As I am going through teaching P132 – Introductory Physics II: What is an electron? What is light? I have noticed a good instructional goal that I did not consider back at the beginning of the semester when I was first planning out the course: developing an appreciation that nonsensical mathematical results can still possess physical meaning. In P132, there are several topics where the formulae can give nonsense answers. Two more straight-forward examples include Snell’s Law n1 sin θ1 = n2 sin θ2 and quantization conditions requiring integers.