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The old example of the change in phase states: water is solid when frozen, gravitational (equilibrious) when liquid, and chaotic when steam.
Except that when it is steam it closely follows the law of ideal gases and is, therefore, a rather simple system with no structure.

If you want chaos and structure you have to look at the critical point.

At the critical point, the scattering is so intense that the system becomes opaque. This phenomenon is called critical opalescence. The domains demonstrate some interesting properties, such as fractal shapes, and there is a peak in the heat capacity. This critical transition temperature is a maximum with respect to the composition. Thus it can be determined by interpolating transition temperatures from known compositions.
Interesting stuff happens not deep in the phases, but on the phase boundaries.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
by Carrie (migeru at eurotrib dot com) on Wed May 7th, 2008 at 11:26:11 AM EST
[ Parent ]
As I pointed out.

Innovation happens near the cusp or critical point or phase state change.

But the tendency of many whole systems, of many kinds, is motion toward homeostasis, even if elements within are chaotic. Supply meets demand, boy meets girl, oxygen meets fire, wasps meet aphids and a fired cannonball meets the earth. They both need each other - and in meeting become equilibrium.

That's why we need unbalanced people. You can't be a genius unless something's missing ;-)

You can't be me, I'm taken

by Sven Triloqvist on Wed May 7th, 2008 at 11:49:21 AM EST
[ Parent ]
Interesting collection of metaphors - I'm not sure I can make use of it.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
by Carrie (migeru at eurotrib dot com) on Wed May 7th, 2008 at 01:42:24 PM EST
[ Parent ]
They are not metaphors, they are examples of of systems that tend to homeostasis. Admittedly it is not a mainstream view to consider boys meeting girls as tending to homeostasis. But a supply and demand system surely does. And when a cannonball falls to earth, is that not tending to homeostasis?

You can't be me, I'm taken
by Sven Triloqvist on Wed May 7th, 2008 at 02:17:33 PM EST
[ Parent ]
Surely the cannonball isn't an example of homeostasis, as it isn't trying to bring its internal systems to balance? Falling to ground and ending up in a steady state is unconnected.

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Wed May 7th, 2008 at 02:21:17 PM EST
[ Parent ]
It's not just the cannonball, of course. You have to think of the whole system - incuding gravitation. The cannonball's 'internal' systems are unconnected yes, but you are looking at the discrete object, not the system as a whole.

Can supply exist without demand?

You can't be me, I'm taken

by Sven Triloqvist on Wed May 7th, 2008 at 02:35:50 PM EST
[ Parent ]
Well, in your gravitational analogy you're wrong. (Classical) gravitational can convert an infinite amount of gravitational energy into kinetic energy and so have a negative heat capacity which makes them unstable.

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
by Carrie (migeru at eurotrib dot com) on Wed May 7th, 2008 at 04:49:38 PM EST
[ Parent ]
So kissing, for you, is basically a delivery system for mononucleosis?

You can't be me, I'm taken
by Sven Triloqvist on Thu May 8th, 2008 at 09:50:41 AM EST
[ Parent ]
Herpes simplex too.

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Thu May 8th, 2008 at 10:19:49 AM EST
[ Parent ]
Non-sequitur alert!

When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
by Carrie (migeru at eurotrib dot com) on Thu May 8th, 2008 at 10:27:40 AM EST
[ Parent ]
See the forest, not just the trees,
Expand your mind. Let your thoughts drift.
You know it makes sense...

You can't be me, I'm taken
by Sven Triloqvist on Thu May 8th, 2008 at 10:54:43 AM EST
[ Parent ]
Is it not a saying in science that 'You never understand a new theory, you just get used to it' ;-)

You can't be me, I'm taken
by Sven Triloqvist on Thu May 8th, 2008 at 02:26:24 PM EST
[ Parent ]

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