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So you'll always be informed at parties, a butterfly flaps its wings in New York, which changes Earth's "initial conditions" to such a small degree, but chaos theory takes over and "magnifies" this change in conditions exponentially, and it rains in Japan. Something big begat by something miniscule.
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And therein lies my difficulty with chaos theory (or at least this famous example). There are probably over 100 trillion variables that, taken together, determine whether or not it will rain in Japan. To connect the rain in Japan to a single one of them with the implicit assumption of causality is preposterous. To suggest that all of the 100 trillion (or whatever) variables were in perfect balance and the lone butterfly tilted the scale just enough is to remove one more shovel full of dirt from a (nearly) bottomless hole.
Unlike the last voice in Horton Hears a Who, all the variables that contribute to an event are not all pointing in the same direction. Some amplify each other, some cancel each other out, some diffract others and the behaviour of others depends on the state of yet still others (if there's no rain in the clouds, then its not going to rain no matter what else happens). To connect events on either side of a stochastic system is in itself a contradiction.