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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. book cover to Douglas Hofstadters GEB This image is a book cover. ...
book cover to Douglas Hofstadters GEB This image is a book cover. ...
The gold medal awarded for Public Service in Journalism The Pulitzer Prize is an American award regarded as the highest honor in print journalism, literary achievements, and musical compositions. ...
Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ...
This page refers to the year 1979. ...
1999 (MCMXCIX) was a common year starting on Friday, and was designated the International Year of Older Persons by the United Nations. ...
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." Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Kurt Gödel (IPA: ) (April 28, 1906 Brno, then Austria-Hungary, now Czech Republic – January 14, 1978 Princeton, New Jersey) was a logician, mathematician, and philosopher of mathematics. ...
Look up Artist in Wiktionary, the free dictionary. ...
Self portrait, 1943¹ Maurits Cornelis Escher (Leeuwarden, June 17, 1898 - Laren, March 27, 1972) was a Dutch artist most known for his woodcuts, lithographs and mezzotints, which tend to feature impossible constructions, explorations of infinity, and tessellations. ...
A composer is a person who writes music. ...
Johann Sebastian Bach (21 March 1685 O.S. – 28 July 1750 N.S.) was a prolific German composer and organist whose sacred and secular works for choir, orchestra and solo instruments drew together almost all of the strands of the baroque style and brought it to its ultimate maturity. ...
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 features 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. A self-portrait of Lewis Carroll, taken with assistance Charles Lutwidge Dodgson (January 27, 1832–January 14, 1898), better known by the pen name Lewis Carroll, was a British author, mathematician, logician, Anglican clergyman and photographer. ...
What the Tortoise Said to Achilles is a brief dialog by Lewis Carroll which playfully problematizes the foundations of logic. ...
In Logic, Modus ponens (Latin: mode that affirms) is a valid, simple argument form (often abbreviated to MP): If P, then Q. P. Therefore, Q. or in logical operator notation: P → Q P ⊢ Q where ⊢ represents the logical assertion. ...
A self-reference occurs when an object refers to itself. ...
Metafiction is a kind of fiction which self-consciously addresses the devices of fiction. ...
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". Word play is a literary technique in which the nature of the words used themselves become part of the subject of the work. ...
Guanine is one of the five main nucleobases found in nucleic acids (, DNA and RNA). ...
Cytosine is one of the 5 main nucleobases used in storing and transporting genetic information within a cell in the nucleic acids DNA and RNA. It is a pyrimidine derivative, with a heterocyclic aromatic ring and two substituents attached (an amine group at position 4 and a keto group at...
Adenine is one of the two purine nucleobases used in forming nucleotides of the nucleic acids DNA and RNA. In DNA, adenine (A) binds to thymine (T) via two hydrogen bonds to assist in stabilizing the nucleic acid structures. ...
Thymine, also known as 5-methyluracil, is a pyrimidine nucleobase. ...
The general structure of a section of DNA Deoxyribonucleic acid (DNA) is a nucleic acid —usually in the form of a double helix— that contains the genetic instructions specifying the biological development of all cellular forms of life, and most viruses. ...
SHRDLU [1] was an early natural language understanding computer program, developed by Terry Winograd at MIT from 1968-1970. ...
Typographical Number Theory (also known as TNT) is a formal axiomatic system describing the natural numbers that appears in Douglas Hofstadters book Gödel, Escher, Bach. ...
Trinitrotoluene (TNT, or Trotyl) is a pale yellow crystalline aromatic hydrocarbon compound that melts at 354 K (178 °F, 81 °C). ...
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.) In mathematical logic, Gödels incompleteness theorems are two celebrated theorems proven by Kurt Gödel in 1931. ...
A strange loop is a case of self-reference which affects (or even damages) the original item, possibly causing a paradox. ...
Drawing Hands (1948) is a lithograph by M. C. Escher. ...
A Sierpinski triangle —a confined recursion of triangles to form a geometric lattice. ...
A self-reference occurs when an object refers to itself. ...
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). Bodhidharma, woodcut print by Yoshitoshi, 1887. ...
This article needs to be cleaned up to conform to a higher standard of quality. ...
Traditional Han character (used in Japanese) for mu Simplified Han character (used in modern Chinese) for wú Mu (Japanese/Korean), Wú/Mou5 (Chinese (Mandarin/Cantonese); ç„¡, simplified: æ— , Cantonese: 冇) is a word which can be roughly translated as without or have not. While typically used as a prefix to imply the absence...
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?" This article is about the musical use of the word canon. For other uses, see canon (disambiguation). ...
Music is a human activity which involves structured and audible sounds, which is used for artistic or aesthetic, entertainment, or ceremonial purposes. ...
Zenos paradoxes are a set of paradoxes devised by Zeno of Elea to support Parmenides doctrine that all is one and that contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. ...
Popping in and out of "levels" is 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. A crab canon is an arrangement of two things that are complementary and backward. ...
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. This article is about the meanings of the word form connected with shape or structure. ...
Look up Function in Wiktionary, the free dictionary The word function may mean: In common parlance, a role of a component in an assembly, or of an element in a systemic aggregate (such as a person within a group). ...
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. A crab canon is an arrangement of two things that are complementary and backward. ...
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. Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0465086454), published by Basic Books in 1997, is a book by Douglas Hofstadter in which he explores the meaning, strengths, failings, and beauty of translation. ...
List of alternate-language titles - 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
- Spanish: Un Eterno y Grácil Bucle
- Swedish: Ett Evigt Gyllene Band
- Turkish: Bir Ebedi Gökçe Belik
Fields of study covered in GEB Metamathematics is mathematics used to study mathematics. ...
Square with symmetry group D4 Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ...
Hondas intelligent humanoid robot Artificial intelligence (AI) is defined as intelligence exhibited by an artificial entity. ...
A self-reference occurs when an object refers to itself. ...
A Sierpinski triangle —a confined recursion of triangles to form a geometric lattice. ...
A strange loop is a case of self-reference which affects (or even damages) the original item, possibly causing a paradox. ...
In logic, mathematics, and computer science, a formal system is a formal grammar used for modelling purposes. ...
Recursion theory, or computability theory, is a branch of mathematical logic dealing with generalizations of the notion of computable function, and with related notions such as Turing degrees and effective descriptive set theory. ...
Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist. ...
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Genetics (from the Greek genno γεννώ= give birth) is the science of genes, heredity, and the variation of organisms. ...
Molecular biology is the study of biology at a molecular level. ...
Typographic work Typography (from the Greek words typos = form and graphein = to write) is the art and technique of setting written subject matter in type using a combination of typeface styles, point sizes, line lengths, line leading, character spacing, and word spacing to produce typeset artwork in physical or digital...
This is not a pipe. ...
Comparative brain sizes In animals, the brain, or encephalon (Greek for in the head), is the control center of the central nervous system. ...
To meet Wikipedias quality standards and appeal to a wider international audience, this article may require cleanup. ...
Look up Cognition in Wiktionary, the free dictionary The term cognition (Latin, cogito: to think) is used in several different loosely related ways. ...
Free will is the philosophical doctrine that holds that our choices are ultimately up to ourselves. ...
Determinism is the philosophical proposition that every event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences. ...
Charles Babbage Charles Babbage (26 December 1791 – 18 October 1871) was an English mathematician, analytical philosopher, mechanical engineer and (proto-) computer scientist who originated the idea of a programmable computer. ...
Alan Turing is often considered the father of modern computer science. ...
See also Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...
The boundary of the Mandelbrot set is a famous example of a fractal. ...
In Douglas Hofstadters Gödel, Escher, Bach, Tumbolia is the land of dead hiccups and extinguished lightbulbs, where dormant software waits for its host hardware to come back up. Tumbolia, viewed by many readers as one of Hofstadters more intriguing inventions, sadly occurs only four times in the...
Rendering of human brain based on MRI data Cognitive science is usually defined as the scientific study either of mind or of intelligence (e. ...
The Chinese room argument is a thought experiment designed by John Searle (1980 [1]) as a counterargument to claims made by strong artificial intelligence (AI, also functionalism). ...
John Randolph Lucas (born 18 June 1929) is a British philosopher. ...
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