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Douglas Richard Hofstadter is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. His 1979 book Gödel, Escher, Bach: An Eternal Golden Braid won both the Pulitzer Prize for general nonfiction and a National Book Award for Science. His 2007 book I Am a Strange Loop won the Los Angeles Times Book Prize for Science and Technology.
Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philosophy, it also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English.
A strange loop is a cyclic structure that goes through several levels in a hierarchical system. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started. Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.
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 short stories, illustrations, and analysis, the book discusses how systems can acquire meaningful context despite being made of "meaningless" elements. It also discusses self-reference and formal rules, isomorphism, 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.
A crab canon is an arrangement of two musical lines that are complementary and backward. If the two lines were placed next to each other, the lines would form something conceptually similar to a palindrome. The name 'crab' refers to the fact that crabs are known to walk backward. It originally referred to a kind of canon in which one line is played backward. An example is found in J. S. Bach's The Musical Offering, which also contains a table canon, which combines retrogression with inversion by having one player turn the music upside down.It is also worth mentioning that "Crab" is Barc.
Metamagical Themas is an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine Scientific American during the early 1980s. The anthology was published in 1985 by Basic Books.
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number. The concept was developed by Kurt Gödel for the proof of his incompleteness theorems.
BlooP and FlooP are simple programming languages designed by Douglas Hofstadter to illustrate a point in his book Gödel, Escher, Bach. BlooP is a non-Turing-complete programming language whose main control flow structure is a bounded loop. All programs in the language must terminate, and this language can only express primitive recursive functions.
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals. The paradox can be expressed as follows:
James Roy Newman (1907–1966) was an American mathematician and mathematical historian. He was also a lawyer, practicing in the state of New York from 1929 to 1941. During and after World War II, he held several positions in the United States government, including Chief Intelligence Officer at the US Embassy in London, Special Assistant to the Undersecretary of War, and Counsel to the US Senate Committee on Atomic Energy. In the latter capacity, he helped to draft the Atomic Energy Act of 1946. He became a member of the board of editors for Scientific American beginning in 1948. He is also credited for coining and first describing the mathematical concept "googol" in his book Mathematics and The Imagination.
A Bongard problem is a kind of puzzle invented by the Russian computer scientist Mikhail Moiseevich Bongard, probably in the mid-1960s. They were published in his 1967 book on pattern recognition. The objective is to spot the differences between the two sides. Bongard, in the introduction of the book credits the ideas in it to a group including M. N. Vaintsvaig, V. V. Maksimov, and M. S. Smirnov.
Hofstadter's law is a self-referential adage, coined by Douglas Hofstadter in his book Gödel, Escher, Bach: An Eternal Golden Braid (1979) to describe the widely experienced difficulty of accurately estimating the time it will take to complete tasks of substantial complexity:
Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law.
The MU puzzle is a puzzle stated by Douglas Hofstadter and found in Gödel, Escher, Bach involving a simple formal system called "MIU". Hofstadter's motivation is to contrast reasoning within a formal system against reasoning about the formal system itself. MIU is an example of a Post canonical system and can be reformulated as a string rewriting system.
This article gives a sketch of a proof of Gödel's first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses, which are discussed as needed during the sketch. We will assume for the remainder of the article that a fixed theory satisfying these hypotheses has been selected.
I Am a Strange Loop is a 2007 book by Douglas Hofstadter, examining in depth the concept of a strange loop to explain the sense of "I". The concept of a strange loop was originally developed in his 1979 book Gödel, Escher, Bach.
In the end, we are self-perceiving, self-inventing, locked-in mirages that are little miracles of self-reference.
Solvitur ambulando is a Latin phrase which means "it is solved by walking" and is used to refer to a problem which is solved by a practical experiment. It is often attributed to Saint Augustine.
Print Gallery is a lithograph printed in 1956 by the Dutch artist M. C. Escher. It depicts a man in a gallery viewing a print of a seaport, and among the buildings in the seaport is the very gallery in which he is standing, making use of the Droste effect with visual recursion. The lithograph has attracted discussion in both mathematical and artistic contexts. Escher considered Print Gallery to be among the best of his works.
The Language of Music is a 1959 book about music by the critic and musician Deryck Cooke.
Dragon is a wood engraving print created by Dutch artist M. C. Escher in April 1952, depicting a folded paper dragon perched on a pile of crystals. It is part of a sequence of images by Escher depicting objects of ambiguous dimension, including also Three Spheres I, Doric Columns, Drawing Hands and Print Gallery.
Day and Night is a woodcut made by the Dutch artist M. C. Escher in 1938.
References
- ↑ Anne H. Soukhanov, ed. (1992). The American Heritage Dictionary of the English Language (Third ed.). Houghton Mifflin Company. p. 1816. ISBN 0-395-44895-6.
- 1 2 Kanfer, Vedi S. (1972-07-03). "Woody Allen: Rabbit Running". Time Magazine. p. 25. Archived from the original on February 20, 2007. Retrieved 2010-05-24.
- ↑ Provenza, Paul (2005). The Aristocrats. Mighty Cheese Productions. IMDB tt0436078.
- ↑ "Aristocrats - Wendy Liebman". YouTube. Archived from the original on 2021-12-21. Retrieved 3 May 2021.
- ↑ Hofstadter, Douglas R. (1979). Gödel, Escher, Bach . Basic Books. p. 187.
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