- Gödel, Escher, Bach
Gödel, Escher, Bach: an Eternal Golden Braid Author(s) Douglas Hofstadter Country USA Language English Subject(s) Consciousness, intelligence Publisher Basic Books Publication date 1979 Pages 777 pages ISBN ISBN 978-0465026562, ISBN 0140179976 OCLC Number 40724766 Dewey Decimal 510/.1 21 LC Classification QA9.8 .H63 1999 Followed by I Am a Strange Loop
Gödel, Escher, Bach: An Eternal Golden Braid (commonly GEB) is a book by Douglas Hofstadter, described by his publishing company as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll".
On its surface, GEB examines logician Kurt Gödel, artist M. C. Escher and composer Johann Sebastian Bach, discussing common themes in their work and lives. At a deeper level, the book is an exposition of concepts fundamental to mathematics, symmetry, and intelligence.
Through illustration and analysis, the book discusses how self-reference and formal rules allow systems to acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.
In response to confusion over the book's theme, Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms. In the book, he presents an analogy about how the individual neurons of the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.
GEB takes the form of an interweaving of various narratives. The main chapters alternate with dialogues between imaginary characters, usually Achilles and the tortoise, first used by Zeno of Elea and later by Lewis Carroll in "What the Tortoise Said to Achilles". These origins are related in the first two dialogues, and later ones introduce new characters such as the Crab. These narratives frequently dip into self-reference and metafiction.
Word play also features prominently in the work. Puns are occasionally used to connect ideas, such as "the Magnificrab, Indeed" with Bach's Magnificat in D; "SHRDLU, Toy of Man's Designing" with Bach's Jesu, Joy of Man's Desiring; and "Typographical Number Theory", or "TNT", which inevitably reacts explosively when it attempts to make statements about itself. One Dialogue contains a story about a genie (from the Arabic "Djinn") and various "tonics" (of both the liquid and musical varieties), which is titled "Djinn and Tonic".
One dialogue in the book is written in the form of a crab canon, in which every line before the midpoint corresponds to an identical line past the midpoint. The conversation still makes sense due to uses of common phrases that can be used as either greetings or farewells ("Good day") and the positioning of lines which double as an answer to a question in the next line. Another is a sloth canon, where one character repeats the lines of another, but slower and negated.
GEB contains many instances of recursion and self-reference, where objects and ideas speak about or refer back to themselves. For instance, there is a phonograph that destroys itself by playing a record titled "I Cannot Be Played on Record Player X" (an analogy to Gödel's incompleteness theorems), an examination of canon form in music, and a discussion of Escher's lithograph of two hands drawing each other. To describe such self-referencing objects, Hofstadter coins the term "strange loop", a concept he examines in more depth in his follow-up book I Am a Strange Loop. To escape many of the logical contradictions brought about by these self-referencing objects, Hofstadter discusses Zen koans. He attempts to show readers how to perceive reality outside their own experience and embrace such paradoxical questions by rejecting the premise — a strategy also called "unasking".
Call stacks are also discussed in GEB, as one dialogue describes the adventures of Achilles and the Tortoise as they make use of "pushing potion" and "popping tonic" involving entering and leaving different layers of reality. Subsequent sections discuss the basic tenets of logic, self-referring statements, ("typeless") systems, and even programming.
The book is filled with puzzles. An example of this is the chapter titled "Contracrostipunctus", which combines the words acrostic and contrapunctus (counterpoint). In a dialogue between Achilles and the Tortoise, the author hints that there is a contrapunctal acrostic in the chapter that refers both to the author (Hofstadter) and Bach. This can be found by taking the first word of each paragraph, to reveal: Hofstadter's Contracrostipunctus Acrostically Backwards Spells "J. S. Bach". The second acrostic is found by taking the first letters of the first (in bold) and reading them backwards to get "J. S. Bach" (just as the first acrostic claims).
For Summer 2007, the Massachusetts Institute of Technology created an online course for high school students built around the book.
In its February 19, 2010 investigative summary on the 2001 anthrax attacks, the Federal Bureau of Investigation revealed that Bruce Edwards Ivins was inspired by GEB to hide secret codes based upon nucleotide sequences in the anthrax-laced letters he allegedly sent in September and October 2001. He used bold letters, as suggested on page 404 of the book. He attempted to hide the book from investigators by throwing it in the trash.
Although Hofstadter claims the idea of translating his book "never crossed [his] mind" when he was writing it, when approached with the idea by his publisher he was "very excited about seeing [the] book in other languages, especially… French". He knew, however, that "there were a million issues to consider" when translating, since the book relies not only on word-play but "structural puns" as well—writing where the form and content of the work mirror each other (such as the "Crab Canon" dialogue, which reads almost exactly the same forwards as backwards).
Hofstadter gives one example of translation trouble in the paragraph "Mr. Tortoise, Meet Madame Tortue", saying translators "instantly ran headlong into the conflict between the feminine gender of the French noun tortue and the masculinity of my character, the Tortoise". Hofstadter decided to translate the French character as "Madame Tortue", and the Italian version as "Signorina Tartaruga". Because of other troubles translators might have retaining the meaning of the book, Hofstadter "painstakingly went through every last sentence of GEB, annotating a copy for translators into any language that might be targeted".
Translation also gave Hofstadter a way to add new meaning and puns. For instance, in Chinese, the subtitle is not a translation of an Eternal Golden Braid, but a seemingly unrelated phrase Jí Yì Bì (集异璧, literally "collection of exotic jades"), which is homophonic to GEB in Chinese. Some material regarding this interplay is to be found in Hofstadter's later book Le Ton beau de Marot, which is mainly about translation.
- ^ Hofstadter, cover.
- ^ By Analogy: A talk with the most remarkable researcher in artificial intelligence today, Douglas Hofstadter, the author of Gödel, Escher, Bach Wired Magazine, November 1995
- ^ Consciousness In The Cosmos: Perspective of Mind: Douglas Hofstadter
- ^ The Prizes, Pulitzer, 1980, http://www.pulitzer.org/awards/1980 .
- ^ GEB, MIT, http://ocw.mit.edu/OcwWeb/hs/geb/geb/ .
- ^ "Amerithrax Investigative Summary" (PDF). United States Department of Justice. February 19, 2010. http://www.justice.gov/amerithrax/docs/amx-investigative-summary.pdf. Retrieved 2010-11-10.
- ^ "Page 404 of Godel, Escher, Bach: An Eternal Golden Braid" (PDF). United States Department of Justice. http://www.justice.gov/amerithrax/docs/j-geb-page-%20404.pdf. Retrieved 2010-11-10.
- ^ Willman, David (2011), The Mirage Man: Bruce Ivins, the Anthrax Attacks, and America's Rush to War; New York: Bantam Books, pg 300.
- ^ a b c Hofstadter 1999, p. 16.
- ^ Hofstadter 1999, p. 17.
- Hofstadter, Douglas R. (1999) , Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books, ISBN 0465026567 .
- GEB video lectures, MIT OpenCourseWare
- Partial contents of 20th Anniversary Edition
- Mårten's GEB site
- Class about GEB, at the University of Michigan
- Java 3D game based on the GEB triplets
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