Quote:
Originally Posted by CraigS
A few definitions may be in order here, (from various sources)…
A non-linear system is one whose output is not directly proportional to its input.
A deterministic system is a system in which no randomness is involved in the development of future states of the system.
Small differences in initial conditions of a system, (such as those due to rounding errors in numerical computation), yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.
This happens even though these systems are deterministic, meaning that their future behaviour is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behaviour is known as deterministic chaos, or simply chaos.
More later .. gotta go.
Cheers
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I know the definitions, Craig, but that still doesn't change what I said. In their strictest sense, they're not truly chaotic. It's a case of bad use of words to describe what's happening. They may not be predictable systems, in so far as their outcomes are concerned, but there is an underlying order driving these systems to whatever outcomes they are heading towards. Once the initial conditions are set, the outcomes are what they'll be, but you have no way of predicting what they'll be. Basically, to be able to predict outcomes in systems such as these, you would have to know of every possible existing variable of the system along with every possible combination/cause for those variables. An indefinite set of variable and cause/effect outcomes. Impossible to model, unless it obeyed something similar to the quantum principle of superposition of state and Heisenberg's Principle.