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Of Spherical Cows and Runaway Trolleys

I remember when I was taking my first college physics course and we were confronted with the standard “cow in the sun” problem that, for ease of solving, directed us to assume a perfectly spherical cow of uniform density in a frictionless environment. I could tell it was intended to be a practical application of the principles we were learning — except it was so unrealistic that it effectively undid any nod to practicality.

I already had enough background in computers to know we had the necessary programs to model the actual processes. In fact, I had been using them at a summer job, and was familiar enough with them to feel comfortable looking for a computer lab where I could access one of them and do the modeling for real.

I’d expected my professor to be pleased with my cleverness when I delivered my printout. Instead he frowned and handed it back to me, telling me it was unacceptable. I was to do the problem as directed, and because I would be handing it in a day late, I would lose one letter grade.

I was a bit of a smart alec, and I just couldn’t resist arguing my case. Looking back, I realize just how lucky I was that Professor Rockwell was a man secure in his abilities, who did not see argument as affront. Instead he very patiently explained to me that he wanted us to do the problem with the mathematical skills we had already mastered, at most using a scientific calculator to speed the calculations. Without a firm understanding of the mathematics involved, using modeling software would be altogether too much like magic, and would not teach us the physical principles, only how to push the buttons marked push and pull the levers marked pull.

Some years later I was taking an ethics of engineering course, and we had to discuss the usual problems of levers that could either kill a beloved family member or a thousand strangers and runaway trolleys that could either kill a crowd of children or one portly businessman. As the class progressed, I grew increasingly frustrated with how artificial and contrived so many of them were, to the point I found it difficult to take them seriously, even as hypotheticals.

Perhaps if this had been an undergraduate course, I might have become the subject of a how-dare-you pile-on. But this was a graduate-level course for doctoral candidates, and instead of everyone trying to humiliate me into silence, the class actually engaged my objection. Although I’d managed to derail the professor’s intended discussion, we ended up reaching a conclusion not dissimilar from Professor Rockwell’s explanation to me back in freshman physics — that using modeling software to create realistic situations full of degrees of risk, of known and unknown unknowns, would make the process altogether too much like magic, an answer box that you put questions in one and and get answers out the other.

—- Ursula Doorne, PhD, Leland Professor of Astronomy, Kennedy University Tycho, oral history interview, October 18, 2067.