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I don't see how these are all chaotic systems. There are plenty of systems in the universe that are not chaotic. In fact living things, and brains in particular

by simonh 5y ago

I don't see how these are all chaotic systems. There are plenty of systems in the universe that are not chaotic. In fact living things, and brains in particular expend a lot of energy expelling entropy. These systems are complex for sure, but that's not at all the same thing. They are very highly ordered, and could not produce consistent repeatable outputs if they weren't. We can't predict very much about the state of a hurricane a week in advance, but my calendar at work is full of events weeks and months in advance that experience tells me have a very high likelihood of happening much as expected. Our projects are extremely complex and can take years to complete. All of that doesn't look much like a chaotic system to me.

mjburgess 5y ago
I need to do more research on the topic, but I think this is a little bit of an illusion. A chaotic system, K, is one in which the probability of measuring a "high order digit" (eg., 10,000) in the output is sensitive to a "low order digit" in the input (eg., 0.000001). Something like: P(log_o K(state) | log_i state) < 1 where o >> i It seems true that a non-chaotic deterministic function, eg., f(t) can be created such that "K(state) is bounded by f(approximation)". Eg., K(state) is the weather, and f(approximation) is the climate model. Or K(state) is the behaviour of gas particles, and f(approximation) is the gases temperature model. Or K(state) is the changing matter distribution of the universe, and f(approximation) is the stable gravitational field model in our solar system. f() is long-run predictable -- but K() isnt. But we know f() fails in the long-run -- K() does eventually change against the predictions of our model f(). Eg., over long periods of time, the climate changes; the non-ideal gasses may spontaneously condense; the sun "explodes". f() is only ever a locally/apparently deterministic approximation.

by simonh 5y ago

mjburgess 5y ago

I need to do more research on the topic, but I think this is a little bit of an illusion. A chaotic system, K, is one in which the probability of measuring a "high order digit" (eg., 10,000) in the output is sensitive to a "low order digit" in the input (eg., 0.000001). Something like: P(log_o K(state) | log_i state) < 1 where o >> i It seems true that a non-chaotic deterministic function, eg., f(t) can be created such that "K(state) is bounded by f(approximation)". Eg., K(state) is the weather, and f(approximation) is the climate model. Or K(state) is the behaviour of gas particles, and f(approximation) is the gases temperature model. Or K(state) is the changing matter distribution of the universe, and f(approximation) is the stable gravitational field model in our solar system. f() is long-run predictable -- but K() isnt. But we know f() fails in the long-run -- K() does eventually change against the predictions of our model f(). Eg., over long periods of time, the climate changes; the non-ideal gasses may spontaneously condense; the sun "explodes". f() is only ever a locally/apparently deterministic approximation.