Alan Turing

List of Contributors

Introduction

Part I. How Do We Compute? What Can We Prove?

Part II. Hiding and Unhiding Information: Cryptology, Complexity and Number Theory

Part III. Building a Brain: Intelligent Machines, Practice and Theory

Part IV. The mathematics of emergence: the mysteries of morphogenesis

Alan Mathison Turing by Max Newman

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

Alan Mathison Turing: 1912–1954

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

Christos Papadimitriou on — Alan and I

On Computable Numbers, with an Application to The Entscheidungsproblem

On Computable Numbers, With an Application to The Entscheidungsproblem. A Correction

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

Martin Davis Illuminates — Three Proofs of The Unsolvability of The Entscheidungsproblem

Samson Abramsky detects — Two Puzzles About Computation

Paul Vitanyi Illustrates the Importance of — Turing Machines and Understanding Computational Complexity

Gregory Chaitin traces the path — From the Halting Problem to the halting probability

Robert Irving Soare expands on — Turing and the Art of Classical Computability

Rainer Glaschick takes us on a trip back to — Turing Machines in Munster

From K. Vela Velupillai — Reflections on Wittgenstein’s Debates with Turing during his Lectures on the Foundations of Mathematics

Jan van Leeuwen and Jin Wiedermann on — the computational power of turing’s Non-Terminating Circular A-Machines

Meurig Beynon puts an empirical slant on — Turing’s Approach to Modelling States of Mind

Henk Barendregt and Antonio Raffone explore — Conscious Cognition as a Discrete, Deterministic and Universal Turing Machine Process

Aaron Sloman develops a distinctive view of — Virtual Machinery and Evolution of Mind (Part 1)

Artur Ekert on the physical reality of —

Cristian Calude, Ludwig Staiger and Michael Stay on — Halting and Non-Halting Turing Computations

Philip Welch leads us — Toward the Unknown Region: On Computing Infinite Numbers

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

Andrew Hodges finds significance in — Church’s Review of Computable Numbers

Computability and λ-Definability

Henk Barendregt, Giulio Manzonetto and Rinus Plasmeijer trace through to today — The Imperative and Functional Programming Paradigm

Computability and λ-Definability

The -Function in λ-K Conversion

Henk Barendregt and Giulio Manzonetto point out the subtleties of —Turing’s Contributions to Lambda Calculus

The -Function in λ-K-Conversion

Systems of Logic Based on Ordinals

Solomon Feferman returns to —Turing’s Thesis: Ordinal Logics and Oracle Computability

Systems of Logic Based on Ordinals

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

Philip Welch takes a set-theoretical view of — Truth and Turing

Alastair Abbott, Cristian Calude and Karl Svozil describe — A Quantum Random Oracle

Practical Forms of Type Theory

Some background remarks from Robin Gandy’s — Preface

Practical Forms of Type Theory

The use of Dots as Brackets in Church’s System

Lance Fortnow discovers — Turing’s dots

The Use of Dots as Brackets in Church’s System

The Reform of Mathematical Notation and Phraseology

Stephen Wolfram connects — Computation, Mathematical Notation and Linguistics

The Reform of Mathematical Notation and Phraseology

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)

On the Gaussian error function

Sandy L. Zabell delivers an authoritative guide to — Alan Turing and the Central Limit Theorem

Turing’s ‘Preface’ (1935) to ‘On the Gaussian error function’

Some Calculations of the Riemann Zeta function: On a Theorem of Littlewood

Dennis Hejhal and Andrew Odlyzko take an in-depth look at — Alan Turing and the Riemann Zeta function

And Dennis Hejhal adds — A Few Comments About Turing’s Method

Some Calculations of the Riemann Zeta-Function

On A Theorem of Littlewood

Solvable and Unsolvable Problems

Gregory Chaitin recommends — Turing’s Small Gem

Solvable and Unsolvable Problems

Examining the Work and Its Later Impact: Wilfried Sieg focuses on — Normal Forms for Puzzles: AVariant of Turing’s Thesis

K. Vela Velupillai connects –: Turing on ‘ Solvable and Unsolvable Problems’ and Simon on ‘Human Problem Solving’

The Word Problem in Semi-Groups with Cancellation

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

While John L. Britton gives us a brief – Introduction to the mathematics

The Word Problem in Semi-Groups with Cancellation

On Permutation Groups

John Leslie Britton’s informative — Introduction

On Permutation Groups

Rounding-off Errors in Matrix Processes

Lenore Blum brings into view —Alan Turing and the Other Theory of Computation

Rounding-Off Errors in Matrix Processes

A Note on Normal Numbers

Andrew Hodges on an interesting connection between — Computable Numbers and Normal Numbers

A Note On Normal Numbers

Examining the Work and Its Later Impact Verónica Becher takes a closer look at — Turing’s Note On Normal Numbers

Turing’s Treatise on the Enigma (Prof’s Book)

Frode Weierud on Alan Turing, Dilly Knox, Bayesian statistics, decoding machines and — Prof’s Book: Seen in the Light of Cryptologic History

Excerpts from the ‘Enigma Paper’

Further Aspects of the Work and Its History Tony Sale delves into the cryptographic background to — Alan Turing, the Enigma and the Bombe

Klaus Schmeh looks at – Why Turing Cracked the Enigma and the Germans Did Not

Speech System ‘Delilah’ – Report on Progress

Andrew Hodges Sets the Scene For — The Secrets of Hanslope Park 1944–1945

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

Examining the Work and Its Later Impact: Craig Bauer presents — Alan Turing and Voice Encryption: A Play in Three Acts

John Harper reports on the — Delilah Rebuild Project

Checking a Large Routine

Cliff B. Jones gives a modern assessment of — Turing’s “Checking a Large Routine”

Friday, 24th June. Checking a large routine. by Dr. A. Turing

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

Toby Howard describes — Turing’s Contributions to the Early Manchester Computers

Excerpt from: Programmer’s Handbook for the Manchester Electronic Computer Mark II

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

Anthony Beavers pays homage to —Alan Turing: Mathematical Mechanist

Lecture to the London Mathematical Society on 20 February 1947

Intelligent Machinery

Rodney A. Brooks and — The Case for Embodied Intelligence

Intelligent Machinery

Examining the Work and Its Later Impact: Christof Teuscher proposes — A Modern Perspective on Turing’s Unorganised Machines

Nicholas Gessler connects past and future — The Computerman, the Cryptographer and the Physicist

Stephen Wolfram looks to reconcile — Intelligence and the Computational Universe

Paul Smolensky asks a key question — Cognition: Discrete or Continuous Computation?

Tom Vickers recalls — Alan Turing at the NPL 1945–47

Douglas Hofstadter engages with — The Gödel–Turing Threshold and the Human Soul

Computing Machinery and Intelligence

Gregory Chaitin discovers Alan Turing ‘The Good Philosopher’ at both sides of — Mechanical Intelligence Versus Uncomputable Creativity

Computing Machinery and Intelligence

Examining the Work and Its Later Impact: Daniel Dennett is inspired by — Turing’s “Strange Inversion of Reasoning”

Aaron Sloman draws together —Virtual Machinery and Evolution of Mind (Part 2)

Mark Bishop examines — The Phenomenal Case of the Turing Test and the Chinese Room

Peter Millican on recognising intelligence and — The Philosophical Significance of the Turing Machine and the Turing Test

Luciano Floridi brings out the value of — The Turing Test and the Method of Levels of Abstraction

Aaron Sloman absolves Turing of —The Mythical Turing Test

David Harel proposes — A Turing-Like Test for Modelling Nature

Huma Shah engages with the realities of — Conversation, Deception and Intelligence: Turing’s Question-Answer Game

Kevin Warwick looks forward to — Turing’s Future

Digital Computers Applied to Games

Alan Slomson introduces — Turing and Chess

Digital Computers Applied to Games

Examining the Work and its Later Impact: David Levy delves deeper into — :Alan Turing on Computer Chess

Can Digital Computers Think?: Intelligent Machinery: A Heretical Theory: Can Automatic Calculating Machines Be Said To Think?

B. Jack Copeland introduces the transcripts — Turing and the Physics of the Mind

Can Digital Computers Think?

Intelligent Machinery: A Heretical Theory

Can Automatic Calculating Machines be Said to Think?

Examining the Work and Its Later Impact: Richard Jozsa takes us forward to — Quantum Complexity and the Foundations of Computing

The Chemical Basis of Morphogenesis

Peter Saunders introduces — Alan Turing’s Work in Biology

And Philip K. Maini wonders at — Turing’s Theory of Morphogenesis

The Chemical Basis of Morphogenesis

Examining the Work and Its Later Impact Henri Berestycki on the visionary power of – Alan Turing and Reaction–Diffusion Equations

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

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

Peter T. Saunders observes Alan Turing — Defeating the Argument from Design

Stephen Wolfram fills out the computational view of — The Mechanisms of Biology

K. Vela Velupillai connects — Four Traditions of Emergence: Morphogenesis, Ulam-von Neumann Cellular Automata, The Fermi-Pasta-Ulam Problem, and British Emergentism

Gregory Chaitin takes the story forward — From Turing to Metabiology and Life as Evolving Software

The Morphogen Theory of Phyllotaxis: 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

Bernard Richards recalls Alan Turing and — Radiolaria: the Result of Morphogenesis

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

Part II. Chemical Theory of Morphogenesis

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

Examining the Work and Its Later Impact: Peter Saunders comments on the background to —: Turing’s Morphogen Theory of Phyllotaxis

Jonathan Swinton explores further —: Turing, Morphogenesis, and Fibonacci Phyllotaxis: Life in Pictures

Aaron Sloman travels forward to —: Virtual Machinery and Evolution of Mind (Part 3): Meta-Morphogenesis: Evolution of Information-Processing Machinery

Outline of the Development of the Daisy

Jonathan Swinton’s updating of the texts — An Editorial Note

Outline of the Development of the Daisy

Afterword

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

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

Bernard Richards shares with us — Recollections of Life In the Laboratory With Alan Turing

Bibliography

A Bibliography of Publications of Alan Mathison Turing

Index