[a1369209993]

> some complicated coordinate-based calculation

Isn't that just what distinguishing scalar/vector/bivector/trivector/etc is for? I don't have problems with coordinates because I don't bother with coordinate-based calculations in the first place. What I don't get is how adding two multivectors of different [ranks? eg scalar + bivector] is supposed to simplify anything.

> > > the geometric product [...] is the sum of a scalar and a bivector

> any expressive language [...] makes it possible to state a wide variety of nonsensical things.

Yes, but if everything the language makes it possible to state is nonsensical, then what's the point?

I assume there's some sort of point to geometric algebra, but I have yet to encounter any convincing explanation of what that point is, and why I shouldn't keep my dot and wedge products properly separated.

[jacobolus]

I just said that for many single calculations, GA has saved me literally hours of headaches, in addition to making the result dramatically clearer and more insightful.

Nobody is going to force you to try something you don’t want to try. I don’t think I’ll be able to convince you.

[a1369209993]

> I just said that for many single calculations, GA has saved me literally hours of headaches, in addition to making the result dramatically clearer and more insightful.

Er, right; I was[0] asking for a example of a such a dramatically clearer and more insightful result, relative to just using normal dot and wedge products. Using vectors at all saves hours of headaches if all it's being compared to is coordinate-based calculations.

0: Well, the comment before that one was asking about the interpretation of the geometric product.