They're not objectively harder to motivate, just preferentially harder for people who aren't interested in them. But they're extremely interesting. They offer a surface for modelling all kinds of geometrical relationships very succinctly, semantically anyway.

This is also super interesting and I don't know why anyone would be uninterested in it philosophically: https://en.wikipedia.org/wiki/Classification_of_Clifford_alg...

There is such a thing of using overly simple abstractions, which can be especially tempting when there's special cases at "low `n`". This is common in the 1D, 2D and 3D cases and then falls apart as soon as something like 4D Special Relativity comes along.

This phenomenon is not precisely named, but "low-dimensional accidents", "exceptional isomorphisms", or "dimensional exceptionalism" are close.

Something that drives me up the wall -- as someone who has studied both computer science and physics -- is that the latter has endless violations of strong typing. I.e.: rotations or vibrations are invariably "swept under the rug" of complex numbers, losing clarity and generality in the process.