Henry Baker <hbaker1@pipeline.com> wrote:
There's a *huge* difference between 'i' and 'j', so the eye might not pick up on this subtlety. In the quaternions, 'i' is perpendicular to 'j', and 'i' doesn't commute with 'j'.
I thought there was perfect symmetry, i.e. that in any quaternion equation you can replace i with j if you also simultaneously replace j with k and k with i. And that you can also swap i with j if you simultaneously stick a minus sign on one (but not both) of them. This is analogous to how in complex numbers you can swap i with -i. And also analogous with the symmetry between electricity and magnetism if you make the Maxwell equations symmetric by removing the bald assertion that there are no magnetic monopoles. Sure, they haven't found any *yet*, but they haven't looked everywhere. As far as I know, nobody has checked under my bed. You can also swap positive for negative electric charges, or north for south magnetic charges.