Contextuality Analysis of Impossible Figures

TL;DR

This paper applies contextuality analysis to impossible figures like Penrose and Escher, evaluating a new hierarchical measure of (non)contextuality to understand their deterministic descriptions under uncertainty.

Contribution

It introduces a hierarchical measure of (non)contextuality and demonstrates its application to impossible figures, advancing the analysis of epistemic systems.

Findings

Hierarchical measure effectively captures contextuality in impossible figures.

Probabilistic mixing models uncertainty in perception of impossible objects.

Analysis shows deterministic descriptions vary with different probabilistic mixtures.

Abstract

This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in earlier publications. As objects of analysis we use impossible figures of the kind created by the Penroses and Escher. We make no assumptions as to how an impossible figure is perceived, taking it instead as a fixed physical object allowing one of several deterministic descriptions. Systems of epistemic random variables are obtained by probabilistically mixing these deterministic systems. This probabilistic mixture reflects our uncertainty or lack of knowledge rather than random variability in the frequentist sense.