Constructing Condensed Memories in Functorial Time
31 Pages Posted: 21 Sep 2022
Abstract
The constructive nature of episodic memory suggests that experienced time is also a construct. We develop an event-based formalism that replaces the traditional objective, agent-independent notion of time with a constructive, agent-dependent notion of time. We show how to make this agent-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render agent-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop a condensed formalism that represents memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor.
Keywords: condensed sets, pro-objects, frame problem, higher category theory, hypergraphs, sheaves
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