The Ishango Artefact: the Missing Base 12 Link
1999; Volume: 14; Issue: 4 Linguagem: Inglês
ISSN
2432-4523
AutoresVladimir Pletser, Dirk Huylebrouck,
Tópico(s)History and Theory of Mathematics
ResumoIn 1950, the Belgian Prof. J. de Heinzelin discovered a bone at Ishango, a Congolese village at the sources of the Nile. The artefact has patterned notches, making it the first tool showing logic reasoning. Here, Pletser proposes his new slide rule interpretation, rejecting former arithmetic game and calendar explanations. Counting methods of present day civilisations in Africa provide circumstantial evidence for Pletser's hypothesis. Moreover, it confirms de Heinzelin's archaeological evidence about relationships between Egypt, West Africa and Ishango. It points towards the use of the base 12, which anthropologist Thomas had studied in West Africa some 80 years ago. It appears that the Ishango artefact is the missing link Thomas was looking for. These results where obtained independently; for instance, space scientist Pletser just stumbled over the Ishango artefact as he favoured the project of carrying it into space, as an African equivalent of the Katachi-symmetry relationship. 1. The Ishango bone The Ishango bone is a 10-cm long curved bone, first described by its discoverer, J. de Heinzelin. He found the tiny bone about fifty years ago, among harpoon heads at a village called Ishango not far from the present border between Congo and Uganda. The fishermen settlement lays on the shores of the Semliki River, one of farthest the sources of the Nile. The bone has a fragment of quartz on the top, most probably for engraving purposes. About 20,000 years old (or even 90,000 years, following other indications), it is the oldest mathematical tool. The bone carries notches distributed in three columns along the bone length. The central column along the most curved side of the bone, is called the M column (French: Milieu), while G and D indicate the Left ( Gauche) and Right (Droite) columns. The M column shows eight groups of respectively 3, 6, 4, 8, 9 or 10, 5, 5, and 7 notches. The G and D columns each show four groups respectively of 11, 13, 17, 19 and of 11, 21, 19, 9 notches. The groups are labelled with an upper case letter for the column and a lower case letter for the actual group, together with the number of notches between parentheses: Ma(4) to Mh(7), Ga(11) to Gd(19), and Da(11) to Dd(9). The notches are approximately parallel
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