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Parts and the Whole
Regardless of how we frame it, all of these instances of emergence share certain characteristics: Emergence is above all a product of coupled, context-dependent interactions. Technically these interactions, and the resulting system, are nonlinear: The behavior of the overall system cannot be obtained by summing the behaviors of its constituent parts. We can no more truly understand strategies in a board game by compiling statistics of the movements of its pieces than we can understand the behavior of an ant colony in terms of averages. Under these conditions, the whole is indeed more than the sum of its parts.[5]
This selection from computer scientist John Holland contains an extremely rich cluster of ideas about emergence. Because Holland moves from the specific to the general, we are going to interpret the text line by line, working from the final statement back to the beginning. In the last sentence Holland tells us that when emergence is in operation, "the whole is indeed more than the sum of its parts." This fits into our general understanding of systems, in which the parts interrelate to form a whole. In an emergent system, there is a special relationship between the parts and the whole. Because an emergent system will play out in unpredictable ways, the whole of the game is more than the sum of the parts.
What does Holland mean by this? Look one sentence earlier: "We can no more truly understand strategies in a board game by compiling statistics of the movements of its pieces than we can understand the behavior of an ant colony in terms of averages." Holland uses board games and an ant colony as examples of emergence, pointing out that these systems cannot be understood merely by taking averages of the behavior of independent objects in the system. This notion is very close to one of the ideas that Campbell mentioned, that "One can describe all the rules, but not necessarily all the products of the rules—not the set of all whole numbers, not every sentence in a language, not all the organisms which may arise from evolution." Campbell is pointing out that in an emergent system, we might know all of the initial rules, but we cannot describe all of the ways that the rules will play out when they are set into motion. He provides the diverse examples of math, language, and evolution. In the case of language, for example, we cannot describe every statement that might be uttered in a language even though we might know all of the words in that language along with the rules of grammar that organize them. Campbell and Holland are both saying the same thing: what makes a system emergent is that there is a special disconnect between the rules of the system and the ways those rules play out. Although the rules might be concise and knowable, the behavior of those rules set into motion in the system creates patterns and results not contained within the rules themselves, results that contain "variety, novelty, and surprise." The rules of grammar might tell us how to organize words into sentences, but they can't account for Huckleberry Finn, The U.S. Constitution, and the lyrics to Britney Spears'"Oops! I Did It Again."The grammatical rules, set into motion through the use of language, exceed the complexity barrier to produce emergent results, which could never have been predicted by a mere consideration of the rules by themselves. This is what Holland means by "The behavior of the overall system cannot be obtained by summing the behaviors of its constituent parts." Merely consolidating all of the rules together in a list can't account for the diverse variety in the behavior of an emergent system. When he mentions that, "Technically these interactions, and the resulting system, are nonlinear," he means nonlinear in the mathematical sense. He is saying that the ways that the objects in the system interact to produce complexity are not just additive, but increase geometrically. This is the kind of complexity seen in the example of the three-planet system. Adding a third planet to the equation did not just increase the complexity of the system by a third: it added orders of magnitude of new complexity. [5]John Holland, Emergence (Reading, PA: Helix Books, 1998), p. 121–122.
