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

Hector Zenil
(editor)

Publisher: Springer Verlag

Four centuries ago, telescopes were turned to the sky for the first time--
and what they saw ultimately launched much of modern science. Over the
past twenty years I have begun to explore a new universe--the
computational universe--made visible not by telescopes but by computers

Stephen Wolfram
A New Kind of Science, 2002

TABLE OF CONTENTS

Foreword
Gregory Chaitin

 

Part I Mechanisms in Programs & Nature

1. Cellular Automata: Models of the Physical World
Herbert W. Franke

2. On the Necessity of Complexity
Joost J. Joosten

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

 

Part II Systems Based in Numbers & Simple Programs

4. Hyperbolic Cellular Automata
Maurice Margenstern

5. Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System
Karl Mainzer

6. A New Kind of Science: Ten Years Later
David H. Bailey

 

Part III Social, Biological Systems & Technology

7. A New Kind of Finance
Philip Z. Maymin

8. The Relevance of Computation Irreducibility and Computation Universality in Economics
K. Vela Velupillai

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

10. Computational Technosphere and Cellular Engineering
Mark Burgin

 

Part IV Fundamental Physics

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

12. Do Particles Evolve?
Tommaso Bolognesi

13. Artificial Cosmogenesis: A New Kind of Cosmology
Clément Vidal

 

Part V Behavior of Systems & the Notion of Computation

14. An Incompleteness Theorem for the Natural World
Rudy Rucker

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

16. A spectral portrait of the elementary cellular automata rule space
Eurico L.P. Ruivo and Pedro P.B. de Oliveira

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

 

Part VI Irreducibility & Computational Equivalence

18. 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

19. Unpredictability and Computational Irreducibility
Hervé Zwirn and Jean-Paul Delahaye

20. Computational Equivalence and Classical Recursion Theory
Klaus Sutner

 

Part VII Reflections and Philosophical Implications

21. Wolfram and the Computing Nature
Gordana Dodig-Crnkovic

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

23. Free Will and A New Kind of Science
Selmer Bringsjord

Afterword
Cristian Calude

 

Length: 500 pages

Expected Publication: Early 2013