Comment by user070223 | Hacker News Reader

Comment by user070223 | Hacker News Reader

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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 https://www.youtube.com/watch?v=60z_hpEAtD8 (And other videos on his channel) Another greate playlist is https://www.youtube.com/watch?v=0VGMxSUDBH8&list=PLLvlxwbzkr...

BTW the author has the following page https://projectivegeometricalgebra.org/ with great infographics and references

Hah! I knew Sudgy would be your first link. There's relatively little content about GA, but once you're hooked you begin to consume it all.

It's like you never got to study Relativity, conformal geometry, electron spins, quaternions, etc then someone comes with a simple cheat code which introduces you to these topics gently. It's like what category theory wants to do for mathematics, but simple.

Here are additional resources:

GA playground: https://enkimute.github.io/ganja.js/examples/coffeeshop.html...

A physics engine in 100 lines (Gravity, Hook, and damping laws are just one line each!), and you can go from 2D to 3D to 4D by changing a single parameter: https://enki.ws/ganja.js/examples/pga_dyn.html

Other resources: https://bivector.net/

And anything by David Hestenes: https://worrydream.com/refs/Hestenes_2002_-_Reforming_the_Ma...

The absolute first video to watch should be the (ironically titled) Why can't you multiply vectors?

https://www.youtube.com/watch?v=htYh-Tq7ZBI

Note though that GA is extremely niche and offers very little beyond exterior algebra. Exterior algebra in the context of differential forms is standard part of the postgrad (and sometimes undergrad) Physics curriculum.

See the applications to physics section here: https://en.m.wikipedia.org/wiki/Differential_form

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