A rather obvious mathematical fact, which I never really noticed before watching this video (perhaps because of notation or the rarity with which it comes up) is that exponentiation and its higher-order forms (arrow notation) is not associative. Is this just a mathematical curiosity or is there any consequence to it? Is there a reason right-associativity was chosen as the default?
I think right associativity was "chosen" because left associativity would be redundant (since (a^b)^c = a^(b*c)), and so it saves on bracketing and generally makes things slicker.
