Irreducibility and Computational Equivalence

10 Years After Wolfram's A New Kind of Science

Editors:

ISBN: 978-3-642-35481-6 (Print) 978-3-642-35482-3 (Online)

Table of contents (24 chapters)

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  1. Front Matter

    Pages 1-12

  2. Mechanisms in Programs and Nature

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-10

      Cellular Automata: Models of the Physical World

    3. No Access

      Book Chapter

      Pages 11-23

      On the Necessity of Complexity

    4. No Access

      Book Chapter

      Pages 25-33

      A Lyapunov View on the Stability of Two-State Cellular Automata

  3. Systems Based on Numbers and Simple Programs

    1. Front Matter

      Pages 35-35

    2. No Access

      Book Chapter

      Pages 37-46

      Cellular Automata and Hyperbolic Spaces

    3. No Access

      Book Chapter

      Pages 47-65

      Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System

    4. No Access

      Book Chapter

      Pages 67-76

      A New Kind of Science: Ten Years Later

  4. Mechanisms in Biology, Social Systems and Technology

    1. Front Matter

      Pages 77-77

    2. No Access

      Book Chapter

      Pages 79-88

      More Complex Complexity: Exploring the Nature of Computational Irreducibility across Physical, Biological, and Human Social Systems

    3. No Access

      Book Chapter

      Pages 89-99

      A New Kind of Finance

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      Book Chapter

      Pages 101-111

      The Relevance of Computation Irreducibility as Computation Universality in Economics

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      Book Chapter

      Pages 113-124

      Computational Technosphere and Cellular Engineering

  5. Fundamental Physics

    1. Front Matter

      Pages 125-125

    2. No Access

      Book Chapter

      Pages 127-134

      The Principle of a Finite Density of Information

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      Book Chapter

      Pages 135-155

      Do Particles Evolve?

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      Book Chapter

      Pages 157-182

      Artificial Cosmogenesis: A New Kind of Cosmology

  6. The Behavior of Systems and the Notion of Computation

    1. Front Matter

      Pages 183-183

    2. No Access

      Book Chapter

      Pages 185-198

      An Incompleteness Theorem for the Natural World

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      Book Chapter

      Pages 199-210

      Pervasiveness of Universalities of Cellular Automata: Fascinating Life-Like Behaviours

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      Book Chapter

      Pages 211-235

      A Spectral Portrait of the Elementary Cellular Automata Rule Space

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      Book Chapter

      Pages 237-259

      Wolfram’s Classification and Computation in Cellular Automata Classes III and IV

  7. Irreducibility and Computational Equivalence

    1. Front Matter

      Pages 261-261

    2. No Access

      Book Chapter

      Pages 263-272

      Exploring Wolfram’s Notion of Computational Irreducibility with a Two-Dimensional Cellular Automaton

    3. No Access

      Book Chapter

      Pages 273-295

      Unpredictability and Computational Irreducibility

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      Book Chapter

      Pages 297-307

      Computational Equivalence and Classical Recursion Theory

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