Spacetimes with Semantics

Abstract: Relationships between objects constitute our notion of space. When these relationships change we interpret this as the passage of time. Observer interpretations are essential to the way we understand these relationships. Hence observer semantics are an integral part of what we mean by spacetime. Semantics make up the essential difference in how one describes and uses the concept of space in physics, chemistry, biology and technology. In these notes, I have tried to assemble what seems to be a set of natural, and pragmatic, considerations about discrete, finite spacetimes, to unify descriptions of these areas. It reviews familiar notions of spacetime, and brings them together into a less familiar framework of promise theory (autonomous agents), in order to illuminate the goal of encoding the semantics of observers into a description of spacetime itself. Autonomous agents provide an exacting atomic and local model for finite spacetime, which quickly reveals the issues of incomplete information and non-locality. From this we should be able to reconstruct all other notions of spacetime. The aim of this exercise is to apply related tools and ideas to an initial unification of real and artificial spaces, e.g. databases and information webs with natural spacetime. By reconstructing these spaces from autonomous agents, we may better understand naming and coordinatization of semantic spaces, from crowds and swarms to datacentres and libraries, as well as the fundamental arena of natural science.