Symbolic Analysis of the Quality of Texts Translated into a Language Preserving Vowel Harmony

To date, the ordinal pattern-based method has been applied to problems in natural and social sciences. We report, for the first time to our knowledge, an attempt to apply this methodology to a topic in the humanities. Specifically, in an effort to investigate the applicability of the methodology in analyzing the quality of texts that are translated into a language preserving the so-called vowel harmony, computed results are presented for the metrics of divergence between the back-translated and the original texts. As a specific language we focus on Japanese, and as metrics the Hellinger distance as well as the chi-square statistic are employed. Here, the former is a typical information-theoretical measure that can be quantified in natural unit, nat for short, while the latter is useful for performing a non-parametric testing of a null hypothesis with a significance level. The methods are applied to three cases: a Japanese novel along with a translated version available, the Preamble to the Constitution of Japan, and seventeen translations of an opening paragraph of a famous American detective story, which include thirteen human and four machine translations using DeepL and Google Translate. Numerical results aptly show unexpectedly high scores of the machine translations, but it still might be too soon to speculate on their unconditional potentialities. Both our attempt and results are not only novel but are also expected to make a contribution toward an interdisciplinary study between physics and linguistics.