Mathematicians From The United States

"Complex adaptive systems have the property that if you run them—by just letting the mathematical variable of "time" go forward—they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously... A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life."

"Even though something like Danny Hillis' "connection machine" is big, it's nothing compared with Avogadro's number of processors that nature has at her disposal."

"We don't know what organization is. ...We do know that complex adaptive systems have to be nonlinear and capable of storing information. ...We know a little bit about what distinguishes an adaptive complex system from a nonadaptive system, such as turbulent fluid flow."

"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 more familiar terms, it is not hard to prove that God is infinite ... but what if you don’t believe that God exists? It may seem hard to doubt that the more impersonal Absolutes–such as “everything,” or the Mindscape–exist, but there are those who do doubt this. The issue under consideration is a version of the old philosophical problem of the One and the Many. What is being asked is whether the cosmos exists as an organic One, or merely as a Many with no essential coherence. It is certainly true that the Mindscape, for instance, does not exist as a single rational thought. For if the Mindscape is a One, then it is a member of itself, and thus can only be known through a flash of mystical vision. No rational thought is a member of itself, so no rational thought could tie the Mindscape into a One."

"Is this all there is? Struggle, loneliness, disease, and death ... Is this all there is? Life can seem so chaotic, so dreary, so grindingly hard. Who among us has not dreamt of some higher reality, some transcendent level of meaning and peace? There actually is such a higher reality ... And it is not so very hard to reach. For many, the fourth dimension has served as a gateway into it. But what is the fourth dimension? No one can point to the fourth dimension, yet it is all around us. Philosophers and mystics meditate upon it; physicists and mathematicians calculate with it. The fourth dimension is part and parcel of many respected scientific theories, yet it is also of great use in such disreputable fields as spiritualism and science fiction."

"In one of our conversations I pressed Gödel to explain what he meant by the “other relation to reality” by which he said one could directly see mathematical objects. He made the point that the same possibilities of thought are open to everyone, so that we can take the world of possible forms as objective and absolute. Possibility is observer-independent, and therefore real, because it is not subject to our will."

"Janna knew full well that the classic dot-com move was to grab that golden parachute and bail like crazy before the investors and employees caught on."

"Tug was fascinated, and not by the money involved. Like many mathematicians, Mesoglea considered money to be one boring, merely bookkeeping subset of the vast mental universe of general computation."

"“Security always soars along with unemployment,” said Pullen, nodding his head at his own wisdom. “We are in a major downturn. I’ve seen this before, so I know the drill. Locks, bolts, Dobermans, they’re all market leaders this quarter. That’s Capitalism 301, girls.”"

"I think of consciousness as a point, an "eye," that moves about in a sort of mental space. All thoughts are already there in this multi-dimensional space, which we might as well call the Mindscape. Our bodies move about in the physical space called the Universe; our consciousnesses move about in the mental space called the Mindscape."

"Just as we all share the same Universe, we all share the same Mindscape. For just as you can physically occupy the same position in the Universe that anyone else does, you can, in principle, mentally occupy the same state of mind or position in the Mindscape that anyone else does."

"Just as a rock is already in the Universe, whether or not someone is handling it, an idea is already in the Mindscape, whether or not someone is thinking it. A person who does mathematical research, writes stories, or meditates is an explorer of the Mindscape in much the same way that Armstrong, Livingstone, or Cousteau are explorers of the physical features of our Universe. The rocks on the Moon were there before the lunar module landed; and all the possible thoughts are already out there in the Mindscape. The mind of an individual would seem to be analogous to the room or to the neighborhood in which that person lives. One is never in touch with the whole Universe through one’s physical perceptions, and it is doubtful whether one’s mind is ever able to fill the entire Mindscape."

"The fourth dimension is a direction different from all the directions in normal space. Some say that time is the fourth dimension ... And this is, in a sense, true. Others say that the fourth dimension is a hyperspace direction quite different from time ... This is also true. There are, in fact, many higher dimensions. One of these higher dimensions is time, another higher dimension is the direction m which space is curved, and still another higher dimension may lead toward some utterly different universes existing parallel to our own. At the deepest level, our world can be regarded as a pattern in infinite-dimensional space, a space in which we and our minds move like fish in water."

"But Charles was the one who finally realized it was nuts to be walking around inside a sewer with a tweaker leading the way. The fact that Charles figured this out before me makes me wonder about myself. I think I’m spending too much time on my computer."

"“Relax, Wag.” “Relaxing makes me tense!” I scream."

"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."

"It was good to be outside, away from the TV and the computer. The natural world had such high bandwidth."

"“How do you remember these things?” “Mathematicians don’t get senile,” he said. “They just go nuts,” I muttered."

"As he mentions this last sin, he looks down my nightgown, which I’m just loving. I press his hand against my warm thigh. “Don’t worry, sweetie. I don’t live in Hell. I live in San Jose.”"

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

"It would take a supercomputer to simulate this puddle in real time—maybe even all the computers in the world. Especially if you included the air currents pushing the raindrops this way and that. Computable or not, it kept happening."

"In short, a gnarly process is complex and unpredictable without being random. If a story hews to some very familiar pattern, it feels stale. But if absolutely anything can happen, a story becomes as unengaging as someone else’s dream. The gnarly zone lies at the interface between logic and fantasy."

"Wit involves describing the world as it actually is. You experience a release of tension when you notice a glitch. Something was off-kilter, and now you see what it was. The elephant in the room has been named. The evil spirit has been incanted. Perceiving an incongruity in our supposedly smooth-running society provokes a shock of recognition and a concomitant burst of laughter. Wit is a critical-satirical process that can be more serious than the “humorous” label suggests."

"Old age is all about killing time."

"Starting with no preconceptions at all, what is the most reasonable model of the world that we can build up? Only two things seem really certain: one exists, and one has perceptions. I may be a meat machine, a soul, an eye of God, a collection of ideas, or who knows what — but I am certain that I exist. I am the thing that writes these words. Of course, you may doubt whether I am real — perhaps you are only dreaming that you read this book — but you do know for certain that you yourself exist. The fact that one has experiences is equally certain; to put it more neutrally, one cannot doubt that perceptions occur."

"The public revealed its single most predictable trait: fickleness."

"“That’s the problem with immortality,” mused Jack. “You never live long enough to get there.”"

"Kelso had the kind of slit-eyed street smarts that came only from Berkeley law classes."

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

"The meaning of life is beauty and love."

"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."

"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."

"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."

"Will molecular manufacture give all of us the luxuries we want? No. Skewed inverse power-law distribution of valued qualities is an intrinsic property of the natural world. That is, roughly speaking, if there are a thousand people at the bottom of the heap, and a hundred immediately above them, there will only be ten farther up, and just one perched on the top in possession of a large proportion of the goodies. Even if we become glowing clouds of ectoplasm, there's going to be something that we’re competing for—and most of us will feel as though we're getting screwed."

"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."

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

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

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

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

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

"“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.”"

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

"“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.”"

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

"I’ve never seen a religion that wasn’t basically evil."

"“Now that’s a fib, I know,” said the black woman. “Is you folks preachers?”"

"This provender was at a double remove from reality; it was artificially made food that had been further treated in an attempt to make it healthy."

"It’s perfect, isn’t it? It just goes to show that everything I’ve ever said about religion is true. The sky’s the limit when it comes to religious stupidity. Here we have a race of alien invaders, and the evangelical true believers are flocking here to get taken over."

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