Quantum Bose-Einstein Statistics for Indistinguishable Concepts in Human Language
This addresses a linguistic modeling problem for researchers in computational linguistics or cognitive science, but it appears incremental as it applies known quantum statistics to a new domain without broad impact.
The paper tackles the problem of modeling the statistical structure of combined concepts like 'eleven animals' in human language, hypothesizing it follows Bose-Einstein statistics due to indistinguishability, and shows that Bose-Einstein distribution fits web-extracted data better than Maxwell-Boltzmann using Kullback-Leibler divergence.
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.