I’m currently playing with the idea that there may be something special to the way chemists use mathematics in explanation. I wrote a quite sketchy seminar paper on the subject, but rather than try to recap it here, I will try something new: a sub-1000 word blog post. Here goes.
I think there is something special about explanation in chemistry because its explanatory aims seem to be so different from those of physics. One of the main things chemists try to explain is how their models work, and why one model makes sense of a class of observed phenomena despite the fact that it is clearly and strictly false. This seems to contrast with some of the explanatory aims of physicists, etc. who are trying to explain how a certain phenomenon came to be, or how classes of phenomena are related to one another.
I’m thinking a lot about Batterman’s account of mathematical explanation in the physical sciences as I write this. Specifically, I can think of explanations in chemistry, say of why we should use the molecular-orbital model in a certain calculation, that rely heavily on mathematical considerations — even on asymptotic considerations of the kind that fascinate Batterman. But they don’t fit into either of Batterman’s explanation-types. Instead, as I claimed in my seminar paper, they use mathematics primarily to distinguish between alternative possible models and then use other considerations from the standard Kuhnian laundry-list — simplicity, scope, etc. — to arbitrate between the models.
I’m a bit concerned that I’m overstating a case here, or that the kind of case I am thinking of is not as prevalent in chemistry as I want it to be. I mean, sure, chemists seek explanations of the origins, behaviors, and universality relations of natural phenomena just like physicists, biologists, etc. But, to come back to the last installment’s productive-science point (although Benny has helpfully pointed out some cautionary notes on taking that distinction too seriously), it seems that some explanations of how synthesis works, how we know we’ve created something new, etc. may not fit the mold of the kinds of explanations other scientists seek.
I don’t know. Maybe I’m grasping at straws. Maybe it’s the end of the semester and I am doing anything I can to avoid finishing my algebraic quantum field theory seminar paper. But there it is. A reasonably-sized blog post.