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

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Feldname	Details
Vorliegende Sprache	eng
Hinweise auf parallele Ausgaben	380919974 Buchausg. u.d.T.: ‡Irreducibility and computational equivalence
ISBN	978-3-642-35481-6
Name	Zenil, Hector
T I T E L	Irreducibility and Computational Equivalence
Zusatz zum Titel	10 Years After Wolfram's A New Kind of Science
Verlagsort	Berlin ; Heidelberg
Verlag	Springer
Erscheinungsjahr	2013
Erscheinungsjahr	2013
Umfang	Online-Ressource (XVI, 358 p. 84 illus, digital)
Reihe	Emergence, Complexity and Computation ; 2
Notiz / Fußnoten	Description based upon print version of record
Weiterer Inhalt	Title Page; Foreword; Preface; Table of Contents; Part I: Mechanisms in Programs and Nature; Cellular Automata: Models of the Physical World; The Turing Machine and G¨odel's Principle; Cellular World-Models; Locality and Causality; Determinism or Randomness?; Conclusions; References; On the Necessity of Complexity; Why Complexity Abounds; What Is Complexity?; The Principle of Computational Equivalence and the Church-Turing Thesis; Complexity and Evolution; Cognition and Complexity; Relative Complexity; Cognitive Diagonalization; Cognition, Complexity and Evolution. Complexity Everywhere: Small Turing MachinesReferences; A Lyapunov View on the Stability of Two-State Cellular Automata; Introduction; Tracking Perturbations in Cellular Automata; The Inadequacy of the Hamming Distance; Tracking All Perturbations; Stability of Cellular Automata; Lyapunov Exponents of Cellular Automata; Some Examples; Conclusion; References; Part II: Systems Based on Numbers and Simple Programs; Cellular Automata and Hyperbolic Spaces; Introduction; Hyperbolic Geometry: Why Not?; A Quick Look at History; Hyperbolic Geometry in Two Words; Tilings and Cellular Automata. Why Cellular Automata in Hyperbolic Spaces?Practical and Theoretical Applications; Simulations; Universality; Conclusion; References; Symmetry and Complexity of Cellular Automata: Towards an Analytical Theory of Dynamical System; Dynamics in the Universe of Cellular Automata; From Simple Local Rules to Global Complex Patterns; Cellular Automata as Dynamical Systems; Digital Dynamics with Difference Equations; Complexity in the Universe of Cellular Automata; Complexity Index of Cellular Automata; Computational Complexity and Universal Computability. Symmetry in the Universe of Cellular AutomataLocal Equivalence of Cellular Automata; Global Equivalence of Cellular Automata; Symmetry with Global Transformations; Global Symmetry of Klein's Vierergruppe V; The Holy Grail of Symmetry and Computability; Outlook to a Computational Universe of Dynamical Systems; References; A New Kind of Science: Ten Years Later; Highlights of ANKS; Experimental Mathematics; ANewFormulaforPi; Ramanujan's Continued Fraction; Formulas for the Riemann Zeta Function; Proof versus Experiment; Conclusion; References. Part III: Mechanisms in Biology, Social Systems and TechnologyMore Complex Complexity: Exploring the Nature of Computational Irreducibility across Physical, Biological, and Human Social Systems; Introduction; PhysicalSystems; Biological Systems; Human Social Systems; Conclusions; References; A New Kind of Finance; Market-Based Approaches; Government-Based Approaches; Practitioners; Conclusions; References; The Relevance of Computation Irreducibility as Computation Universality in Economics; A Preamble on the Origins of the Visions1. Computational Irreducibility as Computation Universality, Implied by the Principle of Computational Equivalence. From the Contents: Part I Mechanisms in Programs and Nature -- Hyperbolic Cellular Automata -- A Lyapunov View on the Stability of Cellular Automata.- Part II The World of Numbers & Simple Programs -- Cellular Automata: Models of the Physical World -- Part III Everyday Systems -- A New Kind of Finance -- The Relevance and Importance of Computation Universality in Economics -- Part IV Fundamental Physics -- The Principle of a Finite Density of Information -- Part V The Behavior of Systems & the Notion of Computation -- An Incompleteness Theorem for the Natural World -- Part VI Irreducibility & Computational Equivalence -- Exploring the Computational Limits of Haugeland's Game as a Two-Dimensional Cellular Automaton.- Part VII Deliberations and Philosophical Implications -- Wolfram and the Computing Nature.
Titelhinweis	Buchausg. u.d.T.: ‡Irreducibility and computational equivalence
ISBN	ISBN 978-3-642-35482-3
Klassifikation	GPFC
	TEC000000
	*68-06
	68Q05
	68Q80
	00B15
	511.35
	620
	QA76.9.M35
	SK 130
Kurzbeschreibung	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 PhysicsThe Behavior of Systems & the Notion of ComputationIrreducibility & Computational EquivalenceReflections and Philosophical Implications.
1. Schlagwortkette	Zellularer Automat
1. Schlagwortkette	Berechnungstheorie
1. Schlagwortkette ANZEIGE DER KETTE	Zellularer Automat -- Berechnungstheorie
2. Schlagwortkette	Zellularer Automat
2. Schlagwortkette	Berechnungstheorie
ANZEIGE DER KETTE	Zellularer Automat -- Berechnungstheorie
SWB-Titel-Idn	37759587X
Signatur	Springer E-Book
Bemerkungen	Elektronischer Volltext - Campuslizenz
Elektronische Adresse	$uhttp://dx.doi.org/10.1007/978-3-642-35482-3
Internetseite / Link	Volltext
Siehe auch	Inhaltstext
Siehe auch	Volltext
Siehe auch	Cover
Siehe auch	Inhaltstext

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