DIYbanter - View Single Post

On Wed, 22 Feb 2006 15:17:04 +0000 (UTC),
(Ken Smith) wrote:

In article ,
John Larkin wrote:
[....]
Of course you can't determine what a small change does to a real-life
chaotic system, because there's nothing to use as a no-stimulus
reference. But you can simulate a chaotic system, with and again
without some stimulus, and compare the results. In a healthy chaotic
system, any, even the tiniest, change results in increasing effects;
if you wait long enough, any small disturbance grows to total,
grand-scale differences in system state. The longterm differences
between a small pertubation and a large one are indistinguishable;
*everything* looks different.

When I lift my arm it appears to move smoothly upwards. The nerves and
muscles are in fact a chaotic system. If you look at one cell, for lift
to lift, the action of that cell can't be predicted. My arm, however,
still rises smoothly.

The "hit and miss" regulator's pattern of on and off is hugely different
when you make a small change in the load but the output voltage remains
near constant.

The chaos here is restrained by a larger, slower, but more powerful
overall negative feedback system.

Both these are examples of systems that robustly chaotic and yet the
average results are easy to predict.

But now consider whether your arm will be "up" or "down" at exactly
noon of January 6, 2008. If I had washed my car, the result would
likely be different.

If you wash your car, you may indeed change where the thunderstorm
happens, however, you won't bring on a new ice age, or at least the oddds
are so low they aren't worth bothering with. If instead, you decreased
the output of the sun by 20%, a new ice age is going to happen.

There are many implications to washing my car. Other people who drive
by may slow down to avoid hitting me in the street, or just to admire
my form. That changes the timing of their lives, and of the timing of
the lives of everyone else they interact with. And those disturbances
spread around the world. A male makes something like a billion sperm a
day, and only one sperm gets to fertilize an egg. The slightest
disturbance, like taking the time to notice me washing my car, or even
to read this word stirs up your prostate enough that whatever kids
you might have had are now different kids. And they influence
thousands, millions of other people and change *their* kids. So my
washing my car (which, out of consideration for posterity, I didn't
do) would have entirely changed the population and the political
dynamics of the world a few hundred years from now, including all the
legislatures and UN committees and all the people who attend global
warming conferences.

The Earth oscillates, very noisily and aperiodically, between ice ages
and jungle ages. Whether we'll be hot or cold 200,000 years now could
be changed by the tiniest extra input to the system. Certainly a major
change in solar output would change climate, but the noisy swings
about the mean, the chaos component, are large and exquisitely
sensitive to input.

John