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

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.

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

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

Content:
Front Matter....Pages 1-12
Front Matter....Pages 1-1
Cellular Automata: Models of the Physical World....Pages 3-10
On the Necessity of Complexity....Pages 11-23
A Lyapunov View on the Stability of Two-State Cellular Automata....Pages 25-33
Front Matter....Pages 35-35
Cellular Automata and Hyperbolic Spaces....Pages 37-46
Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System....Pages 47-65
A New Kind of Science: Ten Years Later....Pages 67-76
Front Matter....Pages 77-77
More Complex Complexity: Exploring the Nature of Computational Irreducibility across Physical, Biological, and Human Social Systems....Pages 79-88
A New Kind of Finance....Pages 89-99
Computational Technosphere and Cellular Engineering....Pages 101-111
Front Matter....Pages 113-124
The Principle of a Finite Density of Information....Pages 125-125
Do Particles Evolve?....Pages 127-134
Artificial Cosmogenesis: A New Kind of Cosmology....Pages 135-155
Front Matter....Pages 157-182
An Incompleteness Theorem for the Natural World....Pages 183-183
Pervasiveness of Universalities of Cellular Automata: Fascinating Life-Like Behaviours....Pages 185-198
A Spectral Portrait of the Elementary Cellular Automata Rule Space....Pages 199-210
Wolfram’s Classification and Computation in Cellular Automata Classes III and IV....Pages 211-235
Front Matter....Pages 237-259
Exploring Wolfram’s Notion of Computational Irreducibility with a Two-Dimensional Cellular Automaton....Pages 261-261
Unpredictability and Computational Irreducibility....Pages 263-272
Computational Equivalence and Classical Recursion Theory....Pages 273-295
Front Matter....Pages 297-307
Wolfram and the Computing Nature....Pages 309-309
A New Kind of Philosophy: Manifesto for a Digital Ontology....Pages 311-323
Erratum: Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System....Pages 325-339
Back Matter....Pages 341-350
....Pages E1-E1