Negative Probabilities and Contextuality

There has been a growing interest, both in physics and psychology, in understanding contextuality in experimentally observed quantities. Different approaches have been proposed to deal with contextual systems, and a promising one is contextuality-by-default, put forth by Dzhafarov and Kujala. The goal of this paper is to present a tutorial on a different approach: negative probabilities. We do so by presenting the overall theory of negative probabilities in a way that is consistent with contextuality-by-default and by examining with this theory some simple examples where contextuality appears, both in physics and psychology.

Fillets: Cues for Connections in Focus+Context Views of Graph-Like Diagrams

Brain sensitivity to print emerges when children learn letter-speech sound correspondences

The acquisition of reading skills is a major landmark process in a human’s cognitive development. On the neural level, a new functional network develops during this time, as children typically learn to associate the well-known sounds of their spoken language with unfamiliar characters in alphabetic languages and finally access the meaning of written words, allowing for later reading. A critical component of the mature reading network located in the left occipitotemporal cortex, termed the “visual word-form system” (VWFS), exhibits print-sensitive activation in readers. When and how the sensitivity of the VWFS to print comes about remains an open question. In this study, we demonstrate the i…

All-Possible-Couplings Approach to Measuring Probabilistic Context

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may ‘‘directly’’ influence them, but (iii) other inputs provide a ‘‘context’’ for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or …

Contextuality Analysis of the Double Slit Experiment (with a Glimpse into Three Slits)

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: Has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the Einsten-Podolsky-Rosen-Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of d…