The Once and Future Turing
Computing the World

EDITORS:
S. Barry Cooper, University of Leeds
Andrew Hodges, University of Oxford



Alan Turing (1912–1954) made seminal contributions to mathematical logic, computation, computer science, artificial intelligence, cryptography and theoretical biology. In this volume, outstanding scientific thinkers take a fresh look at the great range of Turing's contributions, on how the subjects have developed since his time, and how they might develop still further. The contributors include Martin Davis, J. M. E. Hyland, Andrew R. Booker, Ueli Maurer, Kanti V. Mardia, S. Barry Cooper, Stephen Wolfram, Christof Teuscher, Douglas Richard Hofstadter, Philip K. Maini, Thomas E. Woolley, Eamonn A. Gaffney, Ruth E. Baker, Richard Gordon, Stuart Kauffman, Scott Aaronson, Solomon Feferman, P. D. Welch and Roger Penrose. These specially commissioned essays will provoke and engross the reader who wishes to understand better the lasting significance of one of the twentieth century's deepest thinkers.

• Discover Alan Turing's legacy in fields as diverse as computer science, mathematical biology, philosophy and cryptology
• Contains original contributions from world-leading experts on Turing and his work
• Approachable essays suitable for any reader interested in the development of science

Table of Contents

List of contributors
Introduction S. Barry Cooper and Andrew Hodges

Part I. Inside our Computable World, and the Mathematics of Universality:
1. Algorithms, equations, and logic Martin Davis
2. The forgotten Turing J. M. E. Hyland
3. Turing and the primes Andrew R. Booker
4. Cryptography and computation after Turing Ueli Maurer
5. Alan Turing and enigmatic statistics Kanti V. Mardia and S. Barry Cooper

Part II. The Computation of Processes, and Not Computing the Brain:
6. What Alan Turing might have discovered Stephen Wolfram
7. Designed versus intrinsic computation Christof Teuscher
8. Dull rigid human meets ace mechanical translator Douglas Richard Hofstadter

Part III. The Reverse Engineering Road to Computing Life:
9. Turing's theory of developmental pattern formation Philip K. Maini, Thomas E. Woolley, Eamonn A. Gaffney and Ruth E. Baker
10. Walking the tightrope: the dilemma of hierarchical instabilities in Turing's morphogenesis Richard Gordon

Part IV. Biology, Mind, and the Outer Reaches of Quantum Computation:
11. Answering Descartes: beyond Turing Stuart Kauffman
12. The ghost in the quantum Turing machine Scott Aaronson

Part V. Oracles, Infinitary Computation, and the Physics of the Mind:
13. Turing's 'oracle': from absolute to relative computability and back Solomon Feferman
14. Turing transcendent: beyond the event horizon P. D. Welch
15. On attempting to model the mathematical mind Roger Penrose

Afterword S. Barry Cooper and Andrew Hodges.



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