Strange loop
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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.
[edit] 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.
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.
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.
