A Swift Introduction to Geometric Algebra
Why Hacker News recommends it
HN calls it the best video on geometric algebra, one that makes the subject click in about 40 minutes.
What it is
An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.
Recommended by 7 HN commenters across 7 different months, 2020 to 2024.
What Hacker News said
Strong rec canjobear · 2020-11 · on “Geometric Algebra (2012)”
I highly recommend the video [this video] linked from the site above ~40 minutes, and I get the point of geometric algebra now.
Strong rec strainer · 2021-10 · on “A few of the best math explainers from this summer [video]”
This little known channel: sudgylacmoe - which doesn't seem present in the list, has the best video by far on Geometric Algebra (imho) [this video]
Strong rec kilovoltaire · 2022-04 · on “Exponentially Better Rotations”
If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video "A Swift Introduction to Geometric Algebra" [this video]
Strong rec BenoitP · 2024-07 · on “Quaternions in Signal and Image Processing”
You should jump straight to geometric algebra. It's actually simple there. Quaternions and Complex Numbers are about just some not so special multivectors. Here are 2 45mn videos you'll not regret: [LINK] [this video]
Recommends skaskaska · 2023-10 · on “Exploring Quaternions (2018)”
Also check out [this video] and [LINK] Some of the perceived complexity of complex numbers and quaternions seems to stem from not knowing the bigger picture.
Recommends user070223 · 2024-08 · on “Poor Foundations in Geometric Algebra”
Note don't to be confused with Algebraic Geometry they are different; When I first came across this topic it was eye opening, especially the fact that you could squeeze Maxwell's equations into one and the fact that pseudovector create by cross product from physics is just a bivector which in 3d could be represented like a vector orthogonal to the plane created by the two vectors in the product Primer on the topic [this video] (And other videos on his channel) Another greate playlist is [LINK] BTW the author has the following page [LINK] with great infographics and references
Recommends mtizim · 2024-12 · on “A visual proof that a^2 – b^2 = (a + b)(a – b)”
You're in for a nice trip, the concept is called Geometric Algebra: [this video] (~50m video) TLDW: Yes, the concept is there, makes much more sense than a cross product (which is just an oriented area) and generalizes really nicely. Alternatively, read: [LINK]