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The Calculus of Friendship by Steven Strogatz

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Bifurcation (2004)

Change can occur in varying degrees of violence and unpredictability. Accordingly, there are different kinds of mathematics for each.

At the mildest extreme lie the orderly changes of a system obeying differential equations, gliding along according to laws of motion. Think of the planets orbiting the sun or the burbling of a brook. Here calculus is in its element. It is designed for systems that evolve according to definite rules.

At the opposite extreme lies wild, irrational change. The kind that comes from senseless shocks to a system, external events bearing no logical relation to the system itself. The asteroid that hit ...

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