Chaos, causation, and describing dynamics
A standard platitude about the function of causal knowledge or theories is that they are valuable because they support prediction, explanation, and control. Knowledge of predator-prey relations enables us to predict future animal populations, as well as design policies or interventions that help influence those populations. If we understand the underlying biochemical mechanisms of some disease, then we can predict who is at risk for it, explain why it produces particular symptoms, and develop interventions to try to reduce its prevalence or the symptom severity. Of course, there are many situations in which one has, for practical reasons, only some of these desiderata; for example, control might be infeasible for technical or ethical reasons. But these remain, for many researchers, the ideal for why causal knowledge is a valuable end of scientific inquiry, including biological inquiry. There are, however, certain types of systems—in particular, chaotic systems—in which it appears that these ends are unattainable, and these systems appear to be widespread in the biological domain, broadly construed (e.g., Benincà et al., 2008; Cushing, Costantino, Dennis, Desharnais, & Henson, 2003; Guastello, Koopmans, & Pincus, 2009; Hastings & Powell, 1991; Skarda & Freeman, 1987; Tsuda, 2001). In this paper, we will show why it is natural to think that causal models of chaotic systems cannot satisfy any of the three functions. But we will also show why this natural thought is wrong: we can have usable causal knowledge about even chaotic systems. Moreover, the ways in which we can have such knowledge lead us naturally to rethink a standard understanding of how causal learning and modeling proceed. In particular, just as we often must find the appropriate variables for a causal system, we also must determine the proper level or granularity of description for the dynamics of that system.