Gödel, Escher, Bach
Gödel, Escher, Bach: an Eternal Golden Braid is a Pulitzer Prize-winning book by Douglas Hofstadter. It explains how the creative achievements of logician Kurt Goedel, lithographer M. C. Escher and composer Johann Sebastian Bach interweave.
The book itself is an interleaving of various narratives. The chapters alternate with dialogues between imaginary characters. One such dialogue is a piece by Lewis Carroll, in which Achilles and the Tortoise discuss 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 are quite atrocious, but forgivable for the breadth of the connection they make between ideas: "the MagnifiCrab, Indeed", "SHRDLU, Toy of Man's Designing", and "Typographical Number Theory", which inevitably reacts explosively when it attempts to make statements about itself, thus "TNT".
Several analogies for Goedel's incompleteness theorem occur in the book, for example a phonograph which destroys itself by playing a record entitled "I Cannot Be Played on Record Player X", an example of a strange loop.
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 Zenos paradoxes to sentient ant colonies. A key question asked by the book is "When are two things the same?"
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