So I am newly excited about quaternions, as I am working with Mentor to talk about them via the Gaussian integers--only now on the subway have I really figured out why they are a noncommutative algebra--otherwise the norm doesn't work out as nicely (is not an integer)! Sad to think I've overlooked that for so long--but hti si the problem with an overpowered approach to higher algebra with an overcommutative focus. It depresses me to think how much of this I have forgotten, and at the same time have never known.