Word: thoms
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...Cartier tank watch, starting at $450, keep it as popular today as when Louis Cartier first designed it in 1917 to commemorate the U.S. Tank Corps in France Advertising campaigns, such as the one for Black & Decker power and home workshop tools, increasingly stress quality and craftsmanship. Thom McAn, once the proud purveyor of low-cost shoes for kids, now also promotes upscale footwear for women, and ads extoll features like cushioned and arched insoles for its new line of track shoes. Maytag Co. commercials emphasize that their repairmen are "the loneliest people in the world" because the company...
...Although Thom described only limited applications to biology and linguistics, his ideas immediately took hold of the scientific community. Led by E.C. Zeeman of Cambridge University, mathematicians everywhere began to apply the theory to discontinuities ranging from shock waves in physics to schizophrenic cycles in psychology...
...Thom's theory possesses the simplicity and elegance that is so appealing to a mathematician. His model is based on principles of topology, a field ofter described as "rubber-sheet geometry" because it concerns forms that may be stretched or distorted without changing their fundamental, qualitative properties. Thom contends that for a wide range of mathematical structures; including almost all natural processes, only seven stable "unfoldings" can occur. By varying the number and arrangement of factors controlling these structures, he determined that apart from the seven "elementary" structures, all others are doomed to degenerate into unstable configurations...
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...
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...