Two ways to open a nut

Alexandre Grothendieck compares proving a theorem to opening a nut. You can set the chisel against the shell and strike, moving around until it gives. Or you can leave it to soak, and wait for the shell to open of its own accord under the light pressure of a hand. He does not hide which is his. What interests me is that in engineering both turn up every week, and are rarely chosen on purpose.

Striking means trying the possibilities until one gets through. The method has a quality the other lacks: it answers at a known hour. On a production outage that is decisive: there is no time to understand, only a need for it to work again. Its flaw is that it teaches nothing. A problem solved that way comes back, and comes back unchanged.

Narrowing means shrinking the region where the problem can be, without yet trying to solve it. It is slower at first, far faster at the end, and the result carries over: what you have bounded stays true after you leave. Its flaw is that it has no delivery hour, which makes it nearly impossible to promise to a steering committee.

Barbara Oakley gives that opposition firmer ground by distinguishing two regimes of attention, one concentrated, one loosened, and showing that the second works too. It is the argument for the walk, for the night, for the shower: not out of mysticism, but because the stage where you are not thinking about the problem is a stage of the work. The corollary is unwelcome: it cannot be scheduled.

• Barbara Oakley, Learning How to Learn

What remains is what makes both regimes possible: regularity. The notebooks of writers, painters and researchers all say the same thing, often with the same odd hours and the same chosen isolation. Stephen Wolfram has described his working setup in detail; what strikes you is not the tooling but its stability. An environment that does not change leaves all the variation to the problem.

• Stephen Wolfram · Seeking the Productive Life (2019)
• Stephen Wolfram · The Personal Analytics of My Life (2012)

Neither is the right method. The chisel on a problem that needed time produces a patch; the soaking on an incident produces an invoice. The skill is not preferring one, it is recognising which of the two cases you are in, and no reading teaches that: only the number of occasions does.