Well, I think my points in the parent article here do stand (I'm aware that you do not). The fact that there is a good interpretation of the geometric product in some cases does not obviate the fact that everyone's writing crappy intuitive things about it. Anyway it has always been my stance that there is a _good_ version of GA, and people need to figure out what it is and write about that instead of bloviating about how good the current version is. Treating the GP as a composition of operators is a start, but it's not the whole picture --- why do operators compose in that particular way? why are these your operators in the first place? My hunch is that GA is really a subset of a larger and more intuitive algebra that has very obvious answers to these questions, probably from a representation-theory perspective.
(I meant to do this followup soon after the first article but I've been been having a lot of difficulty focusing / constant brain fog for the past few years so it's been on the to-do list instead; part of the problem is that to do it right I need to go read and digest everyone's different treatises / expositions on GA ... and that has felt taxing, to say the least.)
(I meant to do this followup soon after the first article but I've been been having a lot of difficulty focusing / constant brain fog for the past few years so it's been on the to-do list instead; part of the problem is that to do it right I need to go read and digest everyone's different treatises / expositions on GA ... and that has felt taxing, to say the least.)