Archives 1996–2012 de l’ancienne équipe REHSEIS
Laboratoire SPHERE – UMR 7219

People comming to the meeting where invited to read two articles by Marc Chemillier, relating his field work in Madagascar :

http://recherche.ircam.fr/equipes/repmus/marc/publi/sikidy/aspmathcog.pdf http://recherche.ircam.fr/equipes/repmus/marc/publi/sikidy/Mathtrad.pdf

They are in French. The meeting starts by a self-presentation of all people present, because there are some new faces :

Dominique Vellard has been studying and doing field work in ethnomathematics for the past twenty years. She has defended a PhD with Daniel Lacombe and Françoise Heritier on computational practices in Mali and Rwanda. She teaches computor science in Nantes, she has just come back from a field work in Togo and has worked also in Mexico and Burundi, always on ethnomathematical themes. In Rwanda, she has worked on the problems related to money conversions in illeterate communities.

Robin Jamet knows a bit people and facts in History of Mathematics since he started a Masters on the subject that he never finished. He works as a scientific journalist and has come by curiosity.

Marc Chemillier then makes a brief presentation of his field work, using videos that give a general overview of his field work but also sheds a specific light onto some technical aspects of the sikidy divination.

One of the sequences in the video illustrates what happens when a translator doesn’t understand what the field work is about. Dominique Vellard explains that the relations between informants, translators and the ethnomathematician is a co-construcion which takes time to become a real relation based on trust. She explains that field work is always a co-construction in which all are transformed. She gives as an illustration the case of her Rwandian interpret, who having trouble to understand the mental conversions the illeterate communities practiced, realized that they indeed had an intellectual activity, and slowly became less dispising with them. Several time the discussion will come back to the quality of the interpret or informor (the quality of which often gives the quality of the field work), the time required for a good field work, etc. One has also to remain focussed on the mathematical activities and not delve into the tentation of a mongraphy, describing everything.

The video enables one to understand things that the paper explanation made difficult, such as the construction of a mother-matrix with a random process (taking a bunch full of seeds) and with a euclidian division (whose remainder is either one or two).

Marc Chemillier comes back to procedures for which he doesn’t understand the logic from the diviner’s (the one who practices divination) point of view : for instance when the 2222 column apears, algebraically a neutral element of the tabular system of sikidy divination, the diviners invert the usual order of column derivation. Mathematically we can understand why this order is inverted, but what are the diviner’s explanations ? When questioned, diviners do not recognize the inversion and claim that thy just do it this way, « by heart ». This doesn’t have any meaning when considered from the point of view of the production of columns, because the mother-matrix is impredictible, and the inversion is done only when the 2222 column appears.

Agathe Keller, suggests to practice the tables to try to understand from the inside the way they function. Eric Vandendriessche replies that this would once again be inventing your own logic to understand these activities, if you do it on your own. The utility there is in practicing such activities this way is only that it gives you a certain dexterity and knowledge which helps once you are out there doing field work. He then asks how is sikidy transmitted at Madagascar. Marc Chemillier replies that he does not know, the diviners always say that they have learned alone, althought they also evoke the name of their masters.

We discuss the different levels of the actor’s thought that Marc Chemillier wants to unravel in his field work :

There is the mathematical description of the grain’s algebra. The knowledge of these algebraical rules to which the tables are submited, provide an angle from which one can attempt to understand what in the diviner’s practice belongs to a given algebraical property (for instance the use of the neutral element). The mathematical knowledge of these rules can also be a language that can be used to understand the reasoning and mental acts of the diviners. Cognitive methods can also be used to try to understand what are the mental acts of the diviners. For instance chronometrical tests show that the diviners do not count the number of grains contained in a princley column (an even number of grains) or those of slavely columns (with an uneven number of grains). They know them so well that they recognize them immediately. This immediate recognition describes a non-conscient mental act of the diviners (as the fact that when we read a letter upside down, our brain rotates it, a well known result of chronometrical tests).

Marc Chemilier is also of course interested in the theorisation diviner’s have of their practice. He has shown that at least one diviner had a subtle concept of parity, a theoretical idea of it, if one takes the ethymological meaning of theory. The aim of course would be to explicit more of the theory of their formal practice, but this requires time. Marc Chemillier remarks that this approach can also imply studying concepts used and created by actors who may not have words to express them. He referst to Maurice Bloch and Dan Sperber, who have reflected on such situations.

The discussion turns on the formal practice of the tables and the interpretation that are given to them by diviners. A. Keller thinks that sometimes it is possible to have theoretical replies on formal questions by looking at the context in which they are inserted. She takes examples taken from the sanskrit mathematical commentary she has studied in which technical grammatical reasonings are often used to in fact reflect mathematical problems (how does one define a square, etc.). If one disregards these reasonings as being scholastic for instance, one doesn’t see the mathematics that are involved in them.

 Marc Chemillier défends the idea that you can discuss formal problems with the diviners without having to get involved in the mystical interpretation they have of such activities. He says that he still needs to be convinced that the context can help him in this case. He says that he has seen some very gruesome vaudou rituals associated with sikidy divination, and didn’t see any link with the formal work on the grains.

 Marc Chemillier talks about the big divide in ethnomusicology between those interested in the context and those interested in musical forms. Both being of course important, all depending on what is the question you ask at the begining. We all agree that what is interesting is the articulation between the formal reasoning and the context, but to do so you need to know what is happening on both levels. Concerning sikidy divination, the devinors know how to explicit the formal rules of the tables, even the rules that aren’t used when they are divining. But they do not say what it means to them. Everybody in Madagascar seems to know the basic rules of table manipulation, which enables one to control that a divinor knows how to makes tables and does it with more or less dexterity and wit.

Dominique Vellard talks about vaudou geomancy and a Togolese colleague who works on this. She will put him into contact with Marc.