hey nebody havin gud knowledge abt mathematics of chaos plz post a gud hyperlink for it...it must be comprehendable 4 beginners tooo..

3 simpl start@ http://www.imho.com/grae/chaos/chaos.html

THE EDGE OF CHAOS, as the optimal state-position for information-processing, creativity and intelligence, biological efficiency and performance

The Edge of Chaos -- a system midway between stable and chaotic domains. The Edge of Chaos is both a simple concept and infinitely difficult: at this point we do not know what will happen, only that something interesting will happen (as new patterns or properties will emerge).
The Edge of Chaos yields self-organizing, self-maintaining dynamic structure that occurs spontaneously in a far-from-equilibrium system. The Edge of Chaos is a place where the parallel processing of the whole system is maximized -- the system performs at its greatest potential and is able to carry out the most complex computations.
Complex adaptive systems, like individuals, families, organizations and nations, are able to adapt more effectively in turbulent environment, when they are functioning in a mode that is described as The Edge of Chaos. Stuart Kauffman, theoretical biologist who studied Phase Transition, points out that dynamic systems are at their optimum performance potential at the phase transition states. It is also a time of great mental turmoil, if the system is a human being. We all have heard the stories of
great thinkers, writers and artists who live at the edge of chaos where creativity evinces itself. It is a poised state between stability and instability, order and chaos, "a self-organized criticality".
"Self-organized criticality is a new way of viewing nature...perpetually out-of-balance, but organized in a poised state." Per Bak, "How Nature Works"
Christopher Langton, one of the founders of artificial life, in his studies of the cellular automata discovered that they display interesting complex life-like behavior near the border between order and chaos -- on the edge of chaos. If they were ordered, they would be too predictable to be interesting; if they were less ordered, they would be too chaotic and, again, boring.
There is no universal constant, or critical value, for the edge of chaos. You have to construct a path and wander along it, looking for the transition between order and chaos.
The complexity scientists claim that evolution tends to push systems towards the edge of chaos where complex, most interesting behavior such as life can occur.
"Chaos often breeds life, when order breeds habit." Henry Adams, american essayist and historian

Wonderful post above on The EDge of Chaos








The problem is when you at least think that a simple time entropically considered, can become increasing complex entropically as we see what lies around us today. But there are some problems when you go to that simplier time and there, you would think this is where chaos rules? Chaos would to me imply "discretism" while continuity and flow of energy, understands the cohesion between all events?

Phase Transitions?

G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1).

Is that possible?

Thanks, Plato !

Complexity Theory, and its three aspects -- fractals, chaos, and self-organized criticality... And The Vortex Theory... To understand the laws of evolution will allow us to live more consciously, to tune into the evolutionary principles within ourselves and the universe.

"Unless we understand how nature works at all levels and in all dimensions, we are on a collision course." Per Bak

One good turn, always deserves another?

Robert Laughlin as a condense matter theorist saids it doesn't matter which building blocks you use? What is the "organizing principal?" Of course, I have thoughts on that. I like to think outside the box too: )

So...what is that "organizing principle"?

...hopefully, it has nothing to do with the anthropomorphic perceptions of the observer. ...or does it? ;O) (Philosophy and science are so weird that way.)

Personally, I no longer accept the idea of "chaos." There is only order that we do not, as yet, understand.

Hello, guys !
Complexity occurs only at one very special point -- at the Edge of Chaos point.
The Edge of Chaos is the state-space where the parallel processing of the whole system is maximized;
in other words, the system is at its best in terms of its efficiency and performance.
Evolution tends to push the complex systems towards the Edge of Chaos -- the point of self-organized criticality.
And it is a new way of viewing nature ... perpetually out-of-balance, but organized in a poised state. (Per Bak, "How Nature Works")

In the past, it has been assumed that large systems, such as those we find in biology and economics, are in a stable balance. Yet, power laws, characteristic of self-organizing critical systems, have an interesting property.
Events are not periodic (though they appear to be, because large events happen rarely). Rather, the opposite holds:
"The power law indicates that the longer you have waited since a large earthquake at a given location, the longer you can expect still to have to wait... Earthquakes are clustered in time, not periodic." Per Bak

It is well-known that any process of creation passes through the stage of chaos -- of uncertainty, instability, emotional turmoil, searches through options among multiple attractors, phase transition, emergence of new properties...
"At the branch points where something new emerges, disruptions of order are in fact necessary. Indeed, the interplay of order and chaos constitutes the creative potential of nature. Much of the order seen in organisms stems from spontaneous generation from systems operating at the edge of chaos."
Stuart Kauffman, "The Origins of Order:Self-Organization and Selection in Evolution"

The importance of chaos was not fully appreciated until the widespread availability of digital computers for numerical simulations and the demonstration of chaos in various physical systems.
This realization has had broad implications for many fields of science, such as biology, economics, chemistry, engineering, fluid mechanics, physics, and so on.

P.S. Ilya Prigogine defines complexity as "the ability to switch between different modes of behavior as the environmental conditions are varied." Sounds like creative adaptability !?

Pasteur saw dissymmetry as the very characteristic of life (DNA takes the form of a left-handed helix).

Well Warren it has been extremely long road to trying to piece this together in my mind, so I might of thought I'd actually accomplished something?

What is the orgqanizing principal? Of course it's music. You knew that though didn't you:)

But having come to understand there is a value in terms of energy to discretism(reductionism), I couldn't help think that there were different ways to color our world.

So of course with all probabilistic thinking how did such things emerge according to the position the mind takes when it has assumed something about the reality we currently live. Is it that, "like begets like?"



So you look for "this beginning" and then, all things secondary emerge from it? Is there ever only "one" beginning, or many? You had to know what the blackhole amounted too, and what was accomplished, with Strominger.

Pattern Recognition


So I looked at Pascal's triangle as well as the Riemann Hypothesis.

Where and how did these numbered systems all begin and emerge from? So in nature, we see different math systems emerge out of microstate perspectives? Conformal theory and what is it telling us about Bekenstein Bound within context of the blackhole?

Can this condition be re-created for us in our atmosphere? Why most certainly. In RHIC? Of course ,and the result is something quite amazing.

Chaos Theory -- http://www.crystalinks.com/chaos.html