Did you know that you can "map" the entire Universe in a circle of radius 1 cm? Yup. It is called Conformal Mapping, and is very useful in advanced Calculus. For every point "out there", you can mathematically define exactly one point "inside" the circle. The further out the real point, the closer to the center of the circle will be the conformal point. The exact center of the circle corresponds to all points at an infinite distance from the circle.

Fascinating !

Intuitively and intellectually it is hard for me to shake idea that this map of the “real” universe is at its very core organized around an attractor that is constantly moving toward an extremely stable point. This “movement” of time we see gravity and organized evolving systems that we perceive as a dynamic universe manifest as an interplay between a single point of stability at the exact center of our sphere and the instability of conscious biological life that surrounds it. “Organized Reality” is generated as a constant oscillation between theses contained points. The center point that has no movement simply because of its central location within the sphere and all the infinite possible points revolving and interacting around that single point. This is not a novel idea in physics until we place it in the sole context of all physical phenomenon existing as a self contained conscious reality.

Dynamical systems theory also deals with probability and can therefore allow us to synthesize thermodynamics and so-called "Chaos", (which is really a highly complex form of hierarchical, enfolded order that appears to be disorder). The really interesting area here though, is the entities at the transition zone between ordered, stable systems at equilibrium (maximum entropy) and "disordered" (but complex) and unstable Chaotic (minimum entropy) ones. According to the Nobel laureate Ilya Prigogine, these far from equilibrium dissipative systems locally minimize their entropy production by being open to their environments --- they export it in fact, back into their environments, whilst importing low entropy. Globally, overall entropy increase is nevertheless preserved, with the important caveat that the dissipative system concerned often experiences a transient increase (or optimization) of its own complexity, or internal sophistication, before it eventually subsides back into the flux.

This is known as the region of alternatively, Emergence, Maximum Complexity, Self-organized Criticality, Autopoiesis, or the Edge of Chaos. (Nascent science debates nomenclature routinely - and appropriately, in this case, the crucial point being that they are all different terms for essentially the same phenomena.)

Life forms, ecosystems, global climate, plate tectonics, celestial mechanics, human economies, history and societies, even consciousness itself - all manifest this feedback-led, reflexive behavior; they maximize their adaptive capacities by entering this region of (maximum) complexity on the edge of Chaos, whenever they are pushed far from their equilibrium states, thereby incrementally increasing their internal complexity, between occasional catastrophes.

Remarkably, this transition zone is mathematically occupied by The Golden Mean. This ratio acts as an optimized probability operator, (a differential equation like an oscillating binary switch), whenever we observe the quasi-periodic evolution of a dynamical system. It appears in fact, to be the optimal, energy-minimizing route to the region of maximum algorithmic complexity, and to be a basin of attraction for the edge of Chaos. Universo: Dynamical Symmetries, by Nigel Reading