Geography Reference
In-Depth Information
How could Lino compare numerical magnitudes if numerals in the graphic decimal
system lacked semantic meaning? To the boy, nothing in “a small dot with a stick
hanging from it and followed by two small dots” led him to believe it was any
higher than “[me] alone [with] dot [on] my head, without a mate.” The fact that
the new numerical system created by the Salesians still used Xavante names for
numeral 1 through 6 magnified the discrepancies. After I explained to Lino the
logic of place value and how much the zeros in 900 represented, the boy replied
that to him,
185 is less than 900 because I am alone ( mitsi 1) in 185 and without a mate
( imrotõ 5). In 900 tomai'ã tomai'ã is strong because it is wanena (the two of
us together).
Lino resorted to a common principle of dialectical societies, according to
which a totality is always conceived of as the sum of its parts. 185 is less of a
totality since it includes both a “lonely” self and a “mateless” self. 900, in turn,
presented Lino with a situation in which a 9 or a “small dot with a stick falling
from it” was joined by 00 or a couple of “two small dots.” These two small dots
are definitely empowered by the concept of wanena - “the two [of us] together,”
an important value of the Xavante's dualistic social organization and the basic
unitary value of the people's traditional numerical system. The complexity
of the situation in which two numerical systems were at stake accounts for
the difficulties experienced by Lino during his classroom problem-solving
activities, and not the boy's cognitive inability to reason abstractly and learn
For Lino, it was like seeing light at the end of a dark tunnel. The boy remarked,
with a big smile on his face: “ Waradzu matemática pipaõredi,” white men's
mathematics is not scary. He mixed Xavante and Portuguese words to convey his
joy in making sense of a decimal numerical system. Most importantly, Lino also
understood that there are different ways of making sense of mathematical concepts.
He felt empowered to realize that Xavante mathematical knowledge is tsiuptedi ,
strong, because it relies on the knowledge of the entire community.
Xavante Cyclical Laws of Numerical Succession
Unlike the Euclidian definition of a unit as “that by virtue of which each of the things
that exist is called one,” among dialectical societies of central Brazil I would suggest
an alternative explanation. Each of the things that exist is called two - maparané -
or a couple, because it is necessarily formed by a pair of ones or mitsi , the lonely
self. As mentioned above, man/woman, house/patio, village/forest, and human/spirit
are only a few of the paired moieties that form, each one of them, a unit . Without
the woman, the man is nothing but half of a unit, or self, because man and woman
together form the fundamental unitary value.
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