Complexity

The natural and social sciences have undergone a key paradigm shift in recent times: a movement away from reductionist modes of analysis, which seek to understand natural and social phenomena by appealing to their most basic and indivisible components, toward more holistic modes of analysis, which also seek to understand natural and social phenomena—but by focusing on the relationship between the various components within a larger system. An emphasis on systems allows one to identify interesting patterns and mechanisms that might otherwise escape attention. One of the features attributed to systems is complexity, arguably among the most theoretically exciting topics in the natural, social, and applied sciences today.

Complexity is a notoriously difficult concept to define, largely because there is no agreement as to what, exactly, complexity entails. Although there is a tendency in practice to distinguish complex from simple systems, or systems of greater and lesser complexity, it is not always apparent which precise standard or measure makes the relevant difference. One is guided from the start by implicit intuitions about the way systems work, and it is by comparing different systems, or the different historical and developmental stages within the life of a single system, that one is able to identify interesting features associated with complexity.

Perhaps the most basic intuition about complexity is that it involves quantitative phenomena: a great many units interacting together according to some more or less intelligible order or pattern. However, what makes complexity interesting is that the units within a system act in such a way as to indicate at least some degree of randomness and chance. Complex systems are not perfectly ordered or absolutely predictable; rather, they defy expectations through novel and surprising behavior. Although the element of chance and uncertainty indicates disorder, it is precisely the creative and dynamic presence of order and disorder that makes a system complex. Perfect order is uninteresting, as it is always predictable and therefore leaves no questions remaining. On the other hand, pure disorder is equally uninteresting, as there is nothing to latch on to and nothing interesting to try to understand. Complexity captivates attention precisely because of its capacity to behave and react, a capacity partially predictable and partially unpredictable.

Unpredictability notwithstanding, a complex system is nonetheless deterministic, a feature associated with chaos. Although suggestive of pure disorder, chaos technically refers to the capacity of a complex system to exhibit unstable, aperiodic behavior within a bounded range of possibility. What is taken to be randomness is in fact governed by some underlying principle. There are several characteristics of chaos. A system is chaotic if (1) it is dynamic, or subject to change and evolution over time, (2) it is sensitive to initial conditions, (3) great changes within a system can result from simple causes, and (4) a system is nonlinear, that is, if its output is different or greater than its input. One common metaphor for chaos is the butterfly effect, in which a relatively miniscule or momentary event can result in enormous change over an extended period of time, a phenomenon observable in quantum behavior, traffic jams, and the weather.

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