dorsal/arxiv
View SchemaAlgorithmic Theories of Everything
| Authors | Juergen Schmidhuber |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011122 |
| URL | https://arxiv.org/abs/quant-ph/0011122 |
| 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. |
Abstract
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.
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"abstract": "The probability distribution P from which the history of our universe is\nsampled represents a theory of everything or TOE. We assume P is formally\ndescribable. Since most (uncountably many) distributions are not, this imposes\na strong inductive bias. We show that P(x) is small for any universe x lacking\na short description, and study the spectrum of TOEs spanned by two Ps, one\nreflecting the most compact constructive descriptions, the other the fastest\nway of computing everything. The former derives from generalizations of\ntraditional computability, Solomonoff\u0027s algorithmic probability, Kolmogorov\ncomplexity, and objects more random than Chaitin\u0027s Omega, the latter from\nLevin\u0027s universal search and a natural resource-oriented postulate: the\ncumulative prior probability of all x incomputable within time t by this\noptimal algorithm should be 1/t. Between both Ps we find a universal\ncumulatively enumerable measure that dominates traditional enumerable measures;\nany such CEM must assign low probability to any universe lacking a short\nenumerating program. We derive P-specific consequences for evolving observers,\ninductive reasoning, quantum physics, philosophy, and the expected duration of\nour universe.",
"arxiv_id": "quant-ph/0011122",
"authors": [
"Juergen Schmidhuber"
],
"categories": [
"quant-ph",
"cs.AI",
"cs.CC",
"cs.LG",
"hep-th",
"math-ph",
"math.MP",
"physics.comp-ph"
],
"journal_ref": "Sections 1-5 in: Hierarchies of generalized Kolmogorov\n complexities and nonenumerable universal measures computable in the limit.\n International Journal of Foundations of Computer Science 13(4):587-612\n (2002). Section 6 in: The Speed Prior: A New Simplicity Measure Yielding\n Near-Optimal Computable Predictions. In J. Kivinen and R. H. Sloan, editors,\n Proceedings of the 15th Annual Conference on Computational Learning Theory\n (COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence,\n pages 216--228. Springer, 2002.",
"title": "Algorithmic Theories of Everything",
"url": "https://arxiv.org/abs/quant-ph/0011122"
},
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