Mathematical Determination of the Cultural Interaction between Medieval Groups
Abstract
A mathematical classification of two-dimensional ornaments into 17 plane symmetry groups is presented, which were created by five medieval cultural groups of Middle East. The data are considered representative for the cultural groups. By applying a correlation algorithm on the individual use of symmetry classes by each cultural group, the strength of the interaction between the pairs of groups are quantitatively determined. The analysis shows that the strongest similarity in the creation of periodic ornaments is between Rum Seljuks and Arab Muslims. It is also found that the Rum Seljuks, followed by Armenians, are the most interactive cultures. This report is the first attempt to quantify cultural communication by mathematical means.
Keywords
References
- [1] C. Brinton, J. B. Christopher, R. L. Wolff, A History of Civilization Vol. I, Prentice Hall, Englewood, NJ, 1960.
- [2] D. K. Washburn, D. W. Crowe, Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, University of Washington Press, Washington DC, 1991.
- [3] D. Schattschneider, The plane symmetry groups: Their recognition and notation, Amer. Math. Monthly, 85(6) (1978), 439-450.
- [4] L. Jones, Between Islam and Byzantium, Ashgate, Burlington, VT, 2007.
- [5] J. J. Norwich, Byzantium, The Early Centuries, The Apogee, The Decline and Fall, Alfred A. Knopf, NY, 1997.
- [6] A. E. Kaldellis, Romanland: Ethnicity and Empire in Byzantium, Harvard University Press, Cambridge, MA, 2019.
- [7] M. Hattstein, P. Delius, Islam, Kunst und Architektur, K¨onemann, K¨oln, 2000.
- [8] S. R. Canby, D. Beyazit, M. Rugiadi, A. C. S. Peacock, Court and Cosmos, The Great Age of the Seljuqs, The Metropolitan Museum of Art, NY, 2016.
- [9] A. Hutt, L. Harrow, Iran 1, Scorpion Publications, London, 1977.
- [10] A. Bas¸an, The Great Seljuks: A History, Routledge, London, 2010.
