loppy

i,j,k for basis vectors is an interesting one. Historically, Hamilton invented his quaternions before any notion of “vector” existed (as an algebraic object; I believe the geometric notion is older). (So, what, did people just write out everything componentwise? Yes, yes they did. For example, that’s how things like Maxwell’s equations were originally presented.) The reason he chose i,j,k for the unit quaternions is because i was already in use for complex numbers, and i was in use for complex numbers probably to stand for “imaginary”.

The notion of “vector” was invented specifically as a “de-algebraicization” of quaternions. People did not like working with quaternions because they thought it was weird, particurlary because they required 4 numbers but space only required 3, so the likes of Gibbs and Heaviside gutted them and gave us modern 3D vector calculus. The reason we work with the dot product and cross product in 3D is specifically because, given pure imaginary quaternions v, w the product (vw) has real part (-v.w) and imaginary part (v x w).

Also, your last paragraph is somewhat misinformed. Sequences of Greek letters are used all the time, and Hebrew letters are also used in set theory to denote cardinalities (though I can only think of aleph and beth, no sequences of such letters). It is also well-known that some people like to use Japanese よ (yo) for the Yoneda embedding in category theory. But beyond Latin and Greek, there is quite a dearth.

This sentence is shit, but I want to point out at least that “magic” is jargon for “well-behaved” or “particularly well-suited (for our application)”. It’s essentially “magic” like in the phrase “it works like magic”.

Have you read the authors current series, Dai Dark? I’ve only read a couple of chapters so I can’t say too much about how it compares to Dorohedoro, but…

You made me realize this is actually pretty common in math, e.g. “Let x, y be real numbers” instead of “Let x and y be real numbers”. I imagine this comes from the infuence of notation like “Let x, y ∈ ℝ”.