Combinatorics, observables, and String Theory

Abstract

We investigate the most general phase space of configurations, consisting of all possible ways of assigning elementary attributes, ``energies'', to elementary positions, ``cells''. We discuss how this space possesses structures that can be approximated by a quantum-relativistic physical scenario. In particular, we discuss how the Heisenberg's Uncertainty Principle and a universe with a three-dimensional space arise, and what kind of mechanics rules it. String Theory shows up as a complete representation of this structure in terms of time-dependent fields and particles. Within this context, owing to the uniqueness of the underlying mathematical structure it represents, one can also prove the uniqueness of string theory.