This short note comments on \citet{Aerts2024Origin}, which proposes that ranked word frequencies in texts should be read through the lens of Bose--Einstein (BE) statistics and even used to illuminate the origin of quantum statistics in physics. The core message here is modest: the paper offers an interesting analogy and an eye-catching fit, but several key steps mix physical claims with definitions and curve-fitting choices. We highlight three such points: (i) a normalization issue that is presented as "bosonic enhancement", (ii) an identification of rank with energy that makes the BE fit only weakly diagnostic of an underlying mechanism, and (iii) a baseline comparison that is too weak to support an ontological conclusion. We also briefly flag a few additional concerns (interpretation drift, parameter semantics, and reproducibility).
This short note comments on \citet{Aerts2024Origin}, which proposes that ranked word frequencies in texts should be read through the lens of Bose--Einstein (BE) statistics and even used to illuminate the origin of quantum statistics in physics. The core message here is modest: the paper offers an interesting analogy and an eye-catching fit, but several key steps mix physical claims with definitions and curve-fitting choices. We highlight three such points: (i) a normalization issue that is presented as "bosonic enhancement", (ii) an identification of rank with energy that makes the BE fit only weakly diagnostic of an underlying mechanism, and (iii) a baseline comparison that is too weak to support an ontological conclusion. We also briefly flag a few additional concerns (interpretation drift, parameter semantics, and reproducibility).
This analysis critically examines the application of quantum mechanical concepts—such as entanglement, indistinguishability, and Bose Einstein statistics — to language and cognitive processes as proposed in the paper. While the interdisciplinary approach is creative, significant theoretical and empirical challenges arise when translating quantum principles to human cognition. Key issues include the contextual and qualitative nature of cognitive processes, which differ fundamentally from the predictable, probabilistic behaviors observed in quantum systems. Cognitive phenomena are shaped by factors like emotional state, social context, and personal memory, which have no direct analogy in quantum mechanics. The assumption that words or cognitive "particles" are indistinguishable, as quantum particles are, overlooks the unique and dynamic contextual dependencies in language. Moreover, empirical support for such quantum-cognitive parallels remains limited, and the paper’s application of quantum statistics to word frequency distributions may reflect a coincidental pattern rather than a fundamental process. This assessment suggests that while the paper’s quantum analogies could foster new interdisciplinary discussions, they risk speculative overreach if treated as foundational principles for understanding cognition. Effective interdisciplinary integration would require rigorous empirical validation within cognitive science, as well as caution against reductionist interpretations that might simplify the rich complexities of human thought. Future research may benefit from more context-sensitive and evidence-based models that align more closely with established cognitive theories, thereby maintaining the intellectual richness of both quantum mechanics and cognitive science without forcing an untested theoretical bridge between them.
This note is a friendly technical check of arXiv:2511.21731v1. I highlight a few places where the manuscript's interpretation of (i) the reported CHSH/Bell-type calculations and (ii) Bose--Einstein (BE) fits to rank-frequency data seems to go beyond what the stated procedures can firmly support. I also point out one internal inconsistency in the "energy-level spacing" analogy. The aim is constructive: to keep the interesting empirical observations, while making clear what they do (and do not) imply about quantum entanglement in the usual Hilbert-space sense, especially when "energy" is defined by rank.
In previous research, we showed that 'texts that tell a story' exhibit a statistical structure that is not Maxwell-Boltzmann but Bose-Einstein. Our explanation is that this is due to the presence of 'indistinguishability' in human language as a result of the same words in different parts of the story being indistinguishable from one another, in much the same way that 'indistinguishability' occurs in quantum mechanics, also there leading to the presence of Bose-Einstein rather than Maxwell-Boltzmann as a statistical structure. In the current article, we set out to provide an explanation for this Bose-Einstein statistics in human language. We show that it is the presence of 'meaning' in 'texts that tell a story' that gives rise to the lack of independence characteristic of Bose-Einstein, and provides conclusive evidence that 'words can be considered the quanta of human language', structurally similar to how 'photons are the quanta of electromagnetic radiation'. Using several studies on entanglement from our Brussels research group, we also show, by introducing the von Neumann entropy for human language, that it is also the presence of 'meaning' in texts that makes the entropy of a total text smaller relative to the entropy of the words composing it. We explain how the new insights in this article fit in with the research domain called 'quantum cognition', where quantum probability models and quantum vector spaces are used in human cognition, and are also relevant to the use of quantum structures in information retrieval and natural language processing, and how they introduce 'quantization' and 'Bose-Einstein statistics' as relevant quantum effects there. Inspired by the conceptuality interpretation of quantum mechanics, and relying on the new insights, we put forward hypotheses about the nature of physical reality. In doing so, we note how this new type of decrease in entropy, and its explanation, may be important for the development of quantum thermodynamics. We likewise note how it can also give rise to an original explanatory picture of the nature of physical reality on the surface of planet Earth, in which human culture emerges as a reinforcing continuation of life.
Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis on the historical development of QM attributes the origin of quantum statistics, in particular, Bose-Einstein statistics, to a lack of statistical independence of the micro-states of identical quantum entities. We have recently identified Bose-Einstein statistics in the combination of words in large texts, as a consequence of the entanglement created by the meaning carried by words when they combine in human language. Relying on this investigation, we put forward the hypothesis that entanglement, hence the lack of statistical independence, is due to a mechanism of contextual updating, which provides deeper reasons for the appearance of Bose-Einstein statistics in human language. However, this investigation also contributes to a better understanding of the origin of quantum mechanical statistics in physics. Finally, we provide new insights into the intrinsically random behaviour of microscopic entities that is generally assumed within classical statistical mechanics.
Abstract Identical systems, or ‘entities’, are ‘indistinguishable’ in quantum mechanics (QM), and the ‘symmetrization postulate’ rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis of the historical development of QM attributes the origin of quantum statistics, in particular, ‘Bose–Einstein statistics’, to a lack of statistical independence of the micro-states of identical quantum entities. We have recently identified Bose–Einstein statistics in the combination of words in large texts, as a consequence of the ‘entanglement’ created by the meaning carried by words when they combine in human language. Relying on this investigation, we put forward the hypothesis that entanglement, hence the lack of statistical independence, is due to a ‘mechanism of contextual updating’, which provides deeper reasons for the appearance of Bose–Einstein statistics in human language. However, this investigation also contributes to a better understanding of the origin of quantum mechanical statistics in physics. Finally, we provide new insights into the ‘intrinsically random behaviour of microscopic entities’ that is generally assumed within classical statistical mechanics. This article is part of the theme issue ‘Newton, Principia, Newton Geneva Edition (17th–19th) and modern Newtonian mechanics: heritage, past & present’.
We reply to the comments by M. Sienicki and K. Sienicki (arXiv:2512.07881) and by K. Sienicki (arXiv:2601.06104) on our work on quantum-mechanical statistics in human language (arXiv:2407.14924) and on quantum structure in AI-generated language (arXiv:2511.21731). We thank the authors for their careful reading and address what we consider to be the main points of criticism: the exploratory nature of the protocol used in the experiments with large language models; the role of marginal-law violations, and of the Contextuality-by-Default criterion, in the identification of entanglement; the limited diagnostic value of a Bose-Einstein fit taken in isolation; the meaning of assigning the lowest energy levels to the most frequent words; and the relation between the vector spaces used by LLMs and quantum state spaces. We also correct a typographical error in Table 3 of arXiv:2511.21731, which does not affect the reported CHSH value.