From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Wed Sep 07 2005 - 18:47:37 MDT
Richard Loosemore wrote:
>
> Take the regularities observed in one of the most trivial systems that
> we can think about, Conway's Life. Can we find a set of equations that
> will generate the "regular" forms that emerge in that game? All of the
> regular forms, not just some. We should plug in the algorithm that
> defines the game, and out the other end should come descriptions of the
> glider guns etc. Maybe there are optimists who think this is possible.
> There are many people, I submit, who consider this kind of solution to
> be impossible. The function that generates regularities given local
> rules, in the Comway system, is *never* going to be found. It does not
> exist.
Provably so. Turing machines can be encoded in the Conway system. The
question of whether a *specific* Life configuration repeats regularly is
equivalent to the halting problem, never mind generating all such forms.
-- Eliezer S. Yudkowsky http://intelligence.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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