欢迎来到得力文库 - 分享文档赚钱的网站! | 帮助中心 好文档才是您的得力助手!
得力文库 - 分享文档赚钱的网站
全部分类
  • 研究报告>
  • 管理文献>
  • 标准材料>
  • 技术资料>
  • 教育专区>
  • 应用文书>
  • 生活休闲>
  • 考试试题>
  • pptx模板>
  • 工商注册>
  • 期刊短文>
  • 图片设计>
  • ImageVerifierCode 换一换

    GEBenGodel Escher Bach-永恒的金色辫子an Eternal Golden Braid.doc

    • 资源ID:76391269       资源大小:17.85MB        全文页数:799页
    • 资源格式: DOC        下载积分:22金币
    快捷下载 游客一键下载
    会员登录下载
    微信登录下载
    三方登录下载: 微信开放平台登录   QQ登录  
    二维码
    微信扫一扫登录
    下载资源需要22金币
    邮箱/手机:
    温馨提示:
    快捷下载时,用户名和密码都是您填写的邮箱或者手机号,方便查询和重复下载(系统自动生成)。
    如填写123,账号就是123,密码也是123。
    支付方式: 支付宝    微信支付   
    验证码:   换一换

     
    账号:
    密码:
    验证码:   换一换
      忘记密码?
        
    友情提示
    2、PDF文件下载后,可能会被浏览器默认打开,此种情况可以点击浏览器菜单,保存网页到桌面,就可以正常下载了。
    3、本站不支持迅雷下载,请使用电脑自带的IE浏览器,或者360浏览器、谷歌浏览器下载即可。
    4、本站资源下载后的文档和图纸-无水印,预览文档经过压缩,下载后原文更清晰。
    5、试题试卷类文档,如果标题没有明确说明有答案则都视为没有答案,请知晓。

    GEBenGodel Escher Bach-永恒的金色辫子an Eternal Golden Braid.doc

    ContentsOverviewviiiList of IllustrationsxivWords of ThanksxixPart I: GEBIntroduction: A Musico-Logical Offering3Three-Part Invention29Chapter I: The MU-puzzle33Two-Part Invention43Chapter II: Meaning and Form in Mathematics46Sonata for Unaccompanied Achilles61Chapter III: Figure and Ground64Contracrostipunctus75Chapter IV: Consistency, Completeness, and Geometry82Little Harmonic Labyrinth103Chapter V: Recursive Structures and Processes127Canon by Intervallic Augmentation153Chapter VI: The Location of Meaning158Chromatic Fantasy, And Feud177Chapter VII: The Propositional Calculus181Crab Canon199Chapter VIII: Typographical Number Theory204A Mu Offering231Chapter IX: Mumon and Gödel246ContentsIIPart II EGBPrelude .275Chapter X: Levels of Description, and Computer Systems285Ant Fugue311Chapter XI: Brains and Thoughts337English French German Suit366Chapter XII: Minds and Thoughts369Aria with Diverse Variations391Chapter XIII: BlooP and FlooP and GlooP406Air on G's String431Chapter XIV: On Formally Undecidable Propositions of TNTand Related Systems438Birthday Cantatatata .461Chapter XV: Jumping out of the System465Edifying Thoughts of a Tobacco Smoker480Chapter XVI: Self-Ref and Self-Rep495The Magn fierab, Indeed549Chapter XVII: Church, Turing, Tarski, and Others559SHRDLU, Toy of Man's Designing586Chapter XVIII: Artificial Intelligence: Retrospects594Contrafactus633Chapter XIX: Artificial Intelligence: Prospects641Sloth Canon681Chapter XX: Strange Loops, Or Tangled Hierarchies684Six-Part Ricercar720Notes743Bibliography746Credits757Index759ContentsIIIOverviewPart I: GEBIntroduction: A Musico-Logical Offering. The book opens with the story of Bach's Musical Offering. Bach made an impromptu visit to King Frederick the Great of Prussia, and was requested to improvise upon a theme presented by the King. His improvisations formed the basis of that great work. The Musical Offering and its story form a theme upon which I "improvise" throughout the book, thus making a sort of "Metamusical Offering". Self-reference and the interplay between different levels in Bach are discussed: this leads to a discussion of parallel ideas in Escher's drawings and then Gödels Theorem. A brief presentation of the history of logic and paradoxes is given as background for Gödels Theorem. This leads to mechanical reasoning and computers, and the debate about whether Artificial Intelligence is possible. I close with an explanation of the origins of the book-particularly the why and wherefore of the Dialogues.Three-Part Invention. Bach wrote fifteen three-part inventions. In this three-part Dialogue, the Tortoise and Achilles-the main fictional protagonists in the Dialogues-are "invented" by Zeno (as in fact they were, to illustrate Zeno's paradoxes of motion). Very short, it simply gives the flavor of the Dialogues to come.Chapter I: The MU-puzzle. A simple formal system (the MIL'-system) is presented, and the reader is urged to work out a puzzle to gain familiarity with formal systems in general. A number of fundamental notions are introduced: string, theorem, axiom, rule of inference, derivation, formal system, decision procedure, working inside/outside the system.Two-Part Invention. Bach also wrote fifteen two-part inventions. This two-part Dialogue was written not by me, but by Lewis Carroll in 1895. Carroll borrowed Achilles and the Tortoise from Zeno, and I in turn borrowed them from Carroll. The topic is the relation between reasoning, reasoning about reasoning, reasoning about reasoning about reasoning, and so on. It parallels, in a way, Zeno's paradoxes about the impossibility of motion, seeming to show, by using infinite regress, that reasoning is impossible. It is a beautiful paradox, and is referred to several times later in the book.Chapter II: Meaning and Form in Mathematics. A new formal system (the pq-system) is presented, even simpler than the MIU-system of Chapter I. Apparently meaningless at first, its symbols are suddenly revealed to possess meaning by virtue of the form of the theorems they appear in. This revelation is the first important insight into meaning: its deep connection to isomorphism. Various issues related to meaning are then discussed, such as truth, proof, symbol manipulation, and the elusive concept, "form".Sonata for Unaccompanied Achilles. A Dialogue which imitates the Bach Sonatas for unaccompanied violin. In particular, Achilles is the only speaker, since it is a transcript of one end of a telephone call, at the far end of which is the Tortoise. Their conversation concerns the concepts of "figure" and "ground" in variousOverviewIVcontexts- e.g., Escher's art. The Dialogue itself forms an example of the distinction, since Achilles' lines form a "figure", and the Tortoise's lines-implicit in Achilles' lines-form a "ground".Chapter III: Figure and Ground. The distinction between figure and ground in art is compared to the distinction between theorems and nontheorems in formal systems. The question "Does a figure necessarily contain the same information as its ground%" leads to the distinction between recursively enumerable sets and recursive sets.Contracrostipunctus. This Dialogue is central to the book, for it contains a set of paraphrases of Gödels self-referential construction and of his Incompleteness Theorem. One of the paraphrases of the Theorem says, "For each record player there is a record which it cannot play." The Dialogue's title is a cross between the word "acrostic" and the word "contrapunctus", a Latin word which Bach used to denote the many fugues and canons making up his Art of the Fugue. Some explicit references to the Art of the Fugue are made. The Dialogue itself conceals some acrostic tricks.Chapter IV: Consistency, Completeness, and Geometry. The preceding Dialogue is explicated to the extent it is possible at this stage. This leads back to the question of how and when symbols in a formal system acquire meaning. The history of Euclidean and non-Euclidean geometry is given, as an illustration of the elusive notion of "undefined terms". This leads to ideas about the consistency of different and possibly "rival" geometries. Through this discussion the notion of undefined terms is clarified, and the relation of undefined terms to perception and thought processes is considered.Little Harmonic Labyrinth. This is based on the Bach organ piece by the same name. It is a playful introduction to the notion of recursive-i.e., nested structures. It contains stories within stories. The frame story, instead of finishing as expected, is left open, so the reader is left dangling without resolution. One nested story concerns modulation in music-particularly an organ piece which ends in the wrong key, leaving the listener dangling without resolution.Chapter V: Recursive Structures and Processes . The idea of recursion is presented in many different contexts: musical patterns, linguistic patterns, geometric structures, mathematical functions, physical theories, computer programs, and others.Canon by Intervallic Augmentation. Achilles and the Tortoise try to resolve the question, "Which contains more information-a record, or the phonograph which plays it This odd question arises when the Tortoise describes a single record which, when played on a set of different phonographs, produces two quite different melodies: B-A-C -H and C-A-G-E. It turns out, however, that these melodies are "the same", in a peculiar sense.Chapter VI: The Location of Meaning. A broad discussion of how meaning is split among coded message, decoder, and receiver. Examples presented include strands of DNA, undeciphered inscriptions on ancient tablets, and phonograph records sailing out in space. The relationship of intelligence to "absolute" meaning is postulated.Chromatic Fantasy, And Feud. A short Dialogue bearing hardly any resemblance, except in title, to Bach's Chromatic Fantasy and Fugue. It concerns the proper way to manipulate sentences so as to preserve truth-and in particular the questionOverviewVof whether there exist rules for the usage of the word "arid". This Dialogue has much in common with the Dialogue by Lewis Carroll.Chapter VII: The Propositional Calculus. It is suggested how words such as .,and" can be governed by formal rules. Once again, the ideas of isomorphism and automatic acquisition of meaning by symbols in such a system are brought up. All the examples in this Chapter, incidentally, are "Zentences"-sentences taken from Zen koans. This is purposefully done, somewhat tongue-in-cheek, since Zen koans are deliberately illogical stories.Crab Canon. A Dialogue based on a piece by the same name from the Musical Offering. Both are so named because crabs (supposedly) walk backwards. The Crab makes his first appearance in this Dialogue. It is perhaps the densest Dialogue in the book in terms of formal trickery and level-play. Gödel, Escher, and Bach are deeply intertwined in this very short Dialogue.Chapter VIII: Typographical Number Theory. An extension of the Propositional Calculus called "TNT" is presented. In TNT, number-theoretical reasoning can be done by rigid symbol manipulation. Differences between formal reasoning and human thought are considered.A Mu Offering. This Dialogue foreshadows several new topics in the book. Ostensibly concerned with Zen Buddhism and koans, it is actually a thinly veiled discussion of theoremhood and nontheoremhood, truth and falsity, of strings in number theory. There are fleeting references to molecular biology- particular) the Genetic Code. There is no close affinity to the Musical Offering, other than in the title and the playing of self-referential games.Chapter IX: Mumon and Gödel. An attempt is made to talk about the strange ideas of Zen Buddhism. The Zen monk Mumon, who gave well known commentaries on many koans, is a central figure. In a way, Zen ideas bear a metaphorical resemblance to some contemporary ideas in the philosophy of mathematics. After this "Zennery", Gödels fundamental idea of Gödel-numbering is introduced, and a first pass through Gödels Theorem is made.Part II: EGBPrelude . This Dialogue attaches to the next one. They are based on preludes and fugues from Bach's Well-Tempered Clavier. Achilles and the Tortoise bring a present to the Crab, who has a guest: the Anteater. The present turns out to be a recording of the W.T.C.; it is immediately put on. As they listen to a prelude, they discuss the structure of preludes and fugues, which leads Achilles to ask how to hear a fugue: as a whole, or as a sum of parts? This is the debate between holism and reductionism, which is soon taken up in the Ant Fugue.Chapter X: Levels of Description, and Computer Systems. Various levels of seeing pictures, chessboards, and computer systems are discussed. The last of these is then examined in detail. This involves describing machine languages, assembly languages, compiler languages, operating systems, and so forth. Then the discussion turns to composite systems of other types, such as sports teams, nuclei, atoms, the weather, and so forth. The question arises as to how man intermediate levels exist-or indeed whether any exist.OverviewVIAnt Fugue. An imitation of a musical fugue: each voice enters with the same statement. The theme-holism versus reductionism-is introduced in a recursive picture composed of words composed of smaller words. etc. The words which appear on the four levels of this strange picture are "HOLISM", "REDLCTIONIsM", and "ML". The discussion veers off to a friend of the Anteater's Aunt Hillary, a conscious ant colony. The various levels of her thought processes are the topic of discussion. Many fugal tricks are ensconced in the Dialogue. As a hint to the reader, references are made to parallel tricks occurring in the fugue on the record to which the foursome is listening. At the end of the Ant Fugue, themes from the Prelude return. transformed considerably.Chapter XI: Brains and Thoughts. "How can thoughts he supported by the hardware of the brain is the topic of the Chapter. An overview of the large scale and small-scale structure of the brain is first given. Then the relation between concepts and neural activity is speculatively discussed in some detail.English French German Suite. An interlude consisting of Lewis Carroll's nonsense poem "Jabberwocky' together with two translations: one into French and one into German, both done last century.Chapter XII: Minds and Thoughts. The preceding poems bring up in a forceful way the question of whether languages, or indeed minds, can be "mapped" onto each other. How is communication possible between two separate physical brains: What do all human brains have in common? A geographical analogy is used to suggest an answer. The question arises, "Can a brain be understood, in some objective sense, by an outsider?"Aria with Diverse Variations. A Dialogue whose form is based on Bach's Goldberg Variations, and whose content is related to number-theoretical problems such as the Goldbach conjecture. This hybrid has as its main purpose to show how number theory's subtlety stems from the fact that there are many diverse variations on the theme of searching through an infinite space. Some of them lead to infinite searches, some of them lead to finite searches, while some others hover in between.Chapter XIII: BlooP and FlooP and GlooP. These are the names of three computer languages. BlooP programs can carry out only predictably finite searches, while FlooP programs can carry out unpredictable or even infinite searches. The purpose of this Chapter is to give an intuition for the notions of primitive recursive and general recursive functions in number theory, for they are essential in Gödels proof.Air on G's String. A Dialogue in which Gödels self-referential construction is mirrored in words.The idea is due to W. V. O. Quine. This Dialogue serves as a prototype for the next Chapter.Chapter XIV: On Formally Undecidable Propositions of TNT and Related Systems. This Chapter's title is an adaptation of the title of Gödels 1931 article, in which his Incompleteness Theorem was first published. The two major parts of Gödels proof are gone through carefully. It is shown how the assumption of consistency of TNT forces one to conclude that TNT (or any similar system) is incomplete. Relations to Euclidean and non-Euclidean geometry are discussed. Implications for the philosophy of mathematics are gone into w

    注意事项

    本文(GEBenGodel Escher Bach-永恒的金色辫子an Eternal Golden Braid.doc)为本站会员(阿***)主动上传,得力文库 - 分享文档赚钱的网站仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对上载内容本身不做任何修改或编辑。 若此文所含内容侵犯了您的版权或隐私,请立即通知得力文库 - 分享文档赚钱的网站(点击联系客服),我们立即给予删除!

    温馨提示:如果因为网速或其他原因下载失败请重新下载,重复下载不扣分。




    关于得利文库 - 版权申诉 - 用户使用规则 - 积分规则 - 联系我们

    本站为文档C TO C交易模式,本站只提供存储空间、用户上传的文档直接被用户下载,本站只是中间服务平台,本站所有文档下载所得的收益归上传人(含作者)所有。本站仅对用户上传内容的表现方式做保护处理,对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私,请立即通知得利文库网,我们立即给予删除!客服QQ:136780468 微信:18945177775 电话:18904686070

    工信部备案号:黑ICP备15003705号-8 |  经营许可证:黑B2-20190332号 |   黑公网安备:91230400333293403D

    © 2020-2023 www.deliwenku.com 得利文库. All Rights Reserved 黑龙江转换宝科技有限公司 

    黑龙江省互联网违法和不良信息举报
    举报电话:0468-3380021 邮箱:hgswwxb@163.com  

    收起
    展开