Alan Turing · His Work and Impact by Cooper, S. Barry -- Read -- Imperial Library of Trantor

Index

Cover image Title page Table of Contents Copyright 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

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