In short: Reposting my comment from https://news.ycombinator.com/item?id=46775758 https://news.ycombinator.com/item?id=46775758 thread: scaling -> real numbers

In short: Reposting my comment from https://news.ycombinator.com/item?id=46775758 https://news.ycombinator.com/item?id=46775758 thread: scaling -> real numbers 2d rotations and scaling -> complex numbers 3d rotations and scaling -> quaternions In the case of quaternions, there is called double-covering, which turns out (rather than being an artefact), play fundamental role in particle physics.