As far as extra dimensions are concerned, very tiny extra dimensions wouldn't be perceived in everyday life, just as atoms aren't: we see many atoms together but we don't see atoms individually.
Edward WittenSuperstring theories provide a framework in which the force of gravity may be united with the other three forces in nature: the weak, electromagnetic and strong forces. Recent progress has shown that the most promising superstring theories follow from a single theory. For the last generation, physicists have studied five string theories and one close cousin. Recently it has become clear that these five or six theories are different limiting cases of one theory which, though still scarcely understood, is the candidate for superunification of the forces of nature.
Edward WittenIn Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything.
Edward WittenAs of now, string theorists have no explanation of why there are three large dimensions as well as time, and the other dimensions are microscopic. Proposals about that have been all over the map.
Edward Witten