Title: Why we should abolish the cross product. 

Abstract:  Cross products plague our physics by "working too hard". They make nonchiral equations (like maxwells) appear chiral.
They obscure symmetries and the meaning of rotation.
And they only work in 3 (or 7 dimensions).
It turns out that by "doing less", we not only solve these problems, we enter a more beautiful world.
One where pauli matricies, spinors, and the mysterious quantum half angle are all completely classical. A world where everything is more .... intuitive.