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

TL;DR

This paper develops a mathematical framework using perfectoid diamonds and higher category theory to model subjective experience and n-awareness, offering new insights into consciousness, time, and personal identity.

Contribution

It introduces a novel meta-model linking perfectoid diamonds with subjective experience, including a new language and temporal scheme for n-awareness and a categorical model of personal identity.

Findings

Proposes that the (infinity, 1)-category of perfectoid diamonds is an (infinity, 1)-topos.

Extends topological localization to the (infinity, 1)-category of diamonds.

Introduces a categorical model of self as a moduli space in K-theory.

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.