Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.
By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can 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 emphasized that Gödel, Escher, Bach is not about the relationships of mathematics, art, and music—but rather about how cognition emerges from hidden neurological mechanisms. One point in the book presents an analogy about how individual neurons in 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.[1][2]The tagline “a metaphorical fugue on minds and machines in the spirit of Lewis Carroll” was used by the publisher to describe the book.[3]
Structure[edit]
Gödel, Escher, Bach takes the form of interweaving 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 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[edit]
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. 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[edit]
The book is filled with puzzles, including Hofstadter’s famous MU puzzle. 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 (shown in bold), and reading them backwards to get “J S Bach” – just as the acrostic sentence self-referentially claims.
Impact[edit]
Gödel, Escher, Bach won the Pulitzer Prize for general non-fiction[4] and the National Book Award for Science.[5][a]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.”[6]For Summer 2007, the Massachusetts Institute of Technology created an online course for high school students built around the book.[7]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,[8] using bold letters, as suggested on page 404 of the book.[9][10] It was also suggested that he attempted to hide the book from investigators by throwing it in the trash.
Translation[edit]
Hofstadter claims the idea of translating his book “never crossed [his] mind” when he was writing it—but when his publisher brought it up, 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,[11] since the book relies not only on word-play, but on “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 an 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.”[11] Hofstadter agreed to the translators’ suggestions of naming the French character Madame Tortue, and the Italian version Signorina Tartaruga.[12] Because of other troubles translators might have retaining meaning, Hofstadter “painstakingly went through every sentence of Gödel, Escher, Bach, annotating a copy for translators into any language that might be targeted.”[11]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 in Hofstadter’s later book, Le Ton beau de Marot, which is mainly about translation.
Editions[edit]
Hofstadter, Douglas R. (1999) [1979], Gödel, Escher, Bach: An Eternal Golden Braid, Basic Books, ISBN 0-465-02656-7, retrieved 2016-03-02See also[edit]
Notes[edit]
References[edit]
^ 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
^ “Perspective of Mind: Douglas Hofstadter”.
^ Hofstadter, cover.
^ The Prizes, Pulitzer, 1980
^
“National Book Awards – 1980”. National Book Foundation. Retrieved 2012-03-07.
^ Somers, James. “The Man Who Would Teach Machines to Think”. The Atlantic. The Atlantic Media Company. Retrieved 25 October 2013.
^ GEB, MIT
^ “Amerithrax Investigative Summary” (PDF). United States Department of Justice. February 19, 2010. Archived from the original (PDF) on 2010-11-28. Retrieved 2010-11-10.
^ “Page 404 of Godel, Escher, Bach: An Eternal Golden Braid” (PDF). United States Department of Justice. Archived from the original (PDF) on 2010-11-28. 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. xxxiv.
^ Hofstadter 1999, pp. xxxiv–xxxv.
External links[edit]
Gödel, Escher, Bach at Open Library
Video lectures from a summer GEB seminar for high schoolers, 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
Gödel, Escher, Bach (PDF)
vteM. C. EscherWorks1910s
Escher’s Father
Bookplate Bastiaan Kist
Chrysanthemum
Head of a child
Skull
Railway Bridge, Oosterbeek
Mascot
Portrait of a Man (I)
Self-Portrait (I)
Baby
Young Thrush
Bookplate M. C. Escher
Self-Portrait (II)
Jug
The Rag Pickers
Fiet van Stolk
Waves
Self-Portrait (III)
White Cat (I)
The Borger Oak
Portrait
Seated Man with cat on his lap
Tree
Self-Portrait (IV)
Parrot
White Cat (II)
Sea-shell1920s
Self Portrait in a Chair
Rabbits
Female Nude in a Landscape
Wild West
The Fall of Men
Escher’s Father with Magnifying Glass
Portrait of a Man (II)
Man Standing
Seated Old Woman
Flower
Seated Female Nude (I)
Seated Female Nude (II)
Seated Female Nude (III)
Roosje Ingen Housz
Poster
Plane-filling Motif with Human Figures
Paradise
Seated Female Nude (IV)
Seated Female Nude (V)
Hand with Fir Cone
St Francis
Eight Heads
Eagle, vignette
Dolphins
San Gimignano
Self-Portrait (V)
Portrait of Jetta
Vitorchiano nel Cimino
The First Day of the Creation
The Sixth Day of Creation
The Fall of Man
Procession in Crypt
Rome
Castle in the Air
Tower of Babel
Fara San Martino, Abruzzi
Corte, Corsica
The Drowned Cathedral
Infant Arthur Escher
Self-Portrait (VI)
Barbarano, Cimino1930s
Street in Scanno, Abruzzi
Castrovalva
The Bridge
Fiumara, Calabria
Tropea, Calabria
Cloister near Rocca Imperiale, Calabria
Atrani, Coast of Amalfi
Covered Alley in Atrani
Ravello and the Coast of Amalfi
Coast of Amalfi
Farmhouse, Ravello
San Cosimo, Ravello
Turello, Southern Italy
Porta Maria dell’Ospidale, Ravello
Lion of the Fountain in the Piazza at Ravello
San Michele dei Frisone, Rome
Mumified Priests in Gangi, Sicily
Temple of Segeste, Sicily
Cave Dwellings (near Sperlinga) Sicily
Palm
Caltavuturo in the Madonie Mountains Sicily
Cloister of Monreale Sicily
Lava Flow of 1928 from Etna Sicily
Pineta of Calvi, Corsica
Phosphorescent Sea
Fireworks
Old Olive Tree, Corsica
Nonza, Corsica
Still Life with Mirror
Nocturnal Rome: Colonade of St Peter’s
Nocturnal Rome: Santa Maria del Popolo
Nocturnal Rome: Trajan’s Column
Nocturnal Rome: Basilica of Constantine
Nocturnal Rome: Castel Sant’ Angelo
Nocturnal Rome: Colosseum
Aeroplane above Snowy Landscape
Still Life with Spherical Mirror
Hand with Reflecting Sphere
Regular Division of the Plane
Inside St Peter’s
Portrait of G.A. Escher
Sengela, Malta
Hell, copy after Hieronymus Bosch
Snow
Prickly Flower
House in the Lava near Nunziata, Sicily
Still Life and Street
Metamorphosis I
Development I
Day and Night
Cycle
Sky and Water I
Sky and Water II
Entrance to the Oude Kerk, Delft
Development II (I)
Development II (II)
Oostpoort, Delft
Nieuwe Kerk, Delft
Town Hall, Delft
Voldersgracht, Delft1940s
Metamorphosis II
Bookplate Dr. P.H.M. Travaglino
Horse (No. 8)
Sea Horse (No. 11)
Lizard (No. 15)
Eagle (No. 17)
Two Birds (No. 18)
Fish (No. 20)
Clowns (No. 21)
Bird / Fish (No. 22)
Lizard (No. 25)
Three Birds (No. 28)
Fish
Plane-filling Motif with Reptiles
Bird / Fish (No. 34)
Bird / Fish (No. 34B)
Dragonfly (No. 38)
Crab (No. 40)
Two Fish (No. 41)
Shells and Starfish (No. 42)
Bird (No. 44)
Angel-Devil (No. 45)
Verbum
Two Fish (No. 46)
Frog (No. 51)
Fish (No. 55)
Lizard (No. 56)
Two Fish (No. 57)
Two Fish (No. 58)
Two Fish (No. 59)
Two Lizards (No. 60)
Reptiles
Ant
Blowball (I)
Blowball (II)
Encounter
Two Creatures (No. 61)
Devil (No. 62)
Pessimist-Optimist (No. 63)
Balcony
Doric Columns
Three Spheres I
Diploma Tijdelijke Academie, Eindhoven
Winged Lion (No. 66)
Magic Mirror
Three Spheres II
Horseman
Mumified Frog
Eye
New Year’s greeting-card
Gallery
Horseman (No. 67)
Another World
Up and Down
Drawing Hands
Dewdrop
Sun and Moon
Study for Stars
Stars
Fish / Duck / Lizard (No. 69)
Butterfly (No. 70)
Fish / Boat (No. 72)
New Year’s greeting card
Plane-filling Motif with Birds
Regular Division of the Plane with Birds
Sea-shells
Fish and Frogs
Double Planetoid
Flying Fish (No. 73)
Horse / Bird (No. 76)1950s
Order and Chaos
Rippled Surface
Devils (vignette)
Unicorn (No. 78)
Flying Fish / Bird (No. 80)
Predestination
Plane Filling I
Curl-up
House of Stairs
Bird / Fish (No. 82)
Thirty-Six Different Motifs (No. 83)
Bird / Fish (No. 8)
Two Intersecting Planes
Puddle
Dragon
Gravitation
Lizard / Fish / Bat (No. 85)
Two Birds (No. 87)
Sea Horse (No. 88)
Concentric Rinds
Relativity
Spirals
Beetle (No. 91)
Bookplate A.R.A. Wertheim
Tetrahedral Planetoide
Fish (No. 93)
Convex and Concave
Liberation
Rind
Depth
Three Worlds
Fish (No. 94)
Swan (No. 96)
Swans
Bond of Union
Print Gallery
Division
Smaller and Smaller
Lizards (No. 101)
Cube with Magic Ribbons
Plane Filling II
Whirlpools
Belvedere
Sphere Surface with Fish
Sphere Spirals
Flatworms
Circle Limit II
Circle Limit III
Fishes and Scales
Lizard (No. 104)
Pegasus (No. 105)1960s
Ascending and Descending
Circle Limit IV
Fish (No. 107)
Möbius Strip I
Waterfall
Creeping Creature (No. 109)
Fish, Fish / Bird (No. 109 II)
Bird / Fish (No. 110)
Möbius Strip II
Knots
Lizard (No. 124)
Path of Life III
Fish / Bird (No. 126)
Bird (No. 128)
Metamorphosis III
SnakesRelated
Escher Museum
Escher in popular culture
George Arnold Escher (father)
Berend George Escher (brother)
Mathematics and art
Video games inspired by Escher
Adventures in Perception (1971 documentary)
Gödel, Escher, Bach (1979 book)
