Gödel, Escher, Bach: an Eternal Golden Braid is a Pulitzer Prize-winning book by Douglas Hofstadter, first published in 1979 by Basic Books. A new preface by Hofstadter accompanied an otherwise unchanged 20th anniversary edition (ISBN 0465026567) released in 1999.

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."

The central theme of the book is more abstract. Hofstadter asks: "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 does have a theme. He stated: "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.

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".

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.

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?"

Popping in and out of "levels" is also discussed in G.E.B. as one dialog describes the adventures of Achilles and the Tortoise as they make use of "pushing" and "popping" tonics. Entering a picture in a book would count as "pushing", entering a picture in a book within a picture in a book would have caused a double "pushing", and "popping" refers to an exit back to the previous layer of reality. The Tortoise humourously remarks that a friend of his performed a "popping" while in their current state of reality and has never been heard from since. (Did the friend simply cease to exist, or has the friend achieved a higher state of reality, i.e. the same level of reality that the readers of G.E.B. currently reside in?) Subsequent sections discuss the basic tenets of logic, self-referring statements ("typeless"), systems, and even programming.

One particularly noteworthy dialog in the book is cleverly written as a fugue, in which every line before the midpoint corresponds to an identical line past the midpoint, yet the conversation strangely makes sense due to uses of common phrases which can be used as either greetings or farewells ("Good day") and the positioning of lines which, upon close inspection, double as an answer to a question in the next line.

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....

Translation

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.

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.

Fields of study covered in GEB

• Metamathematics
• Symmetry
• Artificial intelligence
• recursion, self-reference, strange loops
• formal systems, computability
• paradoxes and logic
• genetics
• typography
• René Magritte
• brain, mind and cognition
• free will and determinism
• Charles Babbage
• Alan Turing

See also

• computer science
• fractals
• Tumbolia
• cognitive science
• Chinese room

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)de:Gödel, Escher, Bach

fr:Gödel, Escher, Bach, les brins d'une guirlande éternelle nl:Gödel, Escher, Bach zh:哥德尔、埃舍尔、巴赫