I always had a hard time trying to visualize these higher dimension objects. I think its because I actually have quite good visualization and spacial awareness.

I always had a hard time trying to visualize these higher dimension objects. I think its because I actually have quite good visualization and spacial awareness. But going to 4d it just breaks and all the concrete ability isn't so useful. eventually after looking at the math and understanding more about complex numbers, i got some intuition for the multiplication of the basis vectors and i feel like I can sort of extend the intuition by linear decomposition (distributivity) multplication by a complex basis vector is like a pair of rotations one of the rotations is in plane spanned by the reals and vector itself and the other is a rotation "orthogonal" to the vector spanned by the 2 other basis vectors. This helped me recover the intuition around scaling and rotating from the complex numbers to quats.