Quantum Bose-Einstein Statistics for Indistinguishable Concepts in Human Language

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-Boltzmann's.