Table of Contents
Computable Universes & Algorithmic Theory of Everything
Talk covers aspects of the following publications:
Physics: Find simple rules that fit real-world observations
Foundations of inductive inference
What does simple mean?
Is simplicity objective?
Simplest explanation of the universe
Zuse’s computable universe
Do quantum physics & Heisenberg uncertainty & Bell’s inequality contradict Zuse’s thesis?
Who can accept Zuse’s thesis?
But isn’t traditional physics continuous?
Then what is the shortest program for our universe?
Nested Great Programmers
But something is still missing!
Anthropic Principle almost useless!
No prediction without prior distribution!
Any constraints on the prior?
1. Weak constraint. Example: discrete universe history
Formally describable distributions
Generalized Turing Machines
Enumerable Output Machines (EOMs, Schmidhuber, 2000)
Generalized Kolmogorov Complexities for generalized Turing machines (Schmidhuber, 2000)
GTM-Example: Limits of virtual realities and programmable universes?
Now back to: Formally describable priors
Interesting theorems
Coding theorems: PE vs KE
Approximable measure ? vs KmG
Now: unknown prior - yet optimal inductive inference via Bayesmix
Bayesmix: sharp loss bounds Marcus Hutter (on Schmidhuber‘s SNF grant; IJFCS / ECML / ICML 2001)
Universal mix
Even “more universal” mixes
Potential practical problem: Universal mixes above are not recursive
2. Stronger constraint / assumption: Ressource postulate
Fastest way of making universes
Ressource postulate + FAST = Speed Prior S via Algorithm GUESS:
Approximating S through AS:
S-based inductive inference
S-based Inference II
Consequences for physics
Summary
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Author: J. Schmidhuber
Email: juergen@idsia.ch
Home Page: http://www.idsia.ch/~juergen/computeruniverse.html
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