"Ричард Фейнман. Surely You're Joking, Mr. Feynman!/Вы, конечно, шутите, мистер Фейнман! (англ.)" - читать интересную книгу автора

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A Different Box of Tools


At the Princeton graduate school, the physics department and the math
department shared a common lounge, and every day at four o'clock we would
have tea. It was a way of relaxing in the afternoon, in addition to
imitating an English college. People would sit around playing Go, or
discussing theorems. In those days topology was the big thing.
I still remember a guy sitting on the couch, thinking very hard, and
another guy standing in front of him, saying, "And therefore such-and-such
is true."
"Why is that?" the guy on the couch asks.
"It's trivial! It's trivial!" the standing guy says, and he rapidly
reels off a series of logical steps: "First you assume thus-and-so, then we
have Kerchoff's this-and-that; then there's Waffenstoffer's Theorem, and we
substitute this and construct that. Now you put the vector which goes around
here and then thus-and-so..." The guy on the couch is struggling to
understand all this stuff, which goes on at high speed for about fifteen
minutes!
Finally the standing guy comes out the other end, and the guy on the
couch says, "Yeah, yeah. It's trivial."
We physicists were laughing, trying to figure them out. We decided that
"trivial" means "proved." So we joked with the mathematicians: "We have a
new theorem - that mathematicians can prove only trivial theorems, because
every theorem that's proved is trivial."
The mathematicians didn't like that theorem, and I teased them about
it. I said there are never any surprises - that the mathematicians only
prove things that are obvious. Topology was not at all obvious to the
mathematicians. There were all kinds of weird possibilities that were
"counterintuitive." Then I got an idea. I challenged them: "I bet there
isn't a single theorem that you can tell me - what the assumptions are and
what the theorem is in terms I can understand - where I can't tell you
right away whether it's true or false."
It often went like this: They would explain to me, "You've got an
orange, OK? Now you cut the orange into a finite number of pieces, put it
back together, and it's as big as the sun. True or false?"
"No holes?"
"No holes."
"Impossible! There ain't no such a thing."
"Ha! We got him! Everybody gather around! It's So-and-so's theorem of
immeasurable measure!"
Just when they think they've got me, I remind them, "But you said an
orange! You can't cut the orange peel any thinner than the atoms."
"But we have the condition of continuity: We can keep on cutting!"
"No, you said an orange, so I assumed that you meant a real orange."
So I always won. If I guessed it right, great. If I guessed it wrong,
there was always something I could find in their simplification that they
left out.