The smallness issue is pretty straightforward. https://en.wikipedia.org/wiki/Compactification_(physics) https://en.wikipedia.org/wiki/Compactification_(physics)

The smallness issue is pretty straightforward. https://en.wikipedia.org/wiki/Compactification_(physics) https://en.wikipedia.org/wiki/Compactification_(physics) Assuming that the universe is closed like the surface of a sphere, heading off in any direction will eventually bring you back to where you started. Compactified dimensions are roughly like directions in which, for example, that trip is very much shorter, maybe too short to observe. It gets complicated and I'm not a physicist, but the idea that the size of the universe is different on different dimensions is the key one. As far as in-between dimensions goes, I don't know. Maybe it was a reference to fractal dimension.