Gödel, Escher, Bach
Gödel, Escher, Bach: an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, 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 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?"
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: the initials of the four main dialog characters are G, C, A, and T—the base-pairs in DNA. Some puns may be 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. (Cf. recursion and self-reference.)
Hofstadter drives readers along many kinds of routes to escape such contradictions stemming from logic. Ultimately tales of Zen masters awaken our minds with koans that force us to think outside the box and embrace those paradoxes with 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?"
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 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 GEB 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 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 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 (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. An author cannot make a sudden ending (sudden from considerations of plot, that is) come 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 in a play of form and function — peculiarities may be noticed.
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 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.
List of alternate-language titles
- Chinese: 集異璧之大成
- Dutch: Een eeuwige gouden band
- French: Les Brins d'une Guirlande Éternelle
- German: Ein Endlos 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
- Spanish: Un Eterno y Grácil Bucle
- Swedish: Ett Evigt Gyllene Band
- Turkish: Bir Ebedi Gökçe Belik
- Portuguese: Gödel Escher Bach - Um Entrelaçamento de Gênios Brilhantes
Fields of study covered in GEB
- Metamathematics
- Symmetry
- Artificial intelligence
- Self-reference, recursion, strange loops
- Formal systems, computability
- Paradoxes and logic
- Genetics
- Molecular biology
- Typography
- René Magritte
- brain, mind, and cognition
- free will and determinism
- Charles Babbage
- Alan Turing
- the Lisp programming language