Ordered Set Correspondence

Abstract

EnglishThis study focuses on the cross-category comparison of one-dimensional ordered-set representations of data. We investigate whether frequency distributions exhibiting strictly monotonic or logarithmic-like priors, such as character frequency, preserve enough structural information to reveal correspondences between categories otherwise considered distinct. We ask whether such correspondences persist or reappear under transformations of the representation, including changes in dimensionality that provide new but plausible spaces in which higher-order structure can be examined. The method allows data from apparently different domains to be compared provided that their elements can be placed in sufficient correspondence under a defined correspondence principle. Comparisons are evaluated against null distributions using metrics including Cayley Distance, Spearman–Rho, and Kendall–Tau, with progressive logarithmic percentile filters used to search a large candidate space. The cross-category searches are designed to identify correspondences beyond those within commonly recognized categorical relationships. As a test case, the study compares ancient abecedaries and language profiles. A short illustration of the resulting candidate comparisons is then discussed, demonstrating how ordered-set comparison can temporarily abstract data from their spatiotemporal context, allowing structural correspondences to be identified before questions of entropy, information change, and directionality are reintroduced into the analysis.FrançaisCette étude propose de comparer entre catégories des représentations de données sous forme d’ensembles ordonnés unidimensionnels. Elle examine si les distributions de fréquence, notamment celles présentant des propriétés strictement monotones ou logarithmiques, conservent suffisamment d’information structurelle pour révéler des correspondances entre catégories distinctes. La méthode compare ces ensembles à des distributions nulles au moyen des distances de Cayley, de Spearman–Rho et de Kendall–Tau par moyen de l’application de filtres progressifs permettant d’explorer un vaste espace de candidats. Le cadre suppose seulement une correspondance suffisante entre les éléments des ensembles ordonnés. Des abécédaires anciens et profils de langues servent de cas d’étude, avec une brève discussion des correspondances candidates obtenues.Bahasa Indonesia Penelitian ini membandingkan data lintas kategori dalam bentuk himpunan terurut satu dimensi untuk menemukan korespondensi struktural yang tidak tampak melalui kategori yang telah ditentukan. Perbandingan diuji terhadap distribusi nol menggunakan Cayley Distance, Spearman–Rho, dan Kendall–Tau. Sebagai studi kasus, metode ini diterapkan pada abjad-abjad kuno dan profil bahasa.