Taylor's law describes the fluctuation characteristics underlying a system in
which the variance of an event within a time span grows by a power law with
respect to the mean. Although Taylor's law has been applied in many natural and
social systems, its application for language has been scarce. This article
describes a new quantification of Taylor's law in natural language and reports
an analysis of over 1100 texts across 14 languages. The Taylor exponents of
written natural language texts were found to exhibit almost the same value. The
exponent was also compared for other language-related data, such as the
child-directed speech, music, and programming language code. The results show
how the Taylor exponent serves to quantify the fundamental structural
complexity underlying linguistic time series. The article also shows the
applicability of these findings in evaluating language models.

本文描述了一种用于自然语言中的泰勒定律度量的新方法，并对跨 14 种语言的 1100 个文本进行了分析，发现书面自然语言文本的泰勒指数呈现几乎相同的值，同时，还比较了其他语言相关数据的泰勒指数，结果显示出泰勒指数可用于量化语言时间序列的基本结构复杂性，文章还展示了这些发现在评估语言模型方面的适用性。

人类语言序列的泰勒定律

Taylor's law for Human Linguistic Sequences

Complex systems consist of many interacting elements which participate in
some dynamical process. The activity of various elements is often different and
the fluctuation in the activity of an element grows monotonically with the
average activity. This relationship is often of the form "$fluctuations \approx
const.\times average^\alpha$", where the exponent $\alpha$ is predominantly in
the range $[1/2, 1]$. This power law has been observed in a very wide range of
disciplines, ranging from population dynamics through the Internet to the stock
market and it is often treated under the names \emph{Taylor's law} or
\emph{fluctuation scaling}. This review attempts to show how general the above
scaling relationship is by surveying the literature, as well as by reporting
some new empirical data and model calculations. We also show some basic
principles that can underlie the generality of the phenomenon. This is followed
by a mean-field framework based on sums of random variables. In this context
the emergence of fluctuation scaling is equivalent to some corresponding limit
theorems. In certain physical systems fluctuation scaling can be related to
finite size scaling.

本文综述了许多领域中复杂系统中的波动标度性结构及其数学模型，并提出了该现象普遍性的基本原理及其在物理系统中的应用，其中包括 Taylor 定律或者波动标度律。