> I'd argue for a third option: don't try to solve it by sitting in your chair. Go out and work on the problem, and see if what you're doing is improving it.
Amen to this. Doing is a strong teacher, sometimes the only teacher.
I've grown a ton as a person from my work, and one of the biggest things I've learned is how easy it is to have confident, empirically-supported, well-argued, and totally wrong opinions. There's no better way to test your views than to bet on them and put them out into the world - even if they don't work, you'll learn something.
Of course, that can go too far in the other direction, because empirical results are often driven by factors outside your control too. So you do need to be doing analysis and not just looking at results. But analysis alone doesn't get you there, even if you're extraordinarily brilliant (and, statistically, you probably aren't).
Amen to this. Doing is a strong teacher, sometimes the only teacher.
Mistakes and failure are awesome and underrated.