Speaking of Nima Arkani-Hamed, I had the pleasure of showing him around the physics department here at Penn a couple of weeks ago, when he was the colloquium speaker. His talk was entitled "Deconstructing Dimensions" (in an intentional jab at postmodern blather). While he's famous for proposing that there exist large extra spatial dimensions, in this talk he was talking about eliminating dimensions! The subtitles of his talk were "Extra Dimensions Suck" and "Destroy All Dimensions".
He's come up with a way in which field theories can dynamically generate "apparent" or "effective" extra dimensions that behave so much like the real thing, that the possibility can't be ruled out that there are fundamentally fewer than the four dimensions we believe ourselves to live in.
He even had some experimental tests that could distinguish between real dimensions and "theory space" dimensions. First we have to discover the graviton, though.