Page 52 - Msingi Afrika Magazine Issue 11
P. 52
MY AFRIKA
people. On encountering this prime numbers among African It is contended here that these
same prejudice he is robust in civilizations; even in the case of ancient Africans' early concept
his rejection: "As is well known, the treatment of ancient Egyp- of number was formed by their
languages exist in which the tian mathematical achievements. experience of recording by
numerals do not exceed 3 or 4. It For this reason, the ingenious making a mark with a stone tool.
has been inferred from this that achievements of the Ishango They conceived of multiplication
people speaking these languages mathematicians in inventing by 2 as the process of a number
are not capable of forming the the worlds first known sieve of making "copies" or replicas of it-
concept of higher numbers. I the prime numbers has been of self. It makes sense to expect that
think this interpretation of the course overlooked. the concept of multiplication
existing conditions is quite er- held by Stone Age people differs
roneous. ...just as soon as these 4. Copying as a Primitive from that of modern comput-
people find themselves in contact Concept of Multiplication in er age humans. In fact, their
with civilization, and when they Ishango Society concept of multiplication by 2
acquire standards of value that would be generated from the act
have to be counted, they adopt It has been a natural progression of making a mark, then making
with perfect ease higher numerals from the above outmoded yet a copy of that singular mark to
from other languages, and devel- still prevalent attitudes, that all denote 2 doubled from 1. Simi-
op a more or less perfect system research into the thinking of so larly, any number of tallies made
of counting." [13]. called primitive societies thus far by striking marks on a bone can
has always focused on abilities of be doubled by making a copy of
We see from the quotation of counting and simple arithmetic. these same tallies.
Boas who is sympathetic that No studies known to this author
nevertheless, there is still the to date entertain the possibili- To support the above conten-
underlying supposition of the ty that an ancient people other tion, we note that on the Ishango
absence of civilization. Similar- than Europeans might be capa- bone, in the middle column M,
ly, Levy-Bruhl who many might ble of actual mathematics and the number 10 is clearly ex-
assess as yet another sympathetic abstract thought. We have already pressed as composed of two
scholar had a penchant for di- commented on the dismissal by copies of 5, hence they are
viding humanity in terms of the modern authors of the idea that displayed immediately below 10
"pre-logical" mentality of "lower prime number awareness might as below
societies" and the "logical" men- have existed before the classical
tality of civilized peoples [14]. period of the ancient Greeks. 10
Thus we find no possible expla-
Given this historical backdrop it nations or models for methods 5
is no surprise that credit is never of multiplication or division in
given to anything ingenious in so called primitive societies in 5
African culture to do with math- literature, since even to entertain
ematics or science. In fact the the idea is an apparent scientific To further support this notion of
topic of mathematical reasoning taboo. numbers composed of "copies"
is never even contemplated. At of another number, we note the
most, discussions on African We are thus forced to work from following observation by Pletser
people will centre on methods first principles in order to arrive and Huylebrouck [15] in their
of simple arithmetic, counting, at a theory of how the Stone 1999 paper: "A remarkable fact
but never abstract reasoning Age mathematicians of Ishango in the denominations and ges-
and mathematics. This is why might have achieved the feat of tures for the numbers from 6 to
mainstream scholars feel at ease multiplication by 2 or doubling 9 is that these can be formed by
with dogmatic assertions about by a process of copying or repli- different principles. Sometimes 6
the absence of awareness of cating stone tool records (marks). and 8 are expressed as 3+3 and
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