typically obfuscating nondimensional analysis, you twosome. space is clearly three-dimensional for several applications (surveying & navigation e.g.), and it is clearly "more complicated that that," for both interatomic & intergalactic processes, hence the enormous effioacy of stringtheory, beginning with the Kaluza theory.
however, the "compactification to a string" of Klein may not be necessary; it is simply an abstuse math-speak.
it is not that Kaluza was wrong, it's just that no-one knew how to treat of such dimensionality, other than through phase-spaces (like Hamiltonians and Lagrangians) -- with the notable exception of quaternions, or "the first-get vector mechanics, wherefrom we get *all* of the lingo thereof."
> How difficult it is to speak of space. The physicists and astronomers of this day insist that space is isotropic. Remove all the material from space and it may be so, but that is not the space I live in. Isotropic space is a misnomer. Space is clearly structured, especially when we unify it with time. But here I don't mean to go this far. I'm back at the first stage hopefully.
> > Th. Kaluza agreed with Einstein and in 1921 tried > > to explain SRT using 5D space.