Figure: Chaos and chaotic evolution

Caption: A cartoon illustrating chaos and chaotic evolution.

Further explication:

1. We will NOT fully explicate chaos, but it is the property that causes a system to have super-sensitivity to initial conditions AND to evolve in a very complex way.

2. A chaotic system, even though completely obeying determinism in principle, evolves eventually in completely unpredictable way as a usual rule. The usual rule is because you can NEVER exactly calculate continuous quantities, and so at some point calculational error will cause you to leave the path of true evolution. At that point, the super-sensivitivty and complex evolution conditions eventually lead the calculated evolution to be far away from true evolution.

3. In the cartoon, the two bodies start from nearly the same initial conditions. But since the system of the two bodies is chaotic, the evolution of the two bodies eventually becomes completely different. Unless, the initial conditions were exactly the same, very different evolution must occur eventually.

4. Many systems actually exhibit chaos. But we do NOT see chaos much in the human world. We do NOT build our devices to be chaotic. No one wants a chaotic car engine.