Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-26T07:49:09.145Z Has data issue: false hasContentIssue false

Some remarks on number concept development in the Near East and Europe

Published online by Cambridge University Press:  20 May 2016

Abstract

In this article I outline the analogies and the differences in number concept development in prehistoric Europe and in the Near East. Research on Near Eastern recording systems is far more advanced, and it provides us with a good theoretical approach. There are, however, more and more finds in Europe that deserve our attention when looking toward a theory of early number concepts, concepts of measure and mathematics. For archaeologists, there is an obvious requirement that such a theory has to be constructed on a material basis. Therefore in the second part of the text I describe some key finds from Europe that in my opinion allow us, on the one hand, to reference current theoretical approaches and, on the other, to connect theoretical considerations and their material basis.

Type
Articles
Copyright
Copyright © Cambridge University Press 2016 

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

Baczyńska, B., 1993: Cmentarzysko kultury mierzanowickiej w Szarbi, woj. Kieleckie. Studium obrządku pogrzebowego, Kraków.Google Scholar
Barrow, J., 1999: Ein Himmel voller Zahlen. Auf den Spuren mathematischer Wahrheit, Reinbeck.Google Scholar
Broadbent, S.R., 1955: Quantum hypotheses, Biometrika 42 (1), 4557.CrossRefGoogle Scholar
Budja, M., 1998: Clay tokens. Accounting before writing in Eurasia. Documenta praehistorica 25, 219–35.Google Scholar
Chapman, J., 2000: Fragmentation in archaeology. People, places and broken objects in the prehistory in south-eastern Europe, London.Google Scholar
Damerow, P., 1999: The material culture of calculation. A conceptual framework for an historical epistemology of the concept of number, Max Planck Institut für Wissenschaftsgeschichte, reprint 117, available at www.mpiwgberlin.mpg.de/Preprints/P117.PDF.Google Scholar
Diakonof, I.M., 1983: Some reflections on numerals in Sumerian towards a history of mathematical speculations, Journal of the American Oriental Society 103 (1), 8393.CrossRefGoogle Scholar
Dzbyński, A., 2004: Metrologische Strukturen in der Kultur mit Schnurkeramik und ihre Bedeutung für die Kulturentwicklung des mitteleuropäischen Raumes, Langenweissbach (Beiträge zur Ur- und Frühgeschichte Mitteleuropas 39).Google Scholar
Dzbyński, A., 2008a: Ritual and understanding. Rational bases of communication and exchange in prehistoric central Europe, Rzeszów.Google Scholar
Dzbyński, A., 2008b: Von Seeberg bis Kelsterbach. Ein Beitrag zur Bedeutung des Kupfers im Äneolithikum und in der Bronzezeit Europas, Prähistorische Zeitschrift 83, 3644.CrossRefGoogle Scholar
Dzbyński, A., 2011: Mr. Blademan. Macrolithic technology – Eneolithic vocabulary and metaphors. Documenta praehistorica 38, Neolithic Studies 18, 172–84.CrossRefGoogle Scholar
Dzbyński, A., 2013: The power of the line. Metaphor, number and material culture in European prehistory, Newcastle upon Tyne.Google Scholar
Dzbyński, A., 2014: From Seeberg to Colmar. Early mathematical concepts in prehistoric Europe at the interface between material culture, technology and metaphors, Praehistorische Zeitschrift 89 (1), 111.CrossRefGoogle Scholar
Jasim, S.A., and Oates, J., 1986: Early tokens and tablets in Mesopotamia. New information from Tell Abada and Tell Brak, World archaeology 17 (3), 352–55.CrossRefGoogle Scholar
Justenson, J., 2010: Numerical cognition and the development of ‘zero’ in Mesoamerica, in Morley, I. and Renfrew, C. (eds), The archaeology of measurement. Comprehending heaven, earth and time in ancient societies, Cambridge, 4353.CrossRefGoogle Scholar
Kadrow, S., and Machnik, J., 1992: Iwanowice, stanowisko Babia Góra, część II. Cmentarzysko z wczesnego okresu epoki brązu, Kraków.Google Scholar
Klassen, L., 2001: Frühes Kupfer im Norden. Untersuchungen zu Chronologie, Herkunft und Bedeutung der Kupferfunde der Nordgruppe der Trichterbecherkultur, Højbjerg.Google Scholar
Kristiansen, K., 1991: Chiefdoms, states, and systems of social evolution, in Earle, T. (ed.), Chiefdoms. Power, economy and ideology, Cambridge, 1643.Google Scholar
Lakoff, G., and Núñez, R., 2000: Where mathematics comes from. How the embodied mind brings mathematics into being, New York.Google Scholar
Lefranc, P., Arbogast, R.-M., Chenal, F., Clerc, P., Thomas, Y. and Wuttmann, J.-L., 2009: Inhumations, dépôts d'animaux et perles en cuivre sur le site néolithique récent de Colmar ‘aérodrome’, in Lefranc, P., Chenal, F. and Arbogast, R.-M. (eds), 10,000 ans d'histoire! Dix ans de fouilles archéologiques en Alsace, Strasbourg, 4345.Google Scholar
Lefranc, P., Arbogast, R.-M., Chenal, F., Hildbrand, E., Merkl, M., Strahm, C., van Willingen, S. and Wörle, M., 2012: Inhumations, dépôts d'animaux et perles en cuivre du IVe millénaire sur le site Néolithique récent de Colmar ‘Aérodrome’ (Haut-Rhin), Bulletin de la Société Préhistorique Française 109 (4), 689730.Google Scholar
Lenerz-de Wilde, M., 1995: Prämonäre Zahlungsmittel in der Kupfer- und Bronzezeit Mitteleuropas, Fundberichte aus Baden-Württemberg 20, 229327.Google Scholar
Lieberman, S.J., 1980: Of clay pebbles, hollow clay balls, and writing. A Sumerian view, American journal of archaeology 84, 339–58.CrossRefGoogle Scholar
Löffler, I., 2010: Studien zu spät- und endneolithischen Kupferartefakten am Bieler See (Schweiz), unpublished written MA dissertation, University of Bochum.Google Scholar
Malafouris, L., 2010: Grasping the concept of number. How did the sapient mind move beyond approximation?, in Morley, I. and Renfrew, C. (eds), The archaeology of measurement. Comprehending heaven, earth and time in ancient societies, Cambridge, 3542.CrossRefGoogle Scholar
Mayer, E.F., 1977: Die Äxte und Beile in Österreich, München.Google Scholar
Nissen, H.J., 1988: The early history of the ancient Near East 9000–2000 BC, Chicago.CrossRefGoogle Scholar
Ottaway, B., and Strahm, C., 1975: Swiss Neolithic copper beads. Currency, ornament or prestige items?, World archaeology 6, 307–21.CrossRefGoogle Scholar
Pare, C., 1999: Weights and weighing in Bronze Age central Europe, in Eliten in der Bronzezeit. Ergebnisse zweier Kolloquien in Mainz und Athen, Mainz, 421514.Google Scholar
Peroni, R., 1998: Bronzezeitliche Gewichtssysteme im Metallhandel zwischen Mittelmeer und Ostsee, in Hänsel, B. (ed.), Mensch und Umwelt in der Bronzezeit Europas, Kiel, 217–24.Google Scholar
Petruso, K.M., 1992: Ayia Irini. The balance weights. An analysis of weight measurement in prehistoric Crete and the Cycladic Islands, Mainz am Rein.Google Scholar
Renfrew, C., 1973: Before civilisation. The radiocarbon revolution and prehistoric Europe, London.Google Scholar
Sachße, C., 2010: Untersuchungen zu den Bestattungssitten der Badener Kultur, Bonn.Google Scholar
Sangmeister, E., and Strahm, C., 1974: Die Funde aus Kupfer in Seeberg, Burgäschisee-Süd, Bern.Google Scholar
Schmandt-Besserat, D., 1978: The earliest precursors of writing, Scientific American 238 (6), 5059.CrossRefGoogle Scholar
Schmandt-Besserat, D., 1982: The emergence of recording, American anthropologist 84, 871–78.CrossRefGoogle Scholar
Schmandt-Besserat, D., 1992: Before writing. From counting to cuneiform, Austin, TX.Google Scholar
Schmandt-Besserat, D., 2007: Jak powstało pismo, Warszawa.Google Scholar
Smith, P.E.L., 1978: An interim report on Ganj Dareh Tepe, Iran, American journal of archaeology 82 (4), 537–40.CrossRefGoogle Scholar
Sommerfeld, C., 1994: Gerätegeld Sichel. Studien zur monetären Struktur bronzezeitlicher Horte im nördlichen Mitteleuropa, Berlin and New York.CrossRefGoogle Scholar
Staaf, B.M., 1996: An essay on copper flat axes, Acta archaeologica Lundensia 21, 139–52.Google Scholar
Strahm, C., 1994: Anfänge der Metallurgie in Mitteleuropa, Helvetia archaeologica 25, 239.Google Scholar
Taylor, T., 1999: Envaluing metal. Theorizing the Eneolithic ‘hiatus’, in Yong, S.S.M., Pollard, A.M., Budd, P. and Ixer, R.A. (eds), Metals in antiquity, Oxford, 2232.Google Scholar