Self-Organization Far-From-Equilibrium
Channel: Systems Innovation
Date: 03/06/2015

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In this module we will be talking about the theory of far-from-equilibrium self-organization. We will firstly discuss the concepts of order and randomness in terms of symmetry and information theory. We will then talk about complexity as the product of an in-between or phase transition state and finally we will discuss the term edge-of-chaos and talk about how self-organization is thought to be dependent upon noise and random fluctuations in order to stay generating variety.

Far-from-equilibrium self-organization is a model that describes the process of self-organization as taking place at a critical phase transitions space between order and chaos when the system is far-from its equilibrium. But lets start by talking about organization. Organization is an ordered structure to the arrangement of elements within a system that enables them to function, as such we can loosely equate it to the concept of order, both order and organization are highly abstract concepts neither of which are well defined within the language of mathematics and science but probably the most powerful method we have for formalizing them is through the theory of symmetry.

The theory of symmetry within mathematics is an ancient area of interest originally coming from classical geometry but within modern mathematics and physics it has been abstracted to the concept of invariance. In this way symmetry describes how two things are the same under some transformation. So if we have two coins one showing heads the other tails, by simply flipping one of the coins over it will come to have the same state as the other, thus we don’t need two pieces of information to describe the states within this system, we can describe this system in terms of just one state and a flipping transformation that when we perform it will give us the other state.

Now say instead of having two coins we had an apple and an orange, well there is no transformation we know of that can map an apple to an orange, they are different things there is no trivial symmetry or order between them and thus we need at least two distinct pieces of information to describe this system. This second system requires more bits of information to describe its state, thus we can say it has higher statistical entropy. The point to take away here is that we can talk about and quantify order and randomness in terms of information theory, that ordered systems can be described in terms of these transformations which we encode in equations, ordered systems are governed by equations whereas random systems are not, but because there is no correlation between the element’s states in these random systems, they are governed by probability theory the branch of mathematics that analyzes random phenomena.

Complex systems are by any definition nonlinear. Complexity is always a product of an irreducible interaction or interplay between two or more things, if we can just do away with this core dynamic and interplay then we simply have a linear system, if the system is homogeneous and everything can be reduced to one level then it might be a complicated system but it is certainly not a complex system.  Thus one of the main ideas or findings of complexity theory is that complexity is found at what is sometimes called the interesting in between, if we take some parameter to a system, say its rate of change or its degree of diversity and turn this parameter fully up what we often get is randomness, continuous change or total divinity of states without any pattern, or if we turn it fully down we get complete stasis and homogeneity with very stable and simple patterns. It is often the case that with too much order the system becomes governed by a simple set of symmetries, too much disorder results in randomness and the system becomes subject to statistical regularities. It is only in-between that we get complexity, on either side of this there is a single dominant regime or attractor that will come to govern the system’s behavior.


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