| Not a fan of the article. It resorts to ad hominem attacks like > GA had gotten a bad reputation because of its tendency to attract bad mathematicians and full-on crackpots. Hestenes honestly sounds like one a lot of the time, and I’m not really sure whether he is or isn’t. It makes sense, really. > GA ended up appealing to a lot of fringes: people who only had undergraduate degrees, people who had dropped out of PhDs, people with PhDs from unrigorous programs, people who had been good at math but were perhaps going a bit senile, random passerbies from engineering or computer programming, run-of-the-mill circle-squarers, people who had a bone to pick with establishment mathematics and felt like all dissenting views were being unfairly suppressed > It didn’t help that a lot of the texts by the actually-competent GA people, like the Cambridge group, tended to say things that sounded and still sound kind of crackpotty as well. After reading the article, the main "case against geometric algebra" I could find in there was that the author does not like the people using/doing research in geometric algebra, such as the ostensibly failed academics from a Cambridge research group [1] which the article links to. I was expecting in the "An Actual Case Against GA" section that the author would demonstrate something like "Geometric Product actually does not work if you apply it to xyz domain". Rather, the section just ended up being mostly about the type of bikeshedding you see about naming of variables in programming. There is I guess merit to the core "there is no good general interpretation or usage for the geometric product or mixed-grade multivectors" thesis of the article but calling other academics crackpots really subtracts from that message. [1] https://corde.phy.cam.ac.uk/ |
Those paragraphs are in the background section, clearly labeled as "this is what other people think", and are followed with a high effort explanation of (presumably) the substance of the theory and why the author considers some of their ideas to be good and others to just increase the confusion.
The technical arguments are less like variable naming discussions and more like arguments against teaching logic circuit design with only nand (without naming the and/or/not operators) or using untyped lamba calculus (with Church numerals, e.g. `3 := λf.λx.f (f (f x))`) to do calculations on numbers.
At the least, the five bolded statements summarizing 5 of the 7 highly technical arguments should count as substantial claims.
Of course, having learned of the subject only from the author, it's hard to know whether it's a good representation of GA or a strawman, but the theory that he teaches as GA indeed seems quite flawed as a tool for thought.