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.

TRANSFORM COMPOSITION!

(sorry, it's not your fault or even his that you didn't know this - GA textbooks should have it as the first thing they teach but they don't)

especially the part about duals -- made me feel like I was going crazy when I was trying to figure out degenerate metrics: every source deals with it in a slightly different (often sloppy) way; you're sure it all must be possible to resolve and get something beautiful and consistent, but not while you're trying to apply it to a specific problem you need to solve

Mathematics is a social activity. The research cultures of different branches matter.

The start of the article makes a specific technical claims:

> Hestenes’ Geometric Product is not a very good operation and we should not be rewriting all of geometry in terms of it

Later he explains why:

> there is no good general interpretation or usage for the geometric product or mixed-grade multivectors