Re: Importance of chaos theory



On 30.7.2010 17:53, unruh wrote:
On 2010-07-30, Tom St Denis <tm@xxxxxxx> wrote:

I don't know if that's considered "chaotic." In my mind a chaotic
function is one which behaves highly non-linear even with respect to a
great many sample points. Like I can know the temperature for the
last 100 days but I still can't plot out to tomorrow let alone next
week, let alone next month.

Sure you can. The temp may well be chaotic, but that does not stop one
being able to talk about climate. The earth's orbit is chaotic, but that
does not stop us from being able to predict the earth's position next
year (or even 1000 years) with amazing accuracy

I'm not nearly an expert but that is, as far as I understand it, at the
heart of it. A chaotic system implies both non-periodicity in the strict
sense - you don't *ever* get exact repeat of a long enough sequence -
and an "attractor", mostly meaning that, as a pattern-seeking minds, we
clearly see some type of patterns in the data set. It's exactly what
happens with multi-body physics: we "see" planetary orbits and can
approximate planets' positions in the future but we can never calculate
100% exact (down do individual atoms) positions.

I think that this difference between what is approximated and what is
"exact" could be a good source of true randomness but probably not easy,
as the "attractor" part of the whole thing means there can be false
periodicity if measured with insufficient precision (for the planetary
example: if we allow loss of precision we can arrive at completely
predictable orbits, useless for randomness, but on the other hand,
unfortunately, we cannot measure planetary positions to within
atom-sized levels of precision and use that for a source of randomness).

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