>> the moment when the solution to a problem emerges “in the shower” unexpectedly after a long period of unconscious incubation.
A lot of responses here seem to place this chain-of-thought on a spectrum between verbal and "vibe". I don't think that solving problems pre-verbally is actually at odds with verbal intelligence, or that a person must by definition be better at one than another. The pregnant, mathematical, nonverbal thought in the shower is only really useful if it can be organized and stated rationally at some point later. Likewise, the wordy explanation is useless without a well-reasoned theory it's explaining.
For me, I find that dreams help bridge this gap. Oftentimes I'll be struggling with a difficult mental model of a problem, and thinking of a lot of math in my head in the shower. But when I sleep, I'll have some dream that acts as a metaphor for the problem. Say, e.g. I'm thinking about how to time two independent processes to deconflict some data. I might have a dream about missing a flight because the plane already arrived but was announced at the wrong gate, and I'm running across the airport. Then I wake up and see the answer to the problem. Moreover, I then see how to explain the problem I just solved, using a metaphor that most people can understand.
As far as actually explaining it formally in writing, I usually test the code a zillion ways first and then write the documentation.
A lot of responses here seem to place this chain-of-thought on a spectrum between verbal and "vibe". I don't think that solving problems pre-verbally is actually at odds with verbal intelligence, or that a person must by definition be better at one than another. The pregnant, mathematical, nonverbal thought in the shower is only really useful if it can be organized and stated rationally at some point later. Likewise, the wordy explanation is useless without a well-reasoned theory it's explaining.
For me, I find that dreams help bridge this gap. Oftentimes I'll be struggling with a difficult mental model of a problem, and thinking of a lot of math in my head in the shower. But when I sleep, I'll have some dream that acts as a metaphor for the problem. Say, e.g. I'm thinking about how to time two independent processes to deconflict some data. I might have a dream about missing a flight because the plane already arrived but was announced at the wrong gate, and I'm running across the airport. Then I wake up and see the answer to the problem. Moreover, I then see how to explain the problem I just solved, using a metaphor that most people can understand.
As far as actually explaining it formally in writing, I usually test the code a zillion ways first and then write the documentation.