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 efficacy of stringtheory for appreciating the many "quantized" phenomena, 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 may not be "hidden variables," but there are "hidden dimensionalities" or spaces, at least in a formal sense.
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."
> > Th. Kaluza agreed with Einstein and in 1921 tried > > to explain SRT using 5D space.