Let's say you've got a light-emitting flat surface and want to describe its power output. I recommend modeling it as a set of real coordinates with an intensity value at each point and integrating to compute the total power output. By all means I invite you to come up with a better model, without using uncountable sets, for which there isn't a straightforward analogue, just as good, that uses uncountable sets.

Edit: Might as well jump straight to explaining how wave functions work without using uncountable sets, and why that's a better description of reality.