Infix notation IS funny, though I figured anyone learning arithmetic would be familiar and we're stuck with it - we probably can't convince grade schools to use

Infix notation IS funny, though I figured anyone learning arithmetic would be familiar and we're stuck with it - we probably can't convince grade schools to use Polish notation for arithmetic by default. In general, my attitude is that you should pick a notation that makes all the similarities with things you already know as obvious as possible and then stress the differences. They've already learned about non-symmetric infix operators if they've learned subtraction and division, and the only reason to expect that ^ would be symmetric was by analogy to multiplication, which is easy to clear up. Take it as a lesson that by default you should never assume operations are symmetric, in preparation for linear algebra ;)