From: Ben Goertzel (ben@goertzel.org)
Date: Fri Jan 28 2005 - 08:27:35 MST
> This is a substantive hypothesis. Here's why I disagree with it.
>
> Let I(P) = the best way to solve problem P given infinite computing power.
>
> Let L(P) = the best way to solve problem P given limited computing
> power; for the sake of definiteness, say a nanotech supercomputer,
> which is the most we can plausibly hope to get our hands on in the
> foreseeable future.
Sure, but let's introduce a different notation
L(P,x) = the best way to solve P given computing power x
We know that
L(P,infinity) = AIXI or some variant
L(P, human brain power) = something with no resemblance to AIXI
It's really an open question what
L(P, nanotech supercomputer) = ???
Probably it will have aspects of AIXI and aspects of brain-ish architecture,
and some entirely different aspects as well.
> We have candidates for (or at least plausible steps in the direction
> of) I(real life); AIXI et al. And we note that some formulations of
> these do, as Marc conjectures, relate to Chaitin's omega. But as I
> remarked in a previous discussion a little while ago, there are good
> reasons AIXI is PDFware rather than running code.
The mixture of references to Chaitin's omega number and Tipler's Omega Point
is a bit confusing, no?
-- Ben
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