A strange loop is a case of self-reference which affects (or even damages) the original item, possibly causing a paradox. For example, Abbie Hoffman once wrote a book called Steal This Book, which thereby tried to undermine its own sales in bookstores. The band System of a Down did the same later with the album Steal This Album!. The liar paradox and Russell's paradox also involve 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 merely self reference, and 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.
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.
The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach.
Related articles