Towards the prehistoric sources of mathematical thinking. From the Paleolithic to the Ancient Greece. 2800-DMMAT
During the course, archaeological sources are
discussed, from the Palaeolithic to historical times,
concerning the shaping of numerosity and
measurement practices in prehistory. Evidences
such as cuts on Palaeolithic bones, ivory and
artworks, beads, Near Eastern tokens and the first
entries on clay tablets, beads, wires and sheets in
the Neolithic period, megalithic structures (the so-
called megalithic yard), metal ingots from various
regions of the Old World, administrative records,
balance scales and weights in the Near East, Egypt
and Europe, as well as the issue of money and coin
making are discussed. In addition, the philosophical,
theoretical and methodological content will be
presented, various interpretations of the above
mentioned finds and a holistic description of the
process of the formation of mathematical thinking in
history.
Type of course
Mode
Course coordinators
Learning outcomes
Participants have in-depth knowledge of archaeological
evidences and their role in shaping the early stages of
mathematical thinking (K_W01). They have extended
knowledge (K_W03) about the possibilities of the
description and interpretation of these evidences
(K_W04). They understand the need for considering a
variety of disciplines, both humanistic and scientific
approaches in the study of number and measure in
prehistory (K_W10), they know and understand methods
of interpretation (K_W14).
Potrafią dostrzegać złożone zależności pomiędzy
2
omawianymi artefaktami a dawnymi procesami
kulturowymi (K_U07).
Assessment criteria
Approve of attendance or an exam
Bibliography
Carl B. Boyer i Uta C. Merzbach, A History of
Mathematics, 3rd edition (Hoboken, N.J: Wiley,
2010).
Alexander Marshack, „A Lunar-Solar Year Calendar
Stick from North America”, American Antiquity 50, nr
1 (styczeń 1985): 27–51,
https://doi.org/10.2307/280632.
Tomasz Gralak, Architecture, Style and Structure in
the Early Iron Age in Central Europe (PL:
Uniwersytet Wrocławski and author, 2017),
https://doi.org/10.23734/22.17.001.
Karl Petruso, Ayia Irini: The Balance Weights : An
Analysis of Weight Measurement in Prehistoric
Crete and the Cycladic Islands (Mainz on Rhine: P.
von Zabern, 1992).
Michał Heller, Bóg i geometria: gdy przestrzeń była
Bogiem (Copernicus Center Press, 2020).
Majolie Lenerz-de Wilde, „Bronzezeitliche
Zahlungsmittel”, Mitteilungen der Anthropologischen
Gesellschaft in Wien 132 (2002): 1–23.
Mihael Budja, „Clay Tokens - Accounting before
Writing in Eurasia”, Dokumenta Praehistorica 25
(1998): 219–35.
J. Peter Denny, „Cultural Ecology of Mathematics:
Ojibway and Inuit Hunters”, w Native American
Mathematics, red. Michael P. Closs (University of
Texas Press, 1996), 129–80.
Jacques Derrida, Edmund Husserl’s Origin of
Geometry, an Introduction (Lincoln: University of
Nebraska Press, 1989).
Jens Hoyrup, In Measure, Number, and Weight:
Studies in Mathematics and Culture (Albany: State
University of New York Press, 1994).
3
John David Barrow - Pi Razy Drzwi. Szkice O
Liczeniu, Myśleniu I Istnieniu.
Denise Schmandt-Besserat, Jak powstało pismo
(Warszawa: Agade, 2007).
Edmund Husserl, Kryzys nauk europejskich i
fenomenologia transcendentalna (Warszawa: vis-a-
vis, 2017).
Witold Kula, Miary i ludzie (Warszawa: Książka i
Wiedza, 2004).
Morley, I., & Renfrew, C. (Eds.). (2010). The
Archaeology of Measurement: Comprehending
Heaven, Earth and Time in Ancient Societies.
Cambridge: Cambridge University Press.
doi:10.1017/CBO9780511760822
Richard Seaford, Money and the Early Greek Mind:
Homer, Philosophy, Tragedy (Cambridge, UK ; New
York: Cambridge University Press, 2004).
Aleksander Dzbyński, From Seeberg to Colmar:
Early mathematical concepts in prehistoric Europe
at the interface between material culture, technology
and metaphors, Prahistorische Zeitschrift, 2014,
https://doi.org/10.1515/pz-2014-0001.
Aleksander Dzbyński, Rytuał i porozumienie :
racjonalne podstawy komunikacji i wymiany w
pradziejach Europy Środkowej = Ritual and
understanding : rational bases of communication
and exchange in prehistoric Central Europe,
Collectio Archaeologica Ressoviensis 8 (Rzeszów,
2008).
Aleksander Dzbynski, The Power of the Line:
Metaphor, Number and Material Culture in
European Prehistory (Newcastle upon Tyne, 2013).
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: