Re: Qualitative Understanding Of Complex Systems

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QUOCS.  Discussion Note 3

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JA = Jon Awbrey
MW = Matthew West

MW: Non-linear systems I know about and deal with all the time.

MW: I've heard of 3-body systems, but I'm not sure what it means.

Okay, same ballpark, then, or same solar system, anyway.
The sun-earth-moon system would be a 3-body system, and
it exhibits irreducible 3-adicity of the physical kind.
In classical dynamics, you can solve the three separate
2-body systems, sun-earth, sun-moon, earth-moon exactly,
but there is a residue of triple interaction that is
not covered by this pairwise approximation technique,
and things like that, involving non-linearities that
can result in chaotic dynamics, amounted to some of
our first clues about the limitations of classical
dynamics, or at least our capacity to compute it.

At any rate, as I said, it makes sense to deal with the easy cases first,
as we don't even have an initial translation between the formalisms yet.
It's just that when I used to teach linear algebra, I found that it was
necessary to advise people ahead of time about the day when the linear
assumptions would break down, so that they would not give up on math
altogether when the linear methods failed to work.  Sometimes folks
do that if they are misled into thinking that everything is linear.

Jon Awbrey

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