3 ms·

Came here to say this! I always felt like quaternions weren't a perfect fit for 3d rotation, and when I finally learned about bivectors my faith in the eleganc

• the__alchemist 5y ago
  > 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∗? Who cares as long as it rotates vectors the right way, right? Yikes! This is the sort of thing that scares people away from complex numbers from a young age.
  • deleted 5y ago
    [deleted]
  • Twisol 5y ago
    Aren't you doing a bit of an injustice to that article by cherry-picking that line? It's obviously written humorously; the very next words are: > Personally, I have always found it important to actually understand the things I am using. I remember learning about Cross Products and Quaternions and being confused about why they worked this way, but nobody talked about it. Later on I learned about Geometric Algebra and suddenly I could see that the questions I had were legitimate, and everything became so much clearer. Clearly, "who cares as long as" is not the true belief of the author, but rather a mocking call-out of teachers who do think that way.