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arXiv:1508.00434 · Foundations of Science

Spin and Wind Directions I: Identifying Entanglement in Nature and Cognition

Diederik Aerts, Jonito Aerts Arguëlles, Lester Beltran, Suzette Geriente, Massimiliano Sassoli de Bianchi, Sandro Sozzo, Tomas Veloz

Published Jun 23, 2017• 22 citations
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Abstract

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions . Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017 ) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.

DOI
10.1007/s10699-017-9528-9

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We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions . Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017 ) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.
We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.
In the first half of this two-part article (Aerts et al. in Found Sci. doi: 10.1007/s10699-017-9528-9 , 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.
We present the results of two tests where a sample of human participants were asked to make judgements about the conceptual combinations {\it The Animal Acts} and {\it The Animal eats the Food}. Both tests significantly violate the Clauser-Horne-Shimony-Holt version of Bell inequalities (`CHSH inequality'), thus exhibiting manifestly non-classical behaviour due to the meaning connection between the individual concepts that are combined. We then apply a quantum-theoretic framework which we developed for any Bell-type situation and represent empirical data in complex Hilbert space. We show that the observed violations of the CHSH inequality can be explained as a consequence of a strong form of `quantum entanglement' between the component conceptual entities in which both the state and measurements are entangled. We finally observe that a quantum model in Hilbert space can be elaborated in these Bell-type situations even when the CHSH violation exceeds the known `Cirel'son bound', in contrast to a widespread belief. These findings confirm and strengthen the results we recently obtained in a variety of cognitive tests and document and image retrieval operations on the same conceptual combinations.
We have proved in both human-based and computer-based tests that natural concepts generally ‘entangle’ when they combine to form complex sentences, violating the rules of classical compositional semantics. In this article, we present the results of an innovative video-based cognitive test on a specific conceptual combination, which significantly violates the Clauser–Horne–Shimony–Holt version of Bell's inequalities (‘CHSH inequality’). We also show that collected data can be faithfully modelled within a quantum-theoretic framework elaborated by ourselves and a ‘strong form of entanglement’ occurs between the component concepts. While the video-based test confirms previous empirical results on entanglement in human cognition, our empirical approach surpasses language barriers and eliminates the need for prior knowledge, enabling universal accessibility. Finally, this transformative methodology allows one to unravel the underlying connections that drive our perception of reality. As a matter of fact, we provide a novel explanation for the appearance of entanglement in both physics and cognitive realms.
Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental data of situations where classical approaches are problematical. In this paper, we analyze the data we collected in an experiment on a specific conceptual combination, showing that Bell's inequalities are violated in the experiment. We present a new refined entanglement scheme to model these data within standard quantum theory rules, where 'entangled measurements and entangled evolutions' occur, in addition to the expected 'entangled states', and present a full quantum representation in complex Hilbert space of the data. This stronger form of entanglement in measurements and evolutions might have relevant applications in the foundations of quantum theory, as well as in the interpretation of nonlocality tests. It could indeed explain some non-negligible 'anomalies' identified in EPR-Bell experiments.
We show that data collected from corpuses of documents violate the Clauser-Horne-Shimony-Holt version of Bell’s inequality (CHSH inequality) and therefore indicate the presence of quantum entanglement in their structure. We obtain this result by considering two concepts and their combination and coincidence operations consisting of searches of co-occurrences of exemplars of these concepts in specific corpuses of documents. Measuring the frequencies of these co-occurrences and calculating the relative frequencies as approximate probabilities entering in the CHSH inequality, we obtain manifest violations of the latter for all considered corpuses of documents. In comparing these violations with those analogously obtained in an earlier work for the same combined concepts in psychological coincidence experiments with human participants, also violating the CHSH inequality, we identify the entanglement as being carried by the meaning connection between the two considered concepts within the combination they form. We explain the stronger violation for the corpuses of documents, as compared to the violation in the psychology experiments, as being due to the superior meaning domain of the human mind and, on the other side, to the latter reaching a broader domain of meaning and being possibly also actively influenced during the experimentation. We mention some of the issues to be analyzed in future work such as the violations of the CHSH inequality being larger than the ‘Cirel’son bound’ for all of the considered corpuses of documents.