Our life in CHAOS: butterfly effect and science

In all chaos there is a cosmos, in all disorder a secret order. (Carl Jung)
 

Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?
While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on.
Can we use chaos for climate predictions? What's the science behind this concept?

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