| Wow, thanks so much for all this. I've yet to digest it fully but it's a terrific intro, I love how you worded some of this. You should consider teaching! :) I can't elaborate much, so just a few "mind blown" moments for posterity: > GA is just "strongly typed" vector algebra. That's one hell of $1B slogan, at least around these parts! :) Shut up and take my money. > in 3D space (only!) the mathematics of areas and vectors is coincidentally isomorphic, so it's possible to cheat and use only vectors and scalars and then everything "works". I never realized that... there's indeed a lot of confusion in my mind between those concepts. I fail to see how "different" they're supposed to be, I guess really need to go back to sane basic in that regard. > Geometric Algebra has various subsets that are also closed algebras in their own right. Just wow. I love this. I actually need this. > GA has no such restrictions and the same formulas work in all dimensions, including high-dimensional or with degenerate metrics. Problems from classical geometry such as finding tangent lines to circles can be trivially extended to finding tangent hyperplanes to hyperspheres, even for very complex problems. So that is the real kicker for me, because it fits my problem space so well. I'm exploring highly-dimensional models (basically letting complexity arise from the dimensionality of rather simple/elementary objects, rather than trying to shoehorn complex functions in low-dimensional space in hope of pretty much randomly finding "better fits" — it's a strong desire to not interpret the data before the fact, to remove bias from modeling itself). There's interesting research around geometric deep learning as well, which seems largely informed by physics as well, and this is sort of the logical conclusion of that for big datasets. I think industrial use may rise greatly based on this first take. But it's always a generational thing with culture — it takes ~25 years give or take for those who "grew up with it" to finally become the majority of the workforce and sway things their way. Same with politics — looking at you, academia. As you said, "but by this point they're so used to wiring up breadboards manually that it's too late to teach them how to do anything properly." > It's nuts. Yeah, it'll take time, never mind how infuriating in the meantime. But good on you, spreading the word about GA is exactly how we move forward, one post, one topic at a time. Eventually, we get there. |