Irreducibility and Computational Equivalence is a collection of contributions by outstanding authors in celebration of Stephen Wolfram’s A New Kind of Science after 10 years of its publication. Published by Springer Verlag it is already available both Paperback and Hardcover, as well as an eBook and CDF (computable document).
It is clear that computation is playing an increasingly prominent role in the development of mathematics, as well as in the natural and social sciences. The work of Stephen Wolfram over the last several decades has been a salient part in this phenomenon helping founding the field of Complex Systems, with many of his constructs and ideas incorporated in his book A New Kind of Science (ANKS) becoming part of the scientific discourse and general academic knowledge–from the now established Elementary Cellular Automata to the unconventional concept of mining the Computational Universe, from today’s widespread Wolfram’s Behavioural Classification to his principles of Irreducibility and Computational Equivalence.
I found this volume fascinating in its efforts to flesh out the computational implications for biology more generally.
— Dr. Mark Changizi
I believe that this book will be an inspiration for future work in interdisciplinary research at the intersection of computer science, natural and social sciences.
— Prof. Ivan Zelinka
The volume, with a Foreword by Gregory Chaitin and an Afterword by Cris Calude, covers these and other topics related to or motivated by Wolfram’s seminal ideas, reporting on research undertaken in the decade following the publication of Wolfram’s NKS book. Featuring 39 authors, its 23 contributions are organized into seven parts.
Table of Contents:
Part I Mechanisms in Programs and Nature
1. Hyperbolic Cellular Automata
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
Part II The World of Numbers & Simple Programs
5. Cellular Automata: Models of the Physical World
Herbert W. Franke
6. Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System
7. A New Kind of Science: 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
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 Cosmogenesis: A New Kind of Cosmology
13. Do Particles Evolve?
Part V The Behavior of Systems & the Notion of Computation
14. An Incompleteness Theorem for the Natural World
15. Pervasiveness of Universalities of Cellular Automata: Fascinating Life-like Behaviours
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
Part VII Deliberations and Philosophical Implications
20. Wolfram and the Computing Nature
21. A New Kind of Philosophy. Manifesto for a Digital Ontology
22. Free Will For Us, not For Robots