THE GALAXY DISTRIBUTION - HOMOGENEOUS, FRACTAL, OR NEITHER

From the standpoint of theoretical physics we can treat Newtonian cosm ology as a problem in nonlinear dynamics. The attempt to average the d ensity, in search of a method of making contact between theory and obs ervation, is replaced by the more systematic idea of coarsegraining. I also explain in this context why two previous attempts at the constru ction of hierarchical models of the universe are not useful for data a nalysis. The main ideas behind two older competing data analyses purpo rting to show evidence from galaxy statistics for either a homogeneous and isotropic universe in one case, and for a mono-fractal universe i n the other, are presented and discussed. I also present the method an d results of a newer data analysis that shows that visible matter prov ides no evidence that would allow us to claim that the cosmological pr inciple holds, or that the universe is fractal (or multifractal). In o ther words, observational data provides us with no evidence that the u niverse is either homogeneous and isotropic, or monofractal.