The Professoriate Considered as a Super-Critical Branching Process

Attention conservation notice: Academic navel-gazing, in the form of basic arithmetic with unpleasant consequences that I leave partially implicit.

A professor at a top-tier research university who graduates only six doctoral students over a thirty year career is likely regarded by their colleagues as a bit of a slacker when it comes to advising work; it's easy to produce many more new Ph.D.s. (Here is a more representative case of some personal relevance.) That slacking professor has nonetheless reproduced their own doctorate six-fold, which works out to $\frac{\log{6}}{30} \approx$ 6% per year growth in the number of Ph.D. holders. Put this as a lower bound --- a very cautious lower bound --- on how quickly the number of doctorates could grow, if all those doctorate-holders became professors themselves. Unless faculty jobs also grow at 6% per year, which ultimately means student enrollment growing at 6% per year, something has to give. Student enrollment does not grow at 6% per year indefinitely (and it cannot, even if you think everyone should go to college); something gives. What gives is that most Ph.D.s will not be employed in the kind of faculty position where they train doctoral students. The jobs they find might be good, and even make essential use of skills which we only know how to transmit through that kind of acculturation and apprenticeship, but they simply cannot be jobs whose holders spawn more Ph.D.s.

The professoriate is a super-critical branching process, and we know how those end. (I am a neutron that didn't get absorbed by a moderator; that makes me luckier than those that did get absorbed, not better.) In the sustainable steady state, the average professor at a Ph.D.-granting institution should expect to have one student who also goes on to be such a professor in their entire career.

Anyone who takes this as a defense of under-funding public universities, of adjunctification, or even of our society having more non-academic use for quantitative skills than for humanistic learning, has trouble with reading comprehension. Also, of course this is Malthusian reasoning; what made Malthus wrong was not anticipating that what he called "vice" could become universal the demographic transition. Let the reader understand.

Learned Folly