Order Out of Chaos — Prigogine and Stenger on Our Dialogue With Complexity

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Order Out of Chaos — Prigogine and Stenger on Our Dialogue With Complexity

Heat and universality

Joseph Fourier made an important contribution to physics in the nineteenth century when he published his mathematical formulation of the manner in which heat propagates. Today, Fourier’s law tells us that heat flows from regions of higher temperature to regions of lower: “that heat flux is proportional to the difference in temperature.” This law is a remarkable insight into universality. Here, we have many disparate macroscopic systems, from solids to gasses to liquids, each containing an inordinate sum of molecules, each conforming to a law of heat conductivity. To the chemist Ilya Prigogine and philosopher Isabelle Stenger, Fourier’s description was the “birth of the science of complexity.”

Around the same time, another universality, the first law of thermodynamics, was formalizing. It tells us that while “energy cannot be created or destroyed, [it] can be transferred from one form to another.” Energy is forever conserved. So as James Prescott Joule writes in Matter, Living Force and Heat, “the phenomena of nature, whether mechanical, chemical, or vital, consist almost entirely in a continual conversion of attraction through space, living force (N.B., kinetic energy) and heat into one another. Thus it is that order is maintained in the universe—nothing is deranged, nothing ever lost, but the entire machinery, complicated as it is, works smoothly and harmoniously.”

Statistical inevitability

Entrepreneurs were already heeding such intuitions during the industrial revolution. The world as a collective was slowly then suddenly moving from fire and oxcart to heat engines. The physicists too were marching on. William Thomson, for example, had noticed the connection between heat propagation, energy conversion, and the inefficiencies of early industrial machines. It culminated in his formulation of the second law of thermodynamics, describing the “universal tendency toward the degradation of mechanical energy.” Ludwig Boltzmann later interpreted the second law as a “law of disorder” following his development of statistical mechanics. As Prigogine and Stenger explain in their book, Order Out of Chaos, such a “world is described as an engine in which heat is converted into motion only at the price of some irreversible waste and useless dissipation… [So] it [all] goes from one conversion to another and tends toward a final state of thermal equilibrium, ‘heat death.’”

Far-from-equilibrium states

But while an isolated system is on an inexorable track toward equilibrium, interesting things can happen in between. And so it is helpful, Prigogine and Stenger note, to distinguish between far-from-equilibrium and close-to-equilibrium regions. Similar parallels, he says, can be drawn to hydrodynamics. Minor disturbances, for example, can transform stable laminar flows of fluid into something wild and turbulent. The authors say, however, that while turbulence may appear chaotic or irregular to us macroscopic beings, there is “coherent behavior” among the masses of interacting molecules. In a sense, this laminar-turbulent-transition can be thought of as an example of self-organization.

Similar processes may apply to macrosystems that are far-from thermal equilibrium. Here, we have new constructions and “dissipative structures” that emerge from thermal chaos. It is a way to reconcile our experience with Darwinian diversity and complexity with the statistical inevitability of oblivion, as suggested by Boltzmann. Earthian life, you see, is an open system—doing as much as it can with the solar energy it receives from our aging Sun. “The living cell represents an incessant metabolic activity, [where] thousands of chemical reactions take place simultaneously,” note Prigogine and Stenger. To them, the energy flows “resemble the flow of a river that generally moves smoothly but that from time to time tumbles down a waterfall.”

Order through fluctuation

Here, self-organization does not always require a sophisticated mechanism. Elaborate structures can come about via fluctuation. Termites, for example, engineer magnificent nests without much information or central planning. They begin randomly by dropping lumps of material as they move about. Inside each lump are secreted hormones that attract other termites to the construct. By chance, some regions grow more and more as termites lump and clump and secrete around particular sites. Before we know it, grand “‘pillars’ are formed, separated by a distance related to the range over which the hormone spreads.” (Perhaps similar processes apply to empire building in society. When you substitute termites for capitalists and hormones for profits, enterprises, big and small, seem to pop up everywhere. Paul Krugman has applied similar concepts to describe a self-organizing economy.)

For another case, a species of soil-dwelling slime molds (dictyostelium discoideum), Prigogine and Stenger note, exhibit a similar sort of self-aggregating behavior. For the most part, these amoebas are happy to go about their lives as separate, single-celled organisms. But when available nutrients grow unexpectedly poor, they “coalesce into a single supra-cellular mass.” What’s more, some of these cells will change and differentiate, sprouting a “foot” with spores. And if this enterprise happens to stumble upon a nutrient-rich scape, the spores detach, spread, and multiply—initiating another colony of liberal individualists to start their lifecycle anew.

Seething and bubbling

Such models of “order through fluctuation” may help to explain the complexities behind self-organizing behavior. This may extend as well to economics, which remains wedded instead to models of optimization. There’s no doubt, of course, that optimizing behavior is commonplace in nature and society because of intense selection pressures. But such models, Prigogine and Stenger note, tend to “ignore both the possibility of radical transformations… and the inertial constraints that may force a system into a [successful or] disastrous way of functioning.”

As Alvin Toffler writes:

“Most of reality, instead of being orderly, stable, and equilibrial, is seething and bubbling with change, disorder, and process… All systems contain subsystems which are continually fluctuating. At times, a single fluctuation or a combination of them may become so powerful, as a result of positive feedback, that it shatters the pre-existing organization.”

Alvin Toffler in the Preface to Order Out of Chaos (1984).

Bifurcation and dissymmetry

It’s also important to pay attention to the bifurcations and lock-in. In nature, they manifest themselves in peculiar ways. “The DNA of every organism on Earth”, for example, “is a right-handed double helix.” Many scientists suspect this was an entirely chance event—that “right-handed genetic strands just happened to pop up first”, setting in motion every building block that followed. (Although recent research suggests that handedness might be explained in part by interactions with cosmic rays that bombard our planet.)

Similar phenomena may occur in ecology and economics when two or more equilibria exist, as is frequently seen in game theory. Here, systems at a tipping point may transition towards one attractor over another by mere fluctuation alone. The point being that when we’re far-from-equilibrium, chance and necessity are star actors in the unfolding play. As Alvin Toffler writes, “chance nudges what remains of the system down a new path of development. And once that path is chosen (from among many), determinism takes over again until the next bifurcation point is reached.” 

Order out of chaos

Science itself is a trajectory, forever branching and reaching. What it tells us today, moreover, as Prigogine and Stenger conclude, is that “nonequilibrium brings order out of chaos.” “Wherever we look we find evolution, diversification, and instabilities… This is true on all levels, in the field of elementary particles, in biology, and in astrophysics, with the expanding universe and the formation of black holes.” Yet it is only when the system is far from its end that wonderful structures as we experience on Earth emerge.

So it becomes difficult to “disentangle the meaning of words such as ‘order’ and ‘chaos’” in an everyday sense. Just how orderly or disorderly, for instance, are rainforests, coral reefs, and market economies? Each, in their immensity, complexity, and diversity, hum and fuss about. Life itself, as Prigogine and Stenger write, is “the supreme expression” of nature’s self-organization. Here, nonlinearity, instability, and fluctuations are simply the “leitmotivs”.   

Sources and further reading

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