JoshuaZ comments on The Curve of Capability - Less Wrong

18 Post author: rwallace 04 November 2010 08:22PM

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Comment author: paulfchristiano 06 November 2010 02:08:52AM 2 points [-]

We have very different beliefs about P != NP. I would be willing to make the following wager, if it could be suitably enforced with sufficiently low overhead. If a proof that P != NP reaches general acceptance, you will pay me $10000 with probability 1/1000000 (expectation $.01). If an algorithm provably solves 3SAT on n variables in time O(n^4) or less, I will pay you $1000000.

This bet is particularly attractive to me, because if such a fast algorithm for SAT appears I will probably cease to care about the million dollars. My actual probability estimate is somewhere in the ballpark of 10^-6, though its hard to be precise about probabilities so small.

Perhaps it was not clear what I meant by an individual going FOOM, which is fair since it was a bit of a misuse. I mean just that an individual with access to such an algorithm could quickly amplify their own power and then exert a dominant influence on human society. I don't imagine a human will physically alter themselves. It might be entertaining to develop and write up a plan of attack for this contingency. I think the step I assume is possible that you don't is the use of a SAT solver to search for a compact program whose behavior satisfies some desired property, which can be used to better leverage your SAT solver.

A similar thought experiment my friends and I have occasionally contemplated is: given a machine which can run any C program in exactly 1 second (or report an infinite loop), how many seconds would it take you to <ridiculous goal here>?

Comment author: JoshuaZ 12 November 2010 01:28:40AM 0 points [-]

Replying a second time to remind you of this subthread in case you still have any interest in making a bet. If we change it to degree 7 rather than degree 4 and changed the monetary aspects as I outlined I'm ok with the bet.