Abstract
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.
Highlights
Quantum entanglement in human language was studied within the Brussels approach (Aerts et al 2016) to quantum cognition (Aerts and Aerts 1995; Aerts and Gabora 2005a, b; Aerts 2009; Pothos and Busemeyer 2009; Khrennikov 2010; Busemeyer et al 2011;1 3 Vol.:(0123456789)L
We have found a violation of the CHSH inequality in Google Books, and Contemporary American English’ (COCA) with values 3.41, 3 and 3.33, respectively, which are all stronger violations of the CHSH inequality than the one we found with the psychological experiments in Aerts and Sozzo (2011), where the value of the violation was 2.42
We have shown that data we collected from three corpuses of text, Google Books, and COCA, violate the CHSH version (Clauser et al 1969) of Bell’s inequality (Bell 1964, 1987), which indicates the presence of entanglement in the combination of the two concepts Animal and Acts into the sentence The Animal Acts
Summary
Quantum entanglement in human language was studied within the Brussels approach (Aerts et al 2016) to quantum cognition The present work contributes to a further study of the presence of entanglement in human cognition (Bruza et al 2009; Aerts and Sozzo 2011, 2014; Bruza et al 2015; Gronchi and Strambini 2017; Aerts et al 2018d, e; Aerts Arguëlles 2018) as studied within the quantum cognition research programme This time we identify entanglement due to the collection of data violating the CHSH inequality in the structure of corpuses of documents, which means that the present result pertains to a domain of research closely related to quantum cognition which investigates the presence of quantum structure in computer science with applications to information retrieval and natural language processing.
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