I’ve been thinking about writing this post for a long time. Normally I haunt the comment section on Hacker News and whenever an article about GA comes up I post something to the effect of: “GA is okay but it’s not as good as those people say, there’s something wrong with it, what you really want is the wedge product on its own!” Which is not especially productive and probably slightly unhinged. So today I want to actually make that point in one central place that I can link to instead.
To be clear I’m not opposed to GA per se. What I have a problem with is some of the details of GA, and the fact that the proponents of GA haven’t fixed those details yet.
In particular: Hestenes’ “geometric product” is a bad mathematical operation that needs to be discarded, and doing so is way overdue. Meanwhile GA is producing more and more enthusiasts every year, and it will take those people a while to realize the things a lot of us have realized, and in the meantime they will go on selling other people on GA and repeating the cycle. As a result GA is stuck in a sort of mediocrity. My purpose in writing this is to push it to improve and address those problems.
Here’s my basic stance: