The author is using geometric algebra to create mathematical objects with all the same properties as quaternions, but to explain and understand them in a more c

The author is using geometric algebra to create mathematical objects with all the same properties as quaternions, but to explain and understand them in a more comprehensive, sensible way. These things have all the same rotational properties as quaternions. In particular, he’s explaining that quaternions are not vectors, they’re actually oriented planes and showing how their multiplication rules arise in a way that’s not ‘out of thin air’.