Word: phenomena
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...from existing economic thought. Since its formulation around 1964, catastrophe theory has emerged as one of few mathematical breakthroughs in recent times to arouse public interest. The controversy lies in its claim to have broadened the scope of science to include the social sciences and humanities, uniting such diverse phenomena as the collapse of a bridge, the crash of the stock market, and the fall of the Roman empire. Yet its subject is not always "catastrophic" in the literal sense: optical scattering, embryonic growth, prison riots, aggressive behavior in dogs, and the rise of the nouveau riche also fall within...
What allows the theory such wide-ranging applications is its emphasis on qualitative rather than quantitative analysis. What matters is not when or not to what extent something will happen, but whether it will take place at all. Thus catastrophe theorists can claim to understand phenomena other mathematical approaches cannot explain: naturally-occuring discontinuities or "jumps." Since the time of Newton and Leibniz, founders of the calculus three centuries ago, mathematical models in science have been concerned with the regular rotation of planets, the gradual increase in pressure of a gas being heated and the continuously-changing velocity...
Even opponents concede that Thom's mathematics is impeccable; the trouble begins only when he applies the theory to phenomena outside the realm of pure mathematics. It turns out that most of the elementary structures are not quite so elementary: although the simplest of these, the "fold" catastrophe, may be depicted by a parabola, the complex "parabolic umbilic" model cannot be represented in fewer than six dimensions. In addition, some of the structures have such a narrow range of stable states that they are practically useless as real-life models...
...objections to the theory: that it is incapable of making useful predictions; that it is so general and qualitative as to reveal nothing we don't already know; that alternative mathematical models already exist; and that its proponents have based their claims of its wide applicability on a few phenomena well-suited to the model. Finally, two of the harshest critics have charged that in substituting pure theory for "the hard work of learning the facts about the world," idealistic mathematicians have used the theory "deduce the world by thought alone...
WHILE THE authors try to deflect these criticisms, their own position, especially in light of some questionable applications, is not entirely convincing. Thom writes that "our use of local models...implies nothing about the 'ultimate nature of reality'." His catastrophe theory purported not to "explain" phenomena but merely to describe them--a crucial distinction the authors, as well as other proponents, refuse to make. If the mark of a science is both to explain and to predict phenomena, and catastrophe theory often does neither, a re-evaluation of its worth may be in order...