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Complexity—An Introduction
John L Casti

I. Complexity as a Systems Concept
In everyday parlance the term “complex” is generally taken to mean a person or thing composed of many interacting components whose behavior and/or structure is difficult to understand. The behavior of national economies, the human brain and a rain forest ecosystem are all good illustrations of complex systems. Theseexamples underscore the point that sometimes a system may be structurally complex, like a mechanical clock, but behave very simply. In fact, it’s the simple, regular behavior of a clock that allows it to serve as a timekeeping device. On the other hand, there are systems, like the toy rotator shown in Figure 1, whose structure is very easy to understand but whose behavior is impossible to predict.And, of course, some systems like the brain are complex in both structure and behavior. The examples just cited show that there’s nothing new about complex systems; they’ve been with us from the time our ancestors crawled up out of the sea. But what is new is that for perhaps the first time in history, we have the knowledge—and the tools—to study such systems in a controlled, repeatable, scientificfashion. So there is reason to believe that this newfound capability will eventually lead to a viable theory of such systems. Prior to the recent arrival of cheap and powerful computing capabilities, we were hampered in our ability to study a complex system like a road-traffic network, a national 1

Figure 1. A toy rotator with unpredictable behavior. economy or a supermarket chain because it wassimply too expensive, impractical, too time-consuming—or too dangerous—to tinker with the system as a whole. Instead, we were limited to biting off bits and pieces of such processes that could be looked at in a laboratory or in some other controlled setting. But with today’s computers we can actually build complete silicon surrogates of these systems, and use these “would-be worlds” as laboratorieswithin which to look at the workings—and behaviors—of the complex systems of everyday life. In coming to terms with complexity as a systems concept, we first have to realize that complexity is an inherently subjective concept; what’s complex depends upon how you look. When we speak of something being complex, what we’re really doing is making use of everyday language to express a feeling orimpression that we dignify with the label “complex.” But the meaning of something depends not only on the language in which it is expressed (i.e., the code), the medium of transmission and the message, but also on the context. In short, meaning is bound up with the whole process of communication and doesn’t reside in just one or another aspect of it. As a result, the complexity of a political 2 structure, an ecosystem or an immune system cannot be regarded as simply a property of that system taken in isolation. Rather, whatever complexity such systems have is a joint property of the system and its interaction with another system, most often an observer and/or controller. This point is easy to see in areas like finance. An individual investor interacts with the stock exchange and thereby affectsthe price of a stock by deciding to buy, to sell or to hold. This investor then sees the market as complex or simple, depending on how he or she perceives the change of prices. But the exchange itself acts upon the investor, too, in the sense that what is happening on the floor of the exchange influences the investor’s decisions. This back interaction causes the market to see the investor as havinga certain degree of complexity, in that the investor’s actions cause the market to be described in terms like nervous, calm or unsettled. The kind of two-way complexity of a financial market becomes especially obvious in situations when the investor is one whose trades make noticeable blips on the ticker without actually dominating the market. So just as with truth, beauty, good and evil,...
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