[jfarmer]

Well, "in some sense" gives a lot of wiggle room! I agree the magnifying glass analogy is bad, but here's one "sense" in which the rationals "have more holes" than the irrationals.

There exists a function of the reals which is continuous at every irrational point but discontinuous at every rational point. However, there is no function of the reals which is discontinuous on the irrationals but continuous on the rationals. In this sense, the irrationals are "more continuous" than the rationals.

That's about the best I can do, though, which I admit is a stretch.