A space of goals: the cognitive geometry of informationally bounded agents

TL;DR

This paper introduces a 'cognitive geometry' that incorporates informational costs into spatial reasoning, revealing how agents' abilities and strategies shape their perception of optimal routes in a given environment.

Contribution

It develops a novel framework for understanding geometry through informational costs, extending traditional geodesics to infodesics that account for cognitive effort and strategy.

Findings

Visualisation of cognitive geometry shows distortions reflecting strategic behaviors.

Introduction of infodesics as a generalization of geodesics considering informational costs.

Highlighting how informational costs influence route optimality and agent strategies.

Abstract

Traditionally, Euclidean geometry is treated by scientists as a priori and objective. However, when we take the position of an agent, the problem of selecting a best route should also factor in the abilities of the agent, its embodiment and particularly its cognitive effort. In this paper we consider geometry in terms of travel between states within a world by incorporating information processing costs with the appropriate spatial distances. This induces a geometry that increasingly differs from the original geometry of the given world as information costs become increasingly important. We visualise this "cognitive geometry" by projecting it onto 2- and 3-dimensional spaces showing distinct distortions reflecting the emergence of epistemic and information-saving strategies as well as pivot states. The analogies between traditional cost-based geometries and those induced by additional informational costs invite a generalisation of the notion of geodesics as cheapest routes towards the notion of infodesics. In this perspective, the concept of infodesics is inspired by the property of geodesics that, travelling from a given start location to a given goal location along a geodesic, not only the goal, but all points along the way are visited at optimal cost from the start.