We are in the first dimension, as we have no visual indication there are dimensions lower than us.
While "visual indication" could mean just about anything, there are at least "indications" that there are "dimensions lower than us". By putting two semiconductors (that fulfill certain conditions that I don't want to get into right now) together, you can actually create a two-dimensional electron-gas (
Wikilink). Naturally, they are
technically three-dimensional, but as long as their energy is lower than a certain tresholdvalue (which you can easily control), they only have two directions to move in, and thus behave like a two-dimensional electron-gas.
If you do the math for such a gas (i.e. assume that there are only two dimensions), you'll find that it explains the behaviour of it.
Maybe not directly related to the discussion, but hey, maybe you're interested.