Re:The Omega Man: "Math is built on randomness"
by gjm11 on Thursday November 27, 2008 @03:28PM
(#378880)
Sounds like you didn't read all of the rest of the article! (Unless you mean you'd have won against the mathematically naive people he mentions at the start who wrote down things like long sequences of 9s.) Aaronson goes on to describe short names for big numbers that get much bigger with fewer symbols than things like your iterated Ackermann.
Specifically, by defining a sequence of numbers in terms of how much a program of given length can do, given that it halts, it turns out that you get a sequence that provably grows faster than any computable sequence. (It's actually traditional to do this with Turing machines rather than conventional programs.) This is in fact rather closely related to Chaitin's stuff at the start of this discussion.
Judging by the rest of the article, I would have won. I would have written "Ackermann function on Graham's number and Graham's number." For added enjoyment, add "Call this B_1. Define B_n = A(B_n-1,B_n-1) for n > 1. Now take B_(B_1)."
EDIT: Or I guess just:
Let G be Graham's number. Let B_n be G if n = 1 and A(B_n-1,B_n-1) if n > 1 (where A is Ackermann's function). Take B_B_2.