Gödel, Escher, Bach
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An Eternal Golden Braid
Douglas R. Hofstadter
简介
Twenty years after it topped the bestseller charts, Douglas R. Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid is still something of a marvel. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. It also looks at the prospects for computers and artificial intelligence (AI) for mimicking human thought. For the general reader and the computer techie alike, this book still sets a standard for thinking about the future of computers and their relation to the way we think.
Topics Covered: J.S. Bach, M.C. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.
contents
Overview
List of Illustrations
Words of Thanks
Pt. I GEB
Introduction: A Musico-Logical Offering : Three-Part Invention
Ch. I The MU-puzzle : Two-Part Invention
Ch. II Meaning and Form in Mathematics : Sonata for Unaccompanied Achilles
Ch. III Figure and Ground : Contracrostipunctus
Ch. IV Consistency, Completeness, and Geometry : Little Harmonic Labyrinth
Ch. V Recursive Structures and Processes : Canon by Intervallic Augmentation
Ch. VI The Location of Meaning : Chromatic Fantasy, And Feud
Ch. VII The Propositional Calculus : Crab Canon
Ch. VIII Typographical Number Theory : A Mu Offering
Ch. IX Mumon and Godel
Pt. II EGB
Prelude ...
Ch. X Levels of Description, and Computer Systems : ... Ant Fugue
Ch. XI Brains and Thoughts : English French German Suite
Ch. XII Minds and Thoughts : Aria with Diverse Variations
Ch. XIII BlooP and FlooP and GlooP : Air on G's String
Ch. XIV On Formally Undecidable Propositions of TNT and Related Systems : Birthday Cantatatata ...
Ch. XV Jumping out of the System : Edifying Thoughts of a Tobacco Smoker
Ch. XVI Self-Ref and Self-Rep : The Magnificrab, Indeed
Ch. XVII Church, Turing, Tarski, and Others : SHRDLU, Toy of Man's Designing
Ch. XVIII Artificial Intelligence: Retrospects : Contrafactus
Ch. XIX Artificial Intelligence: Prospects : Sloth Canon
Ch. XX Strange Loops, Or Tangled Hierarchies : Six-Part Ricercar
Notes
Bibliography
Credits
Index
