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V_V comments on An angle of attack on Open Problem #1 - Less Wrong
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Comments (84)
That's not the case.
Consider a resource-constrained variant of the original game:
Each program receives as input the round number n and the next program, encrypted by repeated xoring with the output of a monotonic computable function f(n).
Let T_f(n) be the runtime of the fastest algorithm that computes f. Note that T_f(n) is monotonically increasing.
At round n, the current program has a time limit T(n) = C_0 + C_1 * T_f(n). Quirrell never submits programs that exceed the time limit.
In this variant of the game, you have to submit the first program, which has to obey a time limit T(0).
The initial program will not be able to compute the relevant strategy of any of its successors (except at most finitely many of them).
And yet, my quining solution still works (just add a decryption step), and I think Wei Dai's solution also works.
It seems to me that the variant with time limits has a simple quining solution:
1) Get the time limit as input.
2) Spend almost all available time trying to prove in some formal theory that the next program is equivalent to this one.
3) Double down if a proof is found, otherwise take winnings.
That's similar to your idea, right? I'm not sure if it addresses Eliezer's objection, because I no longer understand his objection...
Yes.