Now that I know that you accept extra spatial dimensions in Kaluza Klein models, but don't necessarily believe these models are descriptive of reality, I understand what you're telling me better.
I am totally blowing smoke now, and I admit it - but a "very special cancellation condition" sounds like something that could be modeled with destructive interference of waves, and that dimensions describing wavelengths and frequencies might actually be more useful than extra spatial dimensions.
There is a fundamental question I should have asked much earlier - how do you guys define a "space"?
I am aware that there are Minkowski spaces, Riemann spaces, Hilbert spaces, and I'm sure there must be others. I can't adequately describe all these spaces, but I know that they allow for more dimensions, or are n-dimensional.
But I have been using "space" as analogous to "volume".
Can someone tell me how a theoretical physicist defines "space"? I'm afraid I have to ask you to translate into layman's terms, or I won't get your answer.