Dimension in physics

I have a solid understanding of topological dimension. I heard that some string theororists think that the universe is >= 10-dimensional, but that the extra 7+ dimensions are too small for us to encounter. How can a dimension be small; is it just a model for what is observed, or is it based in theory?

Think of a piece of string, it's effectively 1 dimensional as you can move along it but that's all. But now think of it from the point of view of view of a dust mite, it can move along the string and around it, making it 2 dimensional to the mite. The second dimension is curled up tightly around the string so as we pull out it becomes negligable. The same is true in string theory, the extra dimensions are curled up on a very small scale and as we pull out to the length scales we exist on they are also negligable.

You probably think of our three spatial dimensions as infinite. Consider what would happen if they were finite (say, several lightyears across) and would loop back onto themselves. If you moved far enough in one direction, you would eventually return to somewhere near your starting point. Now consider what would happen if one of those three dimensions was really small; it loops back after only a millimeter or so. At larger scales, the universe would then appear to effectively have only two spatial dimensions.