M.C. Escher - Drawing Hands, 1948.

A strange loop arises when, by moving up or down through a hierarchical 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 will presumably be further elaborated in the same author's new book I am a strange loop, which is due to appear in 2007. Image File history File links Download high resolution version (863x723, 224 KB)http://people. ... Image File history File links Download high resolution version (863x723, 224 KB)http://people. ... Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror), 1935. ... A self-reference occurs when an object refers to itself. ... Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist. ... Douglas Richard Hofstadter (born February 15, 1945) is an American academic. ... GEB cover Gödel, Escher, Bach: an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize-winning book by Douglas Hofstadter, published in 1979 by Basic Books. ... 2007 (MMVII) will be a common year starting on Monday of the Gregorian calendar. ...

Examples

Hofstadter points to Bach's Canon per Tonos, M. C. Escher's drawings Waterfall, Drawing Hands, Ascending and Descending, the liar paradox and the proof of Gödel's Incompleteness Theorem as examples of strange loops. In music, the BACH motif is the sequence of notes B flat, A, C, B natural. ... Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror), 1935. ... In philosophy and logic, the liar paradox encompasses paradoxical statements such as: Analyzing the statement I am lying now, if what the speaker says is true, then the statement I am lying now is false, that means when the statement was said, the speaker was actually lying. ... Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... In mathematical logic, Gödels incompleteness theorems are two theorems about the limits of formal systems, proved by Kurt Gödel in 1931. ...

Strange loops often involve violation of hierarchies, in which, for example, a computer program (rather than a person) writes computer programs. This, by itself, is not enough to be a strange loop (it is common practice for a compiler). An example of a strange loop in software is a quine, which is a program that produces a new version of itself without any input from the outside. Metamorphic code is similar. A hierarchy (in Greek: , it is derived from -hieros, sacred, and -arkho, rule) is a system of ranking and organizing things or people, where each element of the system (except for the top element) is subordinate to a single other element. ... A diagram of the operation of a typical multi-language, multi-target compiler. ... In computing, a quine is a program (a form of metaprogram) that produces its complete source code as its only output. ... In computer virus terms, metamorphic code is code that can reprogram itself. ...

Strange loops are frequently intriguing or even humorous. A sketch on Late Night with Conan O'Brien once had Conan (seemingly spontaneously) become upset with a cue-card holder and tell him to leave the set; immediately, the cue-card holder was shown, holding a card with Conan's "you'd better leave" line written on it. Late Night with Conan OBrien is an American late night talk show on NBC, that is also syndicated world-wide. ... In order to meet Wikipedias quality standards, this articles trivia section requires cleanup. ...

See also

• Irony
• Sorcerer's Apprentice mode
• Autopoiesis