Abstract
This chapter addresses the issue of how different counting systems occurred and in particular the theory of counting systems spreading from a centre. The most comprehensive theory of this kind before 1990 was that of Seidenberg. This theory is expounded and then several queries are raised. In general, the argument is put that the counting systems of Papua New Guinea and Oceania did not spread from the Middle East and the prominence of so-called neo-2 cycles and 10 cycles cannot be supported.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The terminology used throughout this book will be used to discuss Seidenberg’s theory; it was not his terminology.
References
Barrow, J. (1992). Pi in the sky: Counting, thinking, and being. Oxford, UK: Clarendon Press.
Bogoshi, J., Naidoo, K., & Webb, J. (1987). The oldest mathematical artefact. Mathematical Gazette, 71, 294.
Brown, N. (2010). The abacus and the cross. New York, NY: Basic Books.
Cashmore, C. (1972). Vocabularies of the Santa Cruz Islands, British Solomon Islands Protectorate. Working Papers in Linguistics, Department of Anthropology, University of Auckland, 17, 1–79.
Conant, L. (1896). The number concept. New York, NY: Macmillan.
Crawfurd, J. (1863). On the numerals as evidence of the progress of civilization. Transactions of the Ethnological Society of London, 2, 84–111.
Crump, S. (1990). The anthropology of numbers. Cambridge, UK: Cambridge University Press.
de Solla Price, D., & Pospisil, L. (1966). A survival of Babylonian arithmetic in New Guinea? Indian Journal of History of Science, 1(1), 30–33.
Flegg, G. (1984). Numbers: Their history and meaning. New Orleans, LA: Pelican Books.
Flegg, G. (1989). Numbers through the ages. London, UK: Macmillan and the Open University.
Galis, K. (1960). Telsystemen in Nederlands-Nieuw-Guinea. Nieuw Guinea Studien, 4(2), 131–150.
GLEC. (2008). EXCEL summary of counting systems in Papua New Guinea based on Lean’s Appendices. 2015, from http://www.uog.ac.pg/glec/counting_sys/t-coutning_sys/t-counting_sys.htm
Henderson, J. (1975). Yeletnye, the language of Rossel Island. In T. Dutton (Ed.), Studies in languages of central and south-east Papua, Pacific Linguistics (Vol. C-29, pp. 817–834). Canberra, Australia: Australian National Univerisity.
Jett, S. C. (1971). Diffusion versus independent development: The bases of controversy. In C. Riley, J. Kelley, C. Pennington, & R. Rands (Eds.), Man across the sea: Problems of pre-Columbian contacts (pp. 5–53). Austin, TX/London, UK: University of Texas Press.
Joseph, G. (1987). Foundations of Eurocentrism in mathematics. Race and Class, 28(3), 13–28.
Kelly, R. (1993). Constructing inequality: The fabrication of a hierarchy of virtue among the Etoro. Ann Arbor, MI: University of Michigan Press.
Kluge, T. (1938). Die Zahlbegriffe der Australier, Papua und Bantuneger nebst einer Einleitung ueber die Zahl, ein Beitrag zur Geistesgeschichte des Menschen. Berlin, Germany: Selbstverlag.
Kluge, T. (1939). Zahlenbergriffe der Völker Americas, Nordeurasiens, der Munda, und der Palaio-africaner. Unpublished manuscript. Berlin, Germany.
Kluge, T. (1941). Die Zahlenbegriffe der Sprachen Central- und Südostasiens, Indonesiens, Micronesiens, Melanesiens und Polynesiens mit Nachträgen zu den Bänden 2-4. Berlin, Germany. Ein fünfter Beitrag zur Geistesgeschichte des Menschen nebst einer principiellen Untersuchung über die Tonsprachen. Original unpublished manuscript held at Yale University, microfilm held at Australian National University, Canberra, Australia.
Lawes, W. (1895). Grammar and vocabulary of the language spoken by Motu tribe. Sydney, Australia: C. Potter (Government Printer).
Lean, G. (1992). Counting systems of Papua New Guinea and Oceania (Unpublished PhD thesis). PNG University of Technology, Lae, Papua New Guinea. Retrieved from http://www.uog.ac.pg/glec/
Lowrie, R. (1937). The history of ethnological theory. Berkeley, CA: University of California Press.
Parkinson, R. (1907). Dreissig jahre in der Südsee. Stuttgart, Germany: Strecker und Schröder.
Raglan (Lord). (1939). How came civilization? London, UK: Methuen & Co.
Ray, S. (1919). The languages of northern Papua. Journal of the Royal Anthropological Institute of Great Britain and Ireland, 49, 317–341.
Riley, C., Kelley, J., Pennington, C., & Rands, R. (Eds.). (1971). Man across the sea: Problems of pre-Columbian contacts. Austin, TX/London, UK: University of Texas Press.
Schmidt, M. (1900). Die sprachlichen Verhältnisse von Deutsch Neu-Guinea. Zeitschrift für Afrikanische und Ozeanische Sprachen, 5, 345–384.
Schmidt, W. (1926). Die Sprachfamilien und Sprachenkreise der Erde. Heidelberg, Germany: Carl Winter’s Universitätsbuchhandlung.
Schmidt, W. (1929). Numeral systems. In Encyclopedia Britannica (14th ed., pp. 614–615). London, UK/New York, NY: Sears Roebuck.
Seidenberg, A. (1960). The diffusion of counting practices. University of California Publications in Mathematics, 3.
Seidenberg, A. (1962). The ritual origin of counting. Archives for History of Exact Sciences, 2, 1–40.
Smith, G. E. (1933). The diffusion of culture. London, UK: Watts and Co.
Spriggs, M. (2006). The Lapita culture and Austronesian prehistory in Oceania. In P. Bellwood, J. Fox, & D. Tyron (Eds.), The Austronesians: The historical and comparative perspectives (pp. 119–142). Canberra, Australia: ANU Press.
Spriggs, M. (2011). Archaeology and the Austronesian expansion: Where are we now? Antiquity, 85(328), 510–528.
Strong, W. (1911). The Maisin language. Royal Anthropological Institute of Great Britain & Ireland, 41, 381–396.
Tryon, D. (1984). The peopling of the Pacific: A linguistic appraisal. Journal of Pacific History, 19(3–4), 147–159.
Tryon, D., & Hackman, B. (1983). Solomon Islands languages: An internal classification. Pacific Linguistics, C-72, 509.
Tylor, E. (1871). Primitive culture: Researches into the development of mythology, philosophy, religion, language, art and custom. London, UK: John Murray.
Van der Waerden, B., & Flegg, G. (1975a). Counting 1: Primitive and more developed counting systems. Milton Keynes, UK: Open University.
Van der Waerden, B., & Flegg, G. (1975b). Counting 2: Decimal counting words, tallies and knots. Milton Keynes, UK: Open University.
Wilder, R. (1974). Evolution of mathematical concepts. London, UK: Transworld.
Wurm, S. (1982). Papuan languages of Oceania. Tübingen, Germany: Gunter Narr Verlag.
Z’graggen, J. (1975). Comparative wordlists of the Admiralty Islands languages collected by W. E. Smythe. Workpapers in Papua New Guinea Languages, 14, 117–216.
Zegura, S. (1985). The initial peopling of the Americas: An overview. In R. Kirk & E. Szathmary (Eds.), Out of Asia: Peopling the Americas and the Pacific (pp. 1–18). Canberra, Australia: Journal of Pacific History, Australian National University.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Owens, K., Lean, G. (2018). Testing the Diffusion Theory. In: History of Number. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-45483-2_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-45483-2_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45482-5
Online ISBN: 978-3-319-45483-2
eBook Packages: EducationEducation (R0)