New Video & Patreon

2024 Progress Report

I'm excited to share a new video with you today and announce that the newsletter is moving to Patreon.

Earlier this year, while finishing the adaptation of 3Blue1Brown's linear algebra series, I used quaternions to visualize 3d space for illustrating and animating key concepts. This was a bit of an indulgence on my part because rotation matrices can achieve the same thing. However, I was impressed with how elegantly quaternions describe rotation and orientation. Afterward, even though I had successfully implemented quaternions, I was still very curious about how the number system works.

Initially, I planned to create a high-level video about how to use quaternions, but the more I got into it, the more I realized how surface-level my understanding of the number system was. Just because I cobbled together a working implementation of quaternions didn’t mean I understood how they worked. Months later, I even did the very thing I said I wouldn’t do — try and visualize 4d space.

Visualizing four dimensions at once is notoriously hard, which is why Grant's excellent video about quaternions does some fancy footwork to visualize 4d space in three dimensions using stereographic projection. For this video, I decided to stick to the special cases where you can partially see what’s happening in four dimensions. Even though this doesn’t work as well for the general case, I still think this is useful for understanding how the number system works.

I’m proud of how the video turned out and believe it complements the existing material on the subject. That said, I also feel guilty about how much time this video took to make. I estimate that I could have made something like 2-3 videos in the time it took to make this one. I do think a fair amount of time was spent figuring out my style, and if I were to take on a project of similar difficulty in the future, it would take less effort to complete.

This brings me to the other part of this update — the newsletter is moving to Patreon. I would be honored if you considered joining as a contributing member. Of course, if you just want to stay up-to-date, you can join the free tier. I will continue to post updates there, just like the ones in this newsletter.

That’s all I have for now. I hope you check out the video and let me know what you think!

Best,

Kurt