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    Making up numbers in Pano languages: idiosyncratic and unconventional base-free quantification inventories in Amazonia
    (Royal Society, 2025-10-20)
    Amazonian languages typically exhibit very small numeral systems or lack numerals altogether. Increasing economic and cultural pressures, however, often motivate the emergence of more complex inventories for exact quantification. Headwaters Pano languages from Amazonia historically had two lexical items that can be rendered as the numerals 'one' and 'two'. We argue here, however, that they are not either etymologically or synchronically proper numerals (like the English ones are) and can be better glossed as 'single/one' (but also 'a few') and 'pair/two'. For larger quantities ('three' to 'ten'), speakers report idiosyncratic quantifying expressions based on different compositional strategies that recruit the lexical items for 'single/one', 'pair/two', but also 'hand' and, in some cases, other body-part expressions and motion verbs as well. We discuss these idiosyncratic quantifying expressions, showing that they do not present systematic and productive number bases; they exhibit unusual patterns of inter- and intra-speaker variability (i.e. they are poorly conventionalized); and they are rarely used in discourse. Based on these properties, we conclude that these quantifying expressions of Headwaters Pano languages are not numerals proper. We then explore the implications of these salient characteristics for the cross-cultural understanding of quantification and the emergence of numerical systems and the study of anumeric languages in Amazonia.This article is part of the theme issue 'A solid base for scaling up: the structure of numeration systems'.
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    Decimal systems around the world
    (Royal Society, 2025-10-20)
    Decimal numeral systems (base-10) are the most widespread type of counting system across the world's languages. Their ubiquity has often been attributed to presumed functional advantages, including ease of use, cognitive efficiency and arithmetical transparency. In principle, decimal systems represent numbers as compositions involving a form representing 10 and smaller atomic numerals (e.g. Mandarin shí sān 'thirteen', literally 'ten three'). In practice, however, many languages exhibit deviations that obscure this compositional logic—such as allomorphy ( fifteen in English, as opposed to five-ten ), suppletion (e.g. Russian sorok 'forty', unrelated to četyre 'four' or desjat' 'ten'), or secondary structures involving other compositional elements (e.g. 5). Despite being frequently mentioned in the literature, these violations have not been systematically analysed at scale. Here, we develop a rule-based classification of decimal systems and apply it to a curated, genealogically and geographically balanced sample of 118 languages. We assess each system along three dimensions— transparency , canonicity and compositionality —and show that, while surface-level irregularities are widespread, the underlying mathematical structure of decimal systems remains highly regular and patterned. These results reveal that deviations from perfect decimality are not random but instead reflect structured variation shaped by historical, cognitive and typological constraints. This article is part of the theme issue 'A solid base for scaling up: the structure of numeration systems'.
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