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Accueil > Archives > Ancients projets de recherche > Anthropologie des mathématiques > Version française > Les séminaires > Compte-rendus > Anthropology of Mathematics

Anthropology of Mathematics

Compte Rendu de la Séance du Séminaire d’Ethnomathématiques consacré aux travaux

de Céline Petit : "Anthropologie des Mathématiques"

7 juin 2006

Since 2001 I have been doing a PhD research on the general theme of « Inuit games » in the Eastern and Central Canadian Arctic. I collected most of my ethnographic data first in Nunavik (Northern Quebec, in the Ungava Bay area : settlement of Kuujjuaq), and then in Nunavut, in the Iglulik area (Iglulik : there are around 1400 inhabitants in the settlement now) .

I have been doing field work for about two years in these areas. Cartes à visualiser.

String games were actually known and practiced all over the Arctic area among Inuit people, from Eastern Siberia to Eastern Greenland. In the past, mostly before the introduction of Christianity (which varied quite a lot depending on the areas), similar prescriptions used to apply regarding the season of the game, and the gender of the player.

It seems that we face a quite homogenous symbolic system here.

Many string games collected from Alaska to Greenland are also common to different Inuit areas (possibly 65-70 % of each corpus, Rousselière 1965 : 12 ), similar figures being known in remote parts of the Arctic (and sometimes without the games being mastered/practiced in the intermediate areas).

On a general level, my research first consisted in collecting the different games that used to be played in a quite recent past (before the introduction of Christianity and the settling process), and those that are played nowadays mostly by the Iglulingmiut (children as well as adults).

The purpose was to identify significant organizing principles, and first some major functions of these games in the Iglulik society. I chose to adopt a comparative approach through time (a diachronic perspective).

By interviewing Iglulingmiut contemporary elders, I tried to understand better the modes of the play activities that characterized the former semi-nomadic lifestyle (prior to the sedentarization), in order to compare them with nowadays’ main principles (logics) expressed through Inuit contemporary games. Considering playful dynamics as embedded in former shamanistic Inuit societies helps to question further, in a contrastive perspective, the ways play is activated - or requested - in contemporary Inuit communities of Nunavut, and in the Iglulik area in particular.

Beyond the understanding of major social functions linked to Inuit games, the purpose of this research is eventually to point out a structural principle governing the relationships between human beings and non-humans (and animals), (at a symbolical level). In my view, play activities represent a major means of regulating the relationships between the different beings that belong to Inuit cosmology.

Inuit play must be first perceived within a socio-cosmic exchange system involving human and non-human beings (including tutelary spirits), and mostly aimed at maintaining the circulation of game (animals) between those entities. An indication in that sense is the prevalence of games that carry propitiatory or divinatory issues.

As for the string games, they were part of a ritual system of prohibition and prescription, and their practice mostly hold propitiatory effects relating to the solar cycle, as we will see.

These games are usually presented - through contemporary Inuit discourse – both as « traditional » (in the sense that they are said to be played by the Inuit from time immemorial), and as a practice that is relevant in contemporary Inuit life, and that should be taught further.

The contextual frames of this play activity have however significantly changed with the settling process and the introduction of mass media (TV and video games) in the Canadian Arctic.

Presenting the object

The string used to be made out of dorsal caribou sinew, which was braided. Nowadays Inuit mostly use imported material (like these little ropes) to play string games.

String games are called ajaraaq in the Central Arctic, which literally means « which is pushed away/further with the hands, several times and repeatedly » .

These games consist in representing - with a string - various figures, items, human beings, animals or non-human beings ( Amajurjuk, Tuutalik, Uliguliarjuk) and spirits ( Tuutannguaq in particular, which is said to be the “spirit of the string games”). Among the main figures, things or beings that are represented in most of the Inuit areas (and particularly in Iglulik) are :

Body parts (apertures like the mouth, the anus ; male and female genitals ; the arm, the ribs).

Hunting and domestic tools (the kayak, the oil lamp, the tent…)

Physical elements (the crack in the ice, ice blocks…) or cosmological figures (the stars…) .

Animals (the caribou, the fox, brown bear, rabbit, wolf, wolverine, lemming, raven, polar bear, beluga, walrus…). It is quite striking here that one of the most common sea-game (widely used in the Inuit diet, especially in the Iglulik area), the various species of seals, are not represented through this game.

Characters or scenes of social life (the drum-dancer, the two who quarrel and fight…).

It seems that in the past, playing string games - usually within the family group in the evening - was a significant way of showing social events experienced by members of the group (either representing a hunting expedition or a shamanistic ritual), by realizing successive figures. Some string games are actually associated with particular narratives including songs.

In that sense, the practice of string games might be regarded as supporting collective memory (regarding the actions of members of the group, or from other groups).

The striking stability & continuity of the corpus throughout the age has often been underlined, as it seems that the Inuit string games repertoire increased very slowly ( Rousselière 1965 : 15). Several string games/figures actually refer to a long past since they represent animals such as the mammoth ( kiligvaq) or the bison ( silaq).

Significantly, the importance of passing on these games (and their narratives) to the younger generations has been largely emphasized by the elders along/during the last 50 years.

Even when the meaning of most of the songs or narratives associated with some figures seems to be unclear to most of the elders nowadays. The symbolic efficiency attributed to these games might be more linked to the act of representing (than to the meaning of the words).

Moreover, these string games not only imply abilities to watch, to reproduce and memorize, but probably as much to experiment. Innovation and creative autonomy within a codified (collective) theme seem to have been encouraged in Inuit communities. Beyond the existence of codified forms for the string figures (and the striking stability of the whole corpus), the multiplicity of combinatory strategies or “ways” to reach one particular figure might have been deeply valorized (within a same camp or area, Mary-Rousselière 1956 ).

The significance of changing viewpoint (to apprehend a same object or being) is still expressed at many levels of the Inuit culture.

The string games might have been - and may still be - part of a global incitation to change one’s point of view to consider the same object. To shift the perspective whether on one thing or one situation is a significant trend in Inuit nomadic societies indeed.

Inscription dans un système de prohibitions-prescriptions marqué par le dualisme saisonnier

Before Christianity was introduced (in the 1920s-1930s in the Iglulik area), the practice of string games was embedded in a prohibition system linked to the seasons’ alternation (according to the major dualism or opposition between winter and summer, sea / land).

In the Iglulik area (like in most of the Inuit areas, from Alaska to Greenland), the game of ajaraaq was not supposed to be performed while the sun could be seen in the sky, otherwise the female deity of the Sun ( Siqiniq) would get hurt by getting deep cuts from the string, or would even fall (the idea being that the sun’s progress would be hampered by the string). This prohibition applied more specifically during the sun’s return (after the period of darkness which lasts from early December to mid-January in the Iglulik area). To ensure that the prohibition would be followed, the Iglulingmiut used to cut the strings (used for the game) into pieces at that time.

Conversely (to this prohibition), there were strong prescriptions regarding the practice of the string games during the period of darkness in winter time.

Performing ajaraaq during the night was actually regarded as a way to prevent the (invisible/hidden) sun from disappearing forever under the earth, by “holding” it with the string ( Mary-Rousselière 1965 and Saladin d’Anglure 1990 ).

In that sense, ajaraaq is to be viewed in a complementary opposition to the game of ajagaq, a kind of “cup-and-ball” made out of a bone that was thrown up as soon as the sun would come back on the horizon, in order to help it to rise higher and quicker (Saladin d’Anglure 1990).

These representations tend to suggest that a propitiatory value was attached to these games, following a symbolical “mimetism” applied to the cycle of the sun.

Several Inuit games were significantly linked to the solar trajectory.

Among the Iglulingmiut, the juggling game of illukittaq, usually played with two rocks which are said to represent the cosmological figures of the sun and the moon, might have been regarded also as a way to encourage the sun to fulfill its cycle and to rise higher.

More generally, many games were performed within rituals that marked the disappearance of the sun (at the beginning of the winter, when the relationship between humans and animals seemed particularly tenuous).

The games embedded in these rituals of the winter solstice mostly aimed at reactivating the cycle of life reproduction. (Dualist competitions like the tug-of-war or the whip-ball game ).

As regards the string games, the prescriptions governing their practice during the dark period were strong enough to incite the members of a camp to appoint a man who would go to another camp in order to learn either a new string game or one that had been forgotten by the group.

This man would then teach the game to the members of his group when he would come back from his trip (which could be quite long as the other camp might be far away).

Iglulingmiut elders referring to this practice make no mention of any payment for this teaching. Most of the contemporary elders insist on the fact that the practice of string games represented therefore « more than a mere amusement or entertainment », and they continuously emphasize the necessity of teaching and sharing these games among the different generations.

The string games used to be performed mostly in a familial context (extended family group), with the parents and grand-parents teaching the games to the children and youth progressively.

This activity is seen as requiring some specific skills.

During the winter time, the string games were performed by men as well as women, but according to Inuit main representations, they are considered as pertaining to female practice. As opposed to the cup-and-ball game ajagaq (played by men & women) which was represented as a male game.

As regards the string games, a number of restrictions actually applied to the young males (hunters to be), who were not supposed to play often with a string, otherwise they would get their hands tangled in the harpoon line while hunting seal at the breathing hole (under the ice). They would therefore miss their catch, and possibly die by being drown into the water.

In other Arctic regions, and mostly in the western areas (among the Inuit and Aleuts), the string games were more clearly presented as a practice designed for the women.

One might notice however that these are men (elderly men mostly) who are considered as experts in string games in the Central and Easter Arctic these past decades.

Since the introduction of Christianity in the 1930s, the ritual system of prohibitions tended to fade away, and string games can be played at any time now. Yet these games are preferably played in winter time still, when the outdoors activities are more restricted.

Nowadays the string games are mainly played by children, and mostly by girls, within the settlement. They are still taught within some families (with this striking example of an Iglulingmiut grandfather who, as he was dying, insisted on passing on the games he knew to his grandchildren), but some string games workshops have also been institutionalized in the school. This teaching at school is seen as pertaining to a “tradition course”, and for now, the string games don’t seem to be considered as a means to teach mathematics or geometric notions to the students (as opposed to the program which have been initiated among Yupiit in Aaska a few years ago, which uses string games as a support for learning geometry).

It is worth noticing that the string games are still valuable pastimes, performed by women and teenagers whenever they are camping out on the land (with no TV around) in spring time.

Contemporary children and youths master some string games belonging to the former corpus (expressed in ethnographic studies such as Rousselière’s collection) :

See the pictures inuksugaq, katakjuk, tupirjuk, ukalirjuk .

In general however, the girls tend to prefer interactive modalities of the game, playing two-by-two, facing each other, each player operating on the string held by the partner-opponent.

The main rule here is to reach and keep a geometrical figure (undefined), which is usually symmetrical. Such a dualistic combinatory method seems to constitute a recent trend, as the figures involving the participation of two players were “extremely rare” in the 1960s-70s still, according to Rousselière. Moreover, symmetrical figures did not seem to be so common then.

Previous studies (collected corpus in the Canadian Arctic)

Dans l’Arctique, les premiers ethnologues ayant collecté des jeux de ficelle sont Franz Boas (1888 : fournit une des premières descriptions d’un jeu de ficelle inuit, dans le Sud Baffin, Cumberland ) et surtout Diamond Jenness qui adopta une perspective comparative (pour l’ensemble de l’Arctique de l’Ouest), en proposant une description des jeux relevés depuis l’Alaska jusqu’au golfe du Couronnement (avec quelques aperçus sur la Sibérie – Tchouktches – et l’Arctique oriental, Cumberland Sound en particulier). Jenness s’est inspiré essentiellement de la terminologie développée par Haddon et Rivers ( Man 1902), et a adopté une classification qui est d’abord fonction des types d’ouvertures mobilisés.

La première grande étude comparative des jeux de ficelle inuit (de l’Alaska au Groenland) est cependant l’œuvre de Paterson. Ce dernier a mis l’accent sur la répartition des figures, and not so much on the sub-procedures as such ?

Father Guy Mary-Rousselière (1965, 1969) collected string games from the Arviligjuarmiut ( Pelly Bay), sub-group belonging to the Nattilingmiut society, in the Central Canadian Arctic.

Ethnographers have been eager to elaborate a terminological system that would describe the string games in their totality, by depicting the different operations and procedures held on the string, instead of apprehending the games only through the result, or their final figures.

The first technical terminologies (developed by Haddon & Rivers, and adopted by Jenness, Paterson and Rousselière) rely mostly on a set of binary oppositions :

Palmar-dorsal / radial-ulnar / proximal-distal

Vernacular terminology (from Central Canadian Arctic : Arviligjuarmiut, Iglulingmiut)

Ajaraarlugu : doing the A opening.

On a general level, this term also means playing the game of ajaraaq, which emphasizes the prevalence of the A opening in many Inuit string games (A as the most classical).

Most of the Inuit figures actually start with the position I and the A opening, which seems to be widely used throughout Oceania also ( Rousselière 1965 : 11, Eskimo).

There are however various initial position and kinds of openings for the Inuit string games.

Anitillugu : inserting a loop inside another one (lit. “to take out, make it go outwards”). Qinirirlugu : putting two loops together (as the first step of joining them actually : katilluik ), lit. “going to look for, searching for”.

Katillutik : Uniting the loops of the thumbs (…)

Qipisimasuirlugu :turning a tight loop on a finger in order to open it, lit. “to unroll it”.

Pakinillugu : to hook on the string, lit. “to hook on, to grip to”

Sapkullugu : to release the string (lit. “to release”).

Qilurqitillugu : to stretch the string between the two hands, lit. « to stretch by pulling ».

Paurialik : initial position with tight (closed) loops around the thumbs and the little fingers, lit. “which is stretched out” ?

Iglupiaq : on one side (single figure). Lit. “one of a pair (by nature), one of twin things”.

Iglugiik : by the two sides (double figure). Lit. “relationship of twin things, paired by nature”.

This terminology reveals that different operations and sub-procedures have actually been perceived as such by Inuit players while manipulating the string.

On a cognitive level however, it does not mean that most of the Inuit players now conceive nor memorize each game through these single categories, or as a series of strict sequences.

In actual practice, many players who are very quick at reaching the final figure have difficulty in demonstrating the game by splitting it up into precise sequences, that is, by performing slowly (with adequate comments on what they are actually doing). They also find it hard to operate further on someone’s else (novice’s) configuration at a given step when it is a matter of reaching the proper final figure.

(As opposed to the dualistic modality of play, where most of the players quickly identify the intermediate configuration or figure on which they will operate in turn).