I have a super basic gap in my understanding of the theory of extra spacial dimensions - one piece of the explanation that never felt right.
As I've heard it, it's theorized that there may be extra dimensions out there (often talked about in connection with string theory). Those dimensions are theorized to be hidden from our every day experience, and are often described as being "tiny", "small" or "curled up".
What I don't understand is: how does being small allow an extra dimension to exist? Isn't it just small in the same 3 spacial dimensions that existed already? Is "small" just a clumsy metaphor for something that's more abstract? Would something unconnected to space like color be a better way to think about it?
Said a different way: How can extra dimensions be described in terms of existing dimensions? Small is a concept I can understand from my experience in 3 dimensions. How can I take the intuitive leap to understand why this is a useful way to think about extra dimensions?