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Davies discusses the work of Ilya Prigogine on self-organizing systems. When energy systems are driven far from equilibrium they can exhibit spontaneous changes in behavior that are unpredictable. New self-organized structures may be formed leading to increased complexity and variety.


Davies, Paul The Cosmic Blueprint Simon & Schuster, New York 1989 [abridged— 1500 words] — self-organized structures

Anyone who has stood by a fast flowing stream cannot fail to have been struck by the endlessly shifting pattern of eddies and swirls. The turmoil of the torrent is revealed, on closer inspection, to be a maelstrom of organized activity as new fluid structures appear, metamorphose and propagate, perhaps to fade back into the flow further downstream. It is as though the river can somehow call into fleeting existence a seemingly limitless variety of forms.

What is the source of the river’s creative ability?

The conventional view of physical phenomena is that they can ultimately all be reduced to a few fundamental interactions described by deterministic laws. This implies that every physical system follows a unique course of evolution. It is usually assumed that small changes in the initial conditions produce small changes in the subsequent behavior.

However, now a completely new view of nature is emerging which recognizes that many phenomena fall outside the conventional framework. Determinism does not necessarily imply predictability: some very simple systems are infinitely sensitive to their initial conditions. Their evolution in time is so erratic and complex that it is essentially unknowable…

Many physical systems behave in the conventional manner under a range of conditions, but may arrive at a threshold at which predictability suddenly breaks down. There is no longer any unique course, and the system may ‘choose’ from a range of alternatives. This usually signals an abrupt transition to a new state that may have very different properties. In many cases the system makes a sudden leap to a much more elaborate and complex state. Especially interesting are those cases where spatial patterns or temporal rhythms spontaneously appear. Such states seem to possess a degree of global cooperation. Systems which undergo transitions to these states are referred to as self-organizing.

Examples of self-organization have been found in astronomy, physics, chemistry and biology. The familiar phenomenon of turbulent flow mentioned already has puzzled scientists and philosophers for millennia. The onset of turbulence depends on the speed of the fluid. At low speed the flow is smooth and featureless, but as the speed is increased a critical threshold occurs at which the fluid breaks up into more complex forms. Further increase in speed can produce additional transitions.

The transition to turbulent flow occurs in distinct stages when a fluid flows past an obstacle such as a cylinder. At low speed the fluid streams smoothly around the cylinder, but as the speed is increased a pair of vortices appears downstream of the obstacle. At higher speeds the vortices become unstable and break away to join the flow. Finally, at yet higher speed the fluid becomes highly irregular… The fluid has available to it unlimited variety and complexity, and its future behaviour is unknowable. Evidently we have found the source of the river’s creativity…

The simplest type of self-organization in physics is a phase transition. The most familiar phase transitions are the changes from a liquid to a solid or a gas. When water vapour condenses to form droplets, or liquid water freezes to ice, an initially featureless state abruptly and spontaneously acquires structure and complexity.

Phase transitions can take many other forms too. For example, a ferromagnet at high temperature shows no permanent magnetization, but as the temperature is lowered a critical threshold is reached at which magnetization spontaneously appears. The ferromagnet consists of lots of microscopic magnets that are partially free to swivel. When the material is hot these magnets are jiggled about chaotically and independently, so that on a macroscopic scale their magnetizations average each other out. As the material is cooled, the mutual interactions between the micromagnets try to align them. At the critical temperature the disruptive effect of the thermal agitation is suddenly overcome, and all the micromagnets cooperate by lining up into an ordered array. Their magnetizations now reinforce to produce a coherent large scale field…

The foregoing examples of self-organization occur when the temperature is gradually lowered under conditions of thermodynamic equilibrium. More dramatic possibilities arise when a system is driven far away from equilibrium. One such case is the laser. Near to thermodynamic equilibrium a hot solid or gas behaves like an ordinary lamp, with each atom emitting light randomly and independently. The resulting beam is an incoherent jumble of wave trains each a few metres long. It is possible to drive the system away from equilibrium by ‘pumping’, which is a means of giving energy to the atoms to put an excessive number of them into excited states. When this is done a critical threshold is reached at which the atoms suddenly organize themselves on a global scale and execute cooperative behaviour to a very high level of precision. Billions of atoms emit wavelets that are exactly in phase, producing a coherent wave train of light that stretches for thousands of miles…

Dissipative structures
Self-organization occurs both in equilibrium and non-equilibrium systems. In both cases the new phase has a more complex spatial form. There is, however, a fundamental difference between the type of structure present in an ice cube and in swirls of water in a stream. The former is a static configuration of matter, frozen in a particular pattern. The latter is a dynamical entity, generated by a continual throughput of matter and energy from its environment.

It is now recognized that, quite generally, systems driven far from equilibrium tend to undergo abrupt spontaneous changes of behaviour. They may start to behave erratically, or to organize themselves into new and unexpected forms. Although the onset of these abrupt changes can sometimes be understood on theoretical grounds, the detailed form of the new phase is essentially unpredictable. [For example] observing convection cells, the physicist can explain, using traditional concepts, why the original homogeneous fluid became unstable. But he could not have predicted the detailed arrangement of the convection cells in advance. The experimenter has no control over, for example, whether a given blob of fluid will end up in a clockwise or anticlockwise rotating cell.

A crucial property of far-from-equilibrium systems that give rise to process structures is that they are open to their environment. Traditional techniques of physics and chemistry are aimed at closed systems near to equilibrium, so an entirely new approach is needed. One of the leading figures in developing this new approach is the chemist Ilya Prigogine. He prefers the term dissipative structure to describe forms such as convection cells.

To understand why, think about the motion of a pendulum. In the idealized case of an isolated frictionless pendulum (closed system), the bob will swing forever, endlessly repeating the same pattern of motion… The situation is very different if friction is introduced. The moving pendulum now dissipates energy in the form of heat. Whatever its initial motion, it will inexorably come to rest…

The pendulum is a simple example of a dissipative structure, but the same principles apply quite generally… Because energy is continually dissipated, a dissipative structure will only survive so long as it is supplied with energy (and perhaps matter too) by the environment.

This is the key to the remarkable self-organizing abilities of far-from-equilibrium systems. Organized activity in a closed system inevitably decays in accordance with the second law of thermodynamics. But a dissipative structure [like the living cell or a city] evades the degenerative effects of the second law by exporting entropy into its environment. In this way, although the total entropy of the universe continually rises, the dissipative structure maintains its coherence and order, and may even increase it [for a period of time].

The study of dissipative structures thus provides a vital clue to understanding the generative capabilities of nature. It has long seemed paradoxical that a universe apparently dying under the influence of the second law nevertheless continually increases its level of complexity and organization. We now see how it is possible for the universe to increase both organization and entropy at the same time. The optimistic and pessimistic arrows of time can coexist: the universe can display creative unidirectional progress even in the face of the second law…

It is hard to overemphasize the importance of the distinction between matter and energy in, or close to, equilibrium — the traditional subject for scientific study — and far-from-equilibrium dissipative systems. Prigogine has referred to the latter as active matter, because of its potential to spontaneously and unpredictably develop new structures… Disequilibrium, claims Prigogine, ‘is the source of order’ in the universe; it brings ‘order out of chaos’.

It is as though, as the universe gradually unfolds from its featureless origin, matter and energy are continually being presented with alternative pathways of development: the passive pathway that leads to simple, static, inert substance, well described by the Newtonian of thermodynamic paradigms, and the active pathway that transcends these paradigms and leads to unpredictable, evolving complexity and variety.