Re: on formally describable universes and measures

From: <>
Date: Thu, 14 Dec 2000 19:35:17 +0100

Thanks to all who have started sending comments on (Version 1.0, Nov 2000)

The recent Version 1.7 tries to incorporate several useful
suggestions (the substance is the same though):

Algorithmic Theories of Everything
Juergen Schmidhuber

The probability distribution P from which the history of our universe
is sampled represents a theory of everything or TOE. We assume P is
formally describable. Since most (uncountably many) distributions are
not, this imposes a strong inductive bias. To study consequences for
evolving observers, we generalize Solomonoff's algorithmic probability,
Kolmogorov complexity, decidability, and the halting problem. We describe
objects more random than Chaitin's Omega, and a universal cumulatively
enumerable measure (CEM) that dominates previous measures for inductive
inference. Any CEM must assign low probability to any universe lacking a
short enumerating program; P(x) must be small for any universe x lacking
a short description. There is a fastest way of generating all computable
universes based on Levin's universal search. This suggests a TOE based on
a natural resource-oriented postulate: the cumulative prior probability
of all x incomputable within time t should be 1/t. We derive consequences
for inductive reasoning, quantum physics, and the expected duration of
our universe.

TR IDSIA-20-00, Version 1.7, 14/12/2000; 47 pages, 10 theorems, 82 refs (gzipped postscript, 179K) (postscript, 469K) (latex, 148K) (gzipped latex, 50K) (various formats)
Received on Thu Dec 14 2000 - 11:09:32 PST

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