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I am admitedly hard-headed but I still do not think that your examples demonstrate chaos theory or explain why my position is flawed.
Neither the domino example nor the 3-body problem are analogous to the butterfly example.
The domino example falls short for several reasons: a) there is only one element (the dominos), there is no intereference from other elements (reinforcing or dampening) and there is no provision for amplifying the magnitude of the effect as it ripples through the system.
The three body problem is also different than the butterfly example. The 3-body problem is one of sensitivity to initial assumptions. For example, how the universe formed (galaxies with space between them) is entirely dependent on (among other things) the mass of electrons and anti-electrons. Change either of those masses in a nearly infinitely small amount and the post- Big Bang universe is very different. Why? Because there are so many electrons and anti-electrons. Change the mass of a single electron (a single butterfly) and nothing happens.
It seems to me that what you are argueing as a chaotic system is more like the following example: a germ microbe infects a flea that bites a mouse that then goes nuts and chews through some wires in a nuclear submarine causing a meltdown that brings down the sub. So, in this example, a butterfly flapping its wings which blew the microbe left instead of right thereby infecting the flea did, in fact, lead directly and traceably to a nuclear explosion. This example, however is not an example of chaos theory in action.
Ultimately, a theory has to aid in our understanding of an event. My problem with the butterfly example is and remains that it really doesn't do or say anything nor does it prove or even allege anything that we didn't already know. When we see it raining in Japan, it is not illuminating to postulate that the rain might have been caused by a minute event that happened over a year ago. Obviously something caused the rain - but chaos theory as explained in the butterfly example brings us not one inch closer to understanding what or why. Nor does it eliminate any false notions of what caused the rain. Basically, its useless -we are no closer to the truth nor are we any further away from a lack of understanding than we were before the "theory" was introduced.
That is why I have such an academic contempt for this example - it sounds really smart but its as empty as outer space.
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