The Once and Future Turing

Until his death in 2015, S. Barry Cooper was Professor of Mathematical Logic at the University of Leeds. He was both a leading figure in the theory of Turing computability, and a noted advocate of multidisciplinary research, especially in connection with the theoretical and practical limits of the computable. As President of Computability in Europe, he was responsible for many international conferences. He chaired the Turing Centenary Committee, and edited the prize-winning critical edition of Turing's publications: Alan Turing: His Work and Impact. Andrew Hodges is a Senior Research Fellow at the Mathematical Institute, University of Oxford. His main research is in fundamental physics, as a colleague of Roger Penrose, but he is also the biographer of Alan Turing. His book Alan Turing: The Enigma (1983) has reached a wide audience and has inspired works of drama, music, art and film.

'The 15 highly readable essays gathered here, each worth a review, celebrate Turing's centenary by exploring current developments and philosophical ramifications descending from many sides of Turing's work, not just his famous theory of computation and his code-breaking exploits but also his interests in logic, artificial intelligence, morphogenesis, pattern formation, the Riemann hypothesis, etc … Summing Up: Recommended. All readers.' D. V. Feldman, CHOICE

• 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.