Topology and Verb Classes Feature Column Archive 4. The fold: ``The day begins.'' The fold catastrophe is exemplified by the critical point of the function f(x) = x^{3}. This critical point is unstable: perturbing the function to f(x) = x^{3} + ax gives a function with a maximum and a minimum near zero if a is negative, no matter how small, and no critical point at all if a is positive. A typical onedimensional section will follow the parameter a : the energy minumum that exists for a < 0 disappears as the section crosses a = 0 . The corresponding verb class is represented by ``The day ends.'' if the section is traversed from negative a to positive and ``The day begins.'' if it is traversed in the opposite direction.

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