I am not sure about this. It looks more intuitive and I kinda agree that it would be more intuitive and easier to grasp.
On the other hand though, wouldn't you lose the generality? Part of my undergraduate geometry and linear algebra course was on fields, groups and rings and that was built in order to show that once you can define a certain set of operations on a mathematical structure you can do "math" on such structures "as if" they were regular numbers (limitations apply).
Think of matrix fields (not sure if it would be the correct translation, in Italian they were called "campi matriciali").
That was kinda mind blowing to me but at the same time it made perfect sense because of the generic definitions underlying.
Not sure how you could go ahead and explain that with regular 3d-world physics.
On the other hand though, wouldn't you lose the generality? Part of my undergraduate geometry and linear algebra course was on fields, groups and rings and that was built in order to show that once you can define a certain set of operations on a mathematical structure you can do "math" on such structures "as if" they were regular numbers (limitations apply).
Think of matrix fields (not sure if it would be the correct translation, in Italian they were called "campi matriciali").
That was kinda mind blowing to me but at the same time it made perfect sense because of the generic definitions underlying.
Not sure how you could go ahead and explain that with regular 3d-world physics.