Dimensionality of the Universe

One of the most mysterious facts about our universe is that, for most purposes, it can be modelled as four-dimensional: with one dimension for time and three dimensions for space. Why four, why not three, why not 42? There have long been proposals that add more dimensions, especially extra spatial dimensions, which are curled up so tightly that we don't normally perceive them.
The following preprint proposes something different. At very small scales (subatomic) there are effectively fewer than three spatial dimensions while at very large scales (cosmological) there are effectively more than three spatial dimensions!
Vanishing Dimensions and Planar Events at the LHC

We propose that the effective dimensionality of the space we live in depends on the length scale we are probing. As the length scale increases, new dimensions open up. At short scales the space is lower dimensional; at the intermediate scales the space is three-dimensional; and at large scales, the space is effectively higher dimensional. This setup allows for some fundamental problems in cosmology, gravity, and particle physics to be attacked from a new perspective. The proposed framework, among the other things, offers a new approach to the cosmological constant problem and results in striking collider phenomenology and may explain elongated jets observed in cosmic-ray data.