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and towards, the basic organizing principles of Xavante social structure. Structural
transformations in Xavante kinship, encompassing recent changes in marriage
arrangements and delayed birth of offspring, for example, have had the potential of
elongating the spiral, because it delays the offset of a new cycle. However, because
moiety systems of dialectical societies are self-regulating systems of transformations,
they are capable of institutionalizing cyclical or repetitive reproductive processes by
incorporating change without changing the basic composition of the system. Exploring
the socionumerical transformations of this cyclical model can yield important insights
into the intrinsic values and properties of dialectical mathematical systems.
The numerals that represent each socionumerical cycle have been limited to 8 in
this representation because some elders say that the Xavante traditional counting
system extended itself up to 8, rather than 6, as stated before. This is due mostly
because of the people's age-set system, mentioned above - yet another institution
that complements their moiety system. One important cycle of Xavante social life is
marked by the successive incorporation of individuals into age-sets. Every 5 years a
new age-set is formed and people are born within specific age-groups. So rather than
define one's age by Western calendar years, a Xavante person is born within a 5-year
age-set period, which is actually composed of 5 pairs of dry and rainy seasons. Since
there are 8 of those 5-year periods, the total cycle adds up to 40 years (8 times 5).
Every 40 years the cycle repeats or reenacts itself.
The 8 Xavante age-set groups are: Tsada'ro, Ai'rere , Hotorã, Tirowa , Etepá,
Abareú , Nodzö'u, and Anorowa . Alternated age-sets (distinguished in bold font),
in turn, form two separate moieties, according to the pervasive dualism of Xavante
society. Therefore, for example, in certain rituals, such as the palm tree buriti
( Mauritia flexuosa ) log-race, or soccer teams today, every-other age-set will pair up,
alternately, forming 2 teams (see Fig. 5.10 ) .
When I arrived in Kuluene in 1978, I was immediately classified as Anorowa , since
that age-set was formed by individuals born from approximately 1958 to 1962. My
classificatory parents, Peri and Abigail (Aracy's parents too, as she was my older sister),
always directed me to hang out with other Anorowa women in our daily activities -
fetching water or washing clothes at the river. We were all about 20 years old at the
time, and all of the women were already married, except for me. So when it was time
to cook, I hung out with the unmarried women, who were in their early teens, since I
didn't have a family to feed. When I asked to go cook with the Tsada'ro , an age-set
younger than me, my mother Abigail replied: “You are mitsi [all alone, the number 1] so
you must go find a partner to become maparané [2 together].” Despite my frustration
in these occasions, at other times, such as in log races or gardening chores, I got to
participate in activities with women from the older alternating age-set, the Hotorã ,
Etepá, and Nodzö'u, who were about 10, 20 and 30 years older than me, respectively.
Theoretically speaking, the age-set system can be considered as a finite and cyclic
progression, composed of moments of time and social relations that qualify the system
as a socionumerical one. In the Xavante age-set system, however, there is not really a
first term, but there is a sucessor to each term. Here, I have designated the first term
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