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I've noticed that it's not math people who are promoting it but CS people or other engineers. E.g. those who took mostly cookbook classes (no offense intended)
by rsj_hn 6y ago
I've noticed that it's not math people who are promoting it but CS people or other engineers. E.g. those who took mostly cookbook classes (no offense intended) rather than theory classes. This tells me there is a large latent desire for deep understanding.
When I first encountered the term "geometric algebra" and read some of the articles, I couldn't understand what was new about the content. In college, we learned about tensor products, wedge products, clifford algebras, and duals, and geometric algebra struck me as a subset of this core knowledge applied to three dimensions, where you can do things like take a wedge product of two vectors to get a 2 form and then take the dual to get back to a one form, and now you have a "geometric" (more of a linear algebra) interpretation of the cross product as a dual to an exterior product -- which is how we were taught what a cross product is.
But I think a lot of people who don't study this stuff were never taught these relationships, so bundling them up in a marketing name and letting them understand why these standard linear algebra relations behave as they do can really help the working engineer, which seems to be a condemnation of the rote learning approach where you are asked to memorize a bunch of stuff but are never told that what an inner or exterior product really is. Then things like calling two vectors "orthognal" if they have an inner product of zero seems mysterious.
By the way, this isn't just linear algebra. There are many deep connections behind well known algorithms in number theory, topology, calculus, algebraic geometry, (co)homology theories, that are ripe for a snazzy name and a presentation of some of the deeper ideas, so that people can start seeing connections between stuff like complex integrals and euler characteristics and winding numbers, holonomy groups and short exact sequences, etc.
So in this sense, I applaud the geometric algebra evangelists, even though this is all standard stuff that a math undergrad should learn, and the name "geometric algebra" is a completely made up term for what are well known mathematical structures.