The butterfly effect is the idea that things can be very sensitively dependent on initial conditions. In terms of prediction, it's important, but I think it's less important than a corresponding problem, which is the slight errors in a model. So if you are making a model of what the future will look like and your model is very slightly wrong, you know, to the flap of a butterfly's wings,. Then the differences in the prediction and the real system can propagate forward in same way.

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