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 this principle at Wolfram Alpha.

Some models are not wrong; they are just simplifications. It’s important to know what information was lost as part of that simplification. Otherwise, we will mistake the map for the terrain. At other times, events, transformations and environments can invalidate our assumptions. But if we don’t know the assumptions, we’d never know when our theories are no longer valid. And we’d continue operating based on faulty models. Then it would just be a case of Garbage In, Garbage Out.