Commutativity and associativity are some weird properties.

Like a few mathematicians I know like commutative algebra quite a bit more than the non-commutative stuff. Symmetry is nice because it is simple. But the basic element of vector spaces, and grammars, is that they are naturally non-commutative. It is like there is something about non-commutativity that does not scale I guess.

And associativity properties is basically the entire parallel programming research field in a nutshell. (at least the PL side, electronics is different)

Eh, I guess a lot of things are age old algebra with a different coat of paint.