How do we know for sure that we live in three dimensions?

Sure, our surroundings certainly appear to exist in three dimensions, but any good Cartesian will tell you that the appearance of a material object alone is insufficient evidence of its true nature. So how do we go about proving that we aren't, in fact, deluded inhabitants of Abott's two-dimensional Flatland, or… » 9/06/11 8:00am 9/06/11 8:00am