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Volumn 319, Issue 5860, 2008, Pages 213-215

The limits of counting: Numerical cognition between evolution and culture

Author keywords

[No Author keywords available]

Indexed keywords

COGNITION; CULTURE; EVOLUTION; KNOWLEDGE; NUMERICAL METHOD;

EID: 38149113939     PISSN: 00368075     EISSN: 10959203     Source Type: Journal    
DOI: 10.1126/science.1148345     Document Type: Article
Times cited : (79)

References (35)
  • 1
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    • P. Gordon, Science 306, 496 (2004); published online 19 August 2004 (10.1126/science.1094492).
    • P. Gordon, Science 306, 496 (2004); published online 19 August 2004 (10.1126/science.1094492).
  • 6
    • 33846280920 scopus 로고    scopus 로고
    • H. Wiese, Lingua 117, 758 (2007).
    • (2007) Lingua , vol.117 , pp. 758
    • Wiese, H.1
  • 16
    • 77950891366 scopus 로고
    • Department of Mathematics and Computer Science, Papua New Guinea University of Technology, Lae
    • G. A. Lean, Counting Systems of Papua New Guinea (Department of Mathematics and Computer Science, Papua New Guinea University of Technology, Lae, 1992).
    • (1992) Counting Systems of Papua New Guinea
    • Lean, G.A.1
  • 20
    • 38149108574 scopus 로고    scopus 로고
    • C. M. Churchward, A New Fijian Grammar (Australasian Medical, Sydney, Australia, 1941).
    • C. M. Churchward, A New Fijian Grammar (Australasian Medical, Sydney, Australia, 1941).
  • 21
    • 38149028684 scopus 로고    scopus 로고
    • Les Missionaires catholiques de cet Archipel, membres de la Congrégation des Sacrés-Coeurs de Picpus, Essai de Grammaire de la Langue des Isles Gambier ou Mangaréva (Imprimerie Zech et Fils, Braine-le-Comte, Belgium, 1908).
    • Les Missionaires catholiques de cet Archipel, membres de la Congrégation des Sacrés-Coeurs de Picpus, Essai de Grammaire de la Langue des Isles Gambier ou Mangaréva (Imprimerie Zech et Fils, Braine-le-Comte, Belgium, 1908).
  • 23
    • 38149138332 scopus 로고    scopus 로고
    • The common ancestor for a group of related languages, if not documented, is reconstructed by way of a systematic comparison of these languages. This method is inductive, but - because of the extensive database and the high convergence - the reconstructed number words for Proto-Oceanic can be regarded as firmly established. They are further supported by a comparison with other Austronesian languages ranging from Madagascar in the West to Easter Island in the East (22). This comparison shows that the development in parts of Melanesia must have taken place early on but still was an exception in the larger Austronesian cluster.
    • The common ancestor for a group of related languages, if not documented, is reconstructed by way of a systematic comparison of these languages. This method is inductive, but - because of the extensive database and the high convergence - the reconstructed number words for Proto-Oceanic can be regarded as firmly established. They are further supported by a comparison with other Austronesian languages ranging from Madagascar in the West to Easter Island in the East (22). This comparison shows that the development in parts of Melanesia must have taken place early on but still was an exception in the larger Austronesian cluster.
  • 24
    • 38149084413 scopus 로고    scopus 로고
    • If varu was the principal counting unit of the specific sequences as indicated by cultural preferences, even the unusual steps (i.e., paua and tataua) could be explained, namely as short cuts to facilitate the representation of the incomplete units. The specific sequence would then be a modulo 40 system, in which units of 40 tauga were counted, and the remainder (if any occurred at all) was decomposed in 20 + 10 + n. This may not be the most efficient method of decomposition, but - given the generally decimal nature of the system - it was surely the most preferable. The next possible decomposition (20 + 10 + 5 + n) would have arbitrarily restricted the single numerals to n ∈ {1, 2, 3, 4}.
    • If varu was the principal counting unit of the specific sequences as indicated by cultural preferences, even the unusual steps (i.e., paua and tataua) could be explained, namely as short cuts to facilitate the representation of the incomplete units. The specific sequence would then be a modulo 40 system, in which units of 40 tauga were counted, and the remainder (if any occurred at all) was decomposed in 20 + 10 + n. This may not be the most efficient method of decomposition, but - given the generally decimal nature of the system - it was surely the most preferable. The next possible decomposition (20 + 10 + 5 + n) would have arbitrarily restricted the single numerals to n ∈ {1, 2, 3, 4}.
  • 28
    • 38149081702 scopus 로고    scopus 로고
    • The switch from 10 to 20 in the general sequence in Mangarevan is atypical in this regard. However, because many of the traditional numeration systems were replaced in colonial times before they were documented, information on a regular system may simply have been lost.
    • The switch from 10 to 20 in the general sequence in Mangarevan is atypical in this regard. However, because many of the traditional numeration systems were replaced in colonial times before they were documented, information on a regular system may simply have been lost.
  • 32
    • 38149125796 scopus 로고    scopus 로고
    • These conclusions can be further corroborated by an analysis of the composition principles for the object-specific counting sequences. It shows that these specific counting sequences are derived from abstract counting sequences with the aid of residuals of numeral classifiers [which, in several languages, are obligatory in counting to specify and classify the counted objects, such as words like sheet in two sheets of paper; for more details see 26
    • These conclusions can be further corroborated by an analysis of the composition principles for the object-specific counting sequences. It shows that these specific counting sequences are derived from abstract counting sequences with the aid of residuals of numeral classifiers [which, in several languages, are obligatory in counting to specify and classify the counted objects, such as words like "sheet" in "two sheets of paper"; for more details see (26)].
  • 35
    • 38149079287 scopus 로고    scopus 로고
    • We are grateful to H. Spada for institutional support, to A. Rothe for assistance with the material, and to S. Mannion as well as two anonymous reviewers for discussion and valuable comments on earlier versions of this paper
    • We are grateful to H. Spada for institutional support, to A. Rothe for assistance with the material, and to S. Mannion as well as two anonymous reviewers for discussion and valuable comments on earlier versions of this paper.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.