Re: how to do something with really small probability?

From: Eliezer S. Yudkowsky (
Date: Thu Nov 01 2007 - 18:57:18 MDT

Wei Dai wrote:
> Suppose an SI wants to do something with a very small, but non-zero
> probability, say 0 < p <= 1/3^^^3 (in Knuth's up-arrow notation). How
> would it go about doing this? The answer seems to be "it can't", because
> algorithmic information theory says there is no way that it can generate
> a sufficiently long random number that it can know is truly random. Can
> anyone see a way around this limitation?

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.

Eliezer S. Yudkowsky                
Research Fellow, Singularity Institute for Artificial Intelligence

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