THE TWO OF US TOGETHER - Mapping Time, Space and the Body - page 180

The philosophy of Xavante mathematics challenges the basic set of ideas that
informs the series of “natural” numbers, according to which the sucessor of 0 is 1,
the sucessor of 1 is 2, and so on. If, according to Xavante thought, the basic unit is 2,
the number 1 can be considered to have a contrastive identity, that is, to be defined
in relation, or in opposition, to 2. That being the case, the “natural order” for the
Xavante numerical sequence would not be 0, 1, 2, 3... n, n + 1, but could possibly be
the dialectical articulation of:
2, 1, 4, 3, 6, 5, 8, 7... n , n - 1, n + 3.. . if n is an even number
and
2, 1, 4, 3, 6, 5, 8, 7... m , m + 3, m + 2.. . if m is an odd number.
There are distinct ordering possibilities and layouts for this cyclical socionumerical
order. Given the fact that several instances of Xavante social life, including their
notion of time, the body, and relation to the environment are expressed in cycles
(Ferreira 1994b, 1998a; Lopes da Silva 1986; Maybury-Lewis 1979; Turner 1979),
perhaps it would be more appropriate to represent their number system in a cyclical
order, which reproduces itself in spiral form, such as:
Figure 5.9. A cyclical configuration of the Xavante numerical system.
The dynamic properties of a cyclical model, as noted above, allow for the reproduction
of the collective institutions, as well as for transformations in the socionumerical order
to take place. The spiraling nature of the curve moves simultaneously away from,