Michael Nielsen on twitter:
One function of good notetaking is that it forces you to confront your own ignorance of things you thought you understood.
To convey the experience, I once said hyperbolically to a friend: “I believe I could barely think before I began to write seriously”. As the words hung in the air, I had quite a shock, as I realized I really believed it. Taking writing seriously made me a different person.
Unless you are a kitchen tool engineer, there’s no reason to actually understand how a can opener works. What everyone else needs is to know (1) what it is for and (2) how to use it. So most of the time “understanding” is really “comfort with.” It means you know how to interact with it well enough to get by, and you are reassured that it is not going to explode without warning. This comfort is provided mainly by familiarity, not understanding. Having used a can opener many times convinces you that you understand it, because you can almost always make one work, and you almost never cut yourself. Tellingly, Rozenblit and Keil found that their subjects did not overestimate their “how-to” knowledge, only their “how-it-works” knowledge.
Visakan Veerasamy adds:
“Everything is vague to a degree you do not realize till you have tried to make it precise, and everything precise is so remote from everything that we normally think, that you cannot for a moment suppose that is what we really mean when we say what we think.”
— Bertrand Russell in The Philosophy of Logical Atomism