"Well, we could imagine some..."


by Zack M. Davis May 15 2016

If the interpretation of the output \(in this case, "player position"\) mismatches the interpretations of at least one of the inputs, then the function likely isn't associative\. However, this heuristic is also imperfect: The most obvious interpretations of the inputs and outputs to the subtraction function are "they're all just numbers," and subtraction still fails to associate\.

Well, we could imagine someone arguing that differences-between-numbers could be interpreted as a philosophically different entity than the numbers themselves: 3 − 5 = -2, but numbers like -2 which are in ℤ but not ℕ don't have the same kind of easy interpretation as a number you would use to count physical objects with in the way natural numbers like 3 and 5 have.