the end. i'm sick and tired of chasing down all the leaps of mathematical logic in all my physics books. it's impossible. you know why everyone screams that you need to do problems to know physics? because there's no other way. the way i see it there exist two ways to know how a construction works: knowing the details of its innards or observing it in tons of scenarios. it's deductive versus inductive reasoning. in my opinion the former is much more efficient but apparently the physicists see it otherwise; that i should learn how to do physics by osmosis. and you know that's fine, it's their prerogative. maybe for experimentalists their method of choice is even comparably as efficient/beneficial but i question how in the hell theorists learn to do anything except solve the problems they've already been taught to solve. summary: math >> physics. note the strict inequality.