  It is well established that at early times, long before the time of
radiation-matter equality, the universe could have been well described by a
spatially flat, radiation only model. In this letter we consider the whole
primeval universe as a black body radiation (BBR) system in an $n-$dimensional
Euclidean space. We propose that the $(3+1)-d$ nature of the universe could be
the result of a kind of thermodynamic selection principle stemming from the
second law of thermodynamics. In regard the three spatial dimensions we suggest
that they were chosen by means of the minimization of the Helmholtz free energy
per hypervolume unit, while the time dimension, as it is well known was the
result of the principle of increment of entropy for closed systems; that is,
the so-called arrow of time.
