This shift is going to encompass all the various and fascinating domains of Science. Here is a good explanatory paper from Micheal Baranger at MIT, if you have the time.
Chaos is a very big subject. There are many technical papers. Many theorems have been proved. But complexity is much, much bigger. It contains lots of ideas which have nothing to do with chaos. Chaos is basically pure mathematics, and by now it is fairly well-known. Complexity is almost totally unknown still. It is not really math. It is more like theoretical physics, or theoretical anything. Of course, once it is in good shape, it will use a lot of math, perhaps a lot of new math. So the field of chaos is a very small subfield of the field of complexity. Perhaps the most striking difference between the two is the following. A complex system always has several scales. While chaos may reign on scale n, the coarser scale above it (scale n−1) may be self-organizing, which in a sense is the opposite of chaos.
Perhaps complex systems, such as biological systems, manage to modify their environment so as to operate as much as possible at this edge-of-chaos place, which would also be the place where self-organization is most likely to occur. It makes sense to expect self-organization to happen when there are strong long-range correlations.
I have thought for a while that the underlying nature of reality isnt gaussian– but fractal. But I cant prove it…yet. Here is my favorite part of Dr. Baranger’s paper–
Complexity involves an interplay between cooperation and competition.Once again this is an interplay between scales. The usual situation is that competition on scale n is nourished by cooperation on the finer scale below it (scale n + 1). Insect colonies like ants, bees, or termites provide a spectacular demonstration of this. For a sociological example, consider the bourgeois families of the 19th century, of the kind described by Jane Austen or Honor ́e de Balzac. They competed with each other toward economic success and toward procuring the most desirable spouses for their young people. And they succeeded better in this if they had the unequivocal devotion of all their members, and also if alltheir members had a chance to take part in the decisions. Then of course there is war between nations and the underlying patriotism that supports it. Once we understand this competition-cooperation dichotomy, we are a long way from the old clich ́e of “the survival of the fittest”, which has done so much damage to the understanding of evolution in thepublic’s mind.
In Complex Systems Analysis it has become empirically obvious that the post-coldwar system of US hegemony is collapsing in MENA (Middle East North Africa) : Iraq, Libya, Syria, and Yemen are fully convolved in civil war, there are millions of refugees and displaced persons, a quarter million dead Syrians, and escalating militaries and military spending (Kuwait has initiated a draft). Many complex systems studies predicted the Arab Spring– not a single political “science” study predicted it. The flashpoint for current MENA conflict was the beginning of the Arab Spring, and the revolutions in Tunisia and Egypt– the desire of muslim populations for self-representation in government, fueled by social media and technology, supported by the youth bulge in the regional population curves. All this set against a background of falling oil prices and global warming. In Nonlinear System Dynamics the relevant analogy is a wildlands fire gradually going out of control: the fuel load is the continuing oppression and massacre of Sunni muslim populations, and demographic population pressure carried on the vector of social media. In this model artificial states become destabilized from both within (internal sympathizers) and without (oil price slump) — Oman being the next likely state to collapse, as the US desperately attempts to shore up client states and avoid further destabilizing non-client states.
But what if the collapse isnt gradual? What if there is a sudden spontaneous collapse like a chemical reaction or a sandpile collapse? Abelian sandpiles are a special interest of mine because of self-organized criticality.
Self-organized criticality is so far the only known mechanism to generate complexity.
Why should we be interested in SOC? Because it is how equilibrium and periodic systems become chaotic and then complex. In complex systems we can only make statistical predictions– so I can’t *predict* there will be a sandpile collapse in MENA. I can explore the possibility of one and how it might happen.
In sandpile models collapse occurs as local avalanches or a global avalanche where the whole pile goes flat. What if nation-states tipping into civil war can be considered as local avalanches? What would a global collapse in MENA look like? WWIII perhaps? Or a spontaneous Caliphate? If KSA tipped into civil war would all the states of MENA tip into civil war? The way to model this would be with computer simulations of adaptive complex systems instead of simulating wargames and the massive quantitative analysis that the US devotedly uses to build threat/risk decision matrices.
Right now its just a thought experiment for me…but it seems every day brings us closer to that sandpile collapse. It will be wondrous to behold.