I find it really fascinating that you use the metaphor to GA of a senior dev sweeping all the cruft away into a single clean abstraction, is that my read/smell of TFA (as a layperson for this depth of math) is that GA runs the exact same risk of leaky abstraction. It's really general and elegant and covers all these cases with a single abstraction, but in doing so it sometimes conflates very similar things (precisely because they are so similar) when they really ought to be separate things. Like a complex number and the rotation operator it performs. My seat-of-pants take is GA is just a bit too DRY.
My understanding is too shallow to get why we don't just go straight for EA/Clifford Algebra when the "lower" systems like cross product are insufficient.
I share the author's intuition that there ought to exist some mathematical object that begets Clifford Algebras and multivectors and GA and all the like that we have yet to discover.
> They're spending their precious time on this Earth learning a dead language instead of learning about the law or bugs
I know this is hyperbole, but it's my opinion Latin/Greek emerged so dominantly in law/bio/medical fields is that it allows at the same time semantic bleaching and composition. "Jargon is a DSL" if you will. Sure, you could say "heart muscle no worky cause insufficient oxygen" but "myocardial infarction" is a) more concise b) comprises reusable composable pieces of meaning (myo + card + -ial, in + farcire + -ion) c) most importantly, is extremely precise. It's like the trouble of using English + LLM to define a program, vs just writing damn code. Sure you can do the former, but it's lossy, and that lossiness causes issues.
My understanding is too shallow to get why we don't just go straight for EA/Clifford Algebra when the "lower" systems like cross product are insufficient.
I share the author's intuition that there ought to exist some mathematical object that begets Clifford Algebras and multivectors and GA and all the like that we have yet to discover.
> They're spending their precious time on this Earth learning a dead language instead of learning about the law or bugs
I know this is hyperbole, but it's my opinion Latin/Greek emerged so dominantly in law/bio/medical fields is that it allows at the same time semantic bleaching and composition. "Jargon is a DSL" if you will. Sure, you could say "heart muscle no worky cause insufficient oxygen" but "myocardial infarction" is a) more concise b) comprises reusable composable pieces of meaning (myo + card + -ial, in + farcire + -ion) c) most importantly, is extremely precise. It's like the trouble of using English + LLM to define a program, vs just writing damn code. Sure you can do the former, but it's lossy, and that lossiness causes issues.