The Os of Ishango , also called Stick of Ishango, gone back closely to 23.000 years before our era, seems to be the oldest certificate of the practice of arithmetic in the history of humanity. The Belgian archeologist Jean de Heinzelin de Braucourt ossement put at the day this in 1950 at the edge of the Lac Edouard in the area of Ishango to the Belgian Congo, nowadays in Democratic republic of Congo, close to the Uganda. Ossement is in exposure to the Natural history museum of the Natural science with Brussels in Belgium.

It is about a bone of 10,2 cm coming from an animal not identified, discovered in layers of volcanic ash, which has at its top an enchased quartz fragment. Several notches are found organized in group on three columns. Although there exists that presumptions of its arithmetic nature, the bone is the subject of many interpretations.

Deciphering

The notches present on this bone were interpreted, according to the authors, like a prehistoric calculator, a lunar calendar or a prehistoric code bar. Jean de Heinzelin was the first to regard it as a Artéfact of interest for the history of mathematics. He compared it to a play of arithmetic and gave an arbitrary order to the various columns, that is to say: the first (b) , the second (c) and the third (A) while following the notations of the diagram below.

The inventor foot-note that the column (c) is compatible with a basic numbering system 10, owing to the fact that the notches are grouped there like 20 + 1,20 - 1,10 + 1,10 - 1. He also recognized, in column (A) , the writing in the order of the prime numbers ranging between 10 and 20, is: 11,13,17 and 19. Lastly, the column (b) seems to illustrate the method of duplication multiplication by 2 used in one period closer to us in the Egyptian multiplication; that is to say: 3 X 2 = 6 and 4 X 2 = 8.

One decade later the scientific journalist Alexander Marshack foot-note that the sum of all the numbers gave 60 for one or the other of the columns (A) and (c) , and 48 for the column (b) . These considerations led it to suggest that the bone of Ishango would be the oldest known lunar calendar.

J. of Heinzelin following its observations admits, in fact, that the paléo-mathematicians of Ishango had the knowledge of the prime numbers. Moreover certain continuators of work of J. of Heinzelin admit that insofar as these mathematicians had the practical knowledge of the prime numbers, they were also naturally to know the two theorems of arithmetic elementary following:

Theorem 1: For entire naturalness N, 2 (N + 1) = 2n + 2

Theorem 2: For entire naturalness N, 3n = 2n + N

More than like a mathematical play, the bone of Ishango seems to be presented in the form of an encrypted document (secret) calling upon arithmetic and founded on the prime numbers and duplications.

Recently, the astrophysicist Jean Paul Mbelek brought new observations:

1°) the sum of all the extreme numbers of the three columns is equal to 60 (10 + 20 + 30 = 60).

2°) the quantity of numbers of the column (b) is equal to the sum of the quantities of numbers of the columns (A) and (c) , is 8 (for a face) and 4 + 4 = 8 (for the other face) and which there exists a regularity stronger than one obtains while adding or by withdrawing the quantity of numbers appearing in a column from the total sum of this column.

3°) There exists a symmetry compared to the median passing by number 17 and number 10. He notes that indeed in the column (c) extremes (9 = 10 -1, 11 = 10 + 1) and means (19 = 20 - 1,21 = 20 + 1)

External bonds

• the Stick of Ishango… 23.000 years… the oldest mathematical object - royal Institute of the Natural science of Belgium
• Eric W. Weisstein. " Ishango Bone." From MathWorld--With Wolfram Web Resource.
• the incised bones of Ishango give birth to numeration in Africa, Le Monde, February 28th, 2007

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