Geometric and algorithmic practices in oral tradition societies: the case of sand drawings and string-figures from Vanuatu

Résumé En

This paper aims to compare—through an ethnomathematical approach—two activities carried out by the Northern Ambrym Islanders (Vanuatu, South Pacific), and locally termed using the same vernacular verb tu (lit. “to write”). These practices consist in making a figure, either with a loop of string (“string-figure making”, using fingers and sometimes feet and mouth) or by drawing a continuous line in the sand with one finger (“sand drawing”). Initially, we examine thecultural and symbolic aspects of both practices, bringing to light that the making of string-figures and sand drawings are both means of recording and expressing knowledge relating to particular mythological entities, or environmental elements in Northern Ambrym society. Secondly, by focusing on concepts such as operation, procedure, sub-procedure, symmetry and iteration, we demonstrate that both practices share geometric and algorithmic properties. Concomitantly, we investigate the links between the procedures involved in the making of these figures and particular forms of memory and tradition embedded in these practices. We conclude that this comparative study of activities bearing a mathematical character should contribute to revealing criteria for identifying “mathematical practices” in an oral tradition cultural context, which is a core issue in ethnomathematics.