String theory and other new proposals require more than three
space dimensions. These extra dimensions could be very small, which
is why we don't see them.
How can there be extra, smaller dimensions?
Think about an acrobat and a flea on a tight rope. The acrobat can
move forward and backward along the rope. But the flea can move
forward and backward as well as side to side. If the flea keeps
walking to one side, it goes around the rope and winds up where it
started. So the acrobat has one dimension, and the flea has two
dimensions, but one of these dimensions is a small closed loop.
So the acrobat cannot detect any more than the one dimension of the rope, just as we
can only see the world in three dimensions, even though it might well have many more. This
is impossible to visualize, precisely because we can only visualize things in three