We generalize Kolmogorov complexity and study the fastest way of computing all computable objects, with consequences for inductive inference, Occam's razor, and the big picture. 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. We show that P(x) is small for any universe x lacking a short description, and study the spectrum of TOEs spanned by two Ps: P1 reflects the most compact constructive descriptions, P2 the fastest way of computing all computable objects. P1 requires generalizations of traditional computability, Solomonoff's algorithmic probability, and Kolmogorov complexity; it leads to describable objects more random than Chaitin's "number of wisdom" Omega. P2 derives from Levin's universal search in program space and a natural resource-oriented postulate: the cumulative prior probability of all x incomputable within time t by this optimal algorithm should be 1/t. Between P1 and P2 we find a universal cumulatively enumerable measure that dominates traditional enumerable measures; any such CEM must assign low probability to any universe lacking a short enumerating program. We derive P-specific consequences for observers evolving in computable universes, inductive reasoning, quantum physics, philosophy, and the expected duration of our universe. 10 theorems, 50 pages, 100 refs TR IDSIA-20-00, Version 2.0, 20 Dec 2000; quant-ph/0011122 Various formats (html, ps, dvi, pdf, tex) to be found in http://www.idsia.ch/~juergen/toesv2/ PS: we have job openings for two postdocs and one PhD student; please see http://www.idsia.ch/jobs.html
