Theory and Applications of Computability
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Theory and Applications of Computability In cooperation with the association Computability in Europe Series editors Laurent Bienvenu Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM) Montpellier France [email protected] Paola Bonizzoni Università degli Studi di Milano-Bicocca Dipartimento di Informatica Sistemistica e Comunicazione (DISCo) Milano Italy [email protected] Vasco Brattka Universität der Bundeswehr München Fakultät für Informatik Neubiberg Germany University of Cape Town Department of Mathematics & Applied Mathematics Rondebosch South Africa [email protected] Elvira Mayordomo Universidad de Zaragoza Departamento de Informática e Ingeniería de Sistemas Zaragoza Spain [email protected] Prakash Panangaden McGill University School of Computer Science Montreal Canada [email protected] Founding Editors: P. Bonizzoni, V. Brattka, S.B. Cooper, E. Mayordomo Books published in this series will be of interest to the research community and graduate students, with a unique focus on issues of computability. The perspective of the series is multidisciplinary, recapturing the spirit of Turing by linking theoretical and real-world concerns from computer science, mathematics, biology, physics, and the philosophy of science. The series includes research monographs, advanced and graduate texts, and books that offer an original and informative view of computability and computational paradigms. Series Advisory Board Samson Abramsky, University of Oxford Eric Allender, Rutgers, The State University of New Jersey Klaus Ambos-Spies, Universität Heidelberg Giorgio Ausiello, Università di Roma, “La Sapienza” Jeremy Avigad, Carnegie Mellon University Samuel R. Buss, University of California, San Diego Rodney G. Downey, Victoria University of Wellington Sergei S. Goncharov, Novosibirsk State University Peter Jeavons, University of Oxford Nataša Jonoska, University of South Florida, Tampa Ulrich Kohlenbach, Technische Universität Darmstadt Ming Li, University of Waterloo Wolfgang Maass, Technische Universität Graz Grzegorz Rozenberg, Leiden University and University of Colorado, Boulder Alan Selman, University at Buffalo, The State University of New York Wilfried Sieg, Carnegie Mellon University Jan van Leeuwen, Universiteit Utrecht Klaus Weihrauch, FernUniversität Hagen Philip Welch, University of Bristol More information about this series at http://www.springer.com/series/8819 S. Barry Cooper • Mariya I. Soskova Editors The Incomputable Journeys Beyond the Turing Barrier 123 Editors S. Barry Cooper Mariya I. Soskova School of Mathematics Dept. of Mathematical Logic University of Leeds & Applications Leeds, United Kingdom Sofia University Sofia, Bulgaria ISSN 2190-619X ISSN 2190-6203 (electronic) Theory and Applications of Computability ISBN 978-3-319-43667-8 ISBN 978-3-319-43669-2 (eBook) DOI 10.1007/978-3-319-43669-2 Library of Congress Control Number: 2016956098 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface As coeditor, I would like to express my very great appreciation to a number of individuals and institutions who supported this project throughout its development. The event that gave rise to this book would not have come to be without the practical and financial support of the Isaac Newton Institute and their staff and the funding from the John Templeton Foundation. The Chicheley Hall International Centre and its Royal Society staff were magnificent in providing the right atmosphere for the workshop. And the remarkable participants were the ones who made the event such an exciting one. I am grateful to Springer and the editorial board of the book series “Theory and Applications of Computability”, who accepted our idea for this book with no hesitation and supported us throughout its development. Ronan Nugent’s advice and encouragement is deeply appreciated and was especially needed during the final stages of this project. I thank all contributors to this book for their diligent work and patience; the numerous reviewers for their valuable suggestions, comments and questions; the Sofia University Science Foundation and the programme “Women in Science” for their financial support; and my husband Joe Miller and my mother Alexandra Soskova for their unwavering moral support. Most of all, I would like to thank Barry Cooper for including me in this great adventure. Madison, WI, USA Mariya I. Soskova 28 March 2016 v Contents Introduction ...................................................................... 1 Mariya I. Soskova Part I Challenging Turing: Extended Models of Computation Ivan Soskov: A Life in Computability ......................................... 11 Hristo Ganchev and Dimiter Skordev Physical Logic .................................................................... 47 Kate Clements, Fay Dowker, and Petros Wallden From Quantum Foundations via Natural Language Meaning toaTheoryofEverything....................................................... 63 Bob Coecke Part II The Search for “Natural” Examples of Incomputable Objects Some Recent Research Directions in the Computably Enumerable Sets ................................................................. 83 Peter A. Cholak Uncomputability and Physical Law ............................................ 95 Seth Lloyd Algorithmic Economics: Incomputability, Undecidability and Unsolvability in Economics ................................................ 105 K. Vela Velupillai Part III Mind, Matter and Computation Is Quantum Physics Relevant for Life? ........................................ 123 Vlatko Vedral vii viii Contents Trouble with Computation: A Refutation of Digital Ontology.............. 133 J. Mark Bishop Part IV The Nature of Information: Complexity and Randomness Complexity Barriers as Independence ......................................... 143 Antonina Kolokolova Quantum Randomness: From Practice to Theory and Back................ 169 Cristian S. Calude Calculus of Cost Functions ...................................................... 183 André Nies Part V The Mathematics of Emergence and Morphogenesis Turing’s Theory of Morphogenesis: Where We Started, Where WeAreandWhereWeWanttoGo............................................ 219 Thomas E. Woolley, Ruth E. Baker, and Philip K. Maini Construction Kits for Biological Evolution.................................... 237 Aaron Sloman Contributors Ruth E. Baker Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK J. Mark Bishop Goldsmiths, University of London, London, UK Cristian S. Calude Department of Computer Science, University of Auckland, Auckland, New Zealand Peter A. Cholak Department of Mathematics, University of Notre Dame, Notre Dame, IN, USA Kate Clements Blackett Laboratory, Imperial College, London, UK Bob Coecke University of Oxford, Oxford, UK Fay Dowker Blackett Laboratory, Imperial College, London, UK Perimeter Institute, Waterloo, ON, Canada Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada Hristo Ganchev Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria Antonina Kolokolova Department of Computer Science, Memorial University of Newfoundland, St. John’s, NL, Canada Seth Lloyd Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA Philip K. Maini Wolfson Centre for Mathematical Biology, Mathematical Insti- tute, University of Oxford, Oxford, UK André Nies Department of Computer Science, University of Auckland, Auckland, New Zealand ix x Contributors Dimiter Skordev Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria Aaron Sloman School of Computer Science, University of Birmingham, Birmingham, UK Mariya I. Soskova Department of Mathematical Logic and Applications, Sofia University, Sofia, Bulgaria Vlatko Vedral Department of Physics, Clarendon Laboratory, University of Ox- ford, Oxford, UK Centre for Quantum Technologies, National University of Singapore, Singapore, Singapore Department of Physics, National University of Singapore, Singapore, Singapore Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, China K. Vela Velupillai Madras School of Economics, Chennai, India Petros Wallden School of Informatics, University of Edinburgh, Edinburgh, UK IPaQS, Heriot-Watt University, Edinburgh, UK Thomas E. Woolley Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK.