A New Scientist article ‘Why space has exactly three dimensions’ by Matthew Chalmers raises the ontological question of why 3-D, as opposed to something else. The article goes on to show that mathematical representations of quantum mechanics work best with three.
Our own Cordus work also provides circumstantial evidence for space having three dimensions. This arises from the requirement for particules to emit discrete forces in three directions.
Our response to the article follows:
Coming at it from a completely different direction, namely applying the design method to a non-local hidden-variable (NLHV) solution, we also find things work out when there are three dimensions to space. In this case explaining string theory is not a big problem, because it happens that we need about the same number of internal variables to define the NLHV design, as are needed in string theory (http://vixra.org/abs/1204.0047). Entanglement and wave-particle duality are readily explained (http://physicsessays.org/doi/abs/10.4006/0836-1398-25.1.132). Obtaining unification of the electro-magneto-gravitational-strong interactions is also conceptually achievable with NLHV solutions (http://dx.doi.org/10.5539/apr.v5n5107). As a plus, it also gives a theory for time, and thereby addresses not only space but spacetime too (accepted, preprint http://vixra.org/abs/1301.0074). (Spoiler: time becomes an emergent property of matter in this theory).
I wouldn’t claim we have really addressed the deeper ontological question of why three dimensions. But we can at least show that three gives a robust and coherent NLHV solution that explains many difficult areas in fundamental physics. See Cordus on vixra for details.