Quotes Gauss: had "positive, negative and imaginary (or worse still, impossible) unity, been given the names say, of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity." I like that! Lateral numbers, like "throwing a lateral" in American football. It's too bad though that that only refers to addition; for multiplying you might talk about stretchy and twisty numbers instead.
don't think it only refers to addition? 'lateral' just lampshades the orthogonality of the imaginary line to the real on the complex plane. the stretchytwistyness of multiplication simply inhabits said laterality.
i mean you could argue that 'lateral' in-itself is insufficient to disambiguate between the complex numbers and other planar algebras like the duals or split-complexes or just plain-ol pairs with pairwise multiplication. but it's clear who's the belle of the ball.
i guess if we want to be more inclusive we could call the pairwise-mults the plain- (pun intended) or boring-laterals, and the three planar complex algebras could collectively be called the stretchy-laterals, having sheary, twisty, and lorentzy (hyperbolic-twisty) subtypes.
Yeah, I only meant that calling them laterals instead of imaginaries brings out their vectorial nature, but complex numbers as just vectors are boring.
What would we call complex numbers if we wanted a short, vivid, inviting name? They ought to be something schoolkids are eager to learn. The name's only a small part of the school "ugh field", but maybe it's a part we can do something about?
I enjoyed that and the books on PI, e, and zero (I may be forgetting one or more). Each one is an excuse to discuss the history of mathematics which is always interesting to me.
