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## Detailed Presentation

PROJECT **ETKnoS** : ENCODING AND TRANSMITTING KNOWLEDGE WITH A STRING: A COMPARATIVE STUDY OF THE CULTURAL USES OF MATHEMATICAL PRACTICES IN STRING-FIGURE MAKING (OCEANIA, NORTH & SOUTH AMERICA)

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The primary objective of this research is to investigate the expressions of a mathematical rationality at work in the activity of “string-figure making”, as it is practiced in societies with oral traditions within different cultural areas (Oceania, South and North America), and especially among the Ni-Vanuatu (Vanuatu) and the Trobriand people of Papua New Guinea, among the Mapuche in Patagonia and the Guarani-Ñandeva in the Chaco, and also among the Inuit in the Arctic.

In general, this activity – described in the terms of a game, by the first foreign observers (explorers, ethnologists) as well as by the indigenous practitioners – consists in making a figure by applying a succession of operations to a string loop, using the fingers, but sometimes also the teeth, wrists or feet. Taking a comparative perspective, this study is based on an interdisciplinary approach that aims to combine the contributions of fundamental mathematical work (knot theory, modelling, topology, coding), ethnomathematics and the history and philosophy of mathematics, with methods (ethnographic research, ethnolinguistic analysis) but also writings in social and cultural anthropology. This approach seeks to promote the development of novel conceptual tools in order to shed new light on certain cognitive actions associated with "mathematical" reasoning, and embedded in common cultural practices. It aims also to contribute to enriching the methodological approach of the fledgling discipline of ethnomathematics, that has emerged from the work of M. Ascher (1986, 1991, 2002), U. D’Ambrosio (1985, 1990, 2001) and P. Gerdes (1994, 1995), as the study of culturally specific uses of mathematical ideas and knowledge (or as the anthropology of mathematical practices and concepts).

The present project includes a notable epistemological issue relating to the understanding of "mathematics": the comparative (and transcultural) study of cognitive actions involved in a procedural activity such as string-figure making should lead to clarifying the criteria for identifying a “mathematical rationality” expressed in the context of oral traditions. The use of ethnomathematical analytical tools, combined with the ethnological/linguistic study of the concepts and vernacular terms associated with the practice, should contribute to highlight some of the elements in the answer to the question of knowing whether an activity presents, or not, a mathematical character. This question, which is at the heart of ethnomathematics, is of interest to various scientific communities, including researchers in philosophy or didactics of science (and of mathematics in particular). Discussing about criteria for characterizing a mathematical practice or object is in fact quite a recent field of research among philosophers of mathematics (Caveing 2004, Van Kerkhove & Van Bendegem 2007) and this discipline does not yet offer efficient conceptual tools to tackle this issue. It is furthermore noticeable that mathematical ideas or skills are often conceived, by scholars, as rooted in activities responding to concrete problems (numbering, counting, measuring distances, angles or surfaces, navigating by referring to stars...), the practices seen as "ludic" or "artistic" – or as guided by an aesthetics (re)search – being more rarely considered in that perspective. And whereas practices that involve numbering and/or measuring are quite readily recognized as related to mathematics, procedural activities requiring “geometrical” abilities (such as string-figure making, weaving, basketry, sand drawing, etc.) are by contrast not so readily analysed as mathematical by academia in general.

While the project ETKnoS is focused on string-figure making, it also involves, for the societies concerned, the consideration of other practices (weaving, net-making, platting, sand drawing, mud drawing or storyknifing, tatooing, etc.) which the actors associate in various ways (in their terminology, for example) with string-figure making, and the practice of which seems to make use of a form of mathematical reasoning. By starting the comparison of cultural and cognitive aspects of these practices (first within the same society), the present project aims to contribute to the definition of a new epistemological framework for the study of such activities (with a geometric and/or algorithmic character).

N° ANR-16-CE27-0005-01, 2016–2020