An interesting counterargument to the recent popularizations of geometric algebra as the ideal language for doing geometry in physics, computer graphics, and so on.
I haven't actually worked with GA enough to have an opinion either way, but their basic argument seems compelling:
"1. The wedge product and the rest of Exterior Algebra is 100% amazing, S-tier stuff, definitely something everybody who uses mathematics should know about [...]
2. The geometric product, though, is kinda weird and bad.
3. A lot of other parts of GA are working around the fact that the geometric product is weird and bad.
4. The “better” version of Geometric Algebra [...] which we are... slowly unearthing... will be mostly the same as GA but it will discard the geometric product as a basic operation, to everyone’s benefit. [...]"
