Algorithmic Theories of Everything
<|reference_start|>Algorithmic Theories of Everything: 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, one reflecting the most compact constructive descriptions, the other the fastest way of computing everything. The former derives from generalizations of traditional computability, Solomonoff's algorithmic probability, Kolmogorov complexity, and objects more random than Chaitin's Omega, the latter from Levin's universal search 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 both Ps 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 evolving observers, inductive reasoning, quantum physics, philosophy, and the expected duration of our universe.<|reference_end|>
@article{schmidhuber2000algorithmic,
    title={Algorithmic Theories of Everything},
    author={Juergen Schmidhuber},
    journal={Sections 1-5 in: Hierarchies of generalized Kolmogorov
  complexities and nonenumerable universal measures computable in the limit.
  International Journal of Foundations of Computer Science 13(4):587-612
  (2002). Section 6 in: The Speed Prior: A New Simplicity Measure Yielding
  Near-Optimal Computable Predictions. In J. Kivinen and R. H. Sloan, editors,
  Proceedings of the 15th Annual Conference on Computational Learning Theory
  (COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence,
  pages 216--228. Springer, 2002.},
    year={2000},
    number={IDSIA-20-00 (Version 2.0)},
    archivePrefix={arXiv},
    eprint={quant-ph/0011122},
    primaryClass={quant-ph cs.AI cs.CC cs.LG hep-th math-ph math.MP physics.comp-ph}
}