What did you calculate for fun?

I earned my bachelor’s in physics at Imperial College London. In my final year there, I took the last of the three courses on quantum mechanics. Tom Kibble, one of the fathers of the Higgs boson, was the lecturer.

Perhaps because Kibble wanted to end his course with a tour de force, he devoted his last lecture to calculating the ionization energy of helium. I can’t remember which approximation method he used (perhaps Hartree–Fock ), but I do remember the multiple blackboards that he filled with equations and the sense of triumph when he chalked up the final value.

In my subsequent career as a astronomer, I didn’t perform a similar calculation. But there have been occasions when, after learning a new method or theory, I’ve played with the equations involved just for fun.

If my memory is correct, my first recreational calculation followed learning, some time in secondary school, Isaac Newton’s laws of motion, x = vt + ½gt ², and other simple kinematic equations. I calculated how long it would take an object dropped from the top of Britain’s tallest building—the Post Office Tower in London—to hit the ground. I also remember calculating the altitude of geostationary satellites and the radiant energy emitted by a spherical triceratops.

From 1965 to 2003, the Post Office Tower was Britain’s tallest building. The tower still serves its original purpose as a telecommunications hub. My copyeditor says it looks like the Doctor’s sonic screwdriver on the BBC series Doctor Who. CREDIT: David Castor

Although none of those otiose calculations—and others I’ve forgotten—was difficult or particularly original, they had one thing in common: No one had asked me to do them.

In fact, when I look back at the 40 or so physics teachers I’ve had from secondary school to grad school, I can’t recall any of them telling his or her students something like, “Well, now that you know how to calculate the scale height of a planet’s atmosphere, have fun estimating the feasibility of jet-powered flight on the moons of Jupiter!”

Granted, such open-ended questions did appear on some of my problem sheets and exams. Still, some spontaneous encouragement would have been welcome. And not just because playing with equations can be fun. Whole fields of science have been opened up by people who have applied well-known equations in new arenas.

In his 1977 paper “Life at low Reynolds number,” Edward Purcell applied 19th-century physics to a problem that, to quote the introduction to his paper, “most physicists almost never think about” and “most engineers aren’t even interested in": fluid motion under conditions when viscous forces utterly dominate inertial forces. People are evidently interested now. According to the American Journal of Physics, Purcell’s paper has garnered 285 citations.

If, unlike me, you were encouraged by a teacher to play with equations, please leave a comment. I doubt I’d be the only one who’d be interested in your experiences.