My husband has straight hair he keeps in a tight fade, like nearly bald on the sides to very short at the top, and gets his hair cut every 2 weeks. I (lady, curly hair) can go a year between, just get it cut in short layers and let them grow out to long layers. The two of my kids who like theirs short but not crazy short go a month or two between.
Basically the shorter it is, the more you have to cut it - hair grows, on average 1/2 inch (13mm) per month, so mine has a 6 inch tolerance (it doesn’t really look like 6 inches of vertical growth since it isn’t straight) but my husband, with such straight and short hair, has a quarter inch tolerance.
Memorization is such a strange thing to try to teach. I was never good at that in school but could sing any song on the radio after hearing it once. In school I was good enough at math up to a point because I was so bad at memorization got good at thinking my way through it. Was much better at word problems than equations in elementary school.
I do agree with the premise of the shower thought - part of being educated is learning through mistakes. Making mistakes is one of the fastest ways to learn something, and is the main reason I’m good at my job. I am happy to work in accounting where mistakes don’t kill anyone.