副标题: An Eternal Golden Braid
作者: Douglas R. Hofstadter
出版社: Basic Books
出版年: 1999-1-15
页数: 832
定价: GBP 12.99
装帧: Paperback
ISBN: 9780465026562
作者: Douglas R. Hofstadter
出版社: Basic Books
出版年: 1999-1-15
页数: 832
定价: GBP 12.99
装帧: Paperback
ISBN: 9780465026562
内容简介 · · · · · ·
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 l... (展开全部)
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.
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.
目录 · · · · · ·
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
· · · · · · (更多)
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
· · · · · · (更多)
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
· · · · · · (收起)
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
· · · · · · (收起)
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按有用程度 按页码先后 最新笔记
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第94页
A full formalization of geometry would take the drastic step of making _every_ term undefined---that is, turning every term into a "meaningless" symbol of a formal system. I put quotes around "meaningless" because ... the symbols automatically pick up passive meanings in accordance with the theorems they occur in. It is another question, though, whether people discover those me... (更多)A full formalization of geometry would take the drastic step of making _every_ term undefined---that is, turning every term into a "meaningless" symbol of a formal system. I put quotes around "meaningless" because ... the symbols automatically pick up passive meanings in accordance with the theorems they occur in. It is another question, though, whether people discover those meanings, for to do so requires finding a set of concepts which can be linked by an isomorphism to the symbols in the formal system. If one begins with the aim of formalizing geometry, presumably one has an _intended_ interpretation for each symbol, so that the passive meanings are built into the system.
(收起)consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.
2011-12-04 09:35:44 回应
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第79页
Tortoise: ... By the way, did you know that each of the four letters in Bach's name is the name of a musical note? Achilles: 'tisn't possible, is it? After all, musical notes only go from 'A' through 'G'. Tortoise: Just so; in most countries, that's the case. But in Germany, Bach's own homeland, the convention has always been similar, except that what we call 'B', they call 'H', and what w... (更多)
(收起)Tortoise: ... By the way, did you know that each of the four letters in Bach's name is the name of a musical note? Achilles: 'tisn't possible, is it? After all, musical notes only go from 'A' through 'G'. Tortoise: Just so; in most countries, that's the case. But in Germany, Bach's own homeland, the convention has always been similar, except that what we call 'B', they call 'H', and what we call 'B-flat', they call 'B'. For instance, we talk about Bach's "Mass in B Minor", whereas they talk about his "H-moll Messe".
2011-12-01 07:28:07 回应
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第78页
By elaborate calculations, its little computer figured out what effects the sounds would have upon its phonograph. If it deduced that the sounds were such that they would cause the machine in its present configuration to break, then it did something very clever. Old omega contained a device which could disassemble large parts of its phonograph subunit, and rebuild them in new ways, so that it coul... (更多)
This is like switching to a new gauge to avoid multi-valuedness in the wavefunction phase. Now, we know the flux can never be avioded simply by gauge transformations... (收起)By elaborate calculations, its little computer figured out what effects the sounds would have upon its phonograph. If it deduced that the sounds were such that they would cause the machine in its present configuration to break, then it did something very clever. Old omega contained a device which could disassemble large parts of its phonograph subunit, and rebuild them in new ways, so that it could, in effect, change its own structure. If the sounds were "dangerous", a new configuration was chosen, one to which the sounds would pose no threat, and this new configuration would then be built by the rebuilding subunit, under direction of the little computer. Only after this rebuilding operation would Record Player Omega attempt to play the record.
2011-12-01 07:14:05 回应
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第10页
What makes this canon different from any other, however, is that when it concludes---or, rather, seems to conclude---it is no longer in the key of C minor, but now is in D minor. Somehow Bach has contrived to modulate (change keys) right under the listener's nose. And it is so constructed that this "ending" ties smoothly onto the beginning again; thus one can repeat the process and retur... (更多)
That's a Wannier flow in the Hofstadter problem right there. (收起)What makes this canon different from any other, however, is that when it concludes---or, rather, seems to conclude---it is no longer in the key of C minor, but now is in D minor. Somehow Bach has contrived to modulate (change keys) right under the listener's nose. And it is so constructed that this "ending" ties smoothly onto the beginning again; thus one can repeat the process and return in the key of E, only to join again to the beginning.
2011-11-20 10:33:04 回应
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第15页
Implicit in the concept of Strange Loops is the concept of infinity, since what else is a loop but a way of representing an endless process in a finite way? (更多)
(收起)Implicit in the concept of Strange Loops is the concept of infinity, since what else is a loop but a way of representing an endless process in a finite way?
2011-11-20 10:49:27 回应
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第18页
Whereas the Epimenides statement creates a paradox since it is neither true nor false, the Godel sentence G is unprovable (inside Principia Mathematica) but true. The grand conclusin? That the system of Principia Mathematica is "incomplete"---there are true statements of number theory which its methods of proof are too weak to demonstrate. In short, Godel showed that provability is a ... (更多)Whereas the Epimenides statement creates a paradox since it is neither true nor false, the Godel sentence G is unprovable (inside Principia Mathematica) but true. The grand conclusin? That the system of Principia Mathematica is "incomplete"---there are true statements of number theory which its methods of proof are too weak to demonstrate.
(收起)In short, Godel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.
2011-11-20 11:01:14 回应
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第94页
A full formalization of geometry would take the drastic step of making _every_ term undefined---that is, turning every term into a "meaningless" symbol of a formal system. I put quotes around "meaningless" because ... the symbols automatically pick up passive meanings in accordance with the theorems they occur in. It is another question, though, whether people discover those me... (更多)A full formalization of geometry would take the drastic step of making _every_ term undefined---that is, turning every term into a "meaningless" symbol of a formal system. I put quotes around "meaningless" because ... the symbols automatically pick up passive meanings in accordance with the theorems they occur in. It is another question, though, whether people discover those meanings, for to do so requires finding a set of concepts which can be linked by an isomorphism to the symbols in the formal system. If one begins with the aim of formalizing geometry, presumably one has an _intended_ interpretation for each symbol, so that the passive meanings are built into the system.
(收起)consistency is not a property of a formal system per se, but depends on the interpretation which is proposed for it. By the same token, inconsistency is not an intrinsic property of any formal system.
2011-12-04 09:35:44 回应
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第79页
Tortoise: ... By the way, did you know that each of the four letters in Bach's name is the name of a musical note? Achilles: 'tisn't possible, is it? After all, musical notes only go from 'A' through 'G'. Tortoise: Just so; in most countries, that's the case. But in Germany, Bach's own homeland, the convention has always been similar, except that what we call 'B', they call 'H', and what w... (更多)
(收起)Tortoise: ... By the way, did you know that each of the four letters in Bach's name is the name of a musical note? Achilles: 'tisn't possible, is it? After all, musical notes only go from 'A' through 'G'. Tortoise: Just so; in most countries, that's the case. But in Germany, Bach's own homeland, the convention has always been similar, except that what we call 'B', they call 'H', and what we call 'B-flat', they call 'B'. For instance, we talk about Bach's "Mass in B Minor", whereas they talk about his "H-moll Messe".
2011-12-01 07:28:07 回应
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第78页
By elaborate calculations, its little computer figured out what effects the sounds would have upon its phonograph. If it deduced that the sounds were such that they would cause the machine in its present configuration to break, then it did something very clever. Old omega contained a device which could disassemble large parts of its phonograph subunit, and rebuild them in new ways, so that it coul... (更多)
This is like switching to a new gauge to avoid multi-valuedness in the wavefunction phase. Now, we know the flux can never be avioded simply by gauge transformations... (收起)By elaborate calculations, its little computer figured out what effects the sounds would have upon its phonograph. If it deduced that the sounds were such that they would cause the machine in its present configuration to break, then it did something very clever. Old omega contained a device which could disassemble large parts of its phonograph subunit, and rebuild them in new ways, so that it could, in effect, change its own structure. If the sounds were "dangerous", a new configuration was chosen, one to which the sounds would pose no threat, and this new configuration would then be built by the rebuilding subunit, under direction of the little computer. Only after this rebuilding operation would Record Player Omega attempt to play the record.
2011-12-01 07:14:05 回应
书评 · · · · · · (共42条) 我来评论这本书
热门评论 最新评论
What is this book really about?
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- 狮子真好吃啊(拼死拼活订了4张票) 我觉得这个问题最好在读这书之前就搞清楚。 太多人觉得这书在玩文字游戏,故弄玄虚。天大的冤枉啊,无论是Bach还是escher, 其实都是用来解释书中概念的analogy. 下面是作者接受wired的采访时说的,标题就叫“by analogy": I can see that many people didn't ...... (12回应)2006-01-06 36/37有用来自 商务印书馆1996版
开卷有益
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- 健柒 读到一半,是看了前面老兄的推荐买的,不过可是原价一分不差买的,看了杭州的兄弟能5元到手,气愤ing.不过到不是很心痛. 先说说表面印象,书是商务出的,北大人翻译,质量应该是可以信任的.但可能是商务体恤我们读书人攮中羞涩的原因,做成一大本,读起来颇不方便,但其好意心领了.否则按目下的风气,还不做成一套四五大本,全套下来...... (17回应)2005-11-24 52/65有用来自 商务印书馆1996版
空前的奇书
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- 丁丁虫(3/3 0/6) 关于这本书,确实只有“奇书”两个字可以形容。它的奇不但在于原文的奇妙,也在于翻译者的奇妙。能将这本书翻译成如此味道,恐怕并不比写出这样一本书更容易。 至于书的内容——就去看介绍吧。我所能说的是,介绍里没有一个字是缪赞。...... (6回应)2005-06-17 21/25有用来自 商务印书馆1996版
艺术和科学的界限和差异
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- 私人青銅(乍寒還暖時候,更難將息) 记得曾经有一本书叫作两种文化,作者试图探讨人文/社会科学和自然科学之间的差异和类似。 毫无疑问,EGB这本书,非常优美的展示了科学和艺术之间,在结构和推演形式上的相似性,而这本书的译者,通过卓越的翻译和再创作工作,指出了在不同语言文化的环境中,还原思想的根本含义,或者说元含义的可能性。 本书是一本关于逻辑拓扑学的基...... (2回应)2006-07-20 13/14有用来自 商务印书馆1996版
集异璧之螃蟹卡农
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- 近乎想象(我需要一块二向箔,清理用。) 试试反着念。 假如书的结局,在你刚开始读时就知道,没有任何悬念的话会很糟糕,不是吗? 不,不!至少这件事你可以得意吧。你读完了那本书:集异璧之大成:哥德尔,艾舍尔,巴赫。 我当然知道,你没听过数学家哥德尔,画家艾舍尔,只知道巴赫。他是个伟大的音乐家。没听过他的“螃蟹卡农”?把一首曲子按正反顺序播出来,结果都一样?...... (6回应)2006-11-19 16/20有用来自 商务印书馆1996版
Untitled
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- Toornaadoo(心一下就变老) "中译本前后费时十余年,译者都是数学和哲学的专家,还得到原作者的直接参与,译文严谨通达,特别是在原作者的帮助下,把西方的文化典故和说法,尽可能转换为中国文化的典故和说法,使这部译本甚至可看作是一部新的创作,也是中外翻译史上的一个创举。" 书的创意很赞,翻译更是杰出的第二次创作。这种翻译方式我还是第一次见到。 ......2012-01-27 来自 商务印书馆1996版
螃蟹卡农,莫比乌斯。怪圈自指,悖论丛生。层叠穿梭...
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- Cliff Cui 绝壁:大义觉迷(节选) 仰望苍穹,浩渺烟波。物之博大,无若天地。阴阳四时,刚柔四维。天体动静,日月星辰。地体太少,水火土石。暑寒昼夜,性情形体承变有感。雨风露雷,走飞草木受化有应。春夏秋冬,生长收藏。动植类起,人灵万物。体用交备,人物之理。万世万物,昊圣一道。以物观物,窥开物理照破人情。明镜止水,出入造化进退古今......2012-01-25 来自 商务印书馆1996版
三十岁的时候……
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- 黑猫阿姨(自强不息,厚德载物) 三十岁的时候,我们在干什么? 三十岁的时候,侯世达已经写出了《哥德尔、艾舍尔、巴赫》一书; 三十岁的时候,我开始读这本“集异璧之大成”…… 从古典的音乐、数学、绘画到现代的计算机科学、人工智能、认知科学,侯世达似乎无所不能; 从“禅宗公案”到“对位藏头诗”,侯世达对中国文化的精通又令我等汗颜…… 在所有这些的...... (3回应)2011-11-26 来自 商务印书馆1996版
歌德尔不完全性定理
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- 勤天(智慧是一个由知识构成的生态系统) 本来这个国庆是想好好搞搞iPhone开发的。无奈这本书实在是给大脑做马杀机,舒爽无比。所以整个国庆节就耗在这本书上了,导致计划没有执行,节过完了还有一种负罪感。 在这上面花的时间究竟值不值? 这本书丰富了我的思维模型,带了一种新的思维的维度。 看了这本书之后再拿起编译原理来看,再拿起Lisp的书来看,居然可......2011-10-10 来自 商务印书馆1996版
本书序言, 即我的哲学笔记(篇六)2010-05-21
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- STONEMAN 相比于厚厚的正文部份,《哥德尔、埃舍尔、巴赫》这本书的序言在我看它的第一眼起就一下子吸引了我。著者显然对这本书的翻译非常满意并津津乐道——作者序通篇讲述了本书的翻译过程。 本书的作者是一位美国人,他在著作《哥德尔、埃舍尔、巴赫》,或称其英文名《GEB》中应用了大量的英文原生态的文字技巧...... (2回应)2011-09-21 来自 商务印书馆1996版
san
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- algebraization 高中时就有,装帧跟商务印书馆同时期出版的[《语言哲学》马蒂尼奇]一摸一样.其内容颇有点像当年莱布尼兹给贵|妇太|太们写得通俗版哲学读物,只是当今快节奏的社会里权|贵的贵|妇太|太们这点附庸风雅的样子也免了. 讲4点: 1 一本元数学方面的科普读物,跟音乐创作和欣赏进行大量类比.个人以为牵强附会.但也容易理解,因为阳......2011-09-05 来自 商务印书馆1996版
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这本书的其他版本 · · · · · · ( 全部18 )
- 商务印书馆版 1996-8 / 1446人读过 / 有售
- 未知出版社版 0
- Penguin版 2000-03-30 / 36人读过 / 有售
- Penguin Books Ltd版 1994-11 / 5人读过
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