Measuring the Diversity of Qualia: Category-Theoretic Indices for Psychophysical Experimental Data

<ns5:p>Abstract* Characterizing qualitative aspects of subjective experiences, qualia, remains a challenging open problem. The recent Qualia structure paradigm proposes capturing qualia through massive relations with other qualia. A concrete method for this involves measuring pairwise similarities. This approach has been successfully applied to reveal similarities and differences in qualia structures between groups of humans (e.g., color typical vs atypical). Here, we propose a complementary methodology to enhance this paradigm, providing a way to directly quantify the diversity of any specific qualia structure. We introduce measures of “diversity”, originally derived from category-theoretic contexts. These measures have a principled mathematical interpretation: they are measures of the size of a mathematical structure or space. To test their empirical applicability, we evaluated two variants of diversity—“generalized magnitude” and “spread”—using dissimilarity matrices derived from a similarity-rating experiment with N = 120 human participants. Participants rated the pairwise similarities between color words and emotion words; these ratings were then transformed into dissimilarities and analyzed using each diversity index. We compare how each index behaved at both the group and individual levels, and discuss the implications of these results from a mathematical viewpoint. These diversity indices are useful not only for quantifying diversity in qualia structures but also for estimating complex graphical features of these structures.</ns5:p>