"Cryptonomicon" - читать интересную книгу автора (Neal Stephenson - Cryptonomicon (The Whole Book))

"Pi is from geometry--ze same story," Rudy put in.

"Yes, it was believed that Euclid's geometry was really a kind of physics, that his lines and so on represented properties of the physical world. But--you know Einstein?"

"I'm not very good with names."

"That white-haired chap with the big mustache?"

"Oh, yeah," Lawrence said dimly, "I tried to ask him my sprocket question. He claimed he was late for an appointment or something."

"That fellow has come up with a general relativity theory, which is sort of a practical application, not of Euclid's, but of Riemann's geometry--"

"The same Riemann of your zeta function?"

"Same Riemann, different subject. Now let's not get sidetracked here Lawrence--"

"Riemann showed you could have many many different geometries that were not the geometry of Euclid but that still made sense internally," Rudy explained.

"All right, so back to P.M. then," Lawrence said.

"Yes! Russell and Whitehead. It's like this: when mathematicians began fooling around with things like the square root of negative one, and quaternions, then they were no longer dealing with things that you could translate into sticks and bottlecaps. And yet they were still getting sound results."

"Or at least internally consistent results," Rudy said.

"Okay. Meaning that math was more than a physics of bottlecaps."

"It appeared that way, Lawrence, but this raised the question of was mathematics really true or was it just a game played with symbols? In other words--are we discovering Truth, or just wanking?"

"It has to be true because if you do physics with it, it all works out! I've heard of that general relativity thing, and I know they did experiments and figured out it was true."

"Ze great majority of mathematics does not lend itself to experimental testing," Rudy said.

"The whole idea of this project is to sever the ties to physics," Alan said.

"And yet not to be yanking ourselves."

"That's what P.M. was trying to do?"

"Russell and Whitehead broke all mathematical concepts down into brutally simple things like sets. From there they got to integers, and so on.

"But how can you break something like pi down into a set?"

"You can't," Alan said, "but you can express it as a long string of digits. Three point one four one five nine, and so on."

"And digits are integers," Rudy said.

"But no fair! Pi itself is not an integer!"

"But you can calculate the digits of pi, one at a time, by using certain formulas. And you can write down the formulas like so!" Alan scratched this in the dirt: