Mathematicians From The United States

"There are many possible realities, infinitely many. Yet most of them are not . . . alive. Most of them are like books that no one ever actually wrote. A group-mind, like humanity's, lights up one given world. What makes this world different from some ghostly alternative universe is that we actually live here."

"I knew you’d say that. You’re so anal, Fletcher. Too much math."

"Don't you think women would like a man's head that always listens to them and agrees?"

"Thanks to environmental decline, kids of Janna’s age had never seen authentic wildlife. So they flipped for the Goob menagerie: marmosets with butterfly wings, starfish that scuttled like earwigs, long, furry frankfurter cat-snakes."

"The government had recently repealed all speed limits in an attempt to boost oil consumption."

"People always have bad news for you when they call you “sir.”"

"For whatever reason, we find it easier to "read" Hilbert Space patterns in terms of time. Yet the patterns exist outside of time. Thinking timelessly is not some unusual skill; when you remember last night's supper you sense a whole and not a chew-by-chew replay. To know a novel's action is to grasp the four-dimensional spacetime whole described."

"This is just so typical of you, Alwin, to be in love with a giant ass."

"The fifties were supposed to be a golden age when the pig had everything his way. That's what TV and the government wants us to believe: there was a time when no one made trouble. What about Kerouac, you assholes? What about Neal?"

"A person's lifeworm is a tangle of atomic worldlines. A braid. The dotty little atoms trace out smooth lines in spacetime: you are the pattern that these lines make up. there is no one single atom that is exclusively yours. I breathe an atom out, you breathe it in. Your garbage helps my tomatoes grow. And so the little spacetime threads weave us all together. The human race is a single vast tapestry, linked by our shared food and air. There are larger links as well: sperm, egg and umblilicus. Each family tree is an organic whole. Your spacetime body tapers back to the threads of mother's egg and father's sperm. And children, if you have them, are forever rooted in your flesh."

"Was I to be Earth's first casualty in the Attack of the Giant Ass From Hilbert Space?"

"At first the tumbling had me totally disoriented. With each degree that I turned, the images around me would deform and change. Three given blobs might split or merge to two or five, while some other shape's angular facets would sprout interlocking crystals. It was a little like trying to make out a human body by watching a Carousel slideshow of three hundred sixty microtomed cross sections."

"But after a while, some higher brain-center cut in, and I began being mentally able to fit the wildly changing scenery into a coherent four-dimensional whole. The process was really no more devious than the process by which one integrates the two hundred lines of a TV screen into a single two-dimensional image . . . which in turn is interpreted as a three-dimensional scene. It's just a matter of processing information. Impossible? I saw."

"The space of our universe is the hypersurface of a vast expanding hypersphere."

"At the most elemental level, reality evanesces into something called Schröedinger's Wave Function: a mathematical abstraction which is best represented as a pattern in an infinite-dimensional space, Hilbert Space. Each point of the Hilbert Space represents a possible state of affairs. The wave function for some one physical or mental system takes the form of, let us say, a coloring in of Hilbert Space. The brightly colored parts represent likely states for the system, the dim parts represent less probable states of affairs."

"This brought back the sick, ashamed feeling I'd woken up with. I was no better than some geek with a foam-rubber woman's torso like they advertise in Hustler. What a pathetic, twisted version of womanhood: all the "inessential" parts lopped off, nothing left behind but tits and ass and holes. Lifelike washable plastic skin. Greek and French features. But yet, in a way, wasn't the sex sphere always what I'd wanted in a woman? An ugly truth there. "Shut up and spread!" How many times had I told Sybil that, if not in so many words?"

"Although my mood swings were the logical and deterministic results of my inputs, they were dismayingly hard for me to foresee, let alone control."

"There’s only one way that people change the past, Bela. They stop thinking about it. They move on."

"Amazing, the respect that nuclear weapons bring."

"I had formed a vague idea that the sex sphere was a hypersphere extending into the fourth dimension. Which meant that if the sphere's giant cunt swallowed me I could end up somewhere very . . . different."

"Mother Nature doesn’t want power-tripping greedheads looking up her skirts."

"“Do you know computer science?” “I know it’s for lamers who can’t handle real math.”"

"Gödel shared with Einstein a certain mystical turn of thought. The word “mystic” is almost pejorative these days. But mysticism does not really have anything to do with incense or encounter groups or demoniac possession. There is a difference between mysticism and occultism. A pure strand of classical mysticism runs from Plato to Plotinus and Eckhart to such great modern thinkers as Aldous Huxley and D. T. Suzuki. The central teaching of mysticism is this: Reality is One. The practice of mysticism consists in finding ways to experience this higher unity directly. The One has variously been called the Good, God, the Cosmos, the Mind, the Void, or (perhaps most neutrally) the Absolute. No door in the labyrinthine castle of science opens directly onto the Absolute. But if one understands the maze well enough, it is possible to jump out of the system and experience the Absolute for oneself."

"In a sense mathematics is quite objective: the same deductions can become known to everyone who starts with the same axioms and definitions; the same abstract forms can be universally perceived. So it’s perfectly possible to talk math with a cockroach from Galaxy Z."

"The matter of color is more confusing. Not every property of a system can be stated as a definite spatio-temporal state of affairs. A system's tendency, for instance, to move from State A to State B, but not from State B to State A . . . a tendency like this is not any specific event which you can point to in space and time. These nonspecific properties correspond to overall gestalts in the Hilbert Space coloring. Alternating bands of red and green light might, for example, represent a particle which is moving from left to right but which has no specific location. A good mood could be a golden haze not tied to any particular cause."

"“I’ll wish for ten million more bucks while I’m at it.” “And immortality?” “No, no. I don’t want to live forever. Death’s the only thing that keeps me going.”"

"Sybil had an unreal, larger-than-life feeling . . . as if she were a person in a book."

"The surest way to be unhappy is try to be happy all the time."

"The meaning of life is beauty and love."

"See the gnarl. The air is a gnarly ocean; the leaves dance on the trees. I’ve always enjoyed watching clouds and water; and now I realize that the computations they’re carrying out are fully as complex as anything in any book I might read. Each flickering shadow is a reminder of the world’s unsolvable and unpredictable richness."

"One last thought: perhaps our universe is perfect."

"So, okay, I’ll go for the universal-automatist answer to “What is reality?” Reality is made of gnarly computations."

"It was odd, odd, odd to see people die. The world rolled on the same as before, as heedlessly as if a person were an ant or a wildflower or a puff of wind. Nature kept on making more and more of everything, and never mind that birth is a death sentence. And now that I’d been to La Hampa, I knew that creation was even more prodigal than I’d ever imagined. There were worlds upon worlds filled with people struggling and swarming like fretful gnats, all of them doomed to vanish into dust while the cosmic dance spun on."

"He’ll be back. Men always come back when they see you making money."

"“What’s superspace?” I felt around for my body and couldn’t find it. “Thoughtland, Fletch, the cosmos. Pure mentation. Abstract possibility. Infinite dimensions. The class of all sets. God’s mind. The pre-geometric substratum. Hilbert space. Penultimate reality. White...” “Cut the crap, Harry.”"

"In the 1970s I even got to meet Kurt Gödel a few times. The king of the logicians. Gödel once told me, “The a priori is very powerful.” By this he meant that pure logic can take you farther than you might believe possible."

"My roommate says anyone who mails bombs to computer scientists can’t be all bad."

"There is no difference between Time and any of the three dimensions of Space except that our consciousness moves along it. ...space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to these planes, each at right angle to the others. But some philosophical people have been asking why three dimensions particularly—why not another direction at right angles to the other three?—and have even tried to construct a Four Dimensional geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a Three-Dimensional solid, and similarly they think that by models of three dimensions they could represent one of four—if they could master the perspective of the thing. See?"

"In the late 19th century, Newcomb was one of America’s best known and probably one of its most powerful scientists. He had spent most of his career as a professor at the naval observatory in Washington, D. C. He had served as President of the American Academy of Arts and Science and as President of the Political Economy Club in the 1880s. He eventually received numerous awards for his most important astronomical research more accurately measuring the movements of the moon and the planets in our solar system. In the 1880s, Newcomb joined the faculty of Johns Hopkins University and his views regarding the competence of junior faculty were often communicated to President Daniel Gilman. This was especially the case for Peirce and Ely. Newcomb also confronted America’s most prominent theologians on the relationship between theology and science and of course evolution and Christianity. For the nation’s centennial, Newcomb also had offered his harsh appraisals of American science and political economy maintaining that they were way behind European science and British political economy. Newcomb also thwarted Peirce’s career progress on numerous occasions playing a pivotal role in his exclusion from academia after 1885."

"Professor Fisher's The Purchasing Power of Money is dedicated to Simon Newcomb, from whom vid Professor Kemmerer the PT = MV formula ultimately derives. Newcomb was not a professional economist but a mathematician (Professor of Mathematics in the U.S. Navy and at Johns Hopkins). His Principles of Political Economy, published in 1886, is one of those original works which a fresh scientific mind, not perverted by having read too much of the orthodox stuff, is able to produce from time to time in a half -formed subject like economics."

"Is the Airship Possible? That depends, first of all, on whether we are to make the requisite scientific discoveries... the construction of an aerial vehicle ... which could carry even a single man from place-to-place at pleasure requires the discovery of some new metal or some new force."

"One of the most curious of these cases [geometrical paradoxers] was that of a student, I am not sure but a graduate, of the University of Virginia, who claimed that geometers were in error in assuming that a line had no thickness. He published a school geometry based on his views, which received the endorsement of a well-known New York school official and, on the basis of this, was actually endorsed, or came very near being endorsed, as a text-book hi the public schools of New York."

"James R. Wible. "Economics, Christianity, and Creative Evolution: Peirce, Newcomb, and Ely and the Issues Surrounding the Creation of the American Economic Association in the 1880s," 2009."

"I knew that flying machines were impossible; in engineering school I had studied Professor Simon Newcomb's well-known mathematical proof that the efforts of Professor Langley and others to build an aerodyne capable of carrying a man were doomed, useless, because scale theory proved that no such contraption large enough to carry a man could carry a heat-energy plant large enough to lift it off the ground — much less a passenger. That was science's final word on a folly and it put a stop to wasting public monies on a will-o'-the-wisp. Research and development money went into airships, where it belonged, with enormous success. However, in the past few days I had gained a new angle on the idea of "impossible". When a veritable flying machine showed up in our sky, I was not greatly surprised."

"The opinion is widely prevalent that even if the subjects are totally forgotten, a valuable mental discipline is acquired by the efforts made to master them. While the Conference admits that, considered in itself this discipline has a certain value, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill."

"It is a matter of historical record that Newcomb, one of the most eminent American mathematicians of his day, published on the topic of four-dimensional space from 1877, and he spoke about it to the New York Mathematical Society in 1893. Four dimensions (and more) were important research topics in mathematics and physics."

"Number is that property of a group of distinct things which remains unchanged during any change to which the group may be subjected which does not destroy the distinctness of the individual things."

"Judged by the only standards which are admissible in a pure doctrine of numbers i is imaginary in the same sense as the negative, the fraction, and the irrational, but in no other sense; all are alike mere symbols devised for the sake of representing the results of operations even when these results are not numbers (positive integers)."

"The opinion is widely prevalent that even if the subjects are totally forgotten, a valuable mental discipline is acquired by the efforts made to master them. While the Conference admits that, considered in itself this discipline has a certain value, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill."

"Carl B. Boyer … is more or less the Gibbon of math history."