A Spherical Cow

Many years ago, I learned from physics colleagues that when asked to solve a ‘real-world’ problem, they begin with the statement: “Consider a spherical cow…” Little did I know that this is also the name of a book, and my university library had a copy (of the first edition published in 1985). Consider a Spherical Cow is written by John Harte, a professor at UC-Berkeley. It is subtitled “A Course in Environmental Problem Solving”.

 

The book presents 45 problems with worked solutions with interesting ‘real-world’ applications related to geoscience. Each of the ‘solutions’ discusses the approximations made when a simpler model is used (akin to the spherical cow) but also includes discussion and follow-up exercises (no solutions provided) if the model was modified to take more complicated features. Essentially, a cow isn’t really a sphere, so how do we account for that?

 

Chemistry features prominently in a number of the problems. There are problems of atmospheric chemistry, natural elemental cycles (carbon, nitrogen, sulfur, phosphorus). Some problems feature acid rain, trace metal mobilization, fossil fuel burning, and more; for example, “What is the pH in pristine precipitation?” No, it’s not seven. There are several thermodynamics and energy transfer type problems. There are also a number of ecology-type problems including an interesting one about how the population of China might change and when it might approach steady-state. It begins with 1980 data and predicts trends going forward in different age bands every decade through 2040. Today we can compare how well those initial models worked. The results are interesting, and Harte does a good job in discussing the caveats in any model.

 

The math is mostly algebra, albeit quite involved. There is a little bit of vector notation and the occasional differential equation, but these can essentially be transformed into algebraic problems. The appendix has data which students can draw from to solve these ‘real-world’ questions. Since I’d been thinking of transforming my G-Chem courses to include a chunk of data-science techniques, I found Harte’s approach helpful to think about even if I will likely not use many of the actual problems that he poses. It’s the habit of mind that we’re trying to inculcate in our students: how to approach a problem by constructing a simple (model) first and then iteratively improve upon that first guess.

 

I recommend Harte’s book if you are interested in seeing the workflow in his book starting with warm-up exercises and progressing to beyond back-of-the-envelope approaches. I’d also like to come up with the chemists’ equivalent of “Consider a Spherical Cow”. Any suggestions?