I have to admit that I have seen relatively little
of Doctor Who
; however langrage
's explanation of TARDIS
"I presume that the inside of the TARDIS is a curled-up set of dimensions that appear normal size from within,..."
is amazingly similar to string theory
In order for the equations (which granted are mere approximations) to work, the space in which we live -must- be at least 10-dimensional - 1 time-dimension and the rest spatial. There then exist the three regular dimensions which we are familiar with and the rest are curled into special shapes with very particular mathematical properties.
But what's most interesting is at very, very, very small distances. In this realm, which is actually at a sub-quark level, string theory proposes that an examination on a smaller scale is impossible. In fact, there exists no smaller scale.
What happens instead, due to the symmetries of M-Theory, is that as one watches the universe collapse, the normal 3 spatial dimensions which we all know (and love) get smaller but, but the dimensions wrapped into this tiny, tiny little shapes...get larger. That means as the universe collapses on the large scale, it grows at the smallest scale. And when both the big spatial dimensions and the little spatial dimensions are at the same scale, then they flip. The small become the big; the big become the small. Now instead of having a Big Bang there's a Bounce!.
String theorists are not sure of the other implications of this particular symmetry of dimensions, but to me it seems awfully TARDIS-ian.