I was wondering if the notion of a quantity having complex dimension makes sense mathematically? It's maybe just a bad question; I can't attach any physical meaning or intuition to, for example, a vector space of dimension 2 + i, or a quantity with length-dimension -i, but I was wondering if this concept has any mathematical meaning or use.
I did some Google searching, but all I could see were links about complex vector spaces and the like, and I'm not even sure where I should begin looking to find something like this in a textbook or paper... I did come across one post on this site
which mentions complex dimensions in passing, but it has no answer and I hardly understand the question. I will continue digging into the tags once I finish posting.