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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].

References

  1. Tversky, A., Kahneman, D.: Judgements of and by representativeness. In: Kahneman, D., Slovic, P., Tversky, A. (eds.) Judgement Under Uncertainty: Heuristics and Biases, pp. 84–98. Cambridge University Press, Cambridge (1982)

    Chapter  Google Scholar 

  2. Hampton, J.A.: Overextension of conjunctive concepts: evidence for a unitary model for concept typicality and class inclusion. J. Exp. Psychol.: Learn. Mem. Cogn. 14, 12–32 (1988)

  3. Hampton, J.A.: Disjunction of natural concepts. Mem. Cogn. 16, 579–591 (1988)

  4. Tversky, A., Shafir, E.: The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309 (1992)

    Article  Google Scholar 

  5. Aerts, D., Gabora, L.: A theory of concepts and their combinations I: the structure of the sets of contexts and properties. Kybernetes 34, 167–191 (2005)

  6. Aerts, D., Gabora, L.: A theory of concepts and their combinations II: a Hilbert space representation. Kybernetes 34, 192–221 (2005)

    Article  MATH  Google Scholar 

  7. Aerts, D.: Quantum structure in cognition. J. Math. Psychol. 53, 314–348 (2009)

  8. Aerts, D.: Quantum particles as conceptual entities: a possible explanatory framework for quantum theory. Found. Sci. 14, 361–411 (2009)

  9. Khrennikov, A.Y.: Ubiquitous Quantum Structure. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  10. Aerts, D.: Sozzo: Quantum structure in cognition. Why and how concepts are entangled. LNCS 7052, 116–127 (2011)

    MathSciNet  Google Scholar 

  11. Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  12. Aerts, D., Broekaert, J., Gabora, L., Sozzo, S.: Quantum structure and human thought. Behav. Bra. Sci 36, 274–276 (2013)

    Article  Google Scholar 

  13. Aerts, D., Gabora, L., Sozzo, S.: Concepts and their dynamics: a quantum–theoretic modeling of human thought. Top. Cogn. Sci. 5, 737–772 (2013)

    Google Scholar 

  14. Haven, E., Khrennikov, A.Y.: Quantum Social Science. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

  15. Haven, E., Khrennikov, A.Y.: Quantum-like tunnelling and levels of arbitrage. Int. J. Theor. Phys. 52, 4083–4099 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  16. Pothos, E.M., Busemeyer, J.R.: Can quantum probability provide a new direction for cognitive modeling? Behav. Bra. Sci. 36, 255–274 (2013)

    Article  Google Scholar 

  17. Aerts, D., Broekaert, J., Sozzo, S., Veloz, T.: Meaning–focused and quantum–inspired information retrieval. LNCS 8369, 71–83 (2014)

    MathSciNet  Google Scholar 

  18. Aerts, D., Sozzo, S.: Quantum entanglement in conceptual combinations. Int. J. Theor. Phys. 53, 3587–3603 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Aerts, D., Sozzo, S., Tapia, J.: Identifying quantum structures in the Ellsberg paradox. Int. J. Theor. Phys. 53, 3666–3682 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  20. Khrennikov, A.Y., Basieva, I., Dzhafarov, E.N., Busemeyer, J.R.: Quantum models for psychological measurements: an unsolved problem. Plos One 9(10), e110909 (2014)

    Article  Google Scholar 

  21. Khrennikova, P., Haven, E., Khrennikov, A.Y.: An application of the theory of open quantum systems to model the dynamics of party governance in the US Political System. Int. J. Theor. Phys. 53, 1346–1360 (2014)

    Article  MathSciNet  Google Scholar 

  22. Sozzo, S.: A quantum probability explanation in Fock space for borderline contradictions. J. Math. Psychol. 58, 1–12 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Aerts, D.: Foundations of quantum physics: a general realistic and operational approach. Int. J. Theor. Phys. 38, 289–358 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Castellani, E. (ed.): Interpreting Bodies: Classical and Quantum Objects in Modern Physics. Princeton University Press, Princeton (1998)

  25. French, S., Krause, D.: Identity in Physics: A Historical, Philosophical, and Formal Analysis. Oxford University Press, Oxford (2006)

    Book  Google Scholar 

  26. Dieks, D., Versteegh, M.A.M.: Identical quantum particles and weak discernibility. Found. Phys. 38, 923–934 (2008)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Berndl, K., Daumer, M., Dürr, Goldstein, S., Zanghi: A survey of Bohmian mechanics. Nuovo Cim. 110, 737–750 (1995)

    Article  ADS  Google Scholar 

  28. Kolmogorov, A.N.: Grundbegriffe der Wahrscheinlichkeitrechnung, Ergebnisse Der Mathematik (1933); translated as Foundations of Probability. Chelsea Publishing Company, New York (1950)

    Google Scholar 

  29. Pylyshyn, Z.W.: Computation and Cognition. MIT Press, Cambridge (1984)

    Google Scholar 

  30. Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Nuovo Cim. B 37, 1–23 (1977)

    Article  ADS  Google Scholar 

  31. Weinberg, S.: The Quantum Theory of Fields. Cambridge University Press, Cambridge (1995)

    Book  Google Scholar 

  32. Veloz, T.: Quantum cognition on the web: on states of concepts and semantic references (in preparation)

  33. Kass, R.E., Raftery, A.E.: Bayes factors. J. Am. Stat. Assoc. 90(430), 773–795 (1995)

    Article  MATH  Google Scholar 

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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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