Those explanations are really great. I’ve missed such in school when wondering WHY things behave like they do, when I was only shown HOW to use things to get what I want to do. But what do these explanations really explain. I think they are merely satisfying our idea that there is more to it than meets the eye. We think something is missing. What such explanations really do is to show us that the heuristics really work and that they are consistent on more than one level, they are reasonable.
Here are more examples:
Why a negative times a negative should be a positive.
Intuition on why a^-b = 1/(a^b) (and why a^0 =1)
Those explanations are really great. I’ve missed such in school when wondering WHY things behave like they do, when I was only shown HOW to use things to get what I want to do. But what do these explanations really explain. I think they are merely satisfying our idea that there is more to it than meets the eye. We think something is missing. What such explanations really do is to show us that the heuristics really work and that they are consistent on more than one level, they are reasonable.