Perfectoid Diamonds and n-Awareness. A Meta-Model of Subjective Experience

A mathematical model of subjective experience is proposed using hierarchical geometries of representations called n-awareness. The framework draws on higher category theory, homotopy theory, and (infinity, 1)-topoi. Three conjectures enrich the model: that the (infinity, 1)-category of perfectoid diamonds is an (infinity, 1)-topos, that topological localization extends to diamonds, and that Efimov K-theory of diamonds captures structural equivalences between the category of diamonds and subjective experience (privacy, self-containedness, self-reflexivity). A grammar (n-declension) and temporal scheme (n-time) are introduced to express n-awareness. The model revisits philosophical problems of change, simultaneity, and coincidence. Personal identity is modeled as weakly persistent moduli spaces in the K-theory of perfectoid diamonds, resembling a categorical bundle theory.

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Abstract

In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations ("n-awareness"). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity, 1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity, 1)-category of a geometric structure known as perfectoid diamond is an (infinity, 1)-topos. In order to construct a topology on the (infinity, 1)-category of diamonds we then propose that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity, 1)-topoi, extends to the (infinity, 1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity, 1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e. its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar ("n-declension") for a novel language to express n-awareness, accompanied by a new temporal scheme ("n-time"). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of "self" within our framework. A new model of personal identity is introduced which resembles a categorical version of the "bundle theory"; selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds.