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

ISBN-13: 9783642354816 / Angielski / Twarda / 2012 / 360 str.

Hector Zenil

Opis

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. This 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: Mechanisms in Programs & NatureSystems Based on Numbers & Simple Programs Social and Biological Systems & Technology Fundamental Physics The Behavior of Systems & the Notion of Computation Irreducibility & Computational Equivalence Reflections and Philosophical Implications.

Spis treści

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 Automata: Models of the Physical World
Herbert W. Franke

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

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
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 Cosmogenesis: 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 Automata: 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

Blurb

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.

This 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:

Mechanisms in Programs & Nature

Systems Based on Numbers & Simple Programs

Social and Biological Systems & Technology

Fundamental Physics

The Behavior of Systems & the Notion of Computation

Irreducibility & Computational Equivalence

Reflections and Philosophical Implications.

"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