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## December 04 : The work of Marcia Ascher

** Minutes of the meeting of the 17th of february 2005, on Marc Chemillier’s study of Sikidy divination in Madagascar **

Our first meeting starts by a self presentation of all people present. Everybody explained why they came and what they expected from this seminar/brainstorming meeting.

Agathe Keller explains that it is her work on the history of mathema

tics in India that has brought her to read on ethnomathematics. Ethnomathematics can indeed help her contextualize the Sanskrit mathematical texts she studies. Also she has been striked by the multiplicity of living mathematical traditions in today’s India, whether recognized as “mathematics” by those who use them (such as accountants) or recognized as “mathematics” by ethnomathematicians (like south Indian kolams).

Eric Vandendriessche teaches mathematics in high school. After a Masters in History of Science he has started a PhD on string games, conceived of as a mathematical object, and as an ethnomathematical object. He is curious of all oral teachings of mathematics and would also like to define what is “a mathematical idea”.

Sophie Desrosiers is an anthropologist. She studies weaving techniques in the Andes. She has studied the history of pre colombian textiles, especially in Bolivia. She has brought to light a mathematic (or a logic) of weaving techniques using double entry tables, that describe the way strings are combined with one another. Such tabular structures can be found in other social stratas of pre colombian societies and even in contemporay society in the Andes. More generally, Sophie Desrosiers would like to think how mathematical principles can be used in day to day life.

Marc Chemillier is a computor scientist who has come to ethnomathematics through ethnomusicology. He works on the logical and rational structures of divination techniques in Madagascar. He would like to relate the structures of such practices to the way they are spoken of by those who practice them. He is interested in the links between specialized knowledge and scholarly knowledge.

Stella Baruk is a teacher and a well known French specialist of mathematical pedagogy. She insists that one should differentiate cultural practices from mathematical practices. She would like us to define what meaning we give to the word “mathematics” when used in “ethnomathematics”.

Alain Le Mignot teaches logic to future teachers. He is interested in the emergence of logic, and its link to rhetoric and mathematics.

The discussion then starts with a critical synthesis by Eric Vandendriessche of Marcia Ascher’s work and life, especially of Ethnomathematics : A Multicultural View of mathematical Ideas. Pacific Grove, California, Brooks/Cole Publishing Compagny, 1991. The gist of Eric Vandendriessche’s talk is that despite its setbacks the book gives methods to bring to light mathematical ideas and mathematical procedures in activities that didn’t seem mathematical, or in societies that where not deemed to have mathematical activities. The debate then turns to the principles used to judge of the “scientificity” of an activity. For Agathe Keller there is something like a hidden racism in the fact that Marcia Ascher marvels that in societies without writing, or just in isolated communities, people have rational and logical thoughts. Stelle Baruk adds that these thoughts do not tell us anything about their mathematics. Marc Chemillier insists that we shouldn’t look at isolated societies as societies that only strive to survive, the existence of music in all societies testifies that even in very poor communities people have an intellectual and creative life. Eric Vandendriessche questions how the activities described by Marcia Ascher relate to written mathematics. Marc Chemillier quotes Davis & Hirsch, the mathematical Universe, which distinguishes between mathematical discourse and mathematical practice.

Coming back to the criterias by which one can judge of the scientificity of an activity Stella Baruk says that to use quantification (or the notion of number) or geometry (the notion of figure) is not sufficient to qualify an activity as “mathematical”. Marc Chemillier thinks that one should distinguish between analytical reasonings and analogical ones. The first being formal and the latter being intuitive, both belonging to mathematics.

Eric Vandendriessche comes back to Marcia Ascher and to the way she finds mathematics in games, rituals and the links she draws then between these activities. She suggests classifications, especially of algorithmic thoughts and she shows that there are systems of classifications and systems of procedures. Can the latter be considered as mathematics ?

For Stella Baruk mathematics are caracterized by the nature of there objects, not by the processes that transform them.

Maybe the problem here is the question of the unity of mathematics even in the scholarly tradition of today : is computor science mathematics ?

A number of questions are thrown up : how should one characterize the societies/communities studied by Marcia Ascher. In her first book she looks at “isolated societies” in her second one she also looks at non-scholarly practices in communities belonging to societies which have a scholarly traditions. We also talk about those disciplines which use complex structures and for which there is a debate about whether the structures created and used by the actors are conscious or inconscious. Eric Vandendriessche underlines the importance of intentionality in Marcia Ascher’s writings, and also the importance of meaning. Once again then the question is raised : can operations though of and organized intellectually, worked out intellectually, elaorating an abstract system of abstract objects (like the transformation of string fiures or drawings in the sand), can such objects be considered mathematical ? Eric Vandendriessche, Marc Chemillier and Agathe Keller evoke the question of the visualisation of geometrical systems in the corpuses they have studied.

We all agree on field work : Indeed, Marcia Ascher only worked on second hand accounts. To do ethnomathematics we have to do field work and see how things are done and though of. When reading Marcia Ascher’s articles one often doesn’t know if the names given to procedures are her’s or the actor’s.

We thus decide to modify the program of the seiminar to invite people who have done field work to talk about their work.