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