Catastrophe theory, or singularity theory, attempts to explain how discontinuous effects can arise from continuous causes. For example, a forest abruptly terminates and turns into a meadow, even though the weather conditions on each side of the boundary are almost identical. A small increase in tensions between two countries sometimes leads to violent conflict; other times it doesn't. Why?

Unfortunately, catastrophe theory is also known among mathematicians as a fad that failed to live up to its hype. In its heyday--the late 1960s and the 1970s--the advocates of catastrophe theory claimed that it was a new, "qualitative" breed of mathematics that would revolutionize biology or social science in the same way that calculus had revolutionized physics. But the revolution never happened. At best, the theory explained phenomena that people already knew, only in a more obscure and technical language. It had no predictive power, and in...