http://www.siam.org/news/news.php?id=827

Eigenvalues. Fixed points. Stable equilibria. Mathematicians like things that stay put. And if they can't stay put, the objects of study should at least repeat themselves on a regular basis, like orbiting planets or populations of predators and prey. Even in the case of chaotic systems, mathematicians have traditionally gravitated toward invariant features, such as strange attractors, stable manifolds, and periodic points.

What makes this tradition possible is that dynamical systems---at least the ones mathematicians favor---are governed by equations that depend on time either cyclically or not at all. But nature doesn't always oblige. Many phenomena require equations whose coefficients are non-periodic functions of time. Indeed, many---arguably most---phenomena can be described not by equations at all, but only as an amalgam of time-varying data.

http://www.larouchepac.com/news/2007/12/28/larouche-whole-operation-paki...

"People are being idiots," he said, "because they say, well, `You can't say that! Let's concentrate on the facts. Let's concentrate on the facts,' is what they'll say. Now here you have, the fact is, we're in the point of a total breakdown of the international financial and monetary system. This is not a collapse; this is not a depression. It's a disintegration of the very integument upon which the whole civilization has now come to depend. That's the game. And, any developments which don't fit the game, don't explain this kind of thing. It's one thing after the other; it's a chaos operation. The tendency is to create chaos; it's a chaos operation. So, therefore, in a chaos operation,-- don't try to attribute chaos, to some individual who's not chaos.

"We don't know who the culprit is; we don't know which faction, who is the faction," LaRouche concluded. "We can identify the faction by the nature of the faction. But the identity of the faction, we don't have. The guy who's doing this, is doing something. We know what they're doing; we know what the effect is they're playing for. That's clear. WHO that someone is, we don't have."

chaotic systems have "attractors" or stable repeating phenomena by definition, pattern just has to be discovered.

http://en.wikipedia.org/wiki/Chaos_theory

Cool to read up on this.

In quantum mechanics when a quanta is released/absorbed the energy of the particle goes up/down one whole step. A gradual change from point A to B does not happen. I don't see why it should not so happen in economic cricumstances when the enrgy goes out of the system all at once. We fall to a new steady state. Economists, stock market watchers and historians have observed lots of chaotic patterns in history, the chaotic "attractors" seem to be similar to the seasons, 4 year cycle, average human life span, civilizational cycle, etc. If Larouche can't find a cyclical ("chaotic") pattern in this systemic breakdown which fits he could read Diamond.

What you are discribing is a State Change or Phase Change, Like when a whole school of fish suddenly turn right.

Liquid to solid. All at once.

Complex Systems Break Down Chaoticly

Chaotically, and in our case due to multiple forces of environmental friction and degradation, rapidly.

Lyndon LaDouche.

I sure hope you are making sweet, sweet fun of that lunatic by posting his ravings.

While what he says may or may not come to pass, it will not be due to anything he posits.

For more fun info about this fascist demagogue:

http://www.publiceye.org/larouche/

I stand with him when he's correct.

The clearest statement yet on chaos theory and the Power Laws in relation to human self organized criticality.

With chaos theory you have attractors or repellers.

The attractors, as noted above by GS in this thread, are most easily seen-as in smoke rings (the smoke particles adhere to the vapor ring).

Less easily seen are the repellers-the force leaks or repels,
say, liquid particles (blood, for instance).

You can only "see" the repellers from "future rewind".

Think an eddy. The blood hits the eddy before traveling to,
say, the face instead of the brain. Which way will the blood flow?

Same with LaRouche's statement. A repeller is forcing
chaos into a new steady state.

Ok I reread the Larouche quote then your suff again and I got the message. Thanks. Repellers forcing inot a new steady state, very good. I keep learning at TOD all the time.