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
The physicist Michael Faraday believed nothing without being able to experimentally demonstrate it himself, no matter how tedious the demonstation.
Understanding something really deeply is connected to our physical intuition. A simple “words based” understanding can only go so far. Visualizing something, in three dimensions, can help you with a concrete “hook” that your brain can grasp onto and use as a model; understanding then has a physical context that it can “take place in”.
Faraday, again, had this quality in spades – the book makes it clear that this is partly because he was bad at mathematics and thus understood everything through the medium of experiments, and contrasts this with the French scientists (such as Ampere) who understood everything in a highly abstract way.
But Faraday’s physical intuition led him to some of the most crucial discoveries in all of science […]
Nabeel quotes the book “Faraday, Maxwell, and the Electromagnetic Field: How Two Men Revolutionized Physics”:
Simply hearing or reading of such things was never enough for Faraday. When assessing the work of others, he always had to repeat, and perhaps extend, their experiments. It became a lifelong habit—his way of establishing ownership over an idea.
Just as he did countless times later in other settings, he set out to demonstrate this new phenomenon to his own satisfaction. When he had saved enough money to buy the materials, he made a battery from seven copper halfpennies and seven discs cut from a sheet of zinc, interleaved with pieces of paper soaked in salt water. He fixed a copper wire to each end plate, dipped the other ends of the wires in a solution of Epsom salts (magnesium sulfate), and watched.