"For most of us, or perhaps all of us, it's impossible to imagine a world consisting of more than three spatial dimensions. Are we correct when we intuit that such a world couldn't exist? Or is it that our brains are simply incapable of imagining additional dimensions—dimensions that may turn out to be as real as other things we can't detect?
String theorists are betting that extra dimensions do indeed exist; in fact, the equations that describe superstring theory require a universe with no fewer than 10 dimensions. But even physicists who spend all day thinking about extra spatial dimensions have a hard time describing what they might look like or how we apparently feeble-minded humans might approach an understanding of them. That's always been the case, and perhaps always will be."
From, The Elegant Universe.