3 ms·
The basic complaint is that GA adds nothing to exterior algebra, which is well understood, even if under-utilized. That the concepts of EA are under-used is not
by jvanderbot 3y ago
The basic complaint is that GA adds nothing to exterior algebra, which is well understood, even if under-utilized. That the concepts of EA are under-used is not up for debate: Everyone agrees. In fact, by reframing everything from the first introduction to linear algrebra and up in terms of GA, you lose intuition, compatibility, and gain nothing.
https://en.wikipedia.org/wiki/Exterior_algebra https://en.wikipedia.org/wiki/Exterior_algebra
Having read the GA textbook and vector calculus textbook, I can't agree more. The whole thing made me consistently think "Oh cool, so what?". Usually when I read through a grad / undergrad textbook I gain a new way of thinking about problems I want to think about. With GA, it was more of contorting my problems to fit onto GA, and then ... nothing.
However, there were some claims that I did not verify in the GA textbook about being computationally faster and more stable. Those, if borne out, would be valuable.
- blablabla123 3y agoIn my first few semesters of studying Physics I found these commonly used integral identities (Stokes etc.) really odd and wondered why those look so similar. Of course EA/differential forms provide ways to generalize that. Then other QM topics have these absolutely counter-intuitive geometries, although GA seems to provide some consistent intuition. (E.g. why a full rotation is 720 degrees) That said, I think vector algebra/calculus seems to be too much calculation focused to me. It's really hard to develop an intuition without excessive amounts of exercising calculations. (And books about GA still seem scarce) By the way, this article provides some estimations about no. operations compared to just using matrices: https://enkimute.github.io/LookMaNoMatrices/ https://enkimute.github.io/LookMaNoMatrices/