In most professions, most of the time,the job goes as smoothly as driving a bus.
Take medicine, for example. Patient presents with a problem; doctor performs standard diagnosis and consults that big reference book that years of training and experience have lodged in her brain; doctor recommends standard treatment.
Law? Client presents with a problem; lawyer consults the giant law library that years of . . . .
Accountancy, engineering, teaching? Much the same routine, most of the time.
But there are some vocations in which the situation is reversed, professions that do not run as smoothly. In these jobs, the practitioner spends most of his time firmly in limbo. Nothing moves; nothing has moved for an hour, a day, a month. And no solution presents itself.
The practitioner is, in a word, stuck.
I am talking here about mathematics, but I have had similar reports from writers — particularly mystery writers — and architects. And I suspect that physicists and philosophers are in a semi-permanent state of stuck.
The phenomenon of stuck arises whenever we are faced with a demand to devise a new way of solving a problem. The writer wonders, how can I pull together motive and opportunity for the murder without having the reader catch on? The architect wants a giant atrium while preserving the traditional facade of the art gallery he is renovating. And the mathematician wonders, after a month of sporadic attempts to prove a theorem that he was certain was true, whether it may be worth looking for a counter-example.
Sometimes the problem never becomes unstuck: the writer starts over with a new mystery, the architect ditches the atrium and the mathematician lets the unproved theorem gather dust.
But occasionally a light bulb glows in the cartoon balloon. My former colleague Dave, working on his doctoral dissertation was pulling on his socks one morning when he realized that the theorem he had been trying for three months to prove was in fact false. By the time he finished breakfast, a counter-example was forming in his mind. By noon, he had it down on paper. Three weeks later, he handed in his thesis.
My own illumination came to me when I saw how to prove the theorem at the heart of my M.Sc. thesis. I was sitting alone in the graduate student centre, a beer half-way to my lips, when the answer came. Never underestimate the power of beer. As the inestimable Cliff said on an episode of Cheers,
A herd of buffalo can only move as fast as the slowest buffalo. And when the herd is hunted, it is the slowest and weakest ones at the back that are killed first. This natural selection is good for the herd as a whole, because the general speed and health of the whole group keeps improving by the regular killing of the weakest members. In much the same way, the human brain can only operate as fast as the slowest brain cells. Excessive intake of alcohol, as we know, kills brain cells. But naturally, it attacks the slowest and weakest brain cells first. In this way, regular consumption of beer eliminates the weaker brain cells, making the brain a faster and more efficient machine. That’s why you always feel smarter after a few beers.
