Reza on flat ontology as a One God Universe:
In procedurality, we should understand that faraway global behaviors are not simply the similar or homothetic variations of local behaviors. Procedurality or the shift of the perspective according to the shift of landscape of rules is a response to this asymmetry between the global and the local. For example, contingency differs at different levels. We cannot overextend the concept of contingency at the level of the individual gambler to the contingency at the level of a collection of games to the contingency at the level of casino. These have different levels of probability which cannot be over-stretched to one another. By calling this hierarchy of gambles within gambles ‘contingency’ without any regard to the specifications of each distinct level, we are making a flat universe.
A flat universe is a trivial environment in which the content of a local domain is uniformly distributed across the entire horizon. It’s another variation of what Mark Wilson calls “the classical picture of concepts”.5 According to the classical picture, a concept fully and in one-to- one relationship covers the object. The speculative implications of such a universe are indeed appealing because everything can be applied all the way down, concepts can be overextended from one domain to another at will. But as Mark Wilson points out, this conceptual universe is precariously overloaded. It is akin to a house where the basement is leaking, in trying to fix the basement, the kitchen floor sinks in, in repairing the floor, some of the pipes burst. Everything always needs to be patched up because ultimately in this universe nothing works, the entire edifice is a house of cards.
It wouldn’t be too hard to detect this pattern in certain speculative philosophies [lol] where either the object or contingency is the crazy glue – the big idea – that holds everything at the levels of local and global together. Flatness is another name for the condition of triviality where the global structure has the same properties and/or behaviors of its local fields. But when there is an asymmetry between the global and the local – a non-triviality – we cannot solely resort to analysis (locally oriented) to produce or examine a global structure. Conceptual mapping for a non-trivial universe requires various conceptual maps or navigational atlases distributed at different elevations according to their different a priori statuses.
(That’s “One God Universe” as in Burroughs: “Consider the impasse of a one God universe. He is all-knowing and all-powerful. He can’t go anywhere since He is already everywhere. He can’t do anything since the act of doing presupposes opposition. His universe is irrevocably thermodynamic having no friction by definition. So, He has to create friction: War, Fear, Sickness, Death….to keep his dying show on the road…”)
The guiding (mathematical) metaphor here is that of the manifold, which patches together an “atlas” of local spaces, or the sheaf, which ensures the availability of “gluings” for consistent local data. Both entities have the property that local qualities are not globally preserved: a manifold is “locally Euclidean”, but globally may be very weirdly-shaped indeed; sheaves construct a sort of protocol of descent/ascent which determines how local consistency is globally represented and how global data is locally enriched or deformed. To put it another way: they schematise situations in which, to adapt a phrase of Geoffrey Bennington’s, you need more than one idea to think with.
(edit: I have as usual misremembered the phrase, which is from Bennington’s review of books by Gillian Rose and Peter Dews: “the ‘anarchy’ whose spectre is reported to be looming whenever Left or Right finds it needs more than three ideas to think with”)