I've known about quaternions for many years and even used them to program rotation matrices for a few 3d projects but I've never really given them much thought

I've known about quaternions for many years and even used them to program rotation matrices for a few 3d projects but I've never really given them much thought beyond that. For some reason, your comment just completely changed the way I thought about them. To think that the i part of ijk is the same i = sqrt(-1) is mindblowing to me. I had never considered that there may be other "more imaginary" dimensions that were required to solve yet more complicated problems.