Computable Universes & Algorithmic Theory of Everything


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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


Author: J. Schmidhuber


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