A Computable Universe: Understanding and Exploring Nature as Computation PDF
Preview A Computable Universe: Understanding and Exploring Nature as Computation
A COMPUTABLE UNIVERSE Understanding and Exploring Nature as Computation 8306.9789814374293-tp.indd 1 14/9/12 8:49 AM June29,2012 9:45 WorldScientificReviewVolume-9inx6in-8306AComputableUniverse AComputableUniverse TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk A COMPUTABLE UNIVERSE Understanding and Exploring Nature as Computation Foreword by Sir Roger Penrose Editor Hector Zenil University of Sheffield, UK & Wolfram Research, USA World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 8306.9789814374293-tp.indd 2 14/9/12 8:49 AM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. A COMPUTABLE UNIVERSE Understanding and Exploring Nature as Computation Copyright © 2013 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-4374-29-3 Printed in Singapore. ChinAng - A Computable Universe.pmd 1 9/4/2012, 8:56 AM June29,2012 9:45 WorldScientificReviewVolume-9inx6in-8306AComputableUniverse AComputableUniverse To Elena v June29,2012 9:45 WorldScientificReviewVolume-9inx6in-8306AComputableUniverse AComputableUniverse TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk August30,2012 13:35 WorldScientificReviewVolume-9inx6in-8306AComputableUniverse AComputableUniverse Contents Foreword xiii R. Penrose Preface xxxvii Acknowledgements xliii 1. Introducing the Computable Universe 1 H. Zenil Historical, Philosophical & Foundational Aspects of Computation 21 2. Origins of Digital Computing: Alan Turing, Charles Babbage, & Ada Lovelace 23 D. Swade 3. Generating, Solving and the Mathematics of Homo Sapiens. E. Post’s Views on Computation 45 L. De Mol 4. Machines 63 R. Turner vii August30,2012 13:35 WorldScientificReviewVolume-9inx6in-8306AComputableUniverse AComputableUniverse viii Contents 5. Effectiveness 77 N. Dershowitz & E. Falkovich 6. Axioms for Computability: Do They Allow a Proof of Church’s Thesis? 99 W. Sieg 7. The Mathematician’s Bias — and the Return to Embodied Computation 125 S. B. Cooper 8. Intuitionistic Mathematics and Realizability in the Physical World 143 A. Bauer 9. What is Computation? Actor Model versus Turing’s Model 159 C. Hewitt Computation in Nature & the Real World 187 10. Reaction Systems: A Natural Computing Approach to the Functioning of Living Cells 189 A. Ehrenfeucht, J. Kleijn, M. Koutny & G. Rozenberg 11. Bacteria, Turing Machines and Hyperbolic Cellular Automata 209 M. Margenstern 12. Computation and Communication in Unorganized Systems 231 C. Teuscher 13. The Many Forms of Amorphous Computational Systems 243 J. Wiedermann August30,2012 13:35 WorldScientificReviewVolume-9inx6in-8306AComputableUniverse AComputableUniverse Contents ix 14. Computing on Rings 257 G. J. Mart´ınez, A. Adamatzky & H. V. McIntosh 15. Life as Evolving Software 277 G. J. Chaitin 16. Computability and Algorithmic Complexity in Economics 303 K. V. Velupillai & S. Zambelli 17. Blueprint for a Hypercomputer 333 F. A. Doria Computation & Physics & the Physics of Computation 345 18. Information-Theoretic Teleodynamics in Natural and Artificial Systems 347 A. F. Beavers & C. D. Harrison 19. Discrete Theoretical Processes (DTP) 365 E. Fredkin 20. The Fastest Way of Computing All Universes 381 J. Schmidhuber 21. The Subjective Computable Universe 399 M. Hutter 22. What Is Ultimately Possible in Physics? 417 S. Wolfram 23. Universality, Turing Incompleteness and Observers 435 K. Sutner
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