Gödel, Escher, Bach
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Gödel, Escher, Bach: an Eternal Golden Braid: A metaphorical fugue on minds and machines in the spirit of Lewis Carroll (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, published in 1979 by Basic Books. A new preface by Hofstadter accompanied a 20th anniversary re-edition (ISBN 0465026567), which was 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 with no central 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?"
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[edit] Structure
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 is featured 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. These narratives frequently dip into self-reference and metafiction.
Word play features prominently in the work. Puns are occasionally used to connect 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". One Dialogue contains a story about a genie (the name comes from the Arabic "Djinn") and various "tonics" (of both the liquid and musical varieties). The story is titled "Djinn and Tonic". Another example of the book's word play combines a double pun and a Spoonerism with an analogy, whilst simultaneously expressing the main metaphysical theme of the book: "Is the soul greater than the hum of its parts?"
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. (Cf. recursion and self-reference.) Hofstadter examined the idea of a strange loop in depth in this follow-up book I Am a Strange Loop.
Hofstadter drives readers along many kinds of routes to escape such contradictions stemming from logic. Discussion about Zen koans aims to show us how to perceive reality outside the normal confines of our own experience and embrace such paradoxical questions by rejecting the premise, termed "unasking", with the answer Mu (無).
There are other colorful stories about SHRDLU, the Alternative Structure of the Union, self-engulfing TV screens, and canon 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?" Another paradox, the self-referential Hofstadter's law, made its way into geek culture:
- It always takes longer than you expect, even when you take into account Hofstadter's Law.
Call stacks are also discussed in GEB 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 humorously remarks that a friend of his performed a "popping" while in their current state of reality and has never been heard from since; the implied question is, "Did the friend simply cease to exist, or has the friend achieved a higher state of reality?" And since the reader would visit the Tortoise and Achilles, would the friend have ascended to the same level of reality that the readers of GEB currently reside in? Subsequent sections discuss the basic tenets of logic, self-referring statements ("typeless"), systems, and even programming.
One dialog 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, yet the conversation 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 puzzle (in the dialogue Aria with Diverse Variations) is a speculation concerning an author who writes a book and chooses to end the book without actually stopping the text, as is the usual procedure. That an author cannot make a sudden ending (sudden from considerations of plot, that is) comes as a surprise, when the physical fact that there are only a few pages left in the book is obvious to the reader; so such an author might wrap up the 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, when reading the last parts of that same dialogue—or, some might say, GEB as a whole—peculiarities may be noticed. Also, few readers have noticed that the book begins with a cue to the "Author." This follows from the end of the final dialogue whereby the whole book is the author's response to Tortoise's prompt (the last line in the text). In this way, the entire book takes the form of an endlessly rising canon where the author quotes the author, quotes the author, etc.
[edit] 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], 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 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.
[edit] List of alternate-language titles
- Chinese: 集異璧之大成
- Danish: Et evigt gyldent bånd
- Dutch: Een eeuwige gouden band
- French: Les Brins d'une Guirlande Éternelle
- German: Ein endloses geflochtenes Band
- Hungarian: Egybefont Gondolatok Birodalma
- Italian: Un'Eterna Ghirlanda Brillante
- Japanese: ゲーデル,エッシャー,バッハ―あるいは不思議の環
- Korean: 괴델,에셔,바흐 - 영원한 황금 노끈
- Portuguese: Um Entrelaçamento de Gênios Brilhantes
- Russian: Гедель, Эшер, Бах: эта бесконечная гирлянда (variant - Гедель, Эшер, Бах: вечная золотая цепь) (the initials of "эта бесконечная гирлянда" coincide with the initials of "Гедель, Эшер, Бах" - as in the original)
- Spanish: Un Eterno y Grácil Bucle (Una Eterna Trenza Dorada)
- Swedish: Ett Evigt Gyllene Band
- Turkish: Bir Ebedi Gökçe Belik
[edit] People featured in GEB
- Alan Turing
- Charles Babbage
- Johann Sebastian Bach
- Kurt Gödel
- Lewis Carroll
- M. C. Escher
- Marvin Minsky
- René Magritte
[edit] Fields of study covered in GEB
- Metamathematics
- Symmetry
- Artificial intelligence
- Formal systems, computability
- Paradoxes
- Genetics
- Molecular biology
- Logic, number theory
- Typography and syntax
- Brain, mind, and cognition
- Syntax vs. semantics
- Free will vs. determinism
- Holism vs. reductionism
- The Lisp programming language
- Fugue, counterpoint, and musical form
- Isomorphisms and meaning
- Juxtaposed layers of meaning, counterpoint, semiotics, codes
- Self-reference, recursion, strange loops
- Self-organizing, emergent sense of identity: consciousness (e.g. "I am a true statement, and what I state is that I cannot be proven within this system to which I belong" or "I am truthful, but my truth transcends this universe")
- Zen Buddhism
