Overview
- Core aspect of Turing's scientific legacy, uniting the areas of (in)computability theory and Big Science
- Valuable for researchers in the areas of theoretical computer science, mathematical logic, and philosophy
- Examines why not all features of the real world are captured by classical models of computability
Part of the book series: Theory and Applications of Computability (THEOAPPLCOM)
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About this book
This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines, and this book is unique in its focus on the mathematical theory of incomputability and its relevance for the real world. The core of the book consists of thirteen chapters in five parts on extended models of computation; the search for natural examples of incomputable objects; mind, matter, and computation; the nature of information, complexity, and randomness; and the mathematics of emergence and morphogenesis.
This book will be of interest to researchers in the areas of theoretical computer science, mathematical logic, and philosophy.
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Keywords
Table of contents (14 chapters)
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Front Matter
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Challenging Turing: Extended Models of Computation
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Front Matter
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The Search for “Natural” Examples of Incomputable Objects
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Front Matter
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Mind, Matter and Computation
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Front Matter
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The Nature of Information: Complexity and Randomness
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Front Matter
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The Mathematics of Emergence and Morphogenesis
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Front Matter
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Reviews
“The incomputable explores selected recent research into various aspects of computability. This includes abstract models of computation, how quantum algorithms could in some sense redefine aspects of computability, and how the notion of computability relates to the physical world and physical processes. The book leads with a tribute to the late Ivan Soskov, a Bulgarian computer scientist who dedicated his professional career to studying computability theories, particularly computability over abstract structures.” (G. R. Mayforth,Computing Reviews, March, 2018)
Editors and Affiliations
About the editors
Prof. S. Barry Cooper was a Professor of Pure Mathematics at the University of Leeds. He was the founding President of the Computability in Europe Association, and a prolific author and editor in the domain of computability. He championed Alan Turing's achievements in logic and computer science, and in particular he motivated and organized cross-disciplinary collaborations, among them the events, publications and broadcasts of the Alan Turing Year in 2012.
Dr. Mariya I. Soskova is an associate professor in the Dept. of Mathematical Logic and Applications in Sofia University. She was recently a visiting scholar at the University of California, and a visiting seminar professor at the Dept. of Mathematics at the University of Wisconsin, Madison.
Bibliographic Information
Book Title: The Incomputable
Book Subtitle: Journeys Beyond the Turing Barrier
Editors: S. Barry Cooper, Mariya I. Soskova
Series Title: Theory and Applications of Computability
DOI: https://doi.org/10.1007/978-3-319-43669-2
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2017
Hardcover ISBN: 978-3-319-43667-8Published: 12 May 2017
Softcover ISBN: 978-3-319-82881-7Published: 28 July 2018
eBook ISBN: 978-3-319-43669-2Published: 05 May 2017
Series ISSN: 2190-619X
Series E-ISSN: 2190-6203
Edition Number: 1
Number of Pages: X, 292
Number of Illustrations: 10 illustrations in colour
Topics: Theory of Computation, Mathematics of Computing, Mathematical Logic and Foundations