Hello, I've used the search button but the topic I found on it didn't quite answer my questions, so here is my go at it: (I have done one year of maths at college, to know my level in case it's important for formulating your answer)(adsbygoogle = window.adsbygoogle || []).push({});

So I've started reading "The End of Certainty" by Prigogine dealing with the enthralling area of non-equilibrium Thermodynamics, coming to the discussion of determinism and chaos theory.

Is the three body problem important for two things? As I understand it:

No Exact Method Known:but it can be approximated numerically -- am I thus right to assume ithasa solution, in the way that any given, exact, mathematical starting point will result in only one possible evolution?Chaotic Behaviour:in general chaos emerges, and this could mean two things (I don't know which, maybe both, in relation to each other)

in the Approximation:you can approximate the exact solution numerically, but the approximation and the exact solution always diverge for [tex]t \to \infty[/tex] (as an analogy I'm thinking of any finite polynomial approximation (and thus unbounded) to the bounded sine function)in the Starting Points:two very near starting points can have very different evolutions; to make this exact I'd try to say "there is a certain number M so that for all ensembles of starting points (in the phase space), there will always be at least two starting points in that (small) ensemble with their evolutions in phase space, for [tex]t \to \infty[/tex], a greater distance apart than M" (it's just an attempt to grasp it, don't shoot me,notclaiming this is correct).

And then I also wonder: why is this of such importance in the discussion of determinism?

Is it that in making the jump to physics, one has to rely on measurements to find out the starting point, and we know (practically in classical mechanics, theoretically in quantum mechanics) that the 'error' in measurement is never non-zero; this in combination to the fact it's achaotic systemandwe havenoaccess to theanalytical solution, this system becomes indeterminate (practically in classical mechanics, theoretically in quantum mechanics)?

Thank you,

mr. vodka

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# Three Body Problem (and Chaos Theory, Determinism and Prigogine)

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