Dialectal tsunamis emerging from the Simmel effect: a statistical approach to the snail-paced spread of cultural epidemic

Abstract

An attempt is made to settle the controversy on a theory of the concentric distribution of dialectal variants for snails. This theory was presented in 1927 by Kunio Yanagita (1875–1962), outstanding Japanese folklorist. Over more than 95 years, however, its verification remains pending. On the basis of the recent achievement in the linguistic atlas project, time series analysis is made for fitting to the long-tailed rank-frequency relations of cumulative syllabics that are included in the entire dialect sequence of snails. The time reversal asymmetry (TRA) is revealed through comparison between the forward and backward analysis. The validity of the methodology is confirmed through comparison with results for several examples. Computed results show substantial TRAs between the periphery-to-center and center-to-periphery analysis for fitting to the long-tailed distribution in the cumulative frequency versus rank. This feature for the categorial data sequence is consistent with those observed for typical numerical data such as music and heartbeat signals that obey non-Gaussian statistics. Application to the most parsimonious principle yields results being compatible with the above ones, which reproduces the validity of our conclusion. Finally, perturbation analysis is made for several artificially disturbed arrangements of the dialectal strata.