List of Contributors Introduction Part I How Do We Compute？ What Can We Prove？ 1955 Alan Matbison Turing by Max Newman（Bibliographic Memoirs of the Fellows of the Royal Society， 1 （Nov．），253-263） Andrew Hodges contributes——A Comment on Newman's Biographical Memoir Biographical Memoir 1936-7 On Computable Numbers， with an Application to the Entscheidungsproblem（Proc． Lond． Math． Soc． （2）42， 230-265） 1937 - A Correction （ibid： 43， 544-546） Christos Papadimitriou on ——Alan and I Turing texts 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 toTuring 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 Jiri 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 ——NOT 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 1937 On Computable Numbers， with an Application to the Entscheidungsproblem by A． M． Turing - Review by：Alonzo Church（J．Symb．Log．2，42） Andrew Hodges finds significance in ——Church's Review of Computable Numbers 1937 Computability and λ-Definability（J． Symb． Log． 2， 153-63） Henk Barendregt， Giulio Manzonetto and Rinus Plasmeijertrace through to today ——The Imperative and Functional Programming Paradigm Turing text 1937 The p-Function in λ-K Conversion（J．Symb．Log．2，164） Henk Barendregt and Giulio Manzonetto point out the subtleties of——Turing's Contributions to Lambda Calculus Turing text Part Ⅱ Hiding and Unhiding Information： Cryptoloty，Complexity and Unmber Theory Part Ⅲ Building a Brain： Intelligent Machines，Practice and Theory Part Ⅳ The Mathematics of Emergence： The Mysteries of Morphogenesis Afterword Bibliography Index
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