timschochet said:
OK- so why do we have an order of operations rule? I get that we have one but what's the logic of it? Wouldn't it be far simpler to go from left to right unless there were parenthesis?
I know a lot of people laughed at tim for this, but did anyone
really answer it? We use PEMDAS. Why? Why
not left-to-right-except-when-there-are-parentheses, as tim suggested?
In reality, it's just a matter of convention. We use PEMDAS because that's what we've all agreed to do, just like -52 = -25 because that's what we've all (hopefully, finally) agreed that it's equal to. Switching from PEMDAS to something else wouldn't destroy the commutative property, as someone suggested earlier. It's just a convention for communicating in a way that everyone understands. If we all agreed to write math formulas in left-to-right format, instead of PEMDAS, the commutative property of addition and multiplication would still hold. We'd just need to write our formulas in a different order to express the same thing.
We call the sky "blue." In Spain, they call it "azul" - the sky hasn't fallen there, they've just adopted a different convention for communicating. When someone wants to express the color of the sky, there's nothing inherent in the letters "B", "L", "U", and "E" that conveys it. English-speakers just agreed that when you put those shapes together, in that order, it means something.