I immediately and eagerly shared my newfound realization with others, and it impressed absolutely nobody. I was told "How else would the world work?" and "There is lots of math that's not useful, but we choose to work on and formalize the things are are relevant to the real world." These are, of course, perfectly good objections, and I couldn't explain why I found my realization at all remarkable, but I'd had a nagging feeling that I was onto something.
Forward 6 years, and I'm at Market Fresh Books, a bookstore near UIC. As an aside, this bookstore is really interesting -- it sells used books by the pound or for small flat fees. I even once picked up a copy of baby Rudin for just 99¢ (plus tax) to add to my library. Anyhow, I stumbled upon a copy of "Disturbing the Universe," Freeman Dyson's autobiography from 1979, and it looked interesting enough to buy. That evening, while reading it, I came upon the following passage by Dyson:
"Here was I ... doing the most elaborate and sophisticated calculations to figure out how an electron should behave. And here was the electron ... knowing quite well how to behave without waiting for the result of my calculation. How could one seriously believe that the electron really cared about my calculation one way or the other? And yet the experiments ... showed it did care. Somehow or other, all this complicated mathematics that I was scribbling established rules that the electron ... was bound to follow. We know that this is so. Why it is so, why the electron pays attention to our mathematics, is a mystery that even Einstein could not fathom."
I still don't know the answer, and I can't even state the question without it seeming silly, but at least I now know I'm in good company.
image credit, atomicheritage.org