56 Chapter 2: The Actualization of the Virtual in Space
The picture of a relatively differentiated and continuous topological space undergoing discontinuous transitions and progressively acquiring detail until it condenses into the measurable and divisable metric space which we inhabit, is a powerful metaphor for the cosmic genesis of spatial structure.
I attempted before to remove some of its metaphorical content by comparing the relation between topological and metric spaces to that between intensive and extensive properties: the latter are divisable in a simple way, like lengths or volumes are, the former, exemplified by properties like temperature or pressure, are continuous and relatively indivisable.
The cascade of symmetry-breaking events which progressively differentiates a topological space, in turn, compared to a phase transitions occurring at critical values of intensity. I gave an example from contemporary physics whether such a scenario is becoming literally true but the fact is that, as a description of the genesis of space, this picture remained just that, a picture.
It is time now to give a less metaphorical account of how the intensive can engender the extensive, or more exactly, how processes of individuation characterised by intensive properties can yield as their final product individuals with specific spatial structures.