  Changing the dimensionality of the space-time at the smallest and largest
distances has manifold theoretical advantages. If the space is lower
dimensional in the high energy regime, then there are no ultraviolet
divergencies in field theories, it is possible to quantize gravity, and the
theory of matter plus gravity is free of divergencies or renormalizable. If the
space is higher dimensional at cosmological scales, then some cosmological
problems (including the cosmological constant problem) can be attacked from a
completely new perspective. In this paper, we construct an explicit model of
"evolving dimensions" in which the dimensions open up as the temperature of the
universe drops. We adopt the string theory framework in which the dimensions
are fields that live on the string worldsheet, and add temperature dependent
mass terms for them. At the Big Bang, all the dimensions are very heavy and are
not excited. As the universe cools down, dimensions open up one by one. Thus,
the dimensionality of the space we live in depends on the energy or temperature
that we are probing. In particular, we provide a kinematic Brandenberger-Vafa
argument for how a discrete {\it causal set}, and eventually a continuum
$(3+1)$-dim spacetime along with Einstein gravity emerge in the Infrared from
the worldsheet action. The $(3+1)$-dim Planck mass and the string scale become
directly related, {\it without any} compactification. Amongst other
predictions, we argue that LHC might be blind to new physics even if it comes
at the TeV scale. In contrast, cosmic ray experiments, especially those that
can register the very beginning of the shower, and collisions with high
multiplicity and density of particles, might be sensitive to the dimensional
cross-over.
