> Irrational numbers are probably a bad example of what you're talking about. No, they're the perfect example and you're observation about the unit square is g

> Irrational numbers are probably a bad example of what you're talking about. No, they're the perfect example and you're observation about the unit square is glib. Trying to reason about the diagonal of the unit square basically destroyed the Pythagorean world view of integers as the fundamental building blocks of reality. If mathematical entities are simply discovered and that-is-that, then why did it take nearly two millenia after this observation for western math to accept irrationals as numbers? From M. Stifel, 1544: "Now, that cannot be called a true number which is of such a nature that it lacks precision. Therefore, just as an infinite number is not a number, so an irrational number is not a true number, but lies hidden in a kind of cloud of infinity"