By Marcia Ascher
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Extra info for Ethnomathematics
T h e symbols are ours, not theirs. B ut, as often happens in m athem atics, if we assign our symbols w ith care, we can highlight logical and structural relationships that may otherwise escape us. It is the M a lekula who created the tracing systems but it is we who are introducing symbols in an attem pt to capture and convey the structure of their systems. One set of six nitus is characterized by three basic drawing motions that are variously com bined to give rise to a variety of figures. T h e nitus come from at least four islands and have diverse descriptions: a ra t’s track; a pig’s head; a type of nut; the m ark of the grandm other; octopus, food of the ghosts; and the stone on which is seated the ghost guarding the entrance to the Land o f the D ead.
T h e nitus in this group show the general tracing concept o f an iterated procedure com bined with system atic size modification. Also, the initial procedures, although differ ent, share the feature of almost having bilateral or fourfold sym m etry. In each, w hat interferes w ith the sym m etry is the size modification just at the end of the procedure. T h e th ird system is characterized by w hat I call a process algebra. T h e w ord algebra is used in its m ost fundam ental sense: there are variable entities that are operated upon in accordance w ith specific rules.
As before, order is significant— mother of the father is not the same as father of the mother. Some composites are ambiguous; the father of my sister-in-law can be my father-in-law or can be the father of my b ro th er’s wife. And the result of the composite brother of the brother is just the same as brother. The L o g i c of Ki n k e i a i i u n j • Tw o m others and two daughters sleep in the same room. T h ere are only three beds and each one sleeps on one of them . (Rio G rande do Sul, Brazil) • One day three brothers were going past a graveyard.