Re:Calculus Is Deeply Irrational
by hyperpallium on Wednesday August 21, 2019 @03:56AM
(#20755307)
John Von Neumann https://math.stackexchange.com/questions/11267/what-are-some...
Does the followong seem right to you?
Intuition often comes from relating a new thing to something known. So maths, as an abstraction of reality, initially has many sources of intuition.
Later maths never has exactly the same patterns as earlier maths (it's already abstracted; so same patterns would be the same thing, though it cam build-on). Eventually, it doesn't relate to anything known, and you have to create that familiarity from scratch.
That's hard... but if some stuff became known in the first place, why not this too? (One counter is that the other stuff was instinctively known, e.g. 3D space, or at least our minds are pre-shaped to know it, e.g. language).
Assuming math is open-ended, there'll always be new stuff that doesn't relate.
Is that the same as making sense? Well to paraphrase a physicist, you don't so much understand it as get used to it.
One of the fun things about teaching this material is that usually students have been through years of calculus prior to it, and you get to watch the moment when they realize all of this stuff has been "hiding in plain sight".