University of Illinois at Urbana-Champaign, USA, victorhc@illinois.edu
(joint work with Ehtibar N. Dzhafarov)
I will present a hierarchical measure of (non)contextuality that we introduced in [1]. Many systems in which contextuality is studied (e.g., those represented by cyclic systems) have in common that their (non)contextuality is determined by particular configurations of pairwise correlations. This characterization leads to the incorrect intuitive idea that all contextuality appears at the level of pairwise correlations, perhaps even in cyclic subsystems. The hierarchical measure presented helps to determine whether contextuality arises at that level or rather at a higher one (triples, quadruples, etc.).
I will apply this measure to several systems. 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.
[1] Cervantes, V. H. & Dzhafarov, E. N. Contextuality Analysis of Impossible Figures. Entropy 22, 981 (2020).