Absolutely agree.
What's your preferred terminology? I like "Forward" and "Reverse" for positive and negative number and "Lateral" for the imaginary unit, since it is just perpendicular to the Forward and Reverse numbers.
What's your preferred terminology? I like "Forward" and "Reverse" for positive and negative number and "Lateral" for the imaginary unit, since it is just perpendicular to the Forward and Reverse numbers.
"If ... +1, -1, and √-1 had been called direct, inverse and lateral units, instead of positive, negative, and imaginary (or impossible) units, such an obscurity would have been out of the question"
(https://shitohichiumaya.blogspot.com/2016/10/gausss-quote-fo...)
EDIT: similarly, quaternions as a number in 4D, with that extra dimension being handy for avoiding the instability problems when you get near “gimbal lock” in 3D rotations.
On the other hand, dual quaternions do care which is the dual component, since multiplying by complex numbers looks like true rotation, while multiplying by a dual looks like rotation around a point at infinity, aka translation.
So in that case maybe there is something special about the real component.