“Naturally, the four mathematical operations - adding, subtracting, multiplying, and dividing - were impossible. The stones resisted arithmetic as they did the calculation of probability. Forty discs, divided, might become nine; those nine in turn divided might yield 300.”

“If someone were to tell me that there are unicorns on the moon, I could accept or reject the report, or suspend judgement, but it is something I could imagine. If, on the other hand, I were told that six or seven unicorns on the moon could be three, I would declare a priori that such a thing was impossible. The man who has learnt that three plus one are four doesn't have to go through a proof of that assertion with coins, or dice, or chess pieces, or pencils. He knows it, and that's that. He cannot conceive a different sum. There are mathematicians who say that three plus one is a tautology for four, a different way of saying "four" ... But I, Alexander Craigie, of all men on earth, was fated to discover the only objects that contradict that essential law of the human mind. At first I was in a sort of agony, fearing that I'd gone mad; since then, I have come to believe that it would have been better had I been merely insane, for my personal hallucinations would be less disturbing than the discovery that the universe can tolerate disorder. If three plus one can be two, or 14, then reason is madness.”

“The same yearning for order that had created mathematics in the first place made me seek some order in that aberration of mathematics, the insensate stones that propagate themselves.”

“As I manipulated the stones that destroyed the science of mathematics, more than once I thought of those Greek stones that were the first ciphers and that had been passed down to so many languages as the word "calculus". Mathematics I told myself, had its origin, and now has its end, in stones. If Pythagoras had worked with these ...”