Quantum Bose-Einstein Statistics for Indistinguishable Concepts in Human Language

TL;DR

This paper explores the idea that concepts like 'eleven animals' exhibit a Bose-Einstein statistical structure due to the indistinguishability of the concepts involved, supported by web data analysis.

Contribution

It introduces a novel hypothesis linking quantum statistics to human language concepts and provides empirical evidence using web data and divergence analysis.

Findings

Bose-Einstein distribution fits the data better than Maxwell-Boltzmann.

Indistinguishability of concepts influences their statistical structure.

Web data supports quantum-like statistical behavior in language concepts.

Abstract

We investigate the hypothesis that within a combination of a 'number concept' plus a 'substantive concept', such as 'eleven animals,' the identity and indistinguishability present on the level of the concepts, i.e., all eleven animals are identical and indistinguishable, gives rise to a statistical structure of the Bose-Einstein type similar to how Bose-Einstein statistics is present for identical and indistinguishable quantum particles. We proceed by identifying evidence for this hypothesis by extracting the statistical data from the World-Wide-Web utilizing the Google Search tool. By using the Kullback-Leibler divergence method, we then compare the obtained distribution with the Maxwell-Boltzmann as well as with the Bose-Einstein distributions and show that the Bose-Einstein's provides a better fit as compared to the Maxwell-Boltzmanns.