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Topology and Verb Classes

Feature Column Archive


3. The simple minimum: ``I am."

The simple minimum is exemplified by the minimum of the function f(x) = x2. This minimum is stable: every small perturbation of f(x) = x2 will have a minumum near x=0. There is no possibility of a system with this internal dynamics jumping from one state to another: it is always at the single critical point. Any one-dimensional section through any parameter space will be constant, or nearly constant, near x=0. The corresponding verb class is represented by ``I am.'':


3. The simple minimum: ``I am.''