7 HN users recommended this explainer7 months2020–2024score 9
Years with an HN recommendation, 2007–2026
HN calls it the best video on geometric algebra, one that makes the subject click in about 40 minutes.
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.
“If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video” (HN, 2022)
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]
Inspiring overview of the power of geometric algebra
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]
Shows quaternions as simple multivectors in geometric algebra
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.
Gives the bigger picture behind quaternions and complex numbers
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
Primer on geometric algebra with eye-opening physics connections
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]
Introduces geometric algebra, which generalizes cross products
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