Hi, this is my first post. Congratulations to a very interesting forum. The issue, I want to bring up, has probably been discussed already, but hopefully at least not in exactly the same way. I have read the book "Road to Reality" from Roger Penrose, which by the way I found quite interesting, although a little straining , because it was sometimes too hard and sometimes too easy for me. The view of Penrose seems to be, that everything in physics is geometry, which may or may not be true. Anyway coming to my point, Penrose argues against extra dimensions, that they would be unstable on a classical level and he puts forward reasons, why the classical level and not the quantum level applies to this problem. In other parts of the book, Penrose introduces the concept of fibre bundles and explains its success in the context of gauge theory. Now my question is, how is a fibre bundle exactly different from a uniform and stable extra dimension? Isn't a fibre bundle just an extra dimension, which is uniform and stable by definition? I would guess, that the difference is, that a fibre bundle would be regarded as a purely mathematical concept and not as a physical reality like an extra dimension. But can you already draw a clear line between the two concepts on a purely mathematical level?