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Encyclopedia > Gödel, Escher, Bach
GEB cover

Gödel, Escher, Bach: an Eternal Golden Braid is a Pulitzer Prize-winning book by Douglas Hofstadter, first published in by Basic Books. A new preface by Hofstadter accompanied an otherwise unchanged 20th anniversary edition (ISBN 0465026567) released in 1999. book cover to Douglas Hofstadters GEB This image is a book cover. ... book cover to Douglas Hofstadters GEB This image is a book cover. ... The Pulitzer Prize is a United States award regarded as the highest honor in print journalism. ... Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ... 1999 is a common year starting on Friday of the Common Era, and was designated the International Year of Older Persons by the United Nations. ...

At one level, it is a book about how the creative achievements of logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach interweave. As the author states: "I realized that to me, Gödel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object, and came up with this book." Logic (from ancient Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is the study of arguments. ... Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... An artist is someone who employs creative talent to produce works of art. ... Self portrait, 1943¹ Maurits Cornelis Escher (Leeuwarden, June 17, 1898 - Laren, March 27, 1972) was a Dutch artist most known for his woodcuts, lithographs and mezzotints, which tend to feature impossible constructions, explorations of infinity, and tessellations. ... A composer is a person who writes music. ... Johann Sebastian Bach, 1748 portrait by Elias Gottlob Haussmann Johann Sebastian Bach (March 21, 1685[1] (O.S.) – July 28, 1750[2] (N.S.)) was a German composer and organist of the Baroque period, and is universally regarded as one of the greatest composers of all time. ...

At a deeper level, however, the discussion of these three artists is not actually what the book is about. It is used as a device to illuminate the central theme of the book, which Hofstadter states is this: "Do words and thoughts follow formal rules, or do they not?" (In the preface to the twentieth-anniversary edition, Hofstadter laments that his book has been misperceived as a hodge-podge of neat things when it really has a central, organizing theme. He restates that same central theme in this way: "GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle?")

The book takes the form of an interweaving of various narratives. The main chapters alternate with dialogues between imaginary characters, inspired by Lewis Carroll's "What the Tortoise Said to Achilles", which features in the book. In this, Achilles and the Tortoise discuss a paradox related to modus ponens. Hofstadter bases the other dialogues on this one, introducing the Crab and a Genie, among others. Photograph of Lewis Carroll taken by himself, with assistance Charles Lutwidge Dodgson (January 27, 1832 – January 14, 1898), better known by the pen name Lewis Carroll, was a British author, mathematician, logician, Anglican clergyman and photographer. ... What the Tortoise Said to Achilles is a brief dialog by Lewis Carroll which playfully problematizes the foundations of logic. ... For other uses, see Achilles (disambiguation). ... Modus ponens (Latin: mode that affirms) is a valid, simple argument form (often abbreviated to MP): If P, then Q. P. Therefore, Q. or in logical operator notation: where represents the logical assertion. ...

Word play features prominently: the initials of the four main dialog characters are G, C, A, and T -- the base-pairs in DNA. Some puns may be found quite atrocious, but forgivable for the breadth of the connection they make between ideas: "the MagnifiCrab, Indeed" (Bach's Magnificat in D), "SHRDLU, Toy of Man's Designing" (Bach's Jesu, Joy of Man's Desiring), and "Typographical Number Theory", which inevitably reacts explosively when it attempts to make statements about itself, thus "TNT". Word play is a literary technique in which the nature of the words used themselves become part of the subject of the work. ... Space-filling model of a section of DNA molecule Deoxyribose nucleic acid (DNA) is a nucleic acid that contains the genetic instructions specifying the biological development of all cellular forms of life (and many viruses). ... SHRDLU [1] was an early natural language understanding computer program, developed by Terry Winograd at MIT in 1968-70. ... Trinitrotoluene (TNT) is a pale yellow crystalline aromatic hydrocarbon compound that melts at 354 K (178 °F, 81 °C). ...

TNT is an illustration of Gödel's incompleteness theorem and further analogies for it occur in the book, for example a phonograph which destroys itself by playing a record entitled "I Cannot Be Played on Record Player X". This is an example of a strange loop, a term coined by Hofstadter to describe things which speak about or refer back to themselves, such as Escher's lithograph of two hands drawing each other. In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proved by Kurt Gödel in 1931. ... A strange loop is a case of self-reference which affects (or even damages) the original item, possibly causing a paradox. ... Drawing Hands (1948) is a lithograph by M. C. Escher. ...

There are other colorful stories about SHRDLU, the Alternative State of the Union, self-engulfing TV screens, canonical form in music. Other topics range from Zeno's paradoxes to sentient ant colonies. A key question asked by the book is "When are two things the same?" This article is about the musical use of the word canon. For other uses, see canon. ... Wikibooks Wikiversity has more about this subject: School of Music Wikicities has a wiki about Music: Music Look up Music in Wiktionary, the free dictionary All Music Guide: includes a comprehensive and flexible Genre and Style system MusicWiki: A Collaborative Music-related encyclopedia Science of Music: Multimedia exploration of the... Zenos paradoxes are a set of paradoxes devised by Zeno of Elea to support Parmenides doctrine that all is one and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. ...

One quite unnerving puzzle, subtly developed during the first two-thirds of the book, is a speculation concerning an author who writes a book and chooses to end the book without actually stopping the narrative, as is the usual procedure. It is suggested such an author might wrap up his main point, and then continue writing, but drop clues to the reader that the end has already passed, such as wandering and unfocused prose, misstatements, or contradictions. Then, as you read the last sections of G.E.B. you begin to wonder.... A puzzle is a problem or enigma presented as entertainment; that is written down, acted out, etc. ...


The book was for some time considered untranslatable, as it relies heavily on so-called "structural puns", such as the "Crab Canon" dialogue[1] (http://www.barryland.com/canon.html), which reads almost exactly the same, sentence-for-sentence, both forwards and backwards. A crab canon is an arrangement of two things that are complementary and backward. ...

Translation has been a complex task, which has resulted in new material and interplay between the translators and Hofstadter. For instance, in Chinese, the subtitle is not a translation of an Eternal Golden Braid, but a seemingly unrelated (and nonsense) phrase Jí Yì Bì (集异璧, literally "collection of exotic jade") which turns out homophonic with GEB. Some material regarding this interplay is to be found in Hofstadter's later book Le Ton beau de Marot, which is mainly about translation. Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0465086454), published by Basic Books in 1997, is a book by Douglas Hofstadter in which he explores the meaning, strengths, failings, and beauty of translation. ...

Fields of study covered in GEB

Metamathematics is mathematics used to study mathematics. ... Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ... Artificial intelligence (also known as machine intelligence and often abbreviated as AI) is intelligence exhibited by any manufactured (i. ... In mathematics and computer science, recursion is a particular way of specifying (or constructing) a class of objects (or an object from a certain class) with the help of a reference to other objects of the class: a recursive definition defines objects in terms of the already defined objects of... A self-reference occurs when an object refers to itself. ... A strange loop is a case of self-reference which affects (or even damages) the original item, possibly causing a paradox. ... In logic, mathematics, and computer science, a formal system is a formal grammar used for modelling purposes. ... Computability theory is that part of the theory of computation dealing with which problems are solvable by algorithms (equivalently, by Turing machines), with various restrictions and extensions. ... Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines do not exist. ... Logic (from ancient Greek λόγος (logos), originally meaning the word, or what is spoken, but coming to mean thought or reason) is the study of arguments. ... Genetics (from the Greek genno γεννώ= give birth) is the science of genes, heredity, and the variation of organisms. ... Typographic work Typography (from the Greek words typos = form and grapho = write) is the art and technique of selecting and arranging type styles, point sizes, line lengths, line leading, character spacing, and word spacing for typeset applications. ... La trahison des images (The Betrayal Of Images) (1928-1929) Die natürlichen Gnaden (1967) René François Ghislain Magritte (November 21, 1898 – August 15, 1967) was a surrealist artist, born in Lessines, Belgium. ... In the anatomy of animals, the brain, or encephalon, is the supervisory center of the nervous system. ... The mind is the term most commonly used to describe the higher functions of the human brain, particularly those of which humans are subjectively conscious, such as personality, thought, reason, memory, intelligence and emotion. ... Wiktionary has a definition of: Cognition The term cognition is used in several different loosely related ways. ... Free will is the philosophical doctrine that holds that our choices are ultimately up to ourselves. ... Determinism is the philosophical conception which claims that every physical event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences. ... Charles Babbage Charles Babbage (December 26, 1791 – October 18, 1871) was an English mathematician, analytical philosopher and (proto-) computer scientist who was the first person to come up with the idea of a programmable computer. ... Alan Turing, often considered the father of modern computer science. ...

See also

Edsger Dijkstra said: Computer science is no more about computers than astronomy is about telescopes. ... The Mandelbrot set, named after its discoverer, is a famous example of a fractal. ... In Douglas Hofstadters Gödel, Escher, Bach, Tumbolia is the land of dead hiccups and extinguished lightbulbs, where dormant software waits for its host hardware to come back up. Tumbolia, viewed by many readers as one of Hofstadters more intriguing inventions, sadly occurs only four times in the... Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ... The Chinese room argument is a thought experiment designed by John Searle (1980) to debunk the stronger claims made by strong AI (also functionalism). ...

External links

  • Music of Sacred Temperament; The Well Tempered Clavier by J.S.Bach (http://www.geocities.jp/imyfujita/index.html)
  • Music of Intellect The Goldberg Variations by J.S.Bach (http://www.geocities.jp/imyfujita/goldberg/indexe.html)
  • Mårten's page of GEB links (http://geb.stenius.org/old/)
  • <alt.fan.hofstadter> and "GEB" FAQ (http://www.faqs.org/faqs/books/hofstadter-GEB-FAQ/)
  • Crab Canon, from GEB (http://www.evl.uic.edu/swami/crabcanon)



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