Numerals have fascinated and mystified linguists, mathematicians and lay persons alike for centuries. The productive use of numerals (in languages where this happens) exploits recursivity to give rise to what we call the ‘the number line’. While the smaller numerals 1–10 have enjoyed intense scrutiny, the typological study of the formation of the higher numerals has received comparatively less attention. This article contains a comprehensive typological account of how languages in the Indo-European language family code numerals beyond 10 (10–99, 100s, 1,000s), the morphemes involved, and how these are ordered. We use this dataset from eighty-one Indo-European languages with phylogenetic comparative methods to propose diachronic reconstructions of these patterns in the Proto-Indo-European language. Our findings indicate that small numerals (11–19) show the widest cross-linguistic variation, and that higher numerals exhibit more consistency in both component parts and their ordering. Additionally, we show statistical evidence of correlations between the ordering of base and atom morphemes and other word order patterns (noun-postposition, noun-genitive, and verb-object order).

中文翻译：

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印欧语系高级数的类型学和历时性：系统发育比较研究

数个世纪以来，数字一直令语言学家、数学家和外行人着迷和迷惑。数字的有效使用（在发生这种情况的语言中）利用递归性来产生我们所谓的“数字线”。虽然较小的数字 1-10 受到了严格的审查，但对较高数字形成的类型学研究却相对较少受到关注。本文对印欧语系中的语言如何在 10（10–99、100、1,000s）以外的数字、所涉及的语素以及这些语素如何排序进行了全面的类型学说明。我们使用来自 81 种印欧语言的数据集和系统发育比较方法来提出原始印欧语言中这些模式的历时重建。我们的研究结果表明，小数字 (11-19) 显示出最广泛的跨语言变异，并且更高的数字在组成部分及其排序方面表现出更高的一致性。此外，我们还展示了基础语素和原子语素的排序与其他词序模式（名词-后置词、名词-属格和动词-宾语顺序）之间相关性的统计证据。