Numeral Systems of the Languages of California

Dixon, Roland Β.; Kroeber, A. L.

doi:10.1525/aa.1907.9.4.02a00020

Cited by 25 publications

(4 citation statements)

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“…This would suggest that addition by one—application of the successor function—should provide the most natural base system for counting since it would transparently map between words/morphology and meaning. However, even the way that count series are linguistically formed varies beyond the additive, as some systems exhibit multiplication and even subtraction in their construction (Bowern & Zentz, 2012; Carrier, 1981; Dixon & Kroeber, 1907).…”

Section: Forms Of Number Representation Are Diverse Across Culturesmentioning

confidence: 99%

“…The cultural history of mathematics shows that, large, exact, symbolic number is cognitively difficult for humans to create, the product of a long cross-cultural history (Chrisomalis, 2009b; Damerow, 2015; Ifrah, 2000; Joseph, 1987) and that modern conceptions of number are far from universal across human groups. The picture that emerges instead from the ethnographic literature reveals a diversity of culturally contingent approaches to problems of quantity, which are constructed according to local needs, perceptions, practices, and history (Beller et al, 2018; Crossley, 2007; Dixon & Kroeber, 1907; Hymes, 1955; Owens & Lean, 2018; Robson, 2008; Wolfers, 1971). We consider each of (i)–(vi) in turn.…”

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confidence: 99%

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The cultural origins of symbolic number.

O’Shaughnessy¹,

Gibson²,

Piantadosi³

2022

Psychological Review

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In order to explain the unacceptability of certain long-distance dependencies --termed syntactic islands by Ross (1967) --syntacticians proposed constraints on long-distance dependencies which are universal and purely syntactic and thus not dependent on the meaning of the construction (Chomsky 1977(Chomsky , 2006. This predicts that these constraints should hold across constructions and languages. In this paper, we investigate the "subject island" constraint across constructions in English and French, a constraint that blocks extraction out of subjects. In particular, we compare extraction out of nominal subjects with extraction out of nominal objects, in relative clauses and wh-questions, using similar materials across constructions and languages. Contrary to the syntactic accounts, we find that unacceptable extractions from subjects involve (a) extraction in wh-questions (in both languages); or (b) preposition stranding (in English). But the extraction of a whole prepositional phrase from subjects in a relative clause, in both languages, is as good or better than a similar extraction from objects. Following Erteschik-Shir (1973) and Kuno (1987) among others, we propose a theory that takes into account the discourse status of the extracted element in the construction at hand: the extracted element is a focus (corresponding to new information) in wh-questions, but not in relative clauses. The focus status conflicts with the non-focal status of a subject (usually given or discourse-old). These results suggest that most previous discussions of islands may rely on the wrong premise that all extraction types behave alike. Once different extraction types are recognized as different constructions (

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Section: Forms Of Number Representation Are Diverse Across Culturesmentioning

confidence: 99%

mentioning

confidence: 99%

The cultural origins of symbolic number.

O’Shaughnessy¹,

Gibson²,

Piantadosi³

2022

Psychological Review

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“…For example, the Luiseño of California counted “chiefly by means of the fingers and toes” ( Sparkman, 1905 , 657). This method often creates groupings by fives and twenties: “ten,” “all my-hand finished”; “fifteen,” “all my-hand finished and one my-foot”; “twenty,” “another finished my-foot the-side” ( Dixon and Kroeber, 1907 , 689).…”

Section: Counting On the Hand(s)mentioning

confidence: 99%

Finger-Counting and Numerical Structure

Overmann

2021

Front. Psychol.

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Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of whether devices are used in counting, which ones are used, and how they are used.

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“…Seidenberg claimed the two-cycle system was once widespread, but Lean found that there were few systems that were pure two-cycle systems in PNG, and they have not been found en route to South America (e.g., in North America although a paper on California contradicts this (DIXON & KROEBER, 1907). In PNG, as elsewhere, most two-cycle systems, in fact, went on to have a (2, 5) or (2, 5, 20) cycle system and these existed well before the 10-cycle systems introduced mainly by Austronesian (AN) Oceanic speakers.…”

Section: Countering the Diffusionist Theorymentioning

confidence: 99%

Revising the history of number: how Ethnomathematics transforms perspectives on indigenous cultures

Owens¹,

Muke²

2020

Revemop

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Many accounts of the history of number rely on written evidence such as clay, stone, and wood engravings or paintings. However, some of the oldest cultural groups (between 5 000 and 30 000 years old) have had only recent contact with the rest of the world, namely between 80 and 140 years ago but these were oral cultures without written records. Finding out about their understanding of number has involved analysis of the types of counting but also how counting related to the rest of their cultural relationships. There is some surprising evidence of diversity of number systems, longevity of the systems, and the interplay with cultural practices that begs respect for Indigenous cultures. Brief summaries of this history of number in Papua New Guinea and Oceania and the diversity of systems is followed by how this new knowledge can inform school mathematics learning in any part of the world. Revisando la historia de los números: cómo las Etnomatemáticas transforma las perspectivas sobre las culturas indígenasResumen: Muchos relatos de la historia de los números se basan en pruebas escritas como grabados o pinturas de arcilla, piedra y madera. Sin embargo, algunos de los grupos culturales más antiguos (entre 5 000 y 30 000 años) solo han tenido contacto reciente con el resto del mundo, es decir, hace entre 80 y 140 años, pero se trataba de culturas orales sin registros escritos. Conocer su comprensión del número ha implicado el análisis de los tipos de conteo, pero también cómo el conteo se relaciona con el resto de sus relaciones culturales. Hay alguna evidencia sorprendente de la diversidad de sistemas numéricos, la longevidad de los sistemas y la interacción con prácticas culturales que exigen respeto por las culturas indígenas. Breves resúmenes de esta historia del número en Papua Nueva Guinea y Oceanía y la diversidad de sistemas es seguida por cómo este nuevo conocimiento puede informar el aprendizaje matemático escolar en cualquier parte del mundo.Palabras clave: Historia de los Números. Matemáticas indígenas. Papua Nueva Guinea. Melanesia. Pacifico. Longevidad de sistemas numéricos. Revisando a história do número: como a Etnomatemática transforma perspectivas sobre culturas indígenasResumo: Muitos relatos da história do número dependem de evidências escritas como em argila, em pedra, em gravuras, em madeira ou em pinturas. No entanto, alguns dos grupos culturais mais antigos (entre 5.000 e 30.000 anos) tiveram apenas um contacto recente com o resto do mundo, nomeadamente entre 80 e 140 anos atrás, mas esses tinham culturas orais sem registos escritos. Descobrir a compreensão do número envolveu a análise dos tipos de contagem, mas também como a contagem se relacionava com o restante de suas relações culturais. Há algumas evidências surpreendentes da diversidade de sistemas numéricos, longevidade dos sistemas e interação com as práticas culturais que imploram respeito pelas culturas indígenas. Breves sumários desta história de números em Papua Nova Guiné, Oceânia e numa diversidade de sistemas são seguidos por uma

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Numeral Systems of the Languages of California

Cited by 25 publications

References 0 publications

The cultural origins of symbolic number.

The cultural origins of symbolic number.

Finger-Counting and Numerical Structure

Revising the history of number: how Ethnomathematics transforms perspectives on indigenous cultures

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