It must have been just as disturbing for the ancients to see how one could count the sheep using a sack full of pebbles. (We, modern people, are too used to the wonders given to us by the - quite abstract, in fact - notion of a number and never question our faith in the applicability of arithmetical operations to the real world.)
You can hear a band play music from a radio, even though there is no band inside your radio. How? Because electrons in a wire will slosh back and forth in near synchronous response to electrons in a different wire far away. We live in an interactive world where the fact that correlations can occur in matter interactions means that communication is possible.
And the ability to count sheep by counting pebbles is just a generalization of the same principles. One antenna can move in sync with another, without literally being the 'same' antenna. This is indirection or abstraction, depending on how you want to slice it.
The point being, there is no question of why arithmetical operations apply to the real world. The real world permits an infinite variety of valid and useful abstractions. I'd wager it is impossible to imagine a reality where this weren't the case.
