complexity. Why? Well, what does it mean to say that a system is “composed” of a large number of interacting parts? It means (among other things) that the system can be fruitfully redescribed in the language of another science—the one that carves configuration space in terms of whatever the parts for this particular system are. To say that the human body is composed of many interacting cells, for instance, is just to say that we can either treat the body as an individual (as, say, evolutionary biology might) and make use of the patterns that can be identified in the behavior of systems like that, or treat it as a collection of individual cells (as a cellular biologist might) and predict its behavior in terms of those patterns. Systems which can appropriately be said to be made out of many parts are often systems which can be treated by the vocabulary of multiple branches of the scientific project. Moreover, since we’re tying dynamical complexity not to composition but behavior, we don’t need to answer the uncomfortable questions that dog the avid proponent of the mereological size measure—we don’t need to say, for instance, which method of counting parts is the right one. Indeed, the existence of many different ways to count the parts of a system is something that dynamical complexity can embrace whole-heartedly—the fact that the human body can be seen as a collection of organs, or cells, or molecules straightforwardly reflects its status as a complex system: there are many different useful ways to carve it up, and many interesting patterns to be found in its time-evolution.
This leads directly into the hierarchical position measure. Here too the relationship to dynamical complexity is fairly clear. What does it mean to say that one system is “nested more deeply in the hierarchy?” It means that the system can be described (and its behavior predicted)
- Indeed, it was my reading of the canonical articulation of the hierarchical scheme—Oppenheim and Putnam (1954)—that planted the seed which eventually grew into the position I have been defending over the last 60 pages.