How would we know if we were four-dimensional? Well, we would know if we could see and/or turn perpendicular to our three-space. It is somewhat conceivable to me the we just cannot. As someone mentioned in the big-bang thread, the current mode of thinking is that there are really ten dimensions. It just so happens that six of them are less than a
Planck Length in size: 4.05096 x 10<sup>-35</sup> meters. If that were the case, it wouldn't be surprising that we cannot turn our bodies in those directions or that light doesn't seem to fall off as a the ninth power of the radius.
However, if there are any sizeable dimensions beyond our three, then what would stop us from popping out of our hyperplane?
As a side note: In _Slaughterhouse_Five_ by Kurt Vonnegut, the Tralfamadorians see time as simply another spatial dimensions. To
them, we (and they and everything else) look like persistent, twisty extrusions of how we see ourselves.