> I strongly believe that if GA would make this distinction they would lose a lot fewer people. It is a completely interesting and useful thing to talk about “a representation of a particular class of operations that makes composition and inversion easy”, and completely offputting when you blur the distinction between operators and geometric objects themselves, and write every operation in terms of the geometric product when only a few of them are really compositions of operators.
I can't tell what "a few of them" refers to. What is this potential distinction between operators and geometric objects? Sounds like the the distinction between a group action and a group object?
I am willing to believe that GA is an unnecessary renaming of other simpler things, and also that it has these kind of culty vibes, but I'm focusing on the claim that (I understood as) "unifying the operators and geometric objects" is a bad feature rather than a good feature.
I didn't understand this part:
> I strongly believe that if GA would make this distinction they would lose a lot fewer people. It is a completely interesting and useful thing to talk about “a representation of a particular class of operations that makes composition and inversion easy”, and completely offputting when you blur the distinction between operators and geometric objects themselves, and write every operation in terms of the geometric product when only a few of them are really compositions of operators.
I can't tell what "a few of them" refers to. What is this potential distinction between operators and geometric objects? Sounds like the the distinction between a group action and a group object?
I am willing to believe that GA is an unnecessary renaming of other simpler things, and also that it has these kind of culty vibes, but I'm focusing on the claim that (I understood as) "unifying the operators and geometric objects" is a bad feature rather than a good feature.