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You're in for a nice trip, the concept is called Geometric Algebra: https://youtu.be/60z_hpEAtD8?si=HHs_9m0IJ43nfI3S https://youtu.be/60z_hpEAtD8?si=HHs_9m0IJ4
by mtizim 2y ago
You're in for a nice trip, the concept is called Geometric Algebra:
https://youtu.be/60z_hpEAtD8?si=HHs_9m0IJ43nfI3S https://youtu.be/60z_hpEAtD8?si=HHs_9m0IJ43nfI3S
(~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: https://en.m.wikipedia.org/wiki/Bivector https://en.m.wikipedia.org/wiki/Bivector
- hansvm 2y agoGotcha; it's less that my complaint doesn't apply, but more that it isn't relevant (i.e., "squares" and "cubes" aren't especially interesting constructs which need to coexist nicely, and if you relax that constraint then directional geometry can be very interesting). Does that sound right?