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Towards a Prehistory of Number

  • Chapter
History of Number

Part of the book series: History of Mathematics Education ((HME))

Abstract

The previous chapters focused on the cycles of the languages, but this chapter summarises the similarities and differences of the various phyla to indicate how different systems influence others. This provides evidence of much earlier dates for people in this region and a possible timeline with the known movements for counting systems to have been modified especially from the Austronesian 10-cycle. As a result, it is possible to dispute Seidenberg’s timeline and theory of the diffusion of number from civilisations in the Middle East. An alternate timeline is provided based on known events such as the end of the ice-age, uplifts and volcanic activity in island regions, the spread of Lapita pottery, and cultural developments. The variation in counting systems also provides evidence when considered in terms of the other evidence from linguistics, archaeology, geography, genetics and biogeography. Thus a possible timeline for the history of number is suggested indicating the probable antiquity of these counting systems from around 40 000 to 5 000 years ago in Melanesia.

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Notes

  1. 1.

    The 10 languages are: Tehit, Kalabra, Moi, Moraid, Karon-Pantai, Madik, Brat, Hattam, Borai, and Amberbaken. See Lean’s (1992) Appendix D for more details; Figure E2 in Appendix E.

  2. 2.

    The isolates were discussed in Wurm (1982, pp. 252-254). The six languages for which some data exist are: Warenbori, Taurap, Pauwi (Lean’s Appendix D, West Papua); Busa, Yuri, Nagatman (Lean’s Appendix C, Sandaun Province) and. Wurm included Maisin in his list of isolates: this is found in (Lean’s Appendix A, Oro Province) where it has been taken to be an AN language which has been extensively influenced by NAN languages.

  3. 3.

    The exception is the Mioko dialect of the Duke of York language.

  4. 4.

    Trobriands, Marshall Bennet, and islands of the Louisiade Archipelago.

  5. 5.

    The two languages with 10-cycle systems are Bola and Nakanai. The four languages with (5, 10) systems are: Bali-Vitu, Bola, Meramera, and Harua.

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  1. Charles Sturt University, Dubbo, NSW, Australia

    Kay Owens

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  1. Kay Owens
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  2. Glen Lean
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Owens, K., Lean, G. (2018). Towards a Prehistory of Number. In: History of Number. History of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-45483-2_10

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  • DOI: https://doi.org/10.1007/978-3-319-45483-2_10

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