Topology and Verb Classes

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.":

• 1. Natural languages, human thought and topology

• 2. Thom's axioms

• 3. The simple minimum: "I am."

• 4. The fold: "The day begins."

• 5. The cusp: "The fish swallows the bug, " etc.

• 6. The swallowtail: "The bird lays an egg, swallows it and dies."

• 7. Derivatives of the swallowtail: "She repulses his advances," etc.

• References

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