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Complexity
As a preliminary step to understanding emergence and systems, we begin with the concept of complexity. Growing out of classical systems theory, the study of complexity has become its own interdisciplinary field. Researchers in complexity study many different kinds of systems, from computational systems of pure information to biological systems such as cells and organisms to natural ecosystems and human society. The study of complex systems tends to look at systems that are "selforganizing, replicating, learning, and adaptive." [1]In our own brief investigation of complexity, we will admittedly just skim the surface of this fascinating field, perhaps in quite an unconventional way. Let us begin by clarifying the term "complexity." In his book Grammatical Man, Jeremy Campbell weaves together many elements of systems theory to look at relationships between information, language, and DNA. He has this to say about complexity: In living organisms, and even in machines, there exists a "complexity barrier." Beyond this barrier, where systems are of a very high complexity, entirely new principles come into play. Complexity is not just a matter of a system having a lot of parts which are related to one another in nonsimple ways. Instead, it turns out to be a special property in its own right, and it makes complex systems different in kind from simple ones, enabling them to do things and be things we might not have expected. [2]
Campbell doesn't offer a precise definition of complexity, but the passage above does present a useful picture of the concept. Complexity is a property of a system, and according to Campbell, not all systems are complex: only some of them reach what he calls a "complexity barrier." In a complex system, the internal relationships between elements of the system become intricately compounded and extraordinarily complex. Although mathematical models for precisely defining the "complexity barrier" do exist, for our purposes the difference between a simple system and a complex system is more conceptual than numerical. A simple system such as a wooden table does have parts (four legs and a tabletop) that interrelate to form a whole, and the whole is more than the sum of the parts, since a complete table can serve functions that the isolated pieces cannot. But it is clearly a simple system, as the relationships between parts are fixed and entirely predictable.
The table, as a system, is much simpler than even the most elementary game. In Tic-Tac-Toe, the relationships among the parts, the unpredictability of the player's actions, the dynamic shifting of the system over time, the uncertain outcome, all contribute to the complexity of the game, a kind of complexity that is fundamentally different than that demonstrated by a table. As Campbell points out, this complexity is "a special property in its own right," and in the case of games, their special kind of complexity leads to meaningful play. If complexity is not present in a game, meaningful play cannot occur. [1]Jeremy Campbell, Grammatical Man: Information, Entropy, Language, and Life (New York: Simon & Schuster, 1982), p. 105.
[2]Ibid, p. 102.
