I have always felt that the fact that the things we count are not actualy the same invalidates the whole idea of numbers, until...

Understanding fundamental particles requires accepting the fact that some things are exactly the same. There is no subjective categorization goin on when we say a helium atom has 2 electrons.

As it turns out, numbers and counting are real, even though we had no way to know that when we started. Also turns out, Wolfram is a bit of a nut.