© 2017

The Incomputable

Journeys Beyond the Turing Barrier

  • S. Barry Cooper
  • Mariya I. Soskova
  • 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 Theory and Applications of Computability book series (THEOAPPLCOM)

Table of contents

  1. Front Matter
    Pages i-x
  2. Mariya I. Soskova
    Pages 1-8
  3. Challenging Turing: Extended Models of Computation

    1. Front Matter
      Pages 9-9
    2. Hristo Ganchev, Dimiter Skordev
      Pages 11-46
    3. Kate Clements, Fay Dowker, Petros Wallden
      Pages 47-61
  4. The Search for “Natural” Examples of Incomputable Objects

  5. Mind, Matter and Computation

    1. Front Matter
      Pages 121-121
    2. Vlatko Vedral
      Pages 123-131
  6. The Nature of Information: Complexity and Randomness

    1. Front Matter
      Pages 141-141
    2. Antonina Kolokolova
      Pages 143-168
    3. Cristian S. Calude
      Pages 169-181
    4. André Nies
      Pages 183-216
  7. The Mathematics of Emergence and Morphogenesis

    1. Front Matter
      Pages 217-217
    2. Thomas E. Woolley, Ruth E. Baker, Philip K. Maini
      Pages 219-235
    3. Aaron Sloman
      Pages 237-292

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.


Computability Mathematical logic Quantum Computing Turing Barrier Turing Test

Editors and affiliations

  • S. Barry Cooper
    • 1
  • Mariya I. Soskova
    • 2
  1. 1.School of MathematicsUniversity of LeedsLeedsUnited Kingdom
  2. 2.Dept. of Mathematical Logic & ApplicationsSofia UniversitySofiaBulgaria

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
  • Series Abbreviated Title Theory Applications Computability
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science Computer Science (R0)
  • Hardcover ISBN 978-3-319-43667-8
  • Softcover ISBN 978-3-319-82881-7
  • eBook ISBN 978-3-319-43669-2
  • Series ISSN 2190-619X
  • Series E-ISSN 2190-6203
  • Edition Number 1
  • Number of Pages X, 292
  • Number of Illustrations 0 b/w illustrations, 10 illustrations in colour
  • Topics Theory of Computation
    Mathematics of Computing
    Mathematical Logic and Foundations
  • Buy this book on publisher's site
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“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) ​