In this note, we preliminarily discuss the possibility that the expression \alpha_{em}^{-1}=4\pi^{3}+\pi^{2}+\pi has a physical interpretation and can even be helpful in model building. If one interprets this expression in terms of the volumes of l_{p} - sized three-cycles on G_{2} holonomy manifolds and requires that it also comprises effects of the running of the coupling, one can obtain the desired value, but only in a setup which is clearly different from the standard model of particle physics (SM). An understanding of the nature of the link between such putative model and SM is needed. Studying this issue could possibly shed some light on existing problems in model building within string theory (ST), particularly the hierarchy problem. Numerological “success”, which can be achieved if one interprets the formula in terms of volumes of three-cycles on the compactification manifold, as we intend to do here, cannot change the fact that discussion in this note represents merely a heuristic estimate of the feasibility of further research in a certain direction.