# Quantum Bose-Einstein Statistics for Indistinguishable Concepts in Human Language

arXiv: https://arxiv.org/abs/2103.15125 · HTML: https://mlsanity.com/paper/2103.15125/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 41 references that are in the map.
- First posted on arXiv 28 Mar 2021.

## Builds on (most cited first, 5 of 5)

- [Quantum Structure in Cognition: Human Language as a Boson Gas of Entangled Words](https://mlsanity.com/paper/1909.06845/) (2019)
- [Towards a Quantum World Wide Web](https://mlsanity.com/paper/1703.06642/) (2017)
- [The Heart of an Image: Quantum Superposition and Entanglement in Visual Perception](https://mlsanity.com/paper/1802.02216/) (2018)
- [The Quantum Nature of Identity in Human Thought: Bose-Einstein Statistics for Conceptual Indistinguishability](https://mlsanity.com/paper/1410.6854/) (2014)
- [Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach](https://mlsanity.com/paper/1808.03677/) (2018)

## Built on by (most cited first, 5 of 5)

- [A Planck Radiation and Quantization Scheme for Human Cognition and Language](https://mlsanity.com/paper/2201.03306/) (2022)
- [Are Words the Quanta of Human Language? Extending the Domain of Quantum Cognition](https://mlsanity.com/paper/2110.04913/) (2021)
- [Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition](https://mlsanity.com/paper/2511.21731/) (2025)
- [Development of a Thermodynamics of Human Cognition and Human Culture](https://mlsanity.com/paper/2212.12795/) (2022)
- [Identifying Quantum Mechanical Statistics in Italian Corpora](https://mlsanity.com/paper/2412.07919/) (2024)

## Abstract (arXiv)

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.