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Picture for a moment a soccer ball resting in uneasy balance at the top of a hill, primed to roll down into one of two valleys on either side below. But which? That, of course, depends on a number of factors: wind, temperature, the starting position of the ball, maybe some uneven ground or rocks.

It's an example of the so-called butterfly effect, made somewhat famous in pop culture in recent years. At the risk of oversimplifying -- and scandalizing the Ph.D.s in the audience -- it's the ...

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