Page 54 - Msingi Afrika Magazine Issue 11
P. 54
MY AFRIKA
So we write down our resulting namely: 4, 6, 8, 9, 10.
sequence of primes in the series
11- 20 as - All missing numbers from the sequence 10-20 (namely the numbers
composed of copies of others: 12, 14, 15, 16, 18, 20) are deducible
11 from operations continuing the method of doubling from 6 to 10, as
well as the results of previous doubling and additions illustrated.
13
Given the closeness of fit of the prime sieve theory with the data, one
17 is bound to ask why such a simple sieve theory has not been enter-
tained until now? We can only surmise that the negative predisposition
19 of scholarship noted earlier in respect of ancient people and in partic-
ular Africans is to blame. How else could this have been missed?
as required.
The feat of the ancient Ishango mathematicians in devising a tech-
6. Conclusion nique of sifting prime numbers from sequences of the natural num-
bers, using only the most basic tools of addition preceded by a prim-
The Ishango prime sieve theory itive form of multiplication is indeed remarkable. It is the hope that
is perhaps the most consistent this paper will go some way towards according to the ingenious math-
theory on the significance of the ematicians of Ishango the recognition, respect and seminal position in
Ishango bone markings yet pre- world mathematics history that they deeply deserve.
sented. This conclusion is based
on certain results established by
the proof of the Ishango mathe- 7. References
matical sieve:-
[1] De Heinzelin, J., Ishango, Scientific American 206, 6 June 1962, pp 105-114.
[2] Burton, D.M., Elementary Number Theory, McGraw-Hill, 1998, 44-46.
- All columns on the bone are [3] Pletser, V., Does the Ishango Bone indicate the knowledge of Base 12?An Interpre-
employed as essential parts of tation of a Pre-Historic Discovery. The First Mathematical Tool of Mankind. https://
the Ishango mathematical sieve www.researchgate.net/publication/222106237_Does_the_Ishango_Bone_Indicate_
Knowledge_of_the_Base_12_AnInterpretation_of_a_Prehistoric_Discovery_the_First_
- Every single number, every sin- Mathematical_Tool_ofHumankind.
[4] De Heinzelin, J., Ibid.
gle tally on the bone, is employed [5] Pletser, V. and Huylebrouck, D., The Ishango Artefact: The Missing Base 12 Link,
by the theory of the Ishango Forma, 14, 1999, 339-346
mathematical sieve. [6] Pletser, V., Does the Ishango Bone indicate the knowledge of Base 12?An Interpre-
tation of a Pre-Historic Discovery. The First Mathematical Tool of Mankind. https://
- There is no single marking on www.researchgate.net/publication/222106237_Does_the_Ishango_Bone_Indicate_
Knowledge_of_the_Base_12_AnInterpretation_of_a_Prehistoric_Discovery_the_First_
the bone that is not explained by Mathematical_Tool_ofHumankind.
the Ishango mathematical sieve. [7] Pletser, V. and Huylebrouck, D., Ibid.
[8] De Heinzelin, J., Ibid.
- Every number deduced in the [9] Marshack, A., The Roots of Civilization, McGraw-Hill, 1972.
middle calculation column (M) [10] Zaslavsky, C., Africa Counts: Number and Pattern in African Culture, Lawrence
Hill, 1973, p.10.
from the doubling of numbers 1 [11] Zaslavsky, C., Ibid, p.9.
to 5 (omitting 1 and 2), is a num- [12] Zaslavsky, C., op. cit.
ber eliminated from the sequence [13] Boas, F., The Mind of Primitive Man, Macmillan, 1938, p.218.
1,2,3,4,5,6,7,8,9,10 (numbers 1 [14] Levy-Bruhl, L., How Natives Think, New York: Washington Square Press,
and 2 omitted), leaving only the 1966. N.B.: Dr Amon Saba Saakana has informed me on more than one occasion that
Levy-Bruhl recanted on his "pre-logical" statement before his death; and this is hereby
prime sequence: 5, 7. The elim- acknowledged for the record.
inated numbers are those com- [15] Pletser, V. and Huylebrouck, D., Ibid. p.343.
posed of copies of others, and
are all exhibited in the column M *London-based Chair of the Society of African Earth Scientists, amateur number theo-
rist and finance administrator.
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