Visualizing quaternions: An explorable video series

oof, the one thing i am wont to want with 3b1b videos is an interactive suite accompaniment.. unreasonably ungrateful i know ;P i had high hopes this would be it, but this is just a concise lesson form for the series.. which is great! i am a huge fan of both eater's and sanderson's entire ouvre what's great is that 3b1b releases the code that generates these videos and i have cloned the manim(o) library a number of times in…

Freya Holmer, of The Continuity of Splines [0] fame, recently gave a great conference talk about how quaternions naturally arise from the desire to define the multiplication of two vectors if you just agree to one new axiom: v^2 = ||v||^2, or "the square of a vector is equal to the square of its norm". It was fascinating and entertaining and I highly recommend anyone who finds this stuff interesting but confusing (like I do) to check it out: https://www.youtube.com/watch?v=htYh-Tq7ZBI…

I always had a hard time trying to visualize these higher dimension objects. I think its because I actually have quite good visualization and spacial awareness. But going to 4d it just breaks and all the concrete ability isn't so useful. eventually after looking at the math and understanding more about complex numbers, i got some intuition for the multiplication of the basis vectors and i feel like I can sort of extend the intuition by linear decomposition (distributivity) multplication…