should expect out of a concept designed to describe the relationship between how different branches of science view a single physical system. There’s no single correct value for a system’s effective complexity, because there’s no single correct way to carve up a system—no single way to parse it into a string of patterns. Far from making us think that effective complexity gets it wrong, then, this should lead us to think that effective complexity gets things deeply right: the presence of a plurality of values for the effective complexity of a system reflects the methodological plurality of the natural sciences.
McAllister suggests that we might instead choose to sum different values to get a final value, but his proposal is limited to summing over the complexity as defined by algorithmic information content. Because McAllister believes his observation that effective complexity contains an observer-relative element to be a fatal flaw in the concept, he doesn’t consider the possibility that we might obtain a more reliable value by summing over the effective complexity values for the system.
My proposal is that dynamical complexity, properly formalized, is precisely this: a sum of the effective complexity values for the different strings representing the different useful carvings of the system. While there is no single value for effective complexity, we can perfectly coherently talk about summing all the useful ways given our goals and values. The value of this sum will change as we make new scientific discoveries—as we discover new patterns in the world that are worth paying attention to—but this again just serves to emphasize the point from Chapter One: the world is messy, and science is hard. Complexity theory is part of the scientific project, and so inherits all the difficulties and messiness from the rest of the project.
Dynamical complexity, in other words, offers a natural physical interpretation for the