How many bus conductors are there in Jerusalem?

An interesting anecdote.

One of the courses I taught last year was "order of magnitude (OoM) physics". In the course, the physics students learn how to think like physicists, that is, boldly (try to) solve questions, especially those without a precise solution, by carrying out estimates, building simple models, doing dimensional analysis, etc.

I wish I could, but I cannot take credit for thinking of such a course. When I was a post-doc at Caltech more than a decade ago, an equivalent course was given by Profs. Goldreich and Phinney. I went to a few of their fabulous lectures and decided to teach it one day.

Anyway, one of the classical questions in OoM estimates is of course Fermi's question of how many piano tuners are there in Chicago. And, the first question I asked the students in their final exam was, "how many bus conductors are there in Jersualem?" (By bus conductor I mean these people that rarely go aboard and check that everyone has a ticket, with no stowaways). Other questions included, among others, calculating the speed with which a soap bubble bursts, estimate the speed of Alfen waves, and how cold is it in the arctic on average given that it develops a 1.7 meter ice sheet in 6 months, that is, the kind of questions physicists should be able to answer, or at least estimate, with a pen and piece of paper (preferably, the back of an envelope).

A curious graduate student of mine decided to estimate the answer, but later he also carried out an actual experiment, or should I say measurement. He asked a driver who tried to count all the conductors he remembered, and counted 10.

A few days ago, I gave a talk in an unrelated venue. A few of the students approached me later, reminded me that they took the OoM course with me. Then one of them said that he asked a bus conductor how many are there in Jerusalem. The answer was 12, but it was followed by a question by the conductor, "Are you also a student of Nir Shaviv?"

Incidentally, the answer to the typical time it takes the soap bubble to burst is

$$t \sim \sqrt{\Sigma \over \gamma} r ,$$

with $\Sigma$ being the surface density of the bubble, $\gamma$ being the surface tension and $R$ the radius. For a 5cm bubble, one gets ~10ms. (The values of the different constants can be estimated from the fact that a bubble this size will start to significantly deform from its own weight or from a drop of water).