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.Comment: v1: 5 pages revtex, 1 eps figure; v2: includes extensive discussion
on violation of Lorentz invariance, featured in a Nature editorial [Nature
466 (2010) 426] http://www.nature.com/news/2010/100720/full/466426a.html; v3:
discussion expanded, matching journal versio
