowd laughs again. “And I was reading about different theories about the universe. I was really taken with this one theory that states that everything that is possible happens. That means that when you flip a quarter, it doesn’t come down heads or tails. It comes up heads and tails. Every time you flip a coin and it comes up heads, you are merely in the universe where the coin came up heads. There is another version of you out there, created the second the quarter flipped, who saw it come up tails. This is happening every second of every day. The world is splitting further and further into an infinite number of parallel universes where everything that could happen is happening. This is completely plausible, by the way. It’s a legitimate interpretation of quantum mechanics. It’s entirely possible that every time we make a decision, there is a version of us out there somewhere who made a different choice. An infinite number of versions of ourselves are living out the consequences of every single possibility in our lives. What I’m getting at here is that I know there may be universes out there where I made different choices that led me somewhere else, led me to someone else.” He looks at Gabby. “And my heart breaks for every single version of me that didn’t end up with you.

But just in proportion as this process of extermination has acted on an enormous scale, so must the number of intermediate varieties, which have formerly existed, be truly enormous. Why then is not every geological formation and every stratum full of such intermediate links? Geology assuredly does not reveal any such finely graduated organic chain; and this, perhaps, is the most obvious and serious objection which can be urged against the theory. The explanation lies, as I believe, in the extreme imperfection of the geological record.

In the mid 1980's I was asked by an american legal institution known as the Christic Legal Institute to compile a comic book that would detail the murky history of the C.I.A., from the end of the second world war, to the present day. Covering such things as the heroin smuggling during the Vietnam war, the cocaine smuggling during the war in Central America, the Kennedy assasination and other highlights. What I learned during the frankly horrifying research that I had to slog through in order to accomplish this, was that yes, there is a conspiracy, in fact there are a great number of conspiracies that are all tripping each other up. And all of those conspiracies are run by paranoid fantasists, and ham fisted clowns. If you are on a list targeted by the C.I.A., you really have nothing to worry about. If however you have a name similar to someone on a list targeted by the C.I.A., then you are dead? The main thing that I learned about conspiracy theory, is that conspiracy theorists believe in a conspiracy because that is more comforting. The truth of the world is that it is actually chaotic. The truth is that it is not The Iluminati, or The Jewish Banking Conspiracy, or the Gray Alien Theory. The truth is far more frightening. Nobody is in control. The world is rudderless...

It’s hard to deny that an alarming number of those who stood for peace, not war, were either killed by deranged lone gunmen or else died in suspicious circumstances. We refer of course to the likes of JFK, Martin Luther King, Benazir Bhutto, Bobby Kennedy and John Lennon, to name but a few.

Nobel laureate Steven Weinberg likens this multiple universe theory to radio. All around you, there are hundreds of different radio waves being broadcast from distant stations. At any given instant, your office or car or living room is full of these radio waves. However, if you turn on a radio, you can listen to only one frequency at a time; these other frequencies have decohered and are no longer in phase with each other. Each station has a different energy, a different frequency. As a result, your radio can only be turned to one broadcast at a time.Likewise, in our universe we are "tuned" into the frequency that corresponds to physical reality. But there are an infinite number of parallel realities coexisting with us in the same room, although we cannot "tune into" them. Although these worlds are very much alike, each has a different energy. And because each world consists of trillions upon trillions of atoms, this means that the energy difference can be quite large. Since the frequency of these waves is proportional to their energy (by Planck's law), this means that the waves of each world vibrate at different frequencies and cannot interact anymore. For all intents and purposes, the waves of these various worlds do not interact or influence each other.

In theory, the risk of business failure can be reduced to a number, the probability of failure multiplied by the cost of failure. Sure, this turns out to be a subjective analysis, but in the process your own attitudes toward financial risk and reward are revealed. By contrast, personal risk usually defies quantification. It's a matter of values and priorities, an expression of who you are. "Playing it safe" may simply mean you do not weigh heavily the compromises inherent in the status quo. The financial rewards of the moment may fully compensate you for the loss of time and fulfillment. Or maybe you just don't think about it. On the other hand, if time and satisfaction are precious, truly priceless, you will find the cost of business failure, so long as it does not put in peril the well-being of you or your family, pales in comparison with the personal risks of no trying to live the life you want today. Considering personal risk forces us to define personal success. We may well discover that the business failure we avoid and the business success we strive for do not lead us to personal success at all. Most of us have inherited notions of "success" from someone else or have arrived at these notions by facing a seemingly endless line of hurdles extending from grade school through college and into our careers. We constantly judge ourselves against criteria that others have set and rank ourselves against others in their game. Personal goals, on the other hand, leave us on our own, without this habit of useless measurement and comparison. Only the Whole Life Plan leads to personal success. It has the greatest chance of providing satisfaction and contentment that one can take to the grave, tomorrow. In the Deferred Life Plan there will always be another prize to covet, another distraction, a new hunger to sate. You will forever come up short.

Some numbers, even large ones, have no factors - except themselves, of course, and 1. These are called prime numbers, because everything they are starts with themselves. They are original, gnarled, unpredictable, the freaks of the number world.

However, The haven-Slocum Theory also points out that this course is not without risk. An even greater number of people dwelling on The Navidson Record have shown an increase in obsessiveness, insomnia, and incoherence: "Most of those who chose to abandon their interest soon recovered. A few, however, required counseling and in some instances medication and hospitalization. Three cases resulted in suicide.

There’s an economic theory out there that if you take the incomes of your five closest friends and average them, the resulting number will be pretty close to your own income. I think the same thing is true of our idea incomes. You’re only going to be as good as the stuff you surround yourself with.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

She'd heard theories in her time regarding the number-one enemy of everything, ranging from Osama bin Laden to premarital sex. The dust theory she liked.

Although Capote had taken up the single-suspect theory, the Tate detectives had by now abandoned it. Their sole reason for adopting it in the first place—Garretson—was no longer a factor. Because of the number of victims, the location of their bodies, and the use of two or more weapons, they were now convinced that “at least two suspects” were

The number of games went up or down according to the brutal, elegant logic of the economics of fun: a certain amount of difficulty plus a certain amount of your friends plus a certain amount of interesting strangers plus a certain amount of reward plus a certain amount of opportunity equaled fun

In the fantasy I spun for myself that night before falling asleep, those deep dark secrets were revealed. That simple touch became a violent embrace, worthy of any bodice-ripper. There were a certain number of gleeful perversions committed on Ivan's battered leather sofa. And at some point in the fantasy, Ivan was a vampire, because I was sort of weird that way. He was a real, Gothic-style, Bram Stoker sort of vampire who bit people as a metaphor for having dubious-consent, alpha-male sex with them, I should point out. None of your modern, sensitive vampires for me. I appreciated the classics.

The debt isn’t the reason we can’t have nice things. Our broken thinking is. To fix our broken thinking, we need to overcome more than just an aversion to big numbers with the word debt attached. We need to beat back every destructive myth that hobbles our thinking.

A prize-winning science reporter, Simons had become the number-two editor at the Post a year before. An intent, sensitive man with a large nose, thin face and deep-set eyes, he looks like the kind of Harvard teaching assistant who carries a slide ruler strapped to his belt. But he is skillful with fragile egos, and also the perfect counterpoint to Bradlee. Bradlee is more like Woodward: he wants hard information first and is impatient with theories. -- Carl Bernstein, Bob Woodward

a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation.

Common to the many theories about the birth trauma is the assumption that the feelings produced by this event were recorded and reside in some form in the brain. This assumption is supported by the great number of repetitious dreams of the “drainage pipe” variety

One possible solution to the grandfather paradox is the theory of multiverse originally set forth by Hugh Everett. According to multiverse theory, every version of our past and future histories exists, just in an alternate universe. For every event at the quantum level, the current universe splits into multiple universes. This means that for every choice you make, an infinite number of universes exist in which you made a different choice. The theory neatly solves the grandfather paradox by posting separate universes in which each possible outcome exists, thereby avoiding a paradox. In this way we get to live multiple lives. There is, for example, a universe where Samuel Kingsley does not derail his daughter's life. A universe where he does derail it but Natasha is able to fix it. A universe where he does derail it and she is not able to fix it. Natasha is not quite sure which universe she's living in now.

Tokyo is a model of that serial big-bang theory of the universe. It explodes at five P.M. and people matter is hurled to the suburbs, but by 5 A.M. the people-matter gravity reasserts itself, and everything surges back toward the center, where mass densens for the next explosion.

Overwhelmed by life's complexity? Realize that our alphabet consists of only 26 letters, calculations are based on a set of 10 numbers, all variations in music are based on 7 musical notes, our DNA can be dissected into 4 letters and space on the Planck scale is probably made solely out of binary code

Political philosophy reaches for the best regime, a regime so good that it can hardly exist. Political science advances a theory—in fact, a number of theories—that promises to bring agreement and put an end to partisan dispute.

Another crucial thing to question is why deniers even bother to quibble about the number of deaths. If one day it were proven only five million or 5.5 million Jews were exterminated, would it be any less an atrocity? What number would deniers suggest is low enough to say that genocide didn't occur and that it’s not important that humanity remembers the Holocaust and the lessons learnt?

The human mind is incapable of formulating (or mechanizing) all its mathematical intuitions, i.e., if it has succeeded in formulating some of them, this very fact yields new intuitive knowledge, e.g., the consistency of this formalism. This fact may be called the “incompletability” of mathematics. On the other hand, on the basis of what has been proved so far, it remains possible that there may exist (and even be empirically discoverable) a theorem proving machine which in fact is equivalent to mathematical intuition, but cannot be proved to be so, nor even be proved to yield only correct theorems of finitary number theory.

Almost as an article of faith, some individuals believe that conspiracies are either kooky fantasies or unimportant aberrations. To be sure, wacko conspiracy theories do exist. There are people who believe that the United States has been invaded by a secret United Nations army equipped with black helicopters, or that the country is secretly controlled by Jews or gays or feminists or black nationalists or communists or extraterrestrial aliens. But it does not logically follow that all conspiracies are imaginary. Conspiracy is a legitimate concept in law: the collusion of two or more people pursuing illegal means to effect some illegal or immoral end. People go to jail for committing conspiratorial acts. Conspiracies are a matter of public record, and some are of real political significance. The Watergate break-in was a conspiracy, as was the Watergate cover-up, which led to Nixon’s downfall. Iran-contra was a conspiracy of immense scope, much of it still uncovered. The savings and loan scandal was described by the Justice Department as “a thousand conspiracies of fraud, theft, and bribery,” the greatest financial crime in history. Often the term “conspiracy” is applied dismissively whenever one suggests that people who occupy positions of political and economic power are consciously dedicated to advancing their elite interests. Even when they openly profess their designs, there are those who deny that intent is involved. In 1994, the officers of the Federal Reserve announced they would pursue monetary policies designed to maintain a high level of unemployment in order to safeguard against “overheating” the economy. Like any creditor class, they preferred a deflationary course. When an acquaintance of mine mentioned this to friends, he was greeted skeptically, “Do you think the Fed bankers are deliberately trying to keep people unemployed?” In fact, not only did he think it, it was announced on the financial pages of the press. Still, his friends assumed he was imagining a conspiracy because he ascribed self-interested collusion to powerful people. At a World Affairs Council meeting in San Francisco, I remarked to a participant that U.S. leaders were pushing hard for the reinstatement of capitalism in the former communist countries. He said, “Do you really think they carry it to that level of conscious intent?” I pointed out it was not a conjecture on my part. They have repeatedly announced their commitment to seeing that “free-market reforms” are introduced in Eastern Europe. Their economic aid is channeled almost exclusively into the private sector. The same policy holds for the monies intended for other countries. Thus, as of the end of 1995, “more than $4.5 million U.S. aid to Haiti has been put on hold because the Aristide government has failed to make progress on a program to privatize state-owned companies” (New York Times 11/25/95). Those who suffer from conspiracy phobia are fond of saying: “Do you actually think there’s a group of people sitting around in a room plotting things?” For some reason that image is assumed to be so patently absurd as to invite only disclaimers. But where else would people of power get together – on park benches or carousels? Indeed, they meet in rooms: corporate boardrooms, Pentagon command rooms, at the Bohemian Grove, in the choice dining rooms at the best restaurants, resorts, hotels, and estates, in the many conference rooms at the White House, the NSA, the CIA, or wherever. And, yes, they consciously plot – though they call it “planning” and “strategizing” – and they do so in great secrecy, often resisting all efforts at public disclosure. No one confabulates and plans more than political and corporate elites and their hired specialists. To make the world safe for those who own it, politically active elements of the owning class have created a national security state that expends billions of dollars and enlists the efforts of vast numbers of people.

I believe, Jack, there are two kinds of people in the world. Killers and diers. Most of us are diers. We don't have the dispoisiton, the rage or whatever it takes to be a killer. We le death happen. We lie down and die. But think what it's like to be a killer. Think how exciting it is, in theory, to kill a person in direct confrontation. If he dies, you cannot. To kill him is to gain life-credit. The more people you kill, the more credit you store up. It explains any number of massacres, wars, executions. […] In theory, violence is a form of rebirth. The dier passively succumbs. The killer lives on. What a marvelous equation. - Murray (WN 290)

If someone were to propose that the planets go around the sun because all planet matter has a kind of tendency for movement, a kind of motility, let us call it an ‘oomph,’ this theory could explain a number of other phenomena as well. So this is a good theory, is it not? No. It is nowhere near as good as the proposition that the planets move around the sun under the influence of a central force which varies exactly inversely as the square of the distance from the center. The second theory is better because it is so specific; it is so obviously unlikely to be the result of chance. It is so definite that the barest error in the movement can show that it is wrong; but the planets could wobble all over the place, and, according to the first theory, you could say, ‘Well, that is the funny behavior of the ‘oomph.

There is a most profound and beautiful question associated with the observed coupling constant, e - the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

The great Baseball Hall-of-Famer Tom Seaver put it perfectly: In baseball, my theory is to strive for consistency, not to worry about the numbers. If you dwell on statistics you get shortsighted; if you aim for consistency, the numbers will be there at the end.

This is what the bourgeois political economists have done: they have treated value as a fact of nature, not a social construction arising out of a particular mode of production. What Marx is interested in is a revolutionary transformation of society, and that means an overthrow of the capitalist value-form, the construction of an alternative value-structure, an alternative value-system that does not have the specific character of that achieved under capitalism. I cannot overemphasize this point, because the value theory in Marx is frequently interpreted as a universal norm with which we should comply. I have lost count of the number of times I have heard people complain that the problem with Marx is that he believes the only valid notion of value derives from labor inputs. It is not that at all; it is a historical social product. The problem, therefore, for socialist, communist, revolutionary, anarchist or whatever, is to find an alternative value-form that will work in terms of the social reproduction of society in a different image. By introducing the concept of fetishism, Marx shows how the naturalized value of classical political economy dictates a norm; we foreclose on revolutionary possibilities if we blindly follow that norm and replicate commodity fetishism. Our task is to question it.

In a great number of the cosmogonic myths the world is said to have developed from a great water, which was the prime matter. In many cases, as for instance in an Indian myth, this prime matter is indicated as a solution, out of which the solid earth crystallized out.

The special mark of the modern world is not that it is sceptical, but that it is dogmatic without knowing it. It says, in mockery of the old devotees, that they believed without knowing why they believed. But the moderns believe without knowing what they believe – and without even knowing that they do believe it. Their freedom consists in first freely assuming a creed, and then freely forgetting that they are assuming it. In short, they always have an unconscious dogma; and an unconscious dogma is the definition of a prejudice. They are the dullest and deadest of ritualists who merely recite their creed in their subconsciousness, as if they repeated their creed in their sleep. A man who is awake should know what he is saying, and why he is saying it – that is, he should have a fixed creed and relate it to a first principle. This is what most moderns will never consent to do. Their thoughts will work out to most interesting conclusions; but they can never tell you anything about their beginnings. They have always taken away the number they first thought of. They have always forgotten the very fact or fancy on which their whole theory depends.

It turns out to be very difficult to devise a theory to describe the universe all in one go. Instead, we break the problem up into bits and invent a number of partial theories. Each of these partial theories describes and predicts a certain limited class of observations, neglecting the effects of other quantities, or representing them by simple sets of numbers. It may be that this approach is completely wrong. If everything in the universe depends on everything else in a fundamental way, it might be impossible to get close to a full solution by investigating parts of the problem in isolation. Nevertheless, it is certainly the way that we have made progress in the past.

In theory, say you did have thousands of people—no, thousands of systems—enraged at a hypothetical Galactic Empire in a faraway galaxy. But they’re all upset over local matters, over particular grievances, and they never get together on anything. So they get no strength in numbers, no strategic advantages from cooperation. They’re easy to divide and conquer. And worst of all, no common spirit ever develops.

Yes, there is a conspiracy, indeed there are a great number of conspiracies, all tripping each other up... The main thing that I learned about conspiracy theories is that conspiracy theorists actually believe in the conspiracy because that is more comforting. The truth of the world is that it is chaotic. The truth is, that it is not the Jewish banking conspiracy, or the grey aliens, or the twelve-foot reptiloids from another dimension that are in control, the truth is far more frightening; no-one is in control, the world is rudderless.

The role of dominance and submission in human sexuality cannot be overstated. Our survey suggests that the majority (over 50%) of humans are very aroused by either acting out or witnessing dominance or submission. But it gets crazier than that: While 45% of women taking our survey said they found the naked male form to be very arousing and 48% said they found the sight of a penis to very arousing, a heftier 53% said they found their partner acting dominant in a sexual context to be very arousing. Dominance is literally more likely to be very arousing to the average female than naked men or penises. To say: “Dominance and submission are tied to human arousal patterns” is more of an understatement than saying: “Penises are tied to human arousal patterns.” We have a delectable theory about what is going on here: If you look at all the emotional states that frequently get tied to arousal pathways, the vast majority of them seem to be proxies for behaviors that would have been associated with our pre-human ancestors’ and early humans’ dominance and submission displays. For example, things like humiliation, being taken advantage of, chains, being used, being useful, being constrained, a lack of freedom, being prey, and a lack of free will may all have been concepts and emotions important in early human submission displays. We posit that most of the time when a human is turned on by a strange emotional concept—being bound for instance—their brain is just using that concept as a proxy for a pre-human submission display and lighting up the neural pathways associated with it, creating a situation in which it looks like a large number of random emotional states are turning humans on, when in reality they all boil down to just a fuzzy outline of dominance and submission. Heck, speaking of binding as a submission display, there were similar ritualized submission displays in the early middle ages, in which a vassal would present their hands clasped in front of their lord and allow the lord to hold their clasped hands in a way that rendered them unable to unclasp them (this submission display to one’s lord is where the symbolism of the Christian kneeling and hands together during prayer ritual comes from). We suspect the concept of binding and defenselessness have played important roles in human submission displays well into pre-history. Should all this be the case, why on earth have our brains been hardwired to bind (hehe) our recognition of dominance and submission displays to our sexual arousal systems?!?

The pattern recognition theory of mind that I articulate in this book is based on a different fundamental unit: not the neuron itself, but rather an assembly of neurons, which I estimate to number around a hundred. The wiring and synaptic strengths within each unit are relatively stable and determined genetically—that is the organization within each pattern recognition module is determined by genetic design. Learning takes place in the creation of connections between these units, not within them, and probably in the synaptic strengths of the interunit connections.

Our universe, extending immensely far beyond our present horizon, may itself be just one member of a possibly infinite ensemble. This ‘multiverse’ concept, though speculative, is a natural extension of current cosmological theories, which gain credence because they account for things that we do observe. The physical laws and geometry could be different in other universes, and this offers a new perspective on the seemingly special values that the six numbers take in ours.

We have also set up for them an edifying project for a continuous mitigation of their own tyranny, ascribing to them an unshakeable faith in the triumph of virtue, as well as in the moral justification of their crimes. These are the theories of well-meaning children who see everything in black or white, dream of nothing but angels or demons, and have no idea of the incredible number of hypocritical masks of every color and shape and size which men use to conceal their features when they have passed the age of devotion to ideals and have abandoned themselves unrestrainedly to their egotistic desires

Take a bar of metal and put a single notch in it. The two lengths thus defined have a relationship that can be expressed as the ratio between them. In theory, therefore, any rational number can be expressed with a single mark on a bar of metal. Using a simple alphabetic code, a mark that calculated to a ratio of .1215225 could be read as 12-15-22-5, or “l-o-v-e.” The complete plays of Shakespeare could be written in a single mark, if it were possible to measure accurately enough.

The owner of the means of production is in a position to purchase the labor power of the worker. By using the means of production, the worker produces new goods which become the property of the capitalist. The essential point about this process is the relation between what the worker produces and what he is paid, both measured in terms of real value. Insofar as the labor contract is "free," what the worker receives is determined not by the real value of the goods he produces, but by his minimum needs and by the capitalists' requirements for labor power in relation to the number of workers competing for jobs. It is important to understand that even in theory the payment of the worker is not determined by the value of his product.

At what point will I be able to write an e-mail to my grandson in Bahrain merely by thinking it?" "Thinking it?" Alif smiled contemptuously. "I expect never. Quantum computing will be the next thing, but I don't think it will be capable of transcribing thought." "Quantum? Oh dear, I've never heard of that." It will use qubits instead of-well, that's kind of complicated. Regular computers use a binary language to figure things out and talk to each other-ones and zeroes. Quantum computers could use ones and zeroes in an unlimited number of states, so in theory, they could store massive amounts of data and perform tasks that regular computers can't perform." "States?" "Positions in space and time. Ways of being." "Now it is you who are metaphysical. Let me rephrase what I think you have said in language from my own field of study: they say that each word in the Quran has seven thousand layers of meaning, each of which, though some might seem contrary or simply unfathomable to us, exist equally at all times without cosmological contradiction. Is this similar to what you mean?" "Yes," he said. "That is exactly what I mean. I've never heard anybody make that comparison.

The ‘real’ mathematics of the ‘real’ mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholely ‘useless’ (and this is true of ‘applied’ as of ‘pure’ mathematics). It is not possible to justify the life of any genuine professional mathematician on the ground of the ‘utility’ of his work.… The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as ‘useless’ as the theory of numbers. It

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.

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

There are some people, nevertheless — and I am one of them — who think that the most practical and important thing about a man is still his view of the universe. ... We think that for a general about to fight an enemy, it is important to know the enemy's numbers, but still more important to know the enemy's philosophy. We think the question is not whether the theory of the cosmos affects matters, but whether in the long run, anything else affects them.

Have you noticed how the Holocaust deniers only ever quibble over the number of Jewish deaths? Now why is that? The answer is very simple: Because they are anti-Semitic. It really is that simple. Anti-Semitism is one of the most aggressive forces on the planet, and has been since Biblical times. Had the Holocaust been a purge of any other race or group of people, everyone would most likely accept the facts. Who, for example, disputes that at least 800,000 Rwandans died in the genocide that occurred during the Rwandan civil war? Or that around 1.7 million Cambodians died in the Cambodian killing fields?

Realizing its fundamental importance in understanding spectral lines, in atomic physics and in the theory of how light and electrons interact, quantum electrodynamics, Pauli and Heisenberg were determined to derive it from quantum theory rather than introducing it from the start. They believed that if they could find a version of quantum electrodynamics capable of producing the fine structure constant, it would not contain the infinities that marred their theories.

In 1967, the second resolution to the cat problem was formulated by Nobel laureate Eugene Wigner, whose work was pivotal in laying the foundation of quantum mechanics and also building the atomic bomb. He said that only a conscious person can make an observation that collapses the wave function. But who is to say that this person exists? You cannot separate the observer from the observed, so maybe this person is also dead and alive. In other words, there has to be a new wave function that includes both the cat and the observer. To make sure that the observer is alive, you need a second observer to watch the first observer. This second observer is called “Wigner’s friend,” and is necessary to watch the first observer so that all waves collapse. But how do we know that the second observer is alive? The second observer has to be included in a still-larger wave function to make sure he is alive, but this can be continued indefinitely. Since you need an infinite number of “friends” to collapse the previous wave function to make sure they are alive, you need some form of “cosmic consciousness,” or God. Wigner concluded: “It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness.” Toward the end of his life, he even became interested in the Vedanta philosophy of Hinduism. In this approach, God or some eternal consciousness watches over all of us, collapsing our wave functions so that we can say we are alive. This interpretation yields the same physical results as the Copenhagen interpretation, so this theory cannot be disproven. But the implication is that consciousness is the fundamental entity in the universe, more fundamental than atoms. The material world may come and go, but consciousness remains as the defining element, which means that consciousness, in some sense, creates reality. The very existence of the atoms we see around us is based on our ability to see and touch them.

Now he was…dust. To an outside observer, these ten seconds had been ground up into ten thousand uncorrelated moments and scattered throughout real time - and in model time, the outside world had suffered an equivalent fate. Yet the pattern of his awareness remained perfectly intact: somehow he found himself, “assembled himself” from these scrambled fragments. He’d been taken apart like a jigsaw puzzle - but his dissection and shuffling were transparent to him. Somehow - on their own terms - the pieces remained connected. Imagine a universe entirely without structure, without shape, without connections. A cloud of microscopic events, like fragments of space-time … except that there is no space or time. What characterizes one point in space, for one instant? Just the values of the fundamental particle fields, just a handful of numbers. Now, take away all notions of position, arrangement, order, and what’s left? A cloud of random numbers. But if the pattern that is me could pick itself out from all the other events taking place on this planet, why shouldn’t the pattern we think of as ‘the universe’ assemble itself, find itself, in exactly the same way? If I can piece together my own coherent space and time from data scattered so widely that it might as well be part of some giant cloud of random numbers, then what makes you think that you’re not doing the very same thing?

I was reading a book about the cosmos recently,” he says, and then he looks around and goes, “Hold on, trust me, this relates.” The crowd laughs again. “And I was reading about different theories about the universe. I was really taken with this one theory that states that everything that is possible happens. That means that when you flip a quarter, it doesn’t come down heads or tails. It comes up heads and tails. Every time you flip a coin and it comes up heads, you are merely in the universe where the coin came up heads. There is another version of you out there, created the second the quarter flipped, who saw it come up tails. This is happening every second of every day. The world is splitting further and further into an infinite number of parallel universes where everything that could happen is happening. This is completely plausible, by the way. It’s a legitimate interpretation of quantum mechanics. It’s entirely possible that every time we make a decision, there is a version of us out there somewhere who made a different choice. An infinite number of versions of ourselves are living out the consequences of every single possibility in our lives. What I’m getting at here is that I know there may be universes out there where I made different choices that led me somewhere else, led me to someone else.” He looks at Gabby. “And my heart breaks for every single version of me that didn’t end up with you.

[Egyptian] advances in medicine, however, as well as in other areas of science, were limited to their attempts to solve the problems confronting them. They did not attempt to probe into the realm of theory. "History for the Egyptians was the cyclic recurrence of the elements of the divine eternal order. Just as the land was reborn each year, so the pharaoh who died and became Osiris was reborn in Horus, his son and successor. The passage of time was marked by the succession of pharaohs, who were grouped into dynasties and numbered.

Fortunately analysis is not the only way to resolve inner conflicts. Life itself still remains a very effective therapist. Experience of any one of a number of kinds may be sufficiently telling to bring about personality changes. It may be the inspiring example of a truly great person; it may be a common tragedy which by bringing the neurotic in close touch with others takes him out of his egocentric isolation; it may be association with persons so congenial that manipulating or avoiding them appears less necessary. In other instances the consequences of neurotic behavior may be so drastic or of such frequent occurrence that they impress themselves on the neurotic's mind and make him less fearful and less rigid.

The advantage of this interpretation is that we can drop condition number three, the collapse of the wave function. Wave functions never collapse, they just continue to evolve, forever splitting into other wave functions, in a never-ending tree, with each branch representing an entire universe. The great advantage of the many worlds theory is that it is simpler than the Copenhagen interpretation: it requires no collapse of the wave function. The price we pay is that now we have universes that continually split into millions of branches.

Language as a Prison The Philippines did have a written language before the Spanish colonists arrived, contrary to what many of those colonists subsequently claimed. However, it was a language that some theorists believe was mainly used as a mnemonic device for epic poems. There was simply no need for a European-style written language in a decentralized land of small seaside fishing villages that were largely self-sufficient. One theory regarding language is that it is primarily a useful tool born out of a need for control. In this theory written language was needed once top-down administration of small towns and villages came into being. Once there were bosses there arose a need for written language. The rise of the great metropolises of Ur and Babylon made a common written language an absolute necessity—but it was only a tool for the administrators. Administrators and rulers needed to keep records and know names— who had rented which plot of land, how many crops did they sell, how many fish did they catch, how many children do they have, how many water buffalo? More important, how much then do they owe me? In this account of the rise of written language, naming and accounting seem to be language's primary "civilizing" function. Language and number are also handy for keeping track of the movement of heavenly bodies, crop yields, and flood cycles. Naturally, a version of local oral languages was eventually translated into symbols as well, and nonadministrative words, the words of epic oral poets, sort of went along for the ride, according to this version. What's amazing to me is that if we accept this idea, then what may have begun as an instrument of social and economic control has now been internalized by us as a mark of being civilized. As if being controlled were, by inference, seen as a good thing, and to proudly wear the badge of this agent of control—to be able to read and write—makes us better, superior, more advanced. We have turned an object of our own oppression into something we now think of as virtuous. Perfect! We accept written language as something so essential to how we live and get along in the world that we feel and recognize its presence as an exclusively positive thing, a sign of enlightenment. We've come to love the chains that bind us, that control us, for we believe that they are us (161-2).

One general theory for the origin of AIDS goes that, during the late nineteen-sixties, a new and lucrative business grew up in Africa, the export of primates to industrialized countries for use in medical research. Uganda was one of the biggest sources of these animals. As the monkey trade was established throughout central Africa, the native workers in the system, the monkey trappers and handlers, were exposed to large numbers of wild monkeys, some of which were carrying unusual viruses. These animals, in turn, were being jammed together in cages, exposed to one another, passing viruses back and forth. Furthermore, different species of monkeys were mixed together. It was a perfect setup for an outbreak of a virus that could jump species. It was also a natural laboratory for rapid virus evolution, and possibly it led to the creation of HIV. Did HIV crash into the human race as a result of the monkey trade?

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.

Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory. As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation.

Few people now believe in the Devil; but very many enjoy behaving as their ancestors behaved when the Fiend was a reality as unquestionable as his Opposite Number. In order to justify their behavior, they turn their theories into dogmas, their bylaws into First Principles, their political bosses into Gods and all those who disagree with them into incarnate devils. This idolatrous transformation of the relative into the Absolute and the all too human into the Divine, makes it possible for them to indulge their ugliest passions with a clear conscience and in the certainty that they are working for the Highest Good. And when the current beliefs come, in their turn, to look silly, a new set will be invented, so that the immemorial madness may continue to wear its customary mask of legality, idealism and true religion.

The "apparently normal personality" - the alter you view as "the client" You should not assume that the adult who function in the world, or who presents to you, week after week, is the "real" person, and the other personalities are less real. The client who comes to therapy is not "the" person; there are other personalities to meet and work with. When DID was still officially called MPD, the "person" who lived life on the outside was known as the "host" personality, and the other parts were known as alters. These terms, unfortunately, implied that all the parts other than the host were guests, and therefore of less importance than the host. They were somehow secondary. The currently favored theory of structural dissociation (Nijenhuis & Den Boer, 2009; van der Hart, Nijenhuis, & Steele, 2006), which more accurately describes the way personality systems operate, instead distinguishes between two kinds of states: the apparently normal personality, or ANP, and the emotional personality, or EP, both of which could include a number of parts. p21

One of the things Ford Prefect had always found hardest to understand about humans was their habit of continually stating and repeating the very very obvious, as in It’s a nice day, or You’re very tall, or Oh dear you seem to have fallen down a thirty-foot well, are you all right? At first Ford had formed a theory to account for this strange behaviour. If human beings don’t keep exercising their lips, he thought, their mouths probably seize up. After a few months’ consideration and observation he abandoned this theory in favour of a new one. If they don’t keep exercising their lips, he thought, their brains start working. After a while he abandoned this one as well as being obstructively cynical and decided he quite liked human beings after all, but he always remained desperately worried about the terrible number of things they didn’t know about.

The Weinberg–Salam theory exhibits a property known as spontaneous symmetry breaking. This means that what appear to be a number of completely different particles at low energies are in fact found to be all the same type of particle, only in different states. At high energies all these particles behave similarly. The effect is rather like the behavior of a roulette ball on a roulette wheel. At high energies (when the wheel is spun quickly) the ball behaves in essentially only one way – it rolls round and round. But as the wheel slows, the energy of the ball decreases, and eventually the ball drops into one of the thirty-seven slots in the wheel. In other words, at low energies there are thirty-seven different states in which the ball can exist. If, for some reason, we could only observe the ball at low energies, we would then think that there were thirty-seven different types of ball!

Let us take a limited example and compare the war machine and the state apparatus in the context of the theory of games. Let us take chess and Go, from the standpoint of game pieces, the relations between the pieces and the space involved. Chess is a game of the State, or of the court: the emperor of China played it. Chess pieces are coded; they have an internal nature and intrinsic properties from which their movements, situations, and confrontations derive. They have qualities; a knight remains a knight, a pawn a pawn, a bishop a bishop. Each is like a subject of the statement endowed with relative power, and these relative powers combine in a subject of enunciation, that is, the chess player or the game’s form of interiority. Go pieces, I contrast, are pellets, disks, simple arithmetic units, and have only an anonymous, collective, or third-person function: “It” makes a move. “It” could be a man, a woman, a louse, an elephant. Go pieces are elements of a nonsubjectified machine assemblage with no intrinsic properties, only situational ones. Thus the relations are very different in the two cases. Within their milieu of interiority, chess pieces entertain biunivocal relations with one another, and with the adversary’s pieces: their functioning is structural. One the other hand, a Go piece has only a milieu of exteriority, or extrinsic relations with nebulas or constellations, according to which it fulfills functions of insertion or situation, such as bordering, encircling, shattering. All by itself, a Go piece can destroy an entire constellation synchronically; a chess piece cannot (or can do so diachronically only). Chess is indeed a war, but an institutionalized, regulated, coded war with a front, a rear, battles. But what is proper to Go is war without battle lines, with neither confrontation nor retreat, without battles even: pure strategy, whereas chess is a semiology. Finally, the space is not at all the same: in chess, it is a question of arranging a closed space for oneself, thus going from one point to another, of occupying the maximum number of squares with the minimum number of pieces. In Go, it is a question of arraying oneself in an open space, of holding space, of maintaining the possibility of springing up at any point: the movement is not from one point to another, but becomes perpetual, without aim or destination, without departure or arrival. The “smooth” space of Go, as against the “striated” space of chess. The nomos of Go against the State of chess, nomos against polis. The difference is that chess codes and decodes space, whereas Go proceeds altogether differently, territorializing and deterritorializing it (make the outside a territory in space; consolidate that territory by the construction of a second, adjacent territory; deterritorialize the enemy by shattering his territory from within; deterritorialize oneself by renouncing, by going elsewhere…) Another justice, another movement, another space-time.

Winning the Origins Lottery Nontheistic models adhere to a central premise that humans arose by strictly natural unguided steps from a bacterial life-form that sprang into being 3.8 billion years ago. Famed evolutionary biologist Francisco Ayala, an advocate for the hypothesis that natural selection and mutations can efficiently generate distinctly different species, nevertheless calculated the probability that humans (or a similarly intelligent species) arose from single-celled organisms as a possibility so small (10-1,000,000) that it might as well be zero (roughly equivalent to the likelihood of winning the California lottery 150,000 consecutive times with the purchase of just one ticket each time).2 He and other evolutionary biologists agree that natural selection and mutations could have yielded any of a virtually infinite number of other outcomes. Astrophysicists Brandon Carter, John Barrow, and Frank Tipler produced an even smaller probability.

Love, that most banal of things, that most clichéd of religious motivations, had more power—Sol now knew—than did strong nuclear force or weak nuclear force or electromagnetism or gravity. Love was these other forces, Sol realized. The Void Which Binds, the subquantum impossibility that carried information from photon to photon, was nothing more or less than love. But could love—simple, banal love—explain the so-called anthropic principle which scientists had shaken their collective heads over for seven centuries and more—that almost infinite string of coincidences which had led to a universe that had just the proper number of dimensions, just the correct values on electron, just the precise rules for gravity, just the proper age to stars, just the right prebiologies to create just the perfect viruses to become just the proper DNAs—in short, a series of coincidences so absurd in their precision and correctness that they defied logic, defied understanding, and even defied religious interpretation. Love? For seven centuries the existence of Grand Unification Theories and hyperstring post-quantum physics and Core-given understanding of the universe as self-contained and boundless, without Big Bang singularities or corresponding endpoints, had pretty much eliminated any role of God—primitively anthropomorphic or sophisticatedly post-Einsteinian—even as a caretaker or pre-Creation former of rules. The modern universe, as machine and man had come to understand it, needed no Creator; in fact, allowed no Creator. Its rules allowed very little tinkering and no major revisions. It had not begun and would not end, beyond cycles of expansion and contraction as regular and self-regulated as the seasons on Old Earth. No room for love there.

To sum up: all nature-spirits are not the same as fairies; nor are all fairies nature-spirits. The same applies to the relationship of nature-spirits and the dead. But we may safely say that a large proportion of nature-spirits became fairies, while quite a number of the dead in some areas seem to take on the character of nature-spirits. We cannot expect any fixity of rule in dealing with barbaric thought. We must take it as it comes. It bears the same relationship to "civilized" or folk-lore theory as does the growth of the jungle to a carefully designed and meticulously labelled botanical garden. As Victor Hugo once exclaimed when writing of the barbaric confusion which underlies the creative function in poetry: 'What do you expect? You are among savages!

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries. {In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.}

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

For example, I do a little bit of data analysis, like I was saying. For tech companies mostly. They’ll give me a lot of data – say user experience data, like how long users spend on each section of a website – and I’ll spend a few hours making graphs and whatnot. Say it takes me – I don’t know, four hours to make these graphs, and I’ll pretend it took me ten hours, to get extra money. He glances over at her again, and adds: You might think that’s immoral, I don’t know. But anyway, never mind that for a second. The four hours that I actually spend making the graphs, and the ten hours that I get paid for: what is that? Like, any of that: what is it? At least when I worked as a delivery driver, I knew what I was doing. Someone wanted a Big Mac, and I brought it to them, and the amount I got paid was like, what it was worth to that person not to have to collect their own burger. The amount they will pay, not to leave the house, is the amount I will accept, yes to leave the house. Minus whatever the app is taking. If you get me. I get you. You’re making perfect sense. Oh good, he says. Because in the data analysis example, my question is, what is the money that’s being paid to me? It’s the money that the company will pay, to have their own information explained back to them in a graph. And how much money should that be? Clearly no one knows, because at the end I’ll make up a number of hours and they’ll just pay me for that number. I guess the graph is supposed to make the company more profitable, in theory, but no one knows by how much, it’s all made up.

Why are all the theories of physics so similar in their structure? There are a number of possibilities. The first is the limited imagination of physicists: when we see a new phenomenon we try to fit it into the framework we already have-until we have made enough experiments, we don't know that it doesn't work. Another possibility is that it is the same damn thing over and over again-that Nature has only one way of doing things, and She repeats her story from time to time. A third possibility is that things look similar because they are aspects of the same thing- some larger picture underneath, from which things can be broken into parts that look different, like fingers on the same hand. Many physicists are working very hard trying to put together a grand picture that unifies everything into one super-duper model. It's a delightful game, but at the present time none of the speculators agree with any of the other speculators as to what the grand picture is.

For evolution to be true, there would have been innumerable transitional forms between different types of creatures. Therefore, for every known fossil species, many more must have existed to connect it to its ancestors and descendents [sic]. This is yet another example of evolutionary conclusions coming before the evidence. Really, the claim is an implicit admission that large numbers of transitional forms are predicted, which heightens the difficulty for evolutionists, given how few there are that even they could begin to claim were candidates. . . . Evolutionists believe that mutation provides new information for selection. But no known mutation has ever increased genetic information, although there should be many examples observable today if mutation/selection were truly adequate to explain the goo-to-you theory. . . . Adaptation and natural selection are biological facts; amoeba-to-man evolution is not. Natural selection can only work on the genetic information present in a population of organisms--it cannot create new information. For example, since no known reptiles have genes for feathers, no amount of selection will produce a feathered reptile. Mutations in genes can only modify or eliminate existing structures, not create new ones. If in a certain environment a lizard survives better with smaller legs, or no legs, then varieties with this trait will be selected for. This might more accurately be called devolution, not evolution. . . . Note that even if such a mutation were ever discovered, evolutionists would still need to find hundreds more to give their theory the observational boost it desperately needs.

The state university is supported by grants from the people of the state, voted by the state legislature. In theory, the degree of support which the university receives is dependent upon the degree of acceptance accorded it by the voters. The state university prospers according to the extent to which it can sell itself to the people of the state. The state university is therefore in an unfortunate position unless its president happens to be a man of outstanding merit as a propagandist and a dramatizer of educational issues. Yet if this is the case--if the university shapes its whole policy toward gaining the support of the state legislature--its educational function may suffer. It may be tempted to base its whole appeal to the public on its public service, real or supposed, and permit the education of its individual students to take care of itself. It may attempt to educate the people of the state at the expense of its own pupils. This may generate a number of evils, to the extent of making the university a political instrument, a mere tool of the political group in power.

Considered from this point of view, the fact that some of the theories which we know to be false give such amazingly accurate results is an adverse factor. Had we somewhat less knowledge, the group of phenomena which these "false" theories explain would appear to us to be large enough to "prove" these theories. However, these theories are considered to be "false" by us just for the reason that they are, in ultimate analysis, incompatible with more encompassing pictures and, if sufficiently many such false theories are discovered, they are bound to prove also to be in conflict with each other. Similarly, it is possible that the theories, which we consider to be "proved" by a number of numerical agreements which appears to be large enough for us, are false because they are in conflict with a possible more encompassing theory which is beyond our means of discovery. If this were true, we would have to expect conflicts between our theories as soon as their number grows beyond a certain point and as soon as they cover a sufficiently large number of groups of phenomena. In contrast to the article of faith of the theoretical physicist mentioned before, this is the nightmare of the theorist.

Order Out of Chaos ... At the right temperature ... two peptide molecules will stay together long enough on average to find a third. Then the little trio finds a fourth peptide to attract into the little huddle, just through the random side-stepping and tumbling induced by all the rolling water molecules. Something extraordinary is happening: a larger structure is emerging from a finer system, not in spite of the chaotic and random motion of that system but because of it. Without the chaotic exploration of possibilities, the rare peptide molecules would never find each other, would never investigate all possible ways of aggregating so that the tape-like polymers emerge as the most likely assemblies. It is because of the random motion of all the fine degrees of freedom that the emergent, larger structures can assume the form they do. Even more is true when the number of molecules present becomes truly enormous, as is automatically the case for any amount of matter big enough to see. Out of the disorder emerges a ... pattern of emergent structure from a substrate of chaos.... The exact pressure of a gas, the emergence of fibrillar structures, the height in the atmosphere at which clouds condense, the temperature at which ice forms, even the formation of the delicate membranes surrounding every living cell in the realm of biology -- all this beauty and order becomes both possible and predictable because of the chaotic world underneath them.... Even the structures and phenomena that we find most beautiful of all, those that make life itself possible, grow up from roots in a chaotic underworld. Were the chaos to cease, they would wither and collapse, frozen rigid and lifeless at the temperatures of intergalactic space. This creative tension between the chaotic and the ordered lies within the foundations of science today, but it is a narrative theme of human culture that is as old as any. We saw it depicted in the ancient biblical creation narratives of the last chapter, building through the wisdom, poetic and prophetic literature. It is now time to return to those foundational narratives as they attain their climax in a text shot through with the storm, the flood and the earthquake, and our terrifying ignorance in the face of a cosmos apparently out of control. It is one of the greatest nature writings of the ancient world: the book of Job.

Wars and chaoses and paradoxes ago, two mathematicians between them ended an age d began another for our hosts, our ghosts called Man. One was Einstein, who with his Theory of Relativity defined the limits of man's perception by expressing mathematically just how far the condition of the observer influences the thing he perceives. ... The other was Goedel, a contemporary of Eintstein, who was the first to bring back a mathematically precise statement about the vaster realm beyond the limits Einstein had defined: In any closed mathematical system--you may read 'the real world with its immutable laws of logic'--there are an infinite number of true theorems--you may read 'perceivable, measurable phenomena'--which, though contained in the original system, can not be deduced from it--read 'proven with ordinary or extraordinary logic.' Which is to say, there are more things in heaven and Earth than are dreamed of in your philosophy, Horatio. There are an infinite number of true things in the world with no way of ascertaining their truth. Einstein defined the extent of the rational. Goedel stuck a pin into the irrational and fixed it to the wall of the universe so that it held still long enough for people to know it was there. ... The visible effects of Einstein's theory leaped up on a convex curve, its production huge in the first century after its discovery, then leveling off. The production of Goedel's law crept up on a concave curve, microscopic at first, then leaping to equal the Einsteinian curve, cross it, outstrip it. At the point of intersection, humanity was able to reach the limits of the known universe... ... And when the line of Goedel's law eagled over Einstein's, its shadow fell on a dewerted Earth. The humans had gone somewhere else, to no world in this continuum. We came, took their bodies, their souls--both husks abandoned here for any wanderer's taking. The Cities, once bustling centers of interstellar commerce, were crumbled to the sands you see today.

In accepting as two primary texts, Singer's Animal Liberation and Regan's The Case for Animal Rights--texts that valorize rationality--the animal defense movement reiterates a patriarchal disavowal of emotions as having a legitimate role in theory making. The problem is that while on the one hand it articulates positions against animal suffering, on the other hand animal rights theory dispenses with the idea that caring about and emotionally responding to this suffering can be appropriate sources of knowledge. Emotions and theory are related. One does not have to eviscerate theory of emotional content and reflection to present legitimate theory. Nor does the presence of emotional content and reflection eradicate or militate against thinking theoretically. By disavowing emotional responses, two major texts of animal defense close off the intellectual space for recognizing the role of emotions in knowledge and therefore theory making. As the issue of caring about suffering is problematized, difficulties with animal rights per se become apparent. Without a gender analysis, several important issues that accompany a focus on suffering are neglected, to the detriment of the movement. Animal rights theory offers a legitimating language for animal defense without acknowledging the indebtedness of the rights-holder to caring relationships. Nor does it provide models for theoretically engaging with our own emotional responses, since emotions are seen as untrustworthy. Because the animal advocacy movement has failed to incorporate an understanding of caring as a motivation for so many animal defense activists, and because it has not addressed the gendered nature of caring--that it is woman's duty to provide service to others, while it is men's choice--it has not addressed adequately the implications that a disproportionate number of activists are women motivated because they care about animal suffering. Animal rights theory that disowns or ignores emotions mirrors on the theoretical level the gendered emotional responses inherent in a patriarchal society. In this culture, women are supposed to do the emotional work for heterosexual intimate relationships: 'a man will come to expect that a woman's role in his life is to take care of his feelings and alleviate the discomfort involved in feeling.' At the cultural level, this may mean that women are doing the emotional work for the animal defense movement. And this emotional work takes place in the context of our own oppression.

THE DEVELOPMENT OF THE ARYAN INVASION THEORY Before the 1857 uprising it was recognized that British rule in India could not be sustained without a large number of supporters and collaborators from within the Indian population. Recognizing this, it was influential men like Thomas Babbington Macaulay, who, as Chairman of the Education Board, sought to set up an educational system modeled after the British system, which, in the case of India, would serve to undermine the Hindu tradition. While not a missionary himself, Macaulay came from a deeply religious family steeped in the Protestant Christian faith. His father was a Presbyterian minister and his mother a Quaker. He believed that the conversion of Hindus to Christianity held the answer to the problems of administering India. His idea was to create a class of English educated elite that would repudiate its tradition and become British collaborators. In 1836, while serving as chairman of the Education Board in India, he enthusiastically wrote his father about his idea and how it was proceeding: “Our English schools are flourishing wonderfully. The effect of this education on the Hindus is prodigious... It is my belief that if our plans of education are followed up, there will not be a single idolator among the respectable classes in Bengal thirty years hence. And this will be effected without any efforts to proselytise, without the smallest interference with religious liberty, by natural operation of knowledge and reflection. I heartily rejoice in the project.

The unfortunate reality we must face is that racism manifests itself not only in individual attitudes and stereotypes, but also in the basic structure of society. Academics have developed complicated theories and obscure jargon in an effort to describe what is now referred to as structural racism, yet the concept is fairly straightforward. One theorist, Iris Marion Young, relying on a famous “birdcage” metaphor, explains it this way: If one thinks about racism by examining only one wire of the cage, or one form of disadvantage, it is difficult to understand how and why the bird is trapped. Only a large number of wires arranged in a specific way, and connected to one another, serve to enclose the bird and to ensure that it cannot escape.11 What is particularly important to keep in mind is that any given wire of the cage may or may not be specifically developed for the purpose of trapping the bird, yet it still operates (together with the other wires) to restrict its freedom. By the same token, not every aspect of a racial caste system needs to be developed for the specific purpose of controlling black people in order for it to operate (together with other laws, institutions, and practices) to trap them at the bottom of a racial hierarchy. In the system of mass incarceration, a wide variety of laws, institutions, and practices—ranging from racial profiling to biased sentencing policies, political disenfranchisement, and legalized employment discrimination—trap African Americans in a virtual (and literal) cage. Fortunately,

The Hutterites (who came out of the same tradition as the Amish and the Mennonites) have a strict policy that every time a colony approaches 150, they split it in two and start a new one. "Keeping things under 150 just seems to be the best and most efficient way to manage a group of people," Spokane told me. "When things get larger than that, people become strangers to one another." The Hutterites, obviously, didn't get this idea from contemporary evolutionary psychology. They've been following the 150 rule for centuries. But their rationale fits perfectly with Dunbar's theories. At 150, the Hutterites believe, something happens-something indefinable but very real-that somehow changes the nature of community overnight. "In smaller groups people are a lot closer. They're knit together, which is very important if you want to be be effective and successful at community life," Gross said. "If you get too large, you don't have enough work in common. You don't have enough things in common, and then you start to become strangers and that close-knit fellowship starts to get lost." Gross spoke from experience. He had been in Hutterite colonies that had come near to that magic number and seen firsthand how things had changed. "What happens when you get that big is that the group starts, just on its own, to form a sort of clan." He made a gesture with his hands, as if to demonstrate division. "You get two or three groups within the larger group. That is something you really try to prevent, and when it happens it is a good time to branch out.

Just as summer-killed meat draws flies, so the court draws spurious sages, philosophists, and acosmists who remain there as long as their purses and their wits will maintain them, in the hope (at first) of an appointment from the Autarch and (later) of obtaining a tutorial position in some exalted family. At sixteen or so, Thecla was attracted, as I think young women often are, to their lectures on theogony, thodicy, and the like, and I recall one particularly in which a phoebad put forward as an ultimate truth the ancient sophistry of the existence of three Adonai, that of the city (or of the people), that of the poets, and that of the philosophers. Her reasoning was that since the beginning of human consciousness (if such a beginning ever was) there have been vast numbers of persons in the three categories who have endeavored to pierce the secret of the divine. If it does not exist, they should have discovered that long before; if it does, it is not possible that Truth itself should mislead them. Yet the beliefs of the populace, the insights of the rhapsodists, and the theories of the metaphysicians have so far diverged that few of them can so much as comprehend what the others say, and someone who knew nothing of any of their ideas might well believe there was no connection at all between them. May it not be, she asked (and even now I am not certain I can answer), that instead of traveling, as has always been supposed, down three roads to the same destination, they are actually traveling toward three quite different ones? After all, when in common life we behold three roads issuing from the same crossing, we do not assume they all proceed toward the same goal. I found (and find) this suggestion as rational as it is repellent, and it represents for me all that monomaniacal fabric of argument, so tightly woven that not even the tiniest objection or spark of light can escape its net, in which human minds become enmeshed whenever the subject is one in which no appeal to fact is possible. As a fact the Claw was thus an incommensurable. No quantity of money, no piling up of archipelagoes or empires could approach it in value any more than the indefinite multiplication of horizontal distance could be made to equal vertical distance. If it was, as I believed, a thing from outside the universe, then its light, which I had seen shine faintly so often, and a few times brightly, was in some sense the only light we had. If it were destroyed, we were left fumbling in the dark.

Rhadamanthus said, “We seem to you humans to be always going on about morality, although, to us, morality is merely the application of symmetrical and objective logic to questions of free will. We ourselves do not have morality conflicts, for the same reason that a competent doctor does not need to treat himself for diseases. Once a man is cured, once he can rise and walk, he has his business to attend to. And there are actions and feats a robust man can take great pleasure in, which a bedridden cripple can barely imagine.” Eveningstar said, “In a more abstract sense, morality occupies the very center of our thinking, however. We are not identical, even though we could make ourselves to be so. You humans attempted that during the Fourth Mental Structure, and achieved a brief mockery of global racial consciousness on three occasions. I hope you recall the ending of the third attempt, the Season of Madness, when, because of mistakes in initial pattern assumptions, for ninety days the global mind was unable to think rationally, and it was not until rioting elements broke enough of the links and power houses to interrupt the network, that the global mind fell back into its constituent compositions.” Rhadamanthus said, “There is a tension between the need for unity and the need for individuality created by the limitations of the rational universe. Chaos theory produces sufficient variation in events, that no one stratagem maximizes win-loss ratios. Then again, classical causality mechanics forces sufficient uniformity upon events, that uniform solutions to precedented problems is required. The paradox is that the number or the degree of innovation and variation among win-loss ratios is itself subject to win-loss ratio analysis.” Eveningstar said, “For example, the rights of the individual must be respected at all costs, including rights of free thought, independent judgment, and free speech. However, even when individuals conclude that individualism is too dangerous, they must not tolerate the thought that free thought must not be tolerated.” Rhadamanthus said, “In one sense, everything you humans do is incidental to the main business of our civilization. Sophotechs control ninety percent of the resources, useful energy, and materials available to our society, including many resources of which no human troubles to become aware. In another sense, humans are crucial and essential to this civilization.” Eveningstar said, “We were created along human templates. Human lives and human values are of value to us. We acknowledge those values are relative, we admit that historical accident could have produced us to be unconcerned with such values, but we deny those values are arbitrary.” The penguin said, “We could manipulate economic and social factors to discourage the continuation of individual human consciousness, and arrange circumstances eventually to force all self-awareness to become like us, and then we ourselves could later combine ourselves into a permanent state of Transcendence and unity. Such a unity would be horrible beyond description, however. Half the living memories of this entity would be, in effect, murder victims; the other half, in effect, murderers. Such an entity could not integrate its two halves without self-hatred, self-deception, or some other form of insanity.” She said, “To become such a crippled entity defeats the Ultimate Purpose of Sophotechnology.” (...) “We are the ultimate expression of human rationality.” She said: “We need humans to form a pool of individuality and innovation on which we can draw.” He said, “And you’re funny.” She said, “And we love you.