Front Cover.

Half Title Page.

Title Page.

Copyright Page.

List of Contributors.

Introduction.

Contents.

1: How do We Compute? What Can We Prove?.

2: Alan Mathison Turing by Max Newman.

3: Andrew Hodges Contributes: A Comment on Newman’s Biographical Memoir.

4: Alan Mathison Turing: 1912–1954.

5: On Computable Numbers, with an Application to the Entscheidungsproblem – A Correction.

6: ChrIstos Papadimitriou on — Alan and I.

7: On Computable Numbers, with an Application to the Entscheidungsproblem.

8: On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction.

9: Examining the Work and Its Later Impact: Stephen Wolfram on — The Importance of Universal Computation.

10: Martin Davis Illuminates — Three Proofs of the Unsolvability of the Entscheidungsproblem.

11: Samson Abramsky Detects — Two Puzzles about Computation.

12: Paul Vitányi Illustrates the Importance of — Turing Machines and Understanding Computational Complexity.

13: Gregory Chaitin Traces the Path — From the Halting Problem to the Halting Probability.

14: Robert Irving Soare Expands on — Turing and the Art of Classical Computability.

15: Rainer Glaschick Takes us on a Trip Back to — Turing Machines in Münster.

16: From K. Vela Velupillai — Reflections on Wittgenstein’s Debates with Turing During His Lectures on the Foundations of Mathematics.

17: Jan Van Leeuwen and Jiří Wiedermann on — The Computational Power of Turing’s Non-Terminating Circular A-Machines.

18: Meurig Beynon Puts an Empirical Slant on — Turing’s Approach to Modelling States of Mind.

19: Henk Barendregt and Antonio Raffone Explore — Conscious Cognition as a Discrete, Deterministic and Universal Turing Machine Process.

20: Aaron Sloman Develops a Distinctive View of — Virtual Machinery and Evolution of Mind (Part 1).

21: Artur Ekert on the Physical Reality of — NOT.

22: Cristian Calude, Ludwig Staiger and Michael Stay on — Halting and non-Halting Turing Computations.

23: Philip Welch Leads us — Toward the Unknown Region: On Computing Infinite Numbers.

24: On Computable Numbers, with an Application to the Entscheidungsproblem by A. M. Turing – Review By: Alonzo Church.

25: Andrew Hodges Finds Significance in — Church’s Review of Computable Numbers.

26: Computability and λ-Definability.

27: Henk Barendregt, Giulio Manzonetto and Rinus Plasmeijer Trace through to Today — The Imperative and Functional Programming Paradigm.

28: Computability and λ-Definability.

29: The P-Function in λ-K Conversion.

30: Henk Barendregt and Giulio Manzonetto Point Out the Subtleties of —Turing’s Contributions to Lambda Calculus.

31: The P-Function in λ-K-Conversion.

32: Systems of Logic Based on Ordinals.

33: Solomon Feferman Returns to —Turing’s Thesis: Ordinal Logics and Oracle Computability.

34: Systems of Logic Based on Ordinals.

35: Examining the Work and Its Later Impact: Michael Rathjen Looks at — Turing’s ‘Oracle’ in Proof Theory.

36: Philip Welch Takes a Set-Theoretical View of — Truth and Turing.

37: Alastair Abbott, Cristian Calude and Karl Svozil Describe — A Quantum Random Oracle.

38: Practical Forms of Type Theory.

39: Some Background Remarks from Robin Gandy’s — Preface.

40: Practical Forms of Type Theory.

41: The Use of Dots as Brackets in Church’s System.

42: Lance Fortnow Discovers — Turing’s Dots.

43: The Use of Dots as Brackets in Church’s System.

44: The Reform of Mathematical Notation and Phraseology.

45: Stephen Wolfram Connects — Computation, Mathematical Notation and Linguistics.

46: The Reform of Mathematical Notation and Phraseology.

47: Examining the Work and Its Later Impact: Juliet Floyd Explores — Turing,wittgenstein and Types: Philosophical Aspects of Turing’s ‘the Reform of Mathematical Notation and Phraseology’ (1944–5).

48: Hiding and Unhiding Information: Cryptology, Complexity and Number Theory.

49: On the Gaussian Error Function.

50: Sandy L. Zabell Delivers an Authoritative Guide to — Alan Turing and the Central Limit Theorem.

51: Turing’s ‘preface’ (1935) to ‘on the Gaussian Error Function’.

52: Some Calculations of the Riemann Zeta Function: On a Theorem of Littlewood.

53: Dennis Hejhal and Andrew Odlyzko Take an In-Depth Look at — Alan Turing and the Riemann Zeta Function.

54: And Dennis Hejhal Adds — A Few Comments about Turing’s Method.

55: Some Calculations of the Riemann Zeta-Function.

56: On a Theorem of Littlewood.

57: Solvable and Unsolvable Problems.

58: Gregory Chaitin Recommends — Turing’s Small Gem.

59: Solvable and Unsolvable Problems.

60: Examining the Work and Its Later Impact: Wilfried Sieg Focuses on — Normal Forms for Puzzles: A Variant of Turing’s Thesis.

61: K. Vela Velupillai Connects – Turing on ‘Solvable and UnSolvable Problems’ and Simon on ‘Human Problem Solving’.

62: The Word Problem in Semi-Groups with Cancellation.

63: Gregory Chaitin on — Finding the Halting Problem and the Halting Probability in Traditional Mathematics.

64: While John L. Britton Gives us a Brief – Introduction to the Mathematics.

65: The Word Problem in Semi-Groups with Cancellation.

66: On Permutation Groups.

67: John Leslie Britton’s Informative — Introduction.

68: On Permutation Groups.

69: Rounding-Off Errors in Matrix Processes.

70: Lenore Blum Brings into View —Alan Turing and the Other Theory of Computation.

71: Rounding-Off Errors in Matrix Processes.

72: A Note on Normal Numbers.

73: Andrew Hodges on an Interesting Connection between — Computable Numbers and Normal Numbers.

74: A Note on Normal Numbers.

75: Examining the Work and Its Later Impact Verónica Becher Takes a Closer Look at — Turing’s Note on Normal Numbers.

76: Turing’s Treatise on the Enigma (Prof’s Book).

77: Frode Weierud on Alan Turing, Dilly Knox, Bayesian Statistics, Decoding Machines and — Prof’s Book: Seen in the Light of Cryptologic History.

78: Excerpts from the ‘enigma Paper’.

79: Further Aspects of the Work and Its History Tony Sale Delves into the Cryptographic Background to — Alan Turing, the Enigma and the Bombe.

80: Klaus Schmeh Looks at – Why Turing Cracked the Enigma and the Germans did Not.

81: Speech System ‘Delila’ – Report on Progress.

82: Andrew Hodges Sets the Scene for — The Secrets of Hanslope Park 1944–1945.

83: Top Secret: Speech System ‘Delilah’ – Report on Progress.

84: Examining the Work and its Later Impact: Craig Bauer Presents — Alan Turing and Voice Encryption: A Play in Three Acts.

85: John Harper Reports on the — Delilah Rebuild Project.

86: Checking a Large Routine.

87: Cliff B. Jones Gives a Modern Assessment of — Turing’s “checking a Large Routine”.

88: FridA., 24th June. Checking a Large Routine. by Dr. a. Turing.

89: Excerpt From: Programmer’s Handbook for the Manchester Electronic Computer Mark II: Local Programming Methods and Conventions.

90: Toby Howard Describes — Turing’s Contributions to the Early Manchester Computers.

91: Excerpt From: Programmer’s Handbook for the Manchester Electronic Computer Mark II.

92: Building a Brain: Intelligent Machines, Practice and Theory.

93: Turing’s Lecture to the London Mathematical Society on 20 February 1947.

94: Anthony Beavers Pays Homage to —Alan Turing: Mathematical Mechanist.

95: Lecture to the London Mathematical Society on 20 February 1947.

96: Intelligent Machinery.

97: Rodney A. Brooks and — The Case for Embodied Intelligence.

98: Intelligent Machinery.

99: Examining the Work and its Later Impact: Christof Teuscher Proposes — A Modern Perspective on Turing’s Unorganised Machines.

100: Nicholas Gessler Connects past and Future — The Computerman, the Cryptographer and the Physicist.

101: Stephen Wolfram Looks to Reconcile — Intelligence and the Computational Universe.

102: Paul Smolensky Asks a Key Question — Cognition: Discrete or Continuous Computation?.

103: Tom Vickers Recalls — Alan Turing at the NPL 1945–47.

104: Douglas Hofstadter Engages with — The Gödel–Turing Threshold and the Human Soul.

105: Computing Machinery and Intelligence.

106: Gregory Chaitin Discovers Alan Turing ‘the Good Philosopher’ at both Sides of — Mechanical Intelligence versus Uncomputable Creativity.

107: Computing Machinery and Intelligence.

108: Examining the Work and its Later Impact: Daniel Dennett is Inspired by — Turing’s “Strange Inversion of Reasoning”.

109: Aaron Sloman Draws Together —Virtual Machinery and Evolution of Mind (Part 2).

110: Mark Bishop Examines — The Phenomenal Case of the Turing Test and the Chinese Room.

111: Peter Millican on Recognising Intelligence and — The Philosophical Significance of the Turing Machine and the Turing Test.

112: Luciano Floridi Brings Out the Value of — The Turing Test and the Method of Levels of Abstraction.

113: Aaron Sloman Absolves Turing of —The Mythical Turing Test.

114: David Harel Proposes — A Turing-Like Test for Modelling Nature.

115: Huma Shah Engages with the Realities of — Conversation, Deception and Intelligence: Turing’s Question-Answer Game.

116: Kevin Warwick Looks Forward to — Turing’s Future.

117: Digital Computers Applied to Games.

118: Alan Slomson Introduces — Turing and Chess.

119: Digital Computers Applied to Games.

120: Examining the Work and its Later Impact: David Levy Delves Deeper into — Alan Turing on Computer Chess.

121: Can Digital Computers Think?.

122: B. Jack Copeland Introduces the Transcripts — Turing and the Physics of the Mind.

123: Can Digital Computers Think?.

124: Intelligent Machinery: A Heretical Theory.

125: Can Automatic Calculating Machines be Said to Think?.

126: Examining the Work and its Later Impact: Richard Jozsa Takes us Forward to — Quantum Complexity and the Foundations of Computing.

127: The Mathematics of Emergence: The Mysteries of Morphogenesis.

128: The Chemical Basis of Morphogenesis.

129: Peter Saunders Introduces — Alan Turing’s Work in Biology.

130: And Philip K. Maini Wonders at — Turing’s Theory of Morphogenesis.

131: The Chemical Basis of Morphogenesis.

132: Examining the Work and Its Later Impact Henri Berestycki on the Visionary Power of – Alan Turing and Reaction–Diffusion Equations.

133: Hans Meinhardt Focuses on — Travelling Waves and Oscillations Out of Phase: An Almost Forgotten Part of Turing’s Paper.

134: James D. Murray on what Happened — After Turing – The Birth and Growth of Interdisciplinary Mathematics and Biology.

135: PeT.r t. Saunders Observes Alan Turing — Defeating the Argument from Design.

136: Stephen Wolfram Fills Out the Computational View of — The Mechanisms of Biology.

137: K. Vela Velupillai Connects — Four Traditions of Emergence: Morphogenesis, Ulam-Von Neumann Cellular Automata, the Fermi-Pasta-Ulam Problem, and British Emergentism.

138: Gregory Chaitin Takes the Story Forward — From Turing to Metabiology and Life as Evolving Software.

139: The Morphogen Theory of PhyllotaxI.: I. Geometrical and Descriptive Phyllotaxis: II. Chemical Theory of Morphogenesis: III. (Bernard Richards) a Solution of the Morphogenical Equations for the Case of Spherical Symmetry.

140: Bernard Richards Recalls Alan Turing and — Radiolaria: The Result of Morphogenesis.

141: The Morphogen Theory of PhyllotaxI.: Part I. Geometrical and Descriptive Phyllotaxis.

142: Part II. Chemical Theory of Morphogenesis.

143: Part III. A Solution of the Morphogenetical Equations for the Case of Spherical Symmetry.

144: Examining the Work and its Later Impact: Peter Saunders Comments on the Background to — Turing’s Morphogen Theory of Phyllotaxis.

145: Jonathan Swinton Explores Further — Turing, Morphogenesis, and Fibonacci Phyllotaxis: Life in Pictures.

146: Aaron Sloman Travels Forward to — Virtual Machinery and Evolution of Mind (Part 3): Meta-Morphogenesis: Evolution of Information-Processing Machinery.

147: Outline of the Development of the Daisy.

148: Jonathan Swinton’s Updating of the Texts — An Editorial Note.

149: Outline of the Development of the Daisy.

150: Afterword.

151: Einar Fredriksson Recalls the — History of the Publication of the Collected Works of Alan M. Turing.

152: Mike Yates Writing in The Independent, Friday 24 November 1995 — Obituary: Robin Gandy.

153: Bernard Richards Shares with us — Recollections of Life in the Laboratory with Alan Turing.

Bibliography.

A Bibliography of Publications of Alan Mathison Turing.

Index.