  Quantum-gravity renders the space-time dimension to depend on the size of
region; it monotonically increases with the size of region and asymptotically
approaches four for large distances. This effect was discovered in numerical
simulations of lattice quantum gravity in the framework of causal dynamical
triangulation [hep-th/0505113] as well as in renormalization group approach to
quantum gravity [hep-th/0508202]. However, along these approaches the
interpretation and the physical meaning of the effective change of dimension at
shorter scales is not clear. Without invoking particular models in this essay
we show that, box-counting dimension in face of finite resolution of space-time
(generally implied by quantum gravity) shows a simple way how both the
qualitative and the quantitative features of this effect can be understood. In
this way we derive a simple analytic expression of space-time dimension
running, which implies the modification of Newton's inverse square law in a
perfect agreement with the modification coming from one-loop gravitational
radiative corrections.
