Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-7479d7b7d-qs9v7 Total loading time: 0 Render date: 2024-07-14T05:53:53.600Z Has data issue: false hasContentIssue false

5 - Numerical cognition and the development of ‘zero’ in Mesoamerica

Published online by Cambridge University Press:  05 June 2012

By
John Justeson
Edited by
Iain Morley  and
Colin Renfrew
Iain Morley
Affiliation:
The MacDonald Institute for Archaeological Research
Colin Renfrew
Affiliation:
The MacDonald Institute for Archaeological Research
Get access

Summary

Part I. Numeration and numerical cognition

Cognition is a system consisting of representations of knowledge together with the processes that operate on those representations. What is fundamental to numerical cognition is the representation of knowledge about number and numeration, and the operations that are performed on them. This section explores features of numeral systems that relate to several different perspectives on these matters within cognitive and linguistic anthropology. It begins with a selection from Greenberg's (1987) findings on cross-linguistic regularities in the structure of numeral systems in spoken languages.

Number words and phrases

One way to explore how number is conceived is through its representation in language. For many linguistic anthropologists, it seems almost inevitable that the grammatical structure of words relating to regularly relevant semantic categories and domains will help to shape and/or be shaped by the ways they process information involving those categories and domains. Whether or not this is so in the case of number, the relevance of its linguistic representation follows from two empirical observations. (1) The vast majority of languages have numerals – ­conventional terms used widely in a speech community to represent specific numbers. (2) Worldwide, numeral systems – the linguistic organizations of terms representing numbers – show great similarity in their basic structure. The major work relevant to this chapter is by Greenberg (1987; see also Stampe 1977, Hurford 1987), who provides 54 generalizations capturing the structures of a wide variety of documented numeral systems.

Type
Chapter
Information
The Archaeology of Measurement
Comprehending Heaven, Earth and Time in Ancient Societies
 , pp. 43 - 53
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

,Beltrán de Santa Rosa, Pedro, 1746. Arte de el idioma maya reducido a succintas reglas, y semi-lexicon yucateco. Mexico City: Viuda de D. Joseph Bernardo de Hogal.Google Scholar
Berendt, C. Hermann, 1870. Vocabulario de la Lengua Zoque: Año de 1733. Manuscript in the University of Pennsylvania Library.
Blume, A., in press. Maya concepts of zero. In Proceedings of the American Philosophical Society.
Burkitt, Robert, 1902. Notes on the Kekchí language. American Anthropologist 4:441–63.CrossRefGoogle Scholar
Chrisomalis, S. A., 2003. The Comparative History of Numerical Notation. PhD dissertation in Anthropology, McGill University.Google Scholar
Corbett, G. G., 2000. Number. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Davletshin, A., 2002. Once upon a time there was no zero: The evolution of the south-eastern Mesoamerican calendric notation system. Abstract, in Cultural Context from the Archaeoastronomical Data and the Echoes of Cosmic Catastrophic Events: Abstracts Submitted for the SEAC 2002 Tenth Annual Conference, 27–30 August in Tartu, Estonia, eds. Kỡiva, Mare, Mürk, Harry, and Pustỡlnik, Izold. Tartu: Estonian Literary Museum, 25–6.Google Scholar
Dehaene, S., 1997. Number Sense: How the Mind Creates Mathematics. Oxford: Oxford University Press.Google Scholar
Everett, D. L., 2005. Cultural constraints on grammar and cognition in Pirahã: Another look at the design features of human language. Current Anthropology 46:641–6.CrossRefGoogle Scholar
Graham, J. A., Heizer, R. F., and Shook, E. M., 1978. Abaj Takalik 1976: Exploratory investigations. In Studies in Ancient Mesoamerica, III, ed. Graham, J. A. (Contributions of the University of California Archaeological Research Facility, Number 36). Berkeley, California: Archaeological Research Facility, 85–114Google Scholar
Greenberg, J. H., 1987. Generalizations about numeral systems. In Universals of Human Language, vol. 3: Word Formation, eds. Greenberg, J. H., Ferguson, C. A., and Moravcsik, E. A.. Stanford, California: Stanford University Press, 249–95.Google Scholar
Hurford, J. R., 1987. Language and Number: The Emergence of a Cognitive System. Oxford: Oxford University Press.Google Scholar
Justeson, J. S., 2001. Pratiche di calculo nell'antica Mesoamerica. In Storia della Scienza, Vol. II, ed. Aveni, A. F.. Rome: Istituto della Enciclopedia Italiana, Fondata de Giovanni Treccani, 976–90
Kaufman, T. S., with the assistance of J. S. Justeson, 2003. A Preliminary Mayan Etymological Dictionary. Published online at http://www.famsi.org/01051/pmed.pdf.
Kaufman, T. S., and Justeson, J. S., 2007. The history of the word for cacao in ancient Mesoamerica. Ancient Mesoamerica 18(2):193–237.CrossRefGoogle Scholar
Lakoff, G., and Nuñez, R., 2000. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. New York: Basic Books.Google Scholar
Lounsbury, F. G., 1978. Maya numeration, computation, and calendrical astronomy. In Dictionary of Scientific Biography, vol. 17: Anonymous Contributors to Science, ed. Gillispie, C. C.. New York: Charles Scribner's Sons, 759–818.Google Scholar
Lounsbury, F. G. 1990. Some aspects of Mayan numeral syntax pertinent to the opening date of Stela 8 of Copán. In Circumpacifica: Festschrift für Thomas S. Barthel, vol. 1: Mittel- und Südamerika, eds. Illius, B. and Laubscher, M.. Frankfurt am Main: Peter Lang, 289–301.Google Scholar
Pozarenco, Juan de. 1733. Vocabulario de la lengua Çoque. Manuscript in the John Carter Brown Library, Brown University, Providence, Rhode Island.
Stampe, R., 1977. Cardinal number systems. In Papers from the Twelfth Regional Meeting, eds. Mufwene, S. S., Walker, C. A., and Steever, S. B.. Chicago: Chicago Linguistic Society, 594–609.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×