Know Your Assumptions
Most of us have wondered (and cursed) why they taught us the proofs of theorems and formulae at school. Why weren’t we taught only to apply that knowledge instead of deriving what was already known? At that time, it seemed like yet another useless practice of our education system. Only much later have I understood the value of knowing the proofs. It was not the proof itself that was of consequence. Rather, what’s important is to know the assumptions behind that formula, conclusion, model or whatever. Because only by knowing the assumptions can we know when that model is invalid. Or if it is missing anything. Ever seen the flight route from Bangalore to London? It’s a curved path. Why is that? Isn’t the shortest distance between two points a straight line? That “fact” (a line is the shortest distance between two points) only holds for a plane surface . For a curved surface like the earth, a (particular) curved path is the shortest distance between two points. You can see a demo of