"handwaving problems away with division by infinity"
I'm being very pedantic here but it's a bit better to think of it as subtracting infinity from another infinity.
I'm being very pedantic here but it's a bit better to think of it as subtracting infinity from another infinity.
You can easily describe renormalization without math because it's a physical concept. Regularization is more difficult. If the OP decided divergent integral regularization was an interesting conversation topic then I am on your side.
If you do this, you find that you need to choose a scale that "absorbs" the infinities of your calculations (yes, an "infinite" scale). But, the stuff that is not absorbed is a function of energy, and this actually agrees very well with experiment beyond the scale you normalized to.