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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.

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

Douglas Hofstadter is College of Arts and Sciences Professor of Cognitive Science and Computer Science at Indiana University, Bloomington. His other books include the Pulitzer Prize-winning Gödel, Escher, Bach: an Eternal Golden Braid; Metamagical Themas; The Mind’s I; Fluid Concepts and Creative Analogies; Le Ton beau de Marot; and Surfaces and Essences, with Emmanuel Sander. He lives in Bloomington, Indiana.

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禅宗采纳整体论，并且推向逻辑上的极端。如果整体论是断言事物必须作为一个整体被理解，而非其各个部分的总和，那么禅宗走的更远，认为整个世界根本就不能被划分为一个个事物。划分世界就会误入歧途，因而就不能达到顿悟。

一个人永远也不能给出一个最终的、绝对的证明，去阐明在某个系统中的一个证明是正确的。当然，一个人可以给出一个关于证明的证明，或者关于一个证明的证明的证明——但是，最外层的系统有效性总还是一个未经证明的假设，是凭我们的信仰来接收的

丘奇-图灵论题，简化论形式：全部的大脑过程都可以从一个可计算的基质中导出。

这句话大概是能支持“最终可能实现人工智能”这种观点的最强有力的理论基础。

当然，人工智能的研究并不是以模拟神经原网络为目的，因为它建立在另一种信念之上，即：可能有一些意义重大的智能特征是漂浮在一些与生物大脑的基质完全不同种类的基质之上的。

（乌龟对阿喀琉斯说：你要是只蚂蚁！）你怎么会是只蚂蚁！

How could a myrmedian like you be an ant？

道悟趋禅师问曰：“吾欲求真理，吾应修至何等心境方可求之？”

　　 师曰：“本来无心，故无心境可求；本来无真理，故无由求之。”

　　 道悟：“既无心可修，无真可求，聚这些和尚此处习禅修行何故？”

　　 师曰：“此处并无寸地，这些和尚何以聚得？吾口中无舌，何以集而教之？”

　　 道悟：“师何以言谎？”

　　 师曰：“吾既无舌语人，何能言谎？”

　　 道悟：“吾不了师言。”

　 师曰：“吾亦不自了。”

书籍介绍

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.