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 are difficult to understand. The behavior of national economies, the human brain, and a rain forest ecosystem are all good illustrations for complex systems.
These examples show that there is nothing new about complex systems. 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, scientific fashion. 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 economy, or a supermarket chain because it was simply 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 laboratories within 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 is complex depends upon how you look. When we speak of something being complex, what we are really doing is making use of everyday language to express a feeling or impression 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 does not reside in just one or another aspect of it. As a result, the complexity of a political 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.
So just as with truth, beauty, good, and evil, complexity resides as much in the eye of the beholder as it does in the structure and behavior of a system itself. This is not to say that there do not exist 'objective' ways to characterize some aspects of a system's complexity. After all, an amoeba is just plain simpler than an elephant by whatever notion of complexity you happen to believe in. The main point, though, is that these objective measures only arise as special cases of the two-way measures, cases in which the interaction between the system and the observer is much weaker in one direction than in the other.
A second key point is that common usage of the term 'complex' is informal. The word is typically employed as a name for something that seems counterintuitive, unpredictable, or just plain hard to understand. So if it is a genuine 'science' of complex systems we are after and not just anecdotal accounts based on vague personal opinions, we are going to have to translate some of these informal notions about the complex and the commonplace into a more formal, stylized language, one in which intuition and meaning can be more or less faithfully captured in symbols and syntax. The problem is that an integral part of transforming complexity (or anything else) into a science involves making that which is fuzzy precise, not the other way around, an exercise we might more compactly express as 'formalizing the informal'.
To bring home this point a bit more forcefully, let us consider some of the properties associated with 'simple' systems by way of inching our way to a feeling for what is involved with the complex. Generally speaking, simple systems exhibit the following characteristics.
Predictable behavior. There are no surprises in simple systems; simple systems give rise to behaviors that are easy to deduce if we know the inputs (decisions) acting upon the system and the environment. If we drop a stone, it falls; if we stretch a spring and let it go, it oscillates in a fixed pattern; if we put money into a fixed-interest bank account, it grows to a predictable sum in accordance with an easily understood and computable rule. Such predictable and intuitively well understood behavior is one ofthe principal characteristics of simple systems.
Complex processes, on the other hand, generate counterintuitive, seemingly acausal behavior that is full of surprises. Lower taxes and interest rates lead to higher unemployment; low-cost housing projects give rise to slums worse than those the 'better' housing replaced; the construction of new freeways results in unprecedented traffic jams and increased commuting times. For many people, such unpredictable, seemingly capricious, behavior is the defining feature of a complex system.
Few interactions and feedback/feedforward loops. Simple systems generally involve a small number of components, with self-interactions dominating the linkages among the variables. For example, primitive barter economies, in which only a small number of goods (food, tools, weapons, clothing) are traded, seem much simpler and easier to understand than the developed economies of industrialized nations, in which the pathways between raw material inputs and finished consumer goods follow labyrinthine routes involving large numbers of interactions between various intermediate products, labor, and capital inputs.
In addition to having only a few variables, simple systems generally consist of very few feedback/feedforward loops. Loops of this sort enable the system to restructure, or at least modify, the interaction pattern among its variables, thereby opening up the possibility for a wider range of behaviors. To illustrate, consider a large organization that is characterized by variables like employment stability, substitution of capital for human labor, and level of individual action and responsibility (individuality). Increased substitution of work by capital decreases the individuality in the organization, which in turn may reduce employment stability. Such a feedback loop exacerbates any internal stresses initially present in the system, leading possibly to a collapse of the entire organization. This type of collapsing loop is especially dangerous for social structures, as it threatens their ability to absorb shocks, which seems to be a common feature of complex social phenomena.
Centralized decision making. In simple systems, power is generally concentrated in one or at the most a few decision makers. Political dictatorships, privately owned corporations, and the Roman Catholic Church are good examples of this sort of system. These systems are simple because there is very little interaction, if any, between the lines of command. Moreover, the effect of the central authority's decision upon the system is usually rather easy to trace.
By way of contrast, complex systems exhibit a diffusion of real authority. Such systems seem to have a nominal supreme decision maker, but in actuality the power is spread over a decentralized structure. The actions of a number of units then combine to generate the actual system behavior. Typical examples of these kinds of systems include democratic governments, labor unions, and universities. Such systems tend to be somewhat more resilient and stable than centralized structures because they are more forgiving of mistakes by any one decision maker and are more able to absorb unexpected environmental fluctuations.
Decomposable. Typically, a simple system involves weak interactions among its various components. So if we sever some of these connections, the system behaves more or less as before. Relocating American Indians to reservations produced no major effects on the dominant social structure in New Mexico and Arizona, for example, since, for various cultural reasons, the Indians were only weakly coupled to the dominant local social fabric in the first place. Thus, the simple social interaction pattern present could be further decomposed and studied as two independent processes - the Indians and the settlers.
Complex processes, on the other hand, are irreducible. Neglecting any part of the process or severing any of the connections linking its parts usually destroys essential aspects of the system's behavior or structure. You just cannot start slicing up systems of this complexity into subsystems without suffering an irretrievable loss of the very information that makes these systems a 'system'.
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