**From:** Wei Dai (*weidai@weidai.com*)

**Date:** Fri Nov 02 2007 - 04:01:30 MDT

**Next message:**Gissur Þórhallsson: "Re: The 5 stages of evolution"**Previous message:**Dagon Gmail: "Re: The 5 stages of evolution"**In reply to:**Eliezer S. Yudkowsky: "Re: how to do something with really small probability?"**Next in thread:**Rolf Nelson: "Re: how to do something with really small probability?"**Reply:**Rolf Nelson: "Re: how to do something with really small probability?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Eliezer S. Yudkowsky wrote:

*> I don't see it as having anything to do with the algorithm
*

*> information. It's a problem of having to generate 3^^^3 random bits
*

*> in the first place. If you can repeat an action 3^^^3 times and you
*

*> can flip a quantum coin that many times, you're home free; if you live
*

*> in a non-branching universe then you can't do anything random period.
*

Ignoring the non-branching universe for the moment, how do you know that

each quantum coin flip is actually independent from all of the others? If

the flips are not independent, it's possible that your 3^^^3 bits contains

only say 2^100 bits of information but you have no way of telling the

difference. (What I mean is that the laws of physics are such that quantum

coin flips only appear to be independent, but aren't really.)

I'll put this in more formal terms to make it clearer. Let P(x) be the

probability that x is the output of a uniformly random program. Let SI be

the program of a superintelligence such that P(SI) > 1/2^(2^80). (That had

better be true, or we have no hope of ever seeing this SI.) Now is it

possible that SI can take an arbitrary string x and tell us whether P(x) <

1/2^(2^100)? The answer is no, because suppose it could, then we can find

the lexicographically first string S with P(S) < 1/2^(2^100) by writing a

program that uses SI as a subroutine and queries it with all possible

strings in lexicographical order until the SI answers "yes", but since this

program isn't much larger than SI itself, that implies P(S) can't be much

smaller than 1/2^(2^80) which is a contradiction.

**Next message:**Gissur Þórhallsson: "Re: The 5 stages of evolution"**Previous message:**Dagon Gmail: "Re: The 5 stages of evolution"**In reply to:**Eliezer S. Yudkowsky: "Re: how to do something with really small probability?"**Next in thread:**Rolf Nelson: "Re: how to do something with really small probability?"**Reply:**Rolf Nelson: "Re: how to do something with really small probability?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

*
This archive was generated by hypermail 2.1.5
: Wed Jul 17 2013 - 04:01:00 MDT
*