Chaos, Chaos Everywhere
The previous chapter argued that the way we represent the world has a deep influence on what we see. Chaos theory provides an excellent contemporary example of this phenomenon. Today we tend to "see" the world, ourselves, and our organizations in terms of attractors, chaos, self-organization, and the butterfly effect. Economists and financial analysts look for patterns of self-similarity within the daily and hourly fluctuations of the stock market. Therapists speak of strange attractors governing the repetitive behavior of their clients. Community leaders and business consultants are concerned with the dynamics of self-organizing systems. Moviemakers create planetary geographies using fractal generators. Suddenly chaos, complexity, and self-organization surround us to the point where the general public is using terms more generally associated with mathematicians and theoretical physicists, whereas just half a century ago, no one had ever heard of such terms.
Only a few decades ago the fluctuations of the stock market were seen as purely random. Organizations and businesses were studied in terms of rules and hierarchies and good and bad managers. And "chaos" itself? It was simply a word used to mean a pattern without any order, an aberration, something not worth studying or taking seriously. Chaos was the garbage can into which everything was thrown that could not be represented by means of simple rules and behaviors. And what we now know as fractal orders were once called by mathematicians "a gallery of monsters."
How did such a striking change in attitude come about? Why did people begin to take an interest in chaos and notice strange, new, complex patterns of order in what they had previously taken as random events? Again, the short answer is that we mainly see what we already know. Or to put it another way, we could only begin to "see" the inner world of chaos once we had discovered ways of representing it. Once we are given a mental map of the world of chaos we can begin to discern its features.
The development of high-speed computers and new mathematical approaches made it possible to describe the general nature of chaotic systems, apparently random fluctuations, and highly complex patterns. These features of nature had always been present, but until the means to represent them had been discovered they were essentially invisible to us. These very important aspects of the world had been ignored because we had no real way of looking at them. In 1900, we saw a world of law, order, and certainty in which chance and randomness were unwanted exceptions. Today uncertainty and chaos are seen as essential to the hidden order of the cosmos.
Chance
For the past few hundred years Western science, and the Western mind, have been preoccupied with notions of certainty, predictive power, and the exercise of control. Other societies are willing to accept flux and uncertainty. They live in the Tao, within the flow of things, and tolerate the fact that they will never know all there is to know about the universe. By contrast, the Western mind has been seeking a story with a definite ending. Science wants theories that are finite and rounded off. A good theory should not leave gaps, areas of ambiguity, or uncertainty. Moreover, as in some Freudian death wish, physics seeks to bring about its own end. It desires the ultimate answer, the "theory of everything" that will bring closure to its activities. With the ultimate equation, theory will be finished, all questions will be answered. We will know once and for all the story of the universe. In fact that term, "the universe story," has been used by Thomas Berry and Brian Swimm as the title of a book and a project to provide a contemporary scientific account of the universe of similar mythic proportions to that of Dante in the Middle Ages.
Most societies have their origin stories, ways of linking their present world and society to the creation figures of the past. Some stories concern the creation of the world. But often the world is already present as given and the stories are about the naming of things, the origin of medicine, language, cooking, and writing. Berry and Swimm intend something similar with their Universe Story. Yet traditional origin stories have an open quality to them or involve the role of clowns and tricksters such as Coyote, Raven, or Brer Rabbit who turn things upside down and subvert the order of the world.
Until the twentieth century forced us to face the basic uncertainty of the universe, we asked science to present us with comfortable bedtime stories, ones in which "everything comes out all right at the end.” Science believed in the parsimony of the universe and applied Occam's razor. [5] There could only be one right theory and every choice should be judged as being good or bad. Now chaos theory is telling us that if we desire total certainty, if we want to hold the universe in the palm of our hands, we have to leave the human race behind and become godlike beings who can observe and measure a system without in any way disturbing it. As in Laplace's fantasy of being present at the creation of the universe, such beings are omniscient to the point where they can gather complete and total information about a system. They possess computers of infinite power, computers the size of the universe itself, that enable them to understand the inner workings of that same universe.
But we are finite creatures. Total knowledge and predictive power will always be beyond us. We have to accept that we can never know the universe fully and totally. We must learn to live with a measure of uncertainty, paradox, and ambiguity. We must acknowledge that vital pieces of information may always be missing. That is the price we pay for entering fully into the life of the cosmos, for becoming participators in nature instead of mere observers. Living in the universe gives us obligations and responsibilities. Each of our acts of observation will in some way disturb the universe and we must accept full responsibility for the consequences of these actions.
Feeling Out Trends
This does not mean that we must wash our hands of chaotic systems. While their fine details remain forever beyond us, we may still be able to detect patterns within their behavior that are not totally random. Stable systems, such as predator and prey (see the earlier example of pike and trout), are in the grip of what scientists call an attractor. Just as a magnet attracts iron filings into a fixed pattern, so the attractor of a complex system pulls its dynamics, or behavior, into characteristic repetitive directions. Perturb the system and its attractor pulls it back on track. Attractors are a little like Jungian archetypes, always acting in the background. If a person is in the grip of a particular archetype-the hero, the puer aeternis (eternal golden youth), the devouring mother-this will influence the pattern of behavior within relationships, work, and so on. Likewise knowing the shape of an underlying attractor helps us to predict what a system's behavior will be.
Just as an attractor governs a stable system, so a chaotic system is governed by what is called a strange attractor. This means that, although behavior may on the surface appear totally chaotic and infinitely complex, it nevertheless originates from an underlying pattern, for the strange attractor itself has an underlying fractal structure. Fractals are complex patterns in which a particular element of the pattern is repeated at ever decreasing scales ad infinitum. Likewise, while the behavior of a system in the grip of a strange attractor is chaotic, varying unpredictably from moment to moment, these jumps in behavior mirror each other at ever decreasing scale and take place within a certain zone, or range, of possibilities.
Economists have compared the behavior of the stock market to a system in the grip of a strange attractor. While there are overall trends that indicate which stocks are going to rise over the next weeks and which will fall, within these trends can be found fluctuations that, at first glance, appear random. Yet the "random" fluctuations that occur over say, one hour, mimic similar random fluctuations over a day, and over a week. Mathematicians call this self-similar behavior. A fractal displays similar patterns at ever decreasing scales, likewise small fluctuations within the stock market have a fractal structure, and while remaining unpredictable in their fine details, the overall patterns are imitated at smaller and smaller time intervals.
Although the detailed moment-to-moment behavior of a chaotic system cannot be predicted, the overall pattern of its "random" fluctuations may be similar from scale to scale. Likewise, while the fine details of a chaotic system cannot be predicted one can know a little bit about the range of its "random" fluctuation.
Intermittency
Up to now we have looked at systems in which simple order breaks down, or disappears, into that highly complex swirl of behavior called chaos. Yet the theory of nonlinear systems presents us with a paradox, for behind the door marked "chaos" lies a world of order, and behind that door marked "order" can be discovered chaos.
Let us return to the sudden burst of noise from an electronic apparatus-an amplifier connected to a loudspeaker perhaps. Electronic engineers know of a problem called intermittency. This occurs when the regular, ordered output of an amplifier is suddenly swamped by random "noise.” These periods of random noise can also cease suddenly and give way to periods of regular behavior. When intermittency is occurring, we have the alternation of randomness with simple order.
It would be easy to say that a defect in the design of the amplifier (in fact a nonlinear amplifier) results in the occasional breakdown of regular behavior to produce chaos. On the other hand, it is equally true to say that periods of chaos (highly complex behavior) break down to leave regular behavior. In one case, chaos emerges out of simple order, in the other order emerges out of chaos.
Human societies have their periods of chaos-Carnival, Mardi Gras, Oktoberfest-in which normal social rules are abandoned. Men dress in women's clothing, married people indulge in sexual license, there are orgies of eating and drinking, night is turned into day, authority is mocked, and the Fool rules the day. This can be seen as a temporary breakdown of the stable order of society and the lapse of rule. On the other hand it could be that within the apparent chaos of the carnival can be found the source of a society's order over the rest of the year.
Self-Organization
In some cases chaos rules when order is relaxed, in others order has its seeds in the realm of chaos. Go back to that example of a heated pan of water. Competition between hot water rising from the bottom and cooler water descending from the surface produces haphazard, chaotic behavior. But with the right degree of heating these apparently random flows and counterflows suddenly settle down and organize themselves into a regular pattern of hexagonal cells of rising and falling water. This pattern remains stable, provided that there is a constant flow of energy, as heat, through the system. Similar patterns are found in deserts, where the competing flow of hot air rising from the sand meets cooler air falling from above. The result is that regular patterns of rising and falling air move grains of sand until hexagonal patterns form on the desert floor, just like the cells in a bee hive.
The cells in a heated pan of water, or the movement of sand in a desert, are examples of order arising out of chaos. They all occur in what scientists call open systems. When energy flows through a system, such as heat in a pan of water, the system can order itself into a stable structure.
A river provides another example of what is termed self-organization. During the summer it flows slowly with hardly a ripple to disturb its surface. Where there is a rock in the river the water divides and flows gently past the disturbance. But once the spring rains arrive, the river flows faster. In many ways, the movement of particular regions of water appears chaotic and turbulent, but notice what happens as fast-flowing water encounters a rock. Now a vortex appears downstream from the rock. It is a stable form that has emerged out of the chaotic order. These vortices are remarkably stable. Throw in a stone and the vortex may be disturbed for only a moment, but then continues as before.
A vortex is an example of the way an open system organizes itself to produce a stable structure. Unlike the pan of water, in which an energy flow produced stable patterns, this time it is matter-water-that is flowing through the vortex. As long as the river is in spate, this structure is remarkably stable. As soon as the flow subsides, the vortex disappears.
Natural and social open systems exhibit many examples of self-organization, systems in which regular behavior and stable structures emerge out of chaos. These are found in everything from traffic flows, economic systems, the movements of goods and services, to certain types of waves in canals and rivers and even Jupiter's giant Red Spot. Some, like the vortex, are open to a flow of matter, others to a flow of energy, or even information.
A city can be thought of as a self-organized system that has structured itself over a historical period. It maintains its form by virtue of a complex network of flows-money, food, energy, people, and information. Provided that these flows are maintained at a certain level, the city will sustain itself, garbage will be moved, people will have enough to eat, taxes will be paid, and social services will function. But if any one of these flows should be interrupted for a long enough period, the city would collapse and chaos would reign.
Again one of the powerful lessons of this book is being repeated for us. That is, our acceptance of a degree of uncertainty is the very essence of being alive in the universe. Many systems in nature and human society have evolved through processes of self-organization. They were not put together in a mechanical way, by bringing various parts together and arranging them according to some hierarchical scheme and overarching law. Rather they emerged through the interlocking of feedback loops and out of flows to and from the external environment. In this sense, the stabilities of our lives, of our organizations and our social structures, do not arise out of fundamental certainties but from out of the womb of chance, chaos, and openness. Patterns in a pan of heated water and the vortex in a river are particularly simple examples of order emerging out of chaos. Likewise human society itself, with its cities, international governments, and global economics can only exist through this dynamical dance between chaos and order.
The open systems that fall under the umbrella of chaos theory have a large number of components that interact together and engage in mutual feedback. Traditionally, physicists preferred to study isolated systems where all conditions could be carefully controlled. Such systems behave in regular ways and contain no surprises, so that carefully controlled experiments always match the predictions of theory. But today we realize that nature's open systems are far richer and more interesting. Their behavior is a product of their ability to organize themselves and respond in varied ways to changing environments. It is only relatively recently, because of the long-standing theoretical difficulties involved, that such systems have begun to be studied in a systematic way.
This contrast between the versatility and flexibility of self-organization and the behavior of mechanical systems can be illustrated by comparing life in a village to that wi