The Once and Future Turing: Computing the World

doi:10.1017/CBO9780511863196

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.

'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 Source: CHOICE

'The book under review is a collection of 15 papers written by outstanding scientists. It gives a look at the range of A. M. Turing’s contributions and shows how the subjects have been developed since his time and how they might develop still further. The papers are divided into five groups. … Papers collected in this volume will be interesting to all readers who wish to understand better the lasting significance of Alan Turing and his ideas.'

Roman Murawski Source: Mathematical Reviews

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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Contributors
pp ix-x
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Preface
pp xi-xii
- By Andrew Hodges, University of Oxford
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Introduction
pp xiii-xviii
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Part One - Inside Our Computable World, and the Mathematics of Universality
pp 1-3
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1 - Algorithms, Equations, and Logic
pp 4-19
- By Martin Davis, Dwight Way Berkeley CA 94704–2523, USA
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2 - The Forgotten Turing
pp 20-33
- By J.M.E. Hyland, Cambridge University, Wilberforce Road, Cambridge CB3 0WB, UK
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3 - Turing and the Primes
pp 34-52
- By Andrew R. Booker, University of Bristol, University Walk, Clifton, Bristol BS8 1TW, UK
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4 - Cryptography and Computation after Turing
pp 53-77
- By Ueli Maurer, Department of Computer Science, ETH Zürich, CH-8092 Zürich, Switzerland
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5 - Alan Turing and Enigmatic Statistics
pp 78-89
- By Kanti V. Mardia, University of Leeds, Leeds LS2 9JT, UK, S. Barry Cooper, University of Leeds, Leeds LS2 9JT, UK
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Part Two - The Computation of Processes, and Not Computing the Brain
pp 90-91
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6 - What Alan Turing Might Have Discovered
pp 92-105
- By Stephen Wolfram, Wolfram Research Inc., 100 Trade Center Drive, Champaign, IL 61820, USA
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7 - Designed versus Intrinsic Computation
pp 106-116
- By Christof Teuscher, Portland State University, Department of Electrical and Computer Engineering, P.O. Box 751, Portland OR 97207-0751, USA
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8 - Dull Rigid Human meets Ace Mechanical Translator
pp 117-128
- By Douglas Richard Hofstadter, Indiana University, 512 North Fess Avenue, Bloomington, IN 47408, USA
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Part Three - The Reverse Engineering Road to Computing Life
pp 129-130
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9 - Turing's Theory of Developmental Pattern Formation
pp 131-143
- By Philip K. Maini, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK, Thomas E. Woolley, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK, Eamonn A. Gaffney, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK, Ruth E. Baker, Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
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10 - Walking the Tightrope: The Dilemma of Hierarchical Instabilities in Turing's Morphogenesis
pp 144-159
- By Richard Gordon, Wayne State University, Detroit MI 48201, USA
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Part Four - Biology, Mind, and the Outer Reaches of Quantum Computation
pp 160-162
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11 - Answering Descartes: Beyond Turing
pp 163-192
- By Stuart Kauffman, University of Vermont, USA
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12 - The Ghost in the Quantum Turing Machine
pp 193-296
- By Scott Aaronson, Massachusetts Institute of Technology, Cambridge MA 02139, USA
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Part Five - Oracles, Infinitary Computation, and the Physics of the Mind
pp 297-299
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13 - Turing's ‘Oracle’: From Absolute to Relative Computability and Back
pp 300-334
- By Solomon Feferman, Stanford University, Stanford CA 94305–2125, USA
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14 - Turing Transcendent: Beyond the Event Horizon
pp 335-360
- By P.D. Welch, University Walk, Clifton, Bristol BS8 1TW, UK
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15 - On Attempting to Model the Mathematical Mind
pp 361-378
- By Roger Penrose, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK
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Afterword
pp 379-379
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The Once and Future Turing

Computing the World

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