Towards a Derivation of Space
  This attempt to "derive" space is part of the Random Dynamics project. The Random Dynamics philosophy is that what we observe at our low energy level can be interpreted as some Taylor tail of the physics taking place at a higher energy level, and all the concepts like numbers, space, symmetry, as well as the known physical laws, emerge from a "fundamental world machinery" being a most general, random mathematical structure.   Here we concentrate on obtaining spacetime in such a Random Dynamics way. Because of quantum mechanics, we get space identified with about half the dimension of the phase space of a very extended wave packet, which we call "the Snake".   In the last section we also explain locality from diffeomorphism symmetry. 
H. B. Nielsen and A. Kleppe
hep-th