The Fastest Way of Computing All Universes

Is there a short and fast program that can compute the precise history of our universe, including all seemingly random but possibly actually deterministic and pseudo-random quantum fluctuations? There is no physical evidence against this possibility. So let us start searching! We already know a short program that computes all constructively computable universes in parallel, each in the asymptotically fastest way. Assuming ours is computed by this optimal method, we can predict that it is among the fastest compatible with our existence. This yields testable predictions. Note: This paper extends an overview of previous work presented in a survey for the German edition of Scientific American.

[1]  Jürgen Schmidhuber,et al.  New Millennium AI and the Convergence of History: Update of 2012 , 2012 .

[2]  Ray J. Solomonoff,et al.  A Formal Theory of Inductive Inference. Part I , 1964, Inf. Control..

[3]  H. Everett.  "Relative State" Formulation of Quantum Mechanics , 1957 .

[4]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 1997, Texts in Computer Science.

[5]  M. Beeson.  Foundations of Constructive Mathematics , 1985 .

[6]  Gregory J. Chaitin,et al.  A recent technical report , 1974, SIGA.

[7]  L. Levin,et al.  THE COMPLEXITY OF FINITE OBJECTS AND THE DEVELOPMENT OF THE CONCEPTS OF INFORMATION AND RANDOMNESS BY MEANS OF THE THEORY OF ALGORITHMS , 1970 .

[8]  J. Urgen Schmidhuber.  A Computer Scientist's View of Life, the Universe, and Everything , 1997 .

[9]  Gregory J. Chaitin,et al.  On the Length of Programs for Computing Finite Binary Sequences: statistical considerations , 1969, JACM.

[10]  Jürgen Schmidhuber,et al.  Ultimate Cognition à la Gödel , 2009, Cognitive Computation.

[11]  S. Lloyd.  Ultimate physical limits to computation , 1999, Nature.

[12]  Karl Sims,et al.  Evolving virtual creatures , 1994, SIGGRAPH.

[13]  Franka Miriam Bruckler.  History of Mathematics I - 2nd, extended, edition , 2014 .

[14]  Max Tegmark.  Is “the Theory of Everything” Merely the Ultimate Ensemble Theory?☆ , 1997, gr-qc/9704009.

[15]  Jürgen Schmidhuber,et al.  The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions , 2002, COLT.

[16]  E. Mark Gold,et al.  Limiting recursion , 1965, Journal of Symbolic Logic.

[17]  Antonín Kucera,et al.  Randomness and Recursive Enumerability , 2001, SIAM J. Comput..

[18]  Jan Poland.  A coding theorem for Enumerable Output Machines , 2004, Inf. Process. Lett..

[19]  L. E. J. Brouwer,et al.  Over de Grondslagen der Wiskunde , 2009 .

[20]  Jürgen Schmidhuber.  The Computational Universe , 2006 .

[21]  Jürgen Schmidhuber.  2006: Celebrating 75 Years of AI - History and Outlook: The Next 25 Years , 2006, 50 Years of Artificial Intelligence.

[22]  D. C. Cooper,et al.  Theory of Recursive Functions and Effective Computability , 1969, The Mathematical Gazette.

[23]  Günter Hotz,et al.  Analytic Machines , 1999, Theor. Comput. Sci..

[24]  Marcus Hutter,et al.  Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability (Texts in Theoretical Computer Science. An EATCS Series) , 2006 .

[25]  Leopold Löwenheim.  Über Möglichkeiten im Relativkalkül , 1915 .

[26]  C. H. Bennett,et al.  Quantum Information and Computation , 1995 .

[27]  Marcus Hutter.  The Fastest and Shortest Algorithm for all Well-Defined Problems , 2002, Int. J. Found. Comput. Sci..

[28]  Péter Gács.  On the relation between descriptional complexity and algorithmic probability , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[29]  Robert M. Solovay.  A Version of Ω for which ZFC Cannot Predict a Single Bit , 2000, Finite Versus Infinite.

[30]  Schmidhuber Juergen,et al.  The New AI: General & Sound & Relevant for Physics , 2003 .

[31]  H. Cantor.  Ueber eine Eigenschaft des Inbegriffs aller reellen algebraischen Zahlen. , 1984 .

[32]  M. Mahoney,et al.  History of Mathematics , 1924, Nature.

[33]  Jean-Pierre Bourguignon,et al.  Mathematische Annalen , 1893 .

[34]  A. Whitaker.  The Fabric of Reality , 2001 .

[35]  Jürgen Schmidhuber,et al.  Algorithmic Theories of Everything , 2000, ArXiv.

[36]  Jürgen Schmidhuber,et al.  On Fast Deep Nets for AGI Vision , 2011, AGI.

[37]  P. Gács,et al.  KOLMOGOROV'S CONTRIBUTIONS TO INFORMATION THEORY AND ALGORITHMIC COMPLEXITY , 1989 .

[38]  C. Schmidhuber.  Strings from Logic , 2000, hep-th/0011065.

[39]  Risto Miikkulainen,et al.  Efficient Non-linear Control Through Neuroevolution , 2006, ECML.

[40]  J. Bell.  On the Problem of Hidden Variables in Quantum Mechanics , 1966 .

[41]  Thomas S. Ray,et al.  An Approach to the Synthesis of Life , 1991 .

[42]  SolomonoffR..  Complexity-based induction systems , 2006 .

[43]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[44]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[45]  Jürgen Schmidhuber,et al.  Optimal Ordered Problem Solver , 2002, Machine Learning.

[46]  Jürgen Schmidhuber,et al.  Low-Complexity Art , 2017 .

[47]  Gregory. J. Chaitin,et al.  Algorithmic information theory , 1987, Cambridge tracts in theoretical computer science.

[48]  Jürgen Schmidhuber,et al.  A Computer Scientist's View of Life, the Universe, and Everything , 1999, Foundations of Computer Science: Potential - Theory - Cognition.

[49]  A. Church.  Review: A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem , 1937 .

[50]  B. Carter.  Large Number Coincidences and the Anthropic Principle in Cosmology , 1974 .

[51]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[52]  Michael Barr,et al.  The Emperor's New Mind , 1989 .

[53]  T. Munich,et al.  Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks , 2008, NIPS.

[54]  N. Bostrom.  Observational selection effects and probability , 2000 .

[55]  Hilary Putnam,et al.  Trial and error predicates and the solution to a problem of Mostowski , 1965, Journal of Symbolic Logic.

[56]  Bruno Marchal.  Calculabilite, Physique et Cognition , 1998 .

[57]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[58]  T. Erber,et al.  Randomness in quantum mechanics—nature's ultimate cryptogram? , 1985, Nature.

[59]  Claus-Peter Schnorr,et al.  Process complexity and effective random tests , 1973 .

[60]  K. Gödel.  Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I , 1931 .

[61]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[62]  J. Barrow,et al.  The Anthropic Cosmological Principle , 1987 .

[63]  Jürgen Schmidhuber,et al.  Hierarchies of Generalized Kolmogorov Complexities and Nonenumerable Universal Measures Computable in the Limit , 2002, Int. J. Found. Comput. Sci..

[64]  Konrad Zuse,et al.  Rechnender Raum , 1991, Physik und Informatik.

[65]  Cristian S. Calude.  Chaitin Omega numbers, Solovay machines, and Gödel incompleteness , 2002, Theor. Comput. Sci..

[66]  Luca Maria Gambardella,et al.  Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence Flexible, High Performance Convolutional Neural Networks for Image Classification , 2022 .

[67]  G. Hooft.  Quantum gravity as a dissipative deterministic system , 1999, gr-qc/9903084.

[68]  W. Heisenberg.  Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik , 1927 .

[69]  A. Grzegorczyk.  On the definitions of computable real continuous functions , 1957 .

[70]  Jürgen Schmidhuber,et al.  The new AI is general and mathematically rigorous , 2010 .