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From: <juergen.domain.name.hidden>

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

Thanks to all who have started sending comments on

http://arXiv.org/abs/quant-ph/0011122 (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 http://www.idsia.ch/~juergen

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

ftp://ftp.idsia.ch/pub/juergen/toes17.ps.gz (gzipped postscript, 179K)

ftp://ftp.idsia.ch/pub/juergen/toes17.ps (postscript, 469K)

ftp://ftp.idsia.ch/pub/juergen/toes17.tex (latex, 148K)

ftp://ftp.idsia.ch/pub/juergen/toes17.tex.gz (gzipped latex, 50K)

http://www.idsia.ch/~juergen/onlinepub.html (various formats)

Received on Thu Dec 14 2000 - 11:09:32 PST

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

Thanks to all who have started sending comments on

http://arXiv.org/abs/quant-ph/0011122 (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 http://www.idsia.ch/~juergen

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

ftp://ftp.idsia.ch/pub/juergen/toes17.ps.gz (gzipped postscript, 179K)

ftp://ftp.idsia.ch/pub/juergen/toes17.ps (postscript, 469K)

ftp://ftp.idsia.ch/pub/juergen/toes17.tex (latex, 148K)

ftp://ftp.idsia.ch/pub/juergen/toes17.tex.gz (gzipped latex, 50K)

http://www.idsia.ch/~juergen/onlinepub.html (various formats)

Received on Thu Dec 14 2000 - 11:09:32 PST

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