  From the standpoint of theoretical physics we can treat Newtonian cosmology
as a problem in nonlinear dynamics. The attempt to average the density, in
search of a method of making contact between theory and observation, is
replaced by the more systematic idea of coarsegraining. I also explain in this
context why two previous attempts at the construction of hierarchical models of
the universe are not useful in data analysis. The main ideas behind two older
competing data analyses purporting to show evidence from galaxy statistics for
either a homogeneous and isotropic universe in one case, and for a mono-fractal
universe in the other, are presented and discussed. I also present the method
and results of a newer data analysis that shows that visible matter provides no
evidence that would allow us to claim that the cosmological principle holds, or
that the universe is fractal (or multifractal). In other words, observational
data provides us with no evidence that the universe is either homogeneous and
isotropic, or monofractal.
