Word: modell
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Dates: during 1970-1979
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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...
...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...
...MOST COMMONLY-USED model in applications is the "cusp," a three-dimensional structure dependent upon two variables or "control factors" with a third dimension, the "behavior axis," displaying the subject's reaction to these two factors...
Translating this theoretical model into a practicable application involves isolating a particular type of behavior and identifying the control factors affecting it. One use in the social sciences is especially appropriate in view of last week's rally in Washington against nuclear power and the mishap at Three Mile Isle last month. The author's model for determining the rate of power plant construction pits the pro-nuclear lobby against the "ecology" lobby and predicts that at a certain point a nuclear disaster will cause a catastrophic cutback in construction...
...near to reaching that point? There is no way of telling since the evidence is not at all tangible or quantifiable. It seems as if the only hope of verifying the model is to wait for a nuclear disaster to occur and then analyze the effects with hindsight. If we are truly at a "critical turning point" as the authors claim, then it should be apparent very soon whether we are to have many power plants or none...