[diegomacario]

Wow that's fascinating, thanks for sharing it!

Although I disagree with how the author describes quaternions as black boxes. The two questions he asks:

- Why does i2=j2=k2=−1 and ij=k? - Why do we take a vector and upgrade it to an "imaginary" vector in order to transform it, like q(xi+yj+zk)q∗?

Are clearly explained in these interactive videos created by Grant Sanderson and Ben Eater: https://eater.net/quaternions

After I watched those videos, quaternions stopped being so opaque to me. I recommend them :-)

[naikrovek]

yeah, those videos are opaque, too.

if you already understand quaternions, then they're apparently excellent; everyone who understands quaternions recommends them.

I don't understand quaternions. I do not understand videos which attempt to explain them. I've seen them all a dozen times each.

[wyager]

Although I grokked quaternions before learning GA, I am 100% certain that the GA explanation is better and more intuitive.

GA breaks down quaternions (and their generalization to arbitrary dimensions) into smaller pieces that are much more obvious.

It takes hundreds of years to invent quaternions from scratch, but it takes 10 minutes to invent quaternions from GA.