I'm an undergrad just getting into lagrangian fields and symmetry, having my first advanced particle physics lecture tomorrow. I've read around the subject of high energy physics to some degree, but I'm very limited in what I can understand, largely due to the mathematical particulars that I haven't encountered before. I'd like to be able to visualise - or at least explain in a more common-sense way - what compact dimensions represent, why they're required, how they're supposed to come about, and so on. As mentioned, I don't have the mathematical background to understand the jargon - I can get by with being shown an overview of the mathematics involved, however. I find the common pop-science explanation of string theory and ephemera largely useless since they don't give any indication of how one might solve problems. So - is there a reasonable ontological explanation of compact dimensions in terms of what one might be expected to know of rudimentary field theory?