alt Hacker News(This is a nitpick and does not argue against your main claim that GA is a better abstraction to represent and solve physics problems with, that I have no way to evaluate because I don't speak GA, though now I'm curious and will maybe spend an afternoon trying to figure out)
I mean, come on, lawyers and biologists don't really spend half a decade studying Latin. You can tell because smart people that spend a year or two studying Latin are conversationally fluent in it, and lawyers aren't.
They spend a month or two memorizing some latin words that could have been in English, and then (for biologists, lawyers just stop there) years memorizing lots of names of things that they'd have to memorize no matter what language they were in, and it's not really any slower in Latin than it would be in English once you spent that O(1) effort to get used to it.
Like us (systems) programmers don't spend decades studying the C language, we spend a year or two getting comfortable in C and then the rest of our careers learning all sorts of interesting ideas like generational GC that come phrased in pseudo-C but might as well have been phrased in English pseudocode with a similar cognitive load to grokking them.
That wonderful popcnt() algorithm that uses 0x33333333 and 0x55555555 constants would be just as hard to decipher if it was written in plain English.
To be honest I was struggling to phrase my argument in a cohesive narrative without it turning into a ten page blog post.
The point I’m trying to make is that there are necessarily complexities inherent in all areas of study, and there are incidental complexities because of historical reasons, “culture” within certain fields, or juniors putting out their fields’ equivalent of spaghetti code.
Geometric Algebra sweeps away a lot of the rather messy parts of now century-old physics, but the work of doing that substitution is decidedly non-trivial and thankless, so other than Hestenes, nobody seems to be pushing for it.
It’s like the 2pi versus tau fad on the internet.
Mathematicians argue that they’re “the same”, so it doesn’t matter, and ramble on about their equivalent of “learn the Latin to be smart like me”.
No. It’s stupid. It was an error. Tau is the correct circle constant and eliminates magic constants that don’t belong from literally hundreds of famous formulas!
I and many others simply failed to understand radians until I learnt to treat 2pi as a single ligature instead of “two of something”.