GA does not quite do the job.

What does that mean? This is hacker news, you can't just say "that sucks" or "that's great" like on reddit...

Oh right, this is the place where you make a crazy claim and back it up by a Wikipedia link instead of an argument! ;)

What I meant is that, no, I don't think that GA is a substantial improvement of notation, even though a vocal minority might have made you believe otherwise. One piece of evidence is that physicists would have happily picked up the notation otherwise (and no, this is not an appeal to authority ;). Also, I am not sure what you mean by "in the works", since it is quite old of a concept.

GA isn’t really a difference in notation exactly. It’s a difference in model.

Anyway, the model is great, and IMO should be taught in high schools. It would reduce a lot of redundant and obnoxiously inconsistent existing models we use instead, and ultimately save students a lot of time.

It takes a bit of work to get used to reasoning in GA vs. the standard vector model, or via trigonometry, etc., but there’s a pretty big payoff, I find. Many problems are substantially easier to reason about in GA terms, and many bits of bookkeeping can be avoided compared to the standard approaches.

More generally, the study of geometry has in general been systematically deemphasized and devalued over the past 100 years, in favor of analysis. This has IMO caused some serious problems for students’ and scientists’ geometric fluency and reasoning. GA is IMO one way of helping reunify algebraic/analytic with geometric reasoning.

By “in the works” he probably means that since David Hestenes has put in a career’s worth of work reintroducing / popularizing the ideas that were mostly ignored after Grassman’s time with the singular exception of Clifford (except in highly technical pure mathematics contexts, and by a few physicists for studying general relativity), and especially in the last 20 years or so since a slightly bigger community has gotten involved, it seems like GA is picking up some steam. Many more people have heard/thought about it today than 10 years ago, there are now a handful of textbooks, etc. In particular some computer graphics / computer vision / robotics folks have found GA very useful to their work.

As for why physicists haven’t been champing at the bit.. GA as a model doesn’t allow people to solve any new problems that they couldn’t solve before using existing models, it just makes understanding what’s going on a bit easier. It’s sort of like refactoring all your code: it takes a lot of effort to reframe everything in terms of a new model, and the payoff is mostly for the people who are learning the material for the first time rather than for current professional mathematicians and physicists. Radical changes to low-level models take a long time to propagate through society, or sometimes are altogether impossible (which is why we still use base 10 instead of base 12, why America is stuck with imperial units, why we have a completely hacked together calendar of unequal length months, why we use π as a circle constant instead of either 2π or π/2, why we haven’t normalized English spelling, etc. etc.)