True terror—or true enchantment—is produced in man by events that are neither too vast nor too minute.

“In my eschatology there is no such thing as a lesser evil,” said Arago. “With each slain being an entire world dies. For that reason arithmetic provides no measure for ethics. Irreversible evil cannot be measured.”

“The Universe is a labyrinth made of labyrinths. Each leads to another. And wherever we cannot go ourselves, we reach with mathematics. Out of mathematics we build wagons to carry us into the nonhuman realms of the world. It is also possible to construct, out of mathematics, worlds outside the Universe, regardless of whether or not they exist. And

Physics, my friend, is a narrow path drawn across a gulf that the human imagination cannot grasp. It is a set of answers to certain questions that we put to the world, and the world supplies the answers on the condition that we will not then ask it other questions, questions shouted out by common sense. And common sense? It is that which is underst

Nakamura, who heard from Steergard about the midnight argument between the pilot and DEUS, remarked that for what happened in reality one could always come up with a calculation, using tricks known to anyone who ever engaged in applied mathematics.

For the very reason that here nothing served a purpose—not ever, not to anyone—and that here no guillotine of evolution was in play, amputating from every genotype whatever did not contribute to survival, nature, constrained neither by the life she bore nor by the death she inflicted, could achieve liberation, displaying a prodigality characteristi

I don’t recall who proved this to me, or when, but if a man wants to determine the probability of his own birth, by going down the genealogical tree past parents, grandparents, great-grandparents, he can obtain a value as near zero as he likes. If the parents didn’t meet by accident, then the grandparents did, and by the time one gets to the Middle

The reduction of many unknowns to a common unknown denominator represents a gain, not a loss, in information,” replied Lauger easily.

That which mathematically has an extremely low probability also has this characteristic: that it may nevertheless sometimes happen.