I have been following the development of the 4d game Miegakure for a few years. One of the blog posts from the primary developer criticizes quaternions and suggests that rotors are a more natural and generalizable way to represent 3d rotations. Will we learn about rotors in this course?
The blog post in question is here: https://marctenbosch.com/quaternions/
Are there analogues of quaternions for even higher dimensions?
Is there any intuition that would help me understand why it is necessary to have 4 parts to describe a 3d rotation like this?
Doing math instead of going to a party? nerd
Is there a generalization to quaternions that is used in higher dimensional computations (including rotations)? In general, how does one know how many dimensions are needed to generalize to a d-dimensional vector?