case are approximations or idealizations of some as-yet unidentified real patterns. If this is the case, then we have good reason to think that the patterns described by (for instance) Arrhenius deserve some primacy over the approximated or idealized erstaz patterns employed in the construction of computational models.
What counts as an approximation? What counts as an idealization? Are these the same thing? It’s tempting to think that the two terms are equivalent, and that it’s this unified concept that’s at the root of our difficulty here. However, there’s good reason to think that this assumption is wrong on both counts: there’s a significant difference between approximation and idealization in scientific model building, and neither of those concepts accurately captures the nuances of the problem we’re facing here.
Consider our solar system. As we discussed in Chapter Five, the equations describing how the planets’ positions change over time are technically chaotic. Given the dynamics describing how the positions of the planets evolves, two trajectories through the solar system’s state space that begin arbitrarily close together will diverge exponentially over time. However, as we noted before, just noting that a system’s behavior is chaotic leaves open a number of related questions about how well we can predict its long-term behavior. Among other things, we should also pay attention to the spatio-temporal scales over which we’re trying to generate interesting predictions, as well as our tolerance for certain kinds of error in those predictions. In the case of the solar system, for instance, we’re usually interested in the positions of the planets (and some interplanetary objects like asteroids) on temporal and spatial scales that are relevant to our decidedly humanistic goals. We care where the planets will be over the next few thousand years, and at the most are interested in their very general behavior over times ranging from a few
203
