Irreducibility and computational equivalence: 10 years after Wolfram's A new kind of science
<p>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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
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| Schriftenreihe: | Emergence, complexity and computation
2 |
| Schlagworte: | |
| Online-Zugang: | BTU01 FHA01 FHI01 FHN01 FHR01 FKE01 FWS01 UBY01 Volltext Inhaltsverzeichnis Abstract |
| Zusammenfassung: | <p>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.</p><p>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: </p><p>Mechanisms in Programs & Nature</p><p>Systems Based on Numbers & Simple Programs </p><p>Social and Biological Systems & Technology </p><p>Fundamental Physics</p><p>The Behavior of Systems & the Notion of Computation</p><p>Irreducibility & Computational Equivalence</p><p>Reflections and Philosophical Implications.</p><p> |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 358 p. 84 illus) |
| ISBN: | 9783642354823 |
| DOI: | 10.1007/978-3-642-35482-3 |
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| adam_text | IRREDUCIBILITY AND COMPUTATIONAL EQUIVALENCE
/
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
IRREDUCIBILITY AND COMPUTATIONAL EQUIVALENCE
/
: 2013
ABSTRACT / INHALTSTEXT
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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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| title | Irreducibility and computational equivalence 10 years after Wolfram's A new kind of science |
| title_auth | Irreducibility and computational equivalence 10 years after Wolfram's A new kind of science |
| title_exact_search | Irreducibility and computational equivalence 10 years after Wolfram's A new kind of science |
| title_full | Irreducibility and computational equivalence 10 years after Wolfram's A new kind of science Hector Zenil (ed.) |
| title_fullStr | Irreducibility and computational equivalence 10 years after Wolfram's A new kind of science Hector Zenil (ed.) |
| title_full_unstemmed | Irreducibility and computational equivalence 10 years after Wolfram's A new kind of science Hector Zenil (ed.) |
| title_short | Irreducibility and computational equivalence |
| title_sort | irreducibility and computational equivalence 10 years after wolfram s a new kind of science |
| title_sub | 10 years after Wolfram's A new kind of science |
| topic | Ingenieurwissenschaften Künstliche Intelligenz Engineering Artificial intelligence Physics Zellularer Automat (DE-588)4190671-8 gnd Berechnungstheorie (DE-588)4005581-4 gnd |
| topic_facet | Ingenieurwissenschaften Künstliche Intelligenz Engineering Artificial intelligence Physics Zellularer Automat Berechnungstheorie |
| url | https://doi.org/10.1007/978-3-642-35482-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025943980&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025943980&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040889907 |
| work_keys_str_mv | AT zenilhector irreducibilityandcomputationalequivalence10yearsafterwolframsanewkindofscience |