I would say it's a good example of the kinds of behavior that can occur in
nonlinear systems -- a chain of ever-increasing effects starting from a
seemingly insignificant cause. The applied mathematician in me wants to
say it isn't a god example _of_ nonlinearity because it doesn't say
anything about the underlying dynamics :-).
>Chaos theory (after all, many
>nails could be missing, but because of the lack of *this* nail the
>kingdom was lost, surely an unpredictable result)?
Interesting point. I would say yes and no. Yes, because there was no way
of predicting in advance that the loss of that particular nail would cause
such a significant result. But in another sense the answer could be no.
That saying is told to children to warn them of the potential consequences
of small negligence. So in a sense the human race knows about the
potential harm that can be caused by chaotic processes starting from a
seemingly insignificant oversight, and cautions people in their education
to attend to the small details to prevent unexpected bad results.
I read -- or tried to read -- Mandelbrot's book, "The Fractal geometry of
nature" a number of years ago and was quite intrigued by the ability of
nonlinear dynamical systems to build up very detailed fine structures
rapidly.
I was quite symapthetic to the young-earth view at the time, and my
immediate reaction was that nonlinear dynamics might be a part of the
answer to how God could have brought about the complexity of nature as
quickly as the young-earth creationists believed he had. Later on I had to
acknowledge that the geological evidence indicated the earth is 4.6 billion
years old or so, but that didn't change the fact that nonlinear dynamics
may have been one of the methods God used in bringing about the beautiful
complexity we see in nature.
>
>Sort of seriously,
Likewise.
>
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Bill Hamilton | Vehicle Systems Research
GM R&D Center | Warren, MI 48090-9055
810 986 1474 (voice) | 810 986 3003 (FAX)