"you can't multiply vectors" hold my tea
in my research into geometric algebra, I've come up with a neat minimal starting assumption:
v² = ||v||² - a vector multiplied by itself is its length squared
it then follows that multiplying two vectors, gives you a quaternion c:
for those wondering how we can get from v² = ||v||² to knowing that xy = -yx
it's actually really cute! here's how:
I've been wanting to make a video about quaternions (and GA) from this angle, because it's a much more intuitive place to start for me than I've seen elsewhere
many others start by defining the dot and wedge product, but I've never been satisfied with that as a starting point!
@acegikmo I have looked at GA multiple times, and each time I'd really like it to be an interesting way of looking at the world, but each time it's just... slightly different words. It's arguably more elegant, but then in practice it's not, it's just different. I don't get it. Maybe you can make be a believer?
@TomF hopefully! a lot of GA advocates, like a lot of math, tend toward too much generalization, and shooting off to incomprehensible formalism, rather than practicalities
I've found a few areas where I think it really shines!
@dpwiz honestly it's kinda the the same abyss just with slightly prettier colors lol