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Saturday, August 14, 2010

Spontaneous Order and Far-From-Equilibrium Systems

In atomic-chemical environments, we have three states of matter: solid, liquid, and gas. This is what people generally understand to be true, but it's in fact only 3/5 of the picture. In fact, we have transition states between solid and liquid and between liquid and gas. Crystals, for example, are solid and orderly. Water is of course liquid between just above 0 C and just below 100 C. But there is a transition state between crystal order and liquid chaos known as liquid crystals. Another feature of this transition state is that it is far-from-equilibrium, meaning the parts interact in a dynamic fashion, creating strange atractors and, thus, complex dynamics, in their interactions. This is a dynamic order of a different kind than that of crystals, but which appears disordered relative to the simple crystal order. What has all these fatures, of dynamic, far-from-equilibrium liquid crystal order? Living cells, of course. As Peter T. Macklem in "Emergent Phenomena and the Secrets of Life" observed, "We the living exist in a complex regimen in the phase transition between order and chaos. We are there because that is the only place we can be both ordered but adaptable, stable but able to evolve. Crystals are stable and ordered but cannot adapt or evolve. Weather evolves but is unstable and cannot survive" (J. Appl. Physiol. 104: 1844-1846, 2008). However, as we can see from the way I have described it, Macklem is only partly right. Life is not in the transition state between crystals and weather, but between crystals and water. There is in fact something in the transition state between water and weather, and those are known as hurricanes. One will note that hurricanes can and do in fact survive sometimes for days or even weeks at a time. In both kinds of order that occur in the phase transitions, there is a "narrow range of energy consumption over which phase transition occurs" (Macklem). Hurricanes occur if and only if the exact right conditions occur. But if we consider the number of tropical storms and hurricanes in any given year, we can see how often the exact right conditions can in fact occur. And clearly the right conditions occured for the emergence of life becasue, well, here we are.

Of course, what we are talking about here is phase transitions between states of matter. This region will of course be more orderly in the region between solid and liquid than it will be between liquid and gas. The stability of the order between solid and liquid will create more opportunities for the development of strange attractors to create more complex order within such a system. This level of stability is probably why simple cells are able to develop into more complex organisms -- the greater order creates more structural possibilities.

One such structural possibility comes about with the brain. The brain is a complex network of communicating cells with a pretty tight and complex level of communication. Information is able to be transmitted across the entire network of neurons in a more rapid way than a muscle cell in the toe could communicate information to a skin cell on the scalp without neurons (i.e., it would have to rely on chemical diffusion, or at best transmission through the blood stream -- both of which are highly imprecise). The brain is thus more complex than any other organ. Other organs are more orderly -- but it is precisely the brain's disorderliness, pushing it into the realm of phase transition, that makes it more complex. Indeed, the human brain probably lies in the phase transition between order and chaos. A human brain too orderly is likely to be more like an animal's brain, while a human brain too chaotic is likely to exhibit features of mental illness. More creative people perhaps lie closer to the chaotic region, where the brain is farthest-from-equilibrium without falling into complete chaos, allowing them to be highly creative. Indeed, the far-from-equilibrium region is the region of maximum creativity. The healthy human brain thus lies in the phase transition between order and chaos. Too much disorder, the the system falls apart -- gets thrown into chaos (and mental illness in the brain); too much order, and the system rigidifies. How do we get too much order in a complex system? Simplfying processes create too much order. As the system simplifies, it first enters into more and more regular rhythms, becoming more and more predictable in its behavior, until it collapses into a more rigid order lacking growth and creativity. The closer it approaches simple order and, thus an equilibrium state, the closer it approaches death. In the cell this means dying. In the brain, this means collapse into animalistic behaviors.

And what of the kinds fo systems which arise out of the interactions of people? As with each of the systems mentioned, you have to have a certain number of elements before you are able to achieve complex dynamics. This varies from system to system. But one reaches a point where there are enough elements interacting in complex enough fashion that a phase transition occurs, and one gets far-from-equilibrium states with complex dynamics. F. A. Hayek called this spontaneous order. We can find it in social orders of all kinds -- from the arts to morality to language to the economy. Societies range in structure from rigid order to chaos. From a global perspective, a state of wandering tribes would constitute "chaos". Constructivist societies -- various forms of socialism, for example -- would likely consider "rigid order" in this definition. The kind of society that would emerge in the phase transition, made up of networks of people of high enough concentration and population size, would constitute spontaneous orders. Such an economy, for example, would neither be one of rigid order (that is, an economy at equilibrium) nor of chaos. We can compare the state of an economy to that of the brain. One with too much chaos does not have enough structure. It flies apart -- or, more likely, has never come into being. One at equilibrium is dead (one may note that an economic theory where equilibrium is assumed is an economic theory of a dead economy). One approaching equilibrium is dying -- and the first indication of its dying is that it has entered into regular cycles. Of course, an economy may not die at one go. Rather, it may emerge into a less complex state -- move from a typical unemployment rate of 5% to one of 10%, say. Something as complex as an economy could simply ratchet itself into rigidity and death.

A healthy economy, on the other hand, is one with complex dynamics, a network structure that is far-from-equilibrium, structured by both positive aand negative feedback and, as a consequence, creative. Prices, goods, labor, capital do not reach equilibrium and, as a result, create entrepreneurian opportunities. Goods are moved to where they are needed and new products are invented. Resources, including labor and capital, are thus properly allocated within relatively short periods of time. This is a theory of a real economy.

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