Practicing the saxophone only has a payoff in saxophone music. Similarly, abstract exercises will often only have a payoff in nice abstractions. For example, solving the wave equation of the hydrogen atom is a classic, but it cannot gain you anything directly because it is merely knowledge, and that same knowledge can be found in a textbook or wiki faster than it can be derived. You’re just gonna have to be the sort of person for whom solving the wave equation of the hydrogen atom is a juicy project.
Practicing the saxophone only has a payoff in saxophone music. Similarly, abstract exercises will often only have a payoff in nice abstractions. For example, solving the wave equation of the hydrogen atom is a classic, but it cannot gain you anything directly because it is merely knowledge, and that same knowledge can be found in a textbook or wiki faster than it can be derived. You’re just gonna have to be the sort of person for whom solving the wave equation of the hydrogen atom is a juicy project.
That’s a nice quote. I’m working on a handbook for how to self-study. Mind if I (tentatively) use it?
Go for it—though it’s about selection effects as much as it’s advice.