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They say Geometric Algebra is "the new language of physics" and whatever else; my problem with this is that, unlike, say the calculus of differential forms (or
by Koshkin 7y ago
They say Geometric Algebra is "the new language of physics" and whatever else; my problem with this is that, unlike, say the calculus of differential forms (or tensors), it does not make sense in more general manifolds which are at the heart of the modern theoretical physics. Geometric Algebra, therefore, is more like something that, sure, could be taught in high school in an attempt, for example, to streamline elementary vector algebra and thus eliminate some nasty questions (should they arise); yet, there is some mental load to it that may make it not worth the effort...
- moultano 7y agoCan you elaborate on that or provide a link? The OP made it seem like it was strictly more general, and I was getting excited to dive in through that route.
- Koshkin 7y agoWell, nothing wrong with getting excited about and learning this stuff. Point was, in more complicated cases like (non-flat) [co]tangent bundles GA, as an intuitive framework, loses any advantage, perceived or real, over differential forms.
- 6gvONxR4sf7o 7y agoI found that learning geometric algebra in a nice flat space made differential forms much more intuitive for me. I don't think they're so at odds, and teaching one then the other may benefit both.
- BlueTemplar 7y agoUh, getting rid of pseudo-vectors ? Maxwell's Equations? http://www.av8n.com/physics/maxwell-ga.htm http://www.av8n.com/physics/maxwell-ga.htm
- zrkrlc 7y agoHuh, it absolutely does. Alan Macdonald wrote a book about geometric calculus and made a companion video series for it. Here’s the section defining manifolds: https://www.youtube.com/watch?v=jfwdlW7Yr_I https://www.youtube.com/watch?v=jfwdlW7Yr_I That said, tensors are in fact more general than geometric algebra’s multivectors (in that the latter form a quotient algebra of the former). But not all tensors correspond to manifolds as we know them in physics and I argue that GA keeps track of the geometric properties we want better.