The theory has to be interpreted that extra dimensions beyond the ordinary four dimensions the three spatial dimensions plus time are sufficiently small that they haven't been observed yet.

M stands for Magic, Mystery, or Matrixaccording to taste

If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways.

In 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.

But the beauty of Einstein's equations, for example, is just as real to anyone who's experienced it as the beauty of music. We've learned in the 20th century that the equations that work have inner harmony.

1/r^2 has a nasty singularity at r=0, but it did not bother Newton-the Moon is far enough.

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.