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The Quantum Nature of Identity in Human Thought: Bose-Einstein Statistics for Conceptual Indistinguishability

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Abstract

Increasing experimental evidence shows that humans combine concepts in a way that violates the rules of classical logic and probability theory. On the other hand, mathematical models inspired by the formalism of quantum theory are in accordance with data on concepts and their combinations. In this paper, we investigate a new connection between concepts and quantum entities, namely the way both behave with respect to ‘identity’ and ‘indistinguishability’. We do this by considering conceptual entities of the type Eleven Animals, were a number is combined with a noun. In the combination Eleven Animals, indeed the ‘animals’ are identical and indistinguishable, and our investigation aims at identifying the nature of this conceptual identity and indistinguishability. We perform experiments on human subjects and find significant evidence of deviation from the predictions of classical statistical theories, more specifically deviations with respect to Maxwell-Boltzmann statistics. This deviation is of the ‘same type’ of the deviation of quantum mechanical from classical mechanical statistics, due to indistinguishability of microscopic quantum particles, i.e we find convincing evidence of the presence of Bose-Einstein statistics. We also present preliminary promising evidence of this phenomenon in a web-based study.

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Notes

  1. Human subjects generally estimate the exemplar Dog as a more typical example of the concept Pet than the exemplar Spider. This is formalized in the SCoP formalism by saying that the typicality value \(\mu (p_{Dog},1,\hat {p}_{Pet})\) is higher than the typicality value \(\mu (p_{Spider},1,\hat {p}_{Pet})\), where 1 represents the absence of context. On the other hand, human subjects generally estimate the property Being Scary as more applicable to Spider than to Dog. This is formalized in the SCoP formalism by saying that the applicability value ν(p S p i d e r , a S c a r y ) is higher than the applicability value ν(p D o g , a S c a r y ).

  2. It is also worth mentioning that, when the SCoP formalism is applied to quantum entities, one can recognize in μ(q, e, p) the transition probability from state p to state q under the influence of measurement context e, while ν(p, a) corresponds to the probability of property a in state p.

  3. For more information, see http://datamarket.azure.com/dataset/bing/search.

  4. The possibility of the study of meaning using computational techniques in the context of SCoP is mentioned in [13], and planned to be elaborated in great detail in [32].

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Authors and Affiliations

  1. Center Leo Apostel for Interdisciplinary Studies (Clea), VUB University of Brussels, Krijgskundestraat 33, 1160, Brussels, Belgium

    Diederik Aerts, Sandro Sozzo & Tomas Veloz

  2. School of Management and IQSCS, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Sandro Sozzo

  3. Mathematics Departments, University of British Columbia Okanagan Campus, 3333 University Way, Kelowna, BC, Canada

    Tomas Veloz

  4. Instituto de Filosofía y Ciencias de la Complejidad (IFICC), Los Alerces 3024, Ñuñoa, Santiago, Chile

    Tomas Veloz

Authors
  1. Diederik Aerts
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  2. Sandro Sozzo
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  3. Tomas Veloz
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Correspondence to Sandro Sozzo.

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Aerts, D., Sozzo, S. & Veloz, T. The Quantum Nature of Identity in Human Thought: Bose-Einstein Statistics for Conceptual Indistinguishability. Int J Theor Phys 54, 4430–4443 (2015). https://doi.org/10.1007/s10773-015-2620-4

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  • DOI: https://doi.org/10.1007/s10773-015-2620-4

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