Via Aristotle, Leibnitz and Mach to a Fractal D=2 Universe

Abstract

Over the past two decades or so, it has become increasingly appparent that, out to quite large distances, galaxies are distributed in a quasi-fractal fashion with fractal dimension $D \approx 2$. Whether or not this behaviour continues onto indefinitely large scales is a matter of live debate and is a question that can only be settled if, at some scale, there is an unambiguous transition to homogeneity. This point has not yet been reached and may never be. This paper has been written on the basis of the tentative hypothesis that quasi-fractal $D\approx 2$ behaviour is a persistent and fundamental feature of galaxy distribution on all scales and addresses the question of the origins of this putative fractality. Given this tentative hypothesis then, except for the device of putting the fractal behaviour into the initial conditions - which is to by-pass the question, there is no obvious explanation within the framework of conventional cosmology. So we adopt the position that fractality is per-se a signature that different thinking is required. We find that a beautiful solution flows deductively from elementary observations about the world in which we live when we take seriously a view of space and time that can be traced, via Mach, Berkeley and Leibnitz to Aristotle. In summary, we find that a globally inertial space and time can be irreducibly associated with a fractal, D=2, distribution of material if we are prepared to review our understanding of what is meant by the notion of metric on astrophysical scales.