| Sensitivity to initial conditions, popularly called the butterfly effect, does not suffice to establish the presence of chaos. Also required are |
| * arbitrarily close to every state is a periodic state, a pattern of events that repeats, and |
| * for every state, a collection of neighboring states eventually will evolve to intersect a collection of states neighboring every other state. |
| The doubling map gives a simple mathematical example that the butterfly effect does not imply chaos. |
| Part of the appeal of the butterfly effect is its familiarity. Many examples are found in literature. For instance, in "The garden of forking paths" by Borges, if Captain Madden had arrived at the train station a very few seconds earlier, he would not have missed the train carrying Dr. Yu Tsun. Apprehended, Tsun would not have murdered Dr. Stephen Albert, communicating to Berlin the name of the city, Albert, housing the British artillery park which the Germans bombed, delaying the attack on the Serre-Montauban line. |
| Closer to home, with some thought almost everyone can find moments in which seemingly insignificant choices in their lives have lead to substantial changes. For example, ... |
| Michael Schermer presents an example in which a tiny coincidence seems to have had a major consequence in the Civil War. |
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