Comment by dpwm

I tried on multiple occasions to understand Quaternions, but I never found the time to get them. It was like a personal mental block. I also bought into some of the pedagogical FUD surrounding quaternions and understood there were controversies surrounding James Clerk Maxwell's use of them.

In my search I by chance came across a book on "Geometric Algebra" -- or Clifford Algebra. It just so happens that Quaternions form a sub-algebra of the three-dimensional Clifford Algebra.

If you can get complex numbers, you can get Clifford Algebra in 2D. You can then go to Clifford Algebra in 3D.

I believe you can learn enough Clifford Algebra to "get" Quaternions in well under 20 hours, but also have a tool that generalises rotations to higher-dimensional vector spaces.

I'd previously had a topic I just couldn't understand in Fourier Transforms. I just never really got the point until one day it clicked. And when it did, it was no problem to me. That said, I never found any of the videos particularly useful before I understood. Likewise, I still don't find any of the quaternion videos too useful.

I found some course notes to be useful [0]. I then worked through "Linear and Geometric Algebra" by Alan MacDonald.

In short, don't give up. You can come to understand things by the most indirect of paths and your understanding will be all the better for it.

One hard-learnt tip if you do choose to go down this less-travelled route: Many expressions in GA can be simplified into wedge and dot products. I was needlessly writing down the algebraic expressions only to find they expanded back into these. So learn how to manipulate products early on and you'll save yourself from multi-page algebraic expressions.

[0] http://geometry.mrao.cam.ac.uk/2015/10/geometric-algebra-201...