Model of math theory for changing state in phenomenon such as buckling metal under pressure, liquid freezing, government failure, or mob riots. As a study of the mechanism of discontinuous or sudden changed, it says that small changes gradually build to trigger catastrophe, a breaking point in structures, be it metal or people (national frustrations). This breaking point is the catastrophic failure (bridge collapse) or upheaval (empire overthrow). Vladimir Igorevich Arnold, Russian mathematician (1937) and Renee Thom (1923) jointly developed this theory in 1972.

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