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What I tried to say is that I have a hard time establishing any cause-and-effect relationship between an independent (air movement from a butterfly flapping its wings) and a dependent variable (weather in Japan) in a chaotic system.
But how is this different than you pushing a line of dominos, resulting in the last domino falling? It seems like you're arbitrarily "deciding" that a butterfly cannot possibly have an affect a year later around the world. Chaos theory highlights the dependency of massive outcomes on tiny events, that's the entire basis behind it.
Let me put it another way: is anyone saying that had the butterfly not flapped its wings that it would not have rained in Japan? It sounds to me like that is what the example is suggesting and I'm saying that the idea is ridiculous.
That's exactly what the theory states. Allegorically of course. Always keep in mind this is an allegory, the butterfly just REPRESENTS an infinitismally small alteration of the initial conditions.
One initial condition, A, is the butterfly does flap its wings. It rains in Japan a year later.
Initial condition B, is the butterfly does NOT flap its wings. Japan goes through drought.
The initial conditions, tiny and almost identical, have enormous impact on the final outcome: That little deviation, between flapping and not flapping, exponentially propogates into a massive change.
I was saying that a scenario whereby the butterfly is the straw that broke the camel's back is (to put it mildly) not plausible because of the number and frequency of interactions that occur between the butterfly and the rainstorm.
That may be true, but it's not the point. Whether it's the butterfly that actually causes the storm is completely irrelevant. The allegory is demonstrating that something (whatever it is) as small as a butterfly flapping its wings, can determine whether a huge event does or does not happen.
A tiny event results in a massive difference in outcome.
To adopt the butterfly theory is to ascribe an equal liklihood to each of the variables which is to render each of them essentially negligible.
Again, there is no butterfly theory. Chaos theory does not ascribe equal likelyhood to all variables, but states that all variables are capable of enormous impact on the end result, even tiny ones.
To assume that one variable out of a trillion can propogate through the entire system - reinforcing everything in its path or its successor's path so as to rival the magnitude of a weather pattern defies any application of common sense.
Why does it defy common sense? Just because it seems unlikely? I think common sense would say that if you knock over the first domino, the last one eventually falls. There's nothing that should suggest a major event can't start from a tiny, tiny key event.
The 3-body problem, imho is a different problem - the variables are discreet in number and, therefore, traceable.
They are no more traceable than the butterfly scenario. The variables in a 3 body problem could be as numerous as the atoms in each celestial body.
In a chaotic system, the variables are not traceable therefore, the notion of cause and effect has no application. While the butterfly may have flapped its wings and it may have rained in Japan, wether the two events are dependent or independent is unknowable.
It's only unknowable due to the fact that you can't be infinitely accurate. If you had a set of infinitely accurate measuring tools, you could definitely spend an infinite number of years doing calculations that eventually trace back to a butterfly flapping its wings.
In Zen, we can speak about chaos but never of chaos.
Chaos is the supreme ideal of Taoism. Chaos is wholeness, oneness, and Nature. Chaos represents the natural state of the world. Digging holes in the head of Chaos means destroying the natural state of the cosmos.
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