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The Annotated Turing


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Table of Contents

Introduction vii I Foundations 1 1 This Tomb Holds Diophantus 3 2 The Irrational and the Transcendental 13 3 Centuries of Progress 35 II Computable Numbers 55 4 The Education of Alan Turing 57 5 Machines at Work 79 6 Addition and Multiplication 97 7 Also Known as Subroutines 111 8 Everything Is a Number 127 9 The Universal Machine 143 10 Computers and Computability 163 11 Of Machines and Men 189 III Das Entscheidungsproblem 199 12 Logic and Computability 201 13 Computable Functions 231 14 The Major Proof 259 15 The Lambda Calculus 281 16 Conceiving the Continuum 299 IV And Beyond 323 17 Is Everything a Turing Machine? 325 18 The Long Sleep of Diophantus 351 Selected Bibliography 361 Index 366

About the Author

English mathematician Alan Turing (1912?1954) is the author of the 1936 paper "On Computable Numbers, with an Application to the Entscheidungsproblem" that introduced the imaginary computer called the Turing Machine for understanding the nature and limitations of computing. His famous 1950 article "Computing Machinery and Intelligence" introduced the Turing Test for gauging artificial intelligence. American writer Charles Petzold (1953?) is the author of the acclaimed 1999 book Code: The Hidden Language of Computer Hardware and Software, a unique exploration into the digital technologies of computers. He is also the author of hundreds of articles about computer programming, as well as several books on writing programs that run under Microsoft Windows. His Web site is

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