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Taylor's law describes the fluctuation characteristics underlying a system inwhich the variance of an event within a time span grows by a power law withrespect to the mean. Although Taylor's law has been applied in many natural andsocial systems, its application for language has been scarce. This articledescribes a new quantification of Taylor's law in natural language and reportsan analysis of over 1100 texts across 14 languages. The Taylor exponents ofwritten natural language texts were found to exhibit almost the same value. Theexponent was also compared for other language-related data, such as thechild-directed speech, music, and programming language code. The results showhow the Taylor exponent serves to quantify the fundamental structuralcomplexity underlying linguistic time series. The article also shows theapplicability of these findings in evaluating language models.

Taylor's law for Human Linguistic Sequences