Irreducibility and Computational Equivalence: 10 Years After Wolfram's A New Kind of Science

by Hector Zenil (Editor)

Foreword
Gregory Chaitin

Part I Mechanisms in Programs and Nature

1. Hyperbolic Cellular Automata
Maurice Margenstern

2. A Lyapunov View on the Stability of Cellular Automata
Jan M. Baetens & Bernard De Baets

3. On the Necessity of Complexity
Joost J. Joosten

4. Computational Technosphere and Cellular Engineering
Mark Burgin


Part II The World of Numbers & Simple Programs

5. Cellular Models of the Physical World
Herbert W. Franke

6. Symmetry and Complexity of Cellular Towards an Analytical Theory of Dynamical System
Klaus Mainzer

7. A New Kind of Ten Years Later
David H. Bailey


Part III Everyday Systems

8. A New Kind of Finance
Philip Z. Maymin

9. The Relevance and Importance of Computation Universality in Economics
Kumaraswamy Velupillai

10. Exploring the Sources of and Nature of Computational Irreducibility
Brian Beckage, Stuart Kauffman, Louis Gross, Asim Zia, Gabor Vattay and Chris Koliba


Part IV Fundamental Physics

11. The Principle of a Finite Density of Information
Gilles Dowek and Pablo Arrighi

12. Artificial A New Kind of Cosmology
Clément Vidal

13. Do Particles Evolve?
Tommaso Bolognesi


Part V The Behavior of Systems & the Notion of Computation

14. An Incompleteness Theorem for the Natural World
Rudy Rucker

15. Pervasiveness of Universalities of Cellular Fascinating Life-like Behaviours
Emmanuel Sapin

16. Wolfram's Classification and Computation in Cellular Automata Classes III and IV
Genaro J. Martinez, Juan Carlos Seck Tuoh Mora and Hector Zenil


Part VI Irreducibility & Computational Equivalence

17. Exploring the Computational Limits of Haugeland's Game as a Two-Dimensional Cellular Automaton
Drew Reisinger, Taylor Martin, Mason Blankenship, Christopher Harrison, Jesse Squires and Anthony Beavers

18. Irreducibility and Computational Equivalence
Hervé Zwrin and Jean-Paul Delahaye

19. Computational Equivalence and Classical Recursion Theory
Klaus Sutner


Part VII Deliberations and Philosophical Implications

20. Wolfram and the Computing Nature
Gordana Dodig-Crnkovic

21. A New Kind of Philosophy. Manifesto for a Digital Ontology
Jacopo Tagliabue

22. Free Will For Us, not For Robots
Selmer Bringsjord



Afterword
Cristian Calude

376 pages, Paperback

First published December 24, 2012