Post by anansi on Dec 2, 2010 9:58:18 GMT -5
This is part of that double system this is some really unique way of doing numbers
Doubling series in Africa
In some accounts authors have stated that Africans use a “primitive” number system in which they count by multiples of two.It is true that many cases of African arithmetic are based on multiples of two, but as we will see, base two systems are not crude artifacts from a forgotten past. They have surprising mathematical significance, not onlyin relation to African fractals, but to the western history of mathematics and computing as well.
The presence of doubling as a cultural theme occurs in many different African societies, and in many different social domains, connecting the sacredness of twins, spirit doubles, and double vision with material objects, like the blacksmith's twin bellows and the double iron hoe given in bridewealth (figure 7.3). Figure 7.4a shows the Ishango bone, which is dated around 8,000 years old and appears to show a doubling sequence. Doubling is fundamental to many of the counting systems of Africa in modern times as well. It is common, for example, to have the word for an even number 2N mean "N plus N" (e.g. the number 8 in the Shambaa language of Tanzania is “ne na ne,” literally “four and four.”)A similar doubling takes place for the precisely articulated system of number hand gestures (figure 7.4b); for example “four” represented by two groups of two fingers, and “eight” by two groups of four. Petitto (1982) A similar doubling takes place for the precisely articulated system of number hand gestures (figure 7.4b); for example “four” represented by two groups of two fingers, and “eight” by two groups of four. Petitto (1982) found that doubling was used in multiplication and division techniques in west Africa (figure 7.4c).Gillings (1972) details the persistent use of powers of two in ancient Egyptian mathematics as well, andZaslavsky (1973) shows archaeological evidence suggesting that ancient Egypt’s use of base-two calculations derived from the use of base-two in sub-Saharan Africa.
Doubling practices were also used by African descendants in the Americas. Benjamin Banneker, for example, made unusual use of doubling in his calculations, which may have derived from the teachings of his African father and grandfather (Eglash 1997c). Gates (1988) examined the cultural significance of doubling in west African religions such as vodun, and its transfer to “voodoo” in the Americas
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