Gödel, Escher, Bach: An Eternal Golden Braid (1979) by Douglas Hofstadter, is a book about the intellectual themes common to the lives and the works of the logician Kurt Gödel, the artist M. C. Escher, and the composer Johann Sebastian Bach, and shows the thematic connections among mathematics, symmetry, and intelligence. Through short stories, illustrations, and analyses, the book explains how systems acquire meaningful context from the "meaningless" elements that compose a system; self-reference and formal rules; isomorphism; the meaning of communication; how knowledge can be represented and stored; the methods and limitations of symbolic representation; and the notion of "meaning". As a cognitive scientist, Hofstadter said that Gödel, Escher, Bach is not about the relationships of mathematics, art, and music, but about how cognition emerges from hidden neurological mechanisms, e.g. how individual neurons in the brain coordinate to create a coherent mind. Gödel, Escher, Bach won the Pulitzer Prize for General Nonfiction and the National Book Award for Science Hardcover.
Structure Gödel, Escher, Bach is in interweaving narratives and the main chapters alternate dialogues among fictional 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 dialogues introduce new characters such as the Crab. These narratives often are self-referential and metafictional. Word play, such as puns are 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". Sometimes word play has no significant connection, such as the dialogue "A Mu Offering", which has no close affinity to Bach's The Musical Offering. 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 that 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.
Themes The book contains many instances of recursion and self-reference, where objects and ideas speak about or refer back to themselves. One is Quining, a term Hofstadter invented in homage to Willard Van Orman Quine, referring to programs that produce their own source code. Another is the presence of a fictional author in the index, Egbert B. Gebstadter, a man with initials E, G, and B and a surname that partially matches Hofstadter. A phonograph dubbed "Record Player X" 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". Elements of computer science such as call stacks are also discussed in Gödel, Escher, Bach, 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. The same dialogue has a genie with a lamp containing another genie with another lamp and so on. Subsequent sections discuss the basic tenets of logic, self-referring statements, ("typeless") systems, and even programming. Hofstadter further creates BlooP and FlooP, two simple programming languages, to illustrate his point.
Puzzles The book is filled with puzzles, including Hofstadter's MU puzzle, which contrasts reasoning within a defined logical system with reasoning about that system. Another example can be found in the chapter titled Contracrostipunctus, which combines the words acrostic and contrapunctus (counterpoint). In this 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 spelled out 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 words of the first, and reading them backwards to get "J S Bach", as the acrostic sentence self-referentially states.
Reception and impact Gödel, Escher, Bach won the Pulitzer Prize for General Nonfiction and the National Book Award for Science Hardcover. Martin Gardner's July 1979 column in Scientific American stated, "Every few decades, an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event." 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 suggested that Bruce Edwards Ivins was inspired by the book to hide secret codes based upon nucleotide sequences in the anthrax-laced letters he allegedly sent in September and October 2001, using bold letters, as suggested on page 404 of the book. It was also suggested that he attempted to hide the book from investigators by throwing it in the trash. In 2019, British mathematician Marcus du Sautoy curated a series of events at London's Barbican Centre to celebrate the book's fortieth anniversary.
I Am a Strange Loop
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