We can't cut the square, because perfect square is an abstraction and what you are cutting is an approximation of the square. We can't cut across the diagonal,

We can't cut the square, because perfect square is an abstraction and what you are cutting is an approximation of the square. We can't cut across the diagonal, because all cuts are only an approximation of a straight line. We can't directly see the real number being the ratio of square diagonal to its side, because our eyes have finite number of photoreceptors, receiving information from a finite number of photons. It's natural numbers, all the way down...