>>16726618
OP this board is far too one-track minded to ever grasp something like this.

They understand advanced mathematical theorems but not the why. The term is "autism".

If you envision the relationships between quaternions like a physical object like "representation theory" then it'll start to make sense.

It's not like a Rubik's Cube "per se", but it's the same idea.
Turn one side one way and then turn one side the other way.
This sequence of transformations produces the same thing "sometimes", but not always. There's a space where these things commute and the order doesn't matter and a bunch of ones where it doesn't.

The final redpill is (at least appears to be) Octonions. These are neither associative nor commutative but behave like numbers as we understand them.

Here's something weird to chew on:

>all of the number systems are powers of analogous powers of 2
>real (1D)
>complex (2D)
>quaternions (4D)
>octonions (8D)

I don't know why. Neither does anyone.
I have a hunch that it's because the idea of inverses produces the number 2 which is then a corollary to a number of other properties.