Someone on HN proposed "Lateral Number" which I thought was a good one. It's a number, just to the side of the numbers you know.
Re:The Paper That Keeps Showing Up
by cyberbanjo on Monday October 31, 2022 @08:19AM
(#33404721)
"If we call +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."
--Gauss
One of the most helpful things for me when handling imaginary and complex numbers came not from a math class, but a physics class. My HS physics instructor said rather than "imaginary" we could think of -1 as a "hidden" number, because after you do the math fairly often you see where the number would be, but you just can't see it among the "real" numbers. This was literally an aside to something else he was talking about at the time.
Calling the imaginary numbers "lateral" and saying they were "to the side of" other numbers would've been helpful, too. I'm not sure it would have been quite as helpful to me, personally, but either is better than "imaginary" just to juxtapose with the "real" numbers.
> My HS physics instructor said rather than "imaginary" we could think of -1 as a "hidden" number, because after you do the math fairly often you see where the number would be, but you just can't see it among the "real" numbers.
IIRC you often encounter a system where the energy is constant, but only if you consider the imaginary part of some equation holding the potential energy, which then exchanges with "actual" kinetic energy.
Same with quaternions and dual quaternions. They perform rotation and scaling in 3D space. Calling them "hypercomplex numbers" makes it sound like an advanced concept only to be understood after years of dedicated study.
I get that naming things is hard, but they could have gone with something that didn't sound like it was intended to stroke the egos of the learned few who understand.
I prefer the term rotor, because they perform rotation. The actual math involved isn't that difficult if you've learned the basics of geometric/Clifford algebra.