Lawrence,
Let me go back and clarify my distinction of linear vs. non-linear. Obviously linear is sequential, yet this is a very broad category, from simple steps to complex changes. Non-linear is randomness. For example, think molecules of water. Yet there is a great deal of order in this as well. For one thing, it can be measured as a scalar, be it temperature, pressure, weight. There is also the entropic effect, as the various parts bounce into each other and trade energy, speeding the slower and slowing the faster ones, to reach an equilibrium state. There is also Newton's dictum of every action being matched by an equal and opposite reaction. Logically the action, being so defined, is linear, while the reaction of its environment is non-linear, so there is a natural balance between the motion of the particular and the reaction of its environment.
Now these two processes are intimately entwined, like the non-linear gut activity propelling the organism. Evolution is a good example of the situation, as we think in terms of linear progression, such as through generations of organisms. Yet it is much more of a scalar process, as progress needs to be supported by all the activities of the environment, as simple forward action tends to be balanced and negated by the larger quantity of activity. So there has to be the constant feedback and the resulting scalar activity is what actually determines the overall direction. Sort of like a tree has to grow out in all directions for the sequencing of rings to form. Like trying to introduce modern technology into a less complex society that lacks the broad cultural knowledge to use it.
So there is this mutual dichotomy of the actions of the particular and that of the mass of activity. Nodes and networks are a model of this relationship.
You might say the non-linear is the "course-graining" within the particular frame or space.
Now the problem, as I see it, is that there is an overwhelming bias to describe the particular, the node, as fundamental, but the logic doesn't really support this.
Consider how you conflate "state" with one electron. The idea of the entire universe as one "atom" was most forcefully put forward by LeMaitre, in his original argument for what ended up being called Big Bang theory.
Yet "one" is something clearly defined as a unit, ie. is distinct from its environment. On the other hand, a state, particularly a neutral state, is more of a zero. There is no set of boundaries or distinctions. It could well be infinite, as once it is clearly finite, then it becomes, not so much a state, but a set of all that it contains and thus a unit within the larger context.
This goes to the heart of my arguments against Big Bang Theory, in that it argues for the entire universe as a particular unit and attempts to totally erase any concept of a larger context. Now this model is having to admit other universes, yet still cannot condone the idea of any environment to form and contain them. Yet whether we want to admit to a larger context or not, it is essential to creating the unit, by setting boundaries. As it is, our current theories have any number of holes, from the singularity to dark energy, to suggest outside connections.
The electron could as well be a fluctuation of the void. One node popping up in the infinite network of potential.
