Re: Neato chaotic equations for analog computers to display?

From: Dr Chaos (NOSPAM_at_NOSPAM.NOSPAM)
Date: 12/22/04 

Date: Wed, 22 Dec 2004 14:51:53 -0800

Nicholas O. Lindan wrote:
> "John Popelish" <jpopelish@rica.net> wrote
>
>
>>The butterfly effect is an expression of the pinch points that
>>sometimes occur in chaotic systems. At those times and places,
>>infinitesimally small influences change the long term trajectory ...
>
>
> I sit somewhat corrected. Mathematically, I have to concur.
>
> _However_:
>
> o The common man's interpretation of the BE (Butterfly Effect) is
> that this actually happens. Real butterflies, real storms.

True and that may be somehwat misleading. On the space scales
of pressure gradients caused by a butterfly, weather physics damps
it out rather well. In weather the primary instabilities are
mid-latitude storm forming and there instabilities which are still
small on the scale of the planet do make a large difference over
weeks. (much more locally there is strong vertical instability in tropics
and anywhere you get high convection, e.g. thunderstorms).

> o The BE effect as reported in a story about a weather simulation was
> instead a demonstration of the long-term unreliability of the weather
> model.

And why is the weather model long-term unreliable? Wrong physics, or
something else?

>
> o The weather is not a BE system.
>
> o The pinch points in real systems are infintesimal
> and unpredictable.

No, they're the locations in state space with high finite-time
Lyapunov exponents.

> Personally, I believe such a pinch point never existed in reality.
> Large events are driven by large forces from infinitely diverse
> sources.

That's not true---that's the entire point.

>
  No one source has any effect. I can't prove it for love
> or money (or even home-grown tomatoes), but: Go back in time and
> kidnap Edison and the Americans would have to justly admit the
> lightbulb, the record player and movies were invented by the
> French (? TTBOMK), and what's more the French versions were
> better than Edison's.
>
> Ask a Frenchman who invented movies and the answer is the "Pathe brothers".
> Ask an Italian who formulated the laws of motion and it is "Galileo".
> Calculus: Leibnitz. Etc. etc. etc.. So maybe you had to wait a
> few weeks for the next inventor to have the same insight, NBD.
> There is no one _critical_ person/event. [Oh, here I go: Alexander
> the Great, yah?].

general relativity? Nobody was on that trail.