I've been searching trough the internet for more information about Clifford's algebras, and for what I've been reading, Clifford's vector system appears to be "unifying" vector system, in particular I've find some results that show that in a Clifford algebra the Maxwell's equations can be reduced to $$\partial F=J$$ It inded seems a great subject of algebras and it is very interesting. My question is: why can't we just "implement" this algebra in our "daily" system, I mean, why do we learn Gibb's algebra instead of Clifford's one. What is the Gibbs advantage? What is missing in Clifford algebras? Is it not well defined yet?
Thank you and have a great weekend.