Philosophical Interpretation of String Theory I want to know whether string theory is supposed to describe the world exactly, or whether it's just an approximation of some more fundamental theory. Is it similar to how the wave-equation approximates a rubber-band undergoing small vibrations?  
Where could I read some string theorists' views on the relation of mathematics to the real world?
 A: (edit: note that I was responding here to an earlier version of the question which was somewhat different)
I think aspects of this question are a bit too broad and philosophical--asking "How to explain all the mathematical structure that arises in string theory?" reminds me of Wigner's essay puzzling about the question of "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"--but as to the question of whether a completed version of superstring theory might still be an approximation, I can think of two reasons to suspect it wouldn't be:


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*Any quantum theory such as superstring theory should include the Pauli exclusion principle, which says that for any fermion particle (a particle whose spin is an odd number times 1/2, like 1/2, 3/2, 5/2 etc.), only one can occupy a given state at the same time. And a "state" is defined by the values of some set of quantum-mechanical observables, which include position, linear momentum, angular momentum, and spin. The exclusion principle implies that if there were any further undiscovered but in-principle-measurable properties of an electron, we should already know about it, because this would imply for example that more than two electrons would be able to occupy the lowest orbital of a Hydrogen atom (which puts them in the same quantum state for all the known observables except spin, and there are only two possible states for the spin observable of an electron). This does not imply that any quantum theory that includes electrons is exact rather than approximate, since the theory might fail to incorporate some other particles or fields, but it does at least imply that for any given fermion particle, the particle can't have additional bells and whistles that help determine its behavior that we might discover in the future, not unless the basic structure of quantum mechanics is badly wrong (and this doesn't rule out the idea of 'hidden' variables determining electrons' behavior that would be in principle impossible to measure--such variables appear in certain "interpretations" of quantum mechanics such as Bohmian mechanics, but it seems like more of a metaphysical postulate than a physical one since they would remain forever impossible to measure and hidden from view).

*There are some strong arguments from considerations of the thermodynamics of black holes that any future theory of quantum gravity (which string theory aims to be) must include the Bekenstein bound. The Bekenstein bound states that there is an absolute upper limit to the number of distinct physical states that a region with a given volume and total energy can possibly be in. This implied that if you had a theory whose collection of basic entities (strings, branes, whatever) and their observables predicted that number of possible states in such a region, then you shouldn't expect to turn up any further observables or basic entities that could occupy such a region, because this would increase the number of possible states for such a region beyond the Bekenstein bound.
