Irreducibility and Computational Equivalence

10 Years After Wolfram's A New Kind of Science

  • Hector Zenil

Part of the Emergence, Complexity and Computation book series (ECC, volume 2)

Table of contents

  1. Front Matter
    Pages 1-12
  2. Mechanisms in Programs and Nature

    1. Front Matter
      Pages 1-1
    2. Joost J. Joosten
      Pages 11-23
    3. Jan M. Baetens, Bernard De Baets
      Pages 25-33
  3. Systems Based on Numbers and Simple Programs

    1. Front Matter
      Pages 35-35
    2. Maurice Margenstern
      Pages 37-46
    3. David H. Bailey
      Pages 67-76
  4. Mechanisms in Biology, Social Systems and Technology

    1. Front Matter
      Pages 77-77
    2. Brian Beckage, Stuart Kauffman, Louis J. Gross, Asim Zia, Christopher Koliba
      Pages 79-88
    3. Philip Z. Maymin
      Pages 89-99
  5. Fundamental Physics

    1. Front Matter
      Pages 125-125
    2. Pablo Arrighi, Gilles Dowek
      Pages 127-134
    3. Tommaso Bolognesi
      Pages 135-155
  6. The Behavior of Systems and the Notion of Computation

    1. Front Matter
      Pages 183-183
    2. Eurico L. P. Ruivo, Pedro P. B. de Oliveira
      Pages 211-235
    3. Genaro J. Martínez, Juan C. Seck-Tuoh-Mora, Hector Zenil
      Pages 237-259
  7. Irreducibility and Computational Equivalence

    1. Front Matter
      Pages 261-261
    2. Drew Reisinger, Taylor Martin, Mason Blankenship, Christopher Harrison, Jesse Squires, Anthony Beavers
      Pages 263-272
    3. Hervé Zwirn, Jean-Paul Delahaye
      Pages 273-295
  8. Reflections and Philosophical Implications

    1. Front Matter
      Pages 309-309
    2. Gordana Dodig-Crnkovic
      Pages 311-323
    3. Selmer Bringsjord
      Pages 341-350
  9. Back Matter
    Pages 1-8

About this book


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


Complexity Computational Equivalence Irreducibility Wolframs New Kind of Science

Editors and affiliations

  • Hector Zenil
    • 1
  1. 1., Department of Computer Science/The University of SheffieldPortobelloUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-642-35481-6
  • Online ISBN 978-3-642-35482-3
  • Series Print ISSN 2194-7287
  • Series Online ISSN 2194-7295
  • Buy this book on publisher's site