Proto-Mathematics of the Ishango Bone in The DR Congo
Sub-Saharan Africa can claim to be the home of proto-mathematics, given that the two oldest mathematical artifacts, the Ishango and the Lebombo Bones, were found in the region. Today we shall focus on the Ishango Bone.
The Ishango Bone
The Ishango Bone was discovered in 1960 by Jean Heinzelin Braucourt, a Belgian national who was exploring the eastern fringes of the Democratic republic of Congo, then Belgian Congo. The bone was found among the ruins of a human settlement that was located near Lake Edward, an ancient settlement that had been buried by a volcanic eruption.
The bone, which through carbon dating has been estimated to be anywhere between 20,000 to 25,000 years old, is believed to be the second oldest mathematical artefact because of a series of notches etched on it. The notches were made by a quartz crystal attached on one end of the bone.
The Ishango bone has three columns with groups of notches that seem to suggest more than just keeping a simple tally.
The notches on the left column consist of the prime numbers 11, 13, 17 and 19, which add up to 60, similar to the odd numbers etched on the right column; 11, 21, 19 and 9. The middle column seems to display some understanding of multiplication and division, as the middle column starts with 3 notches, followed by 6 notches. There are then 4 notches, followed by 8. The third pair of notches begins with 10 notches, followed by 5. The last pair of notches is an odd one, as it begins with 5 notches, followed by 7, but if you carefully observe at the sequence of numbers in all columns, you should notice that each number is a product of mathematical manipulation using 2 as the base value.
Let me elucidate. The column on the left is thus: 11, 13, 17 and 19. The differences between each value is 2, 4 and 2 respectively.
The column in the middle denotes multiplication by 2 for the first 2 pairs, then division by 2 for the 3rd pair, and finally some more addition (and 5 and 7 are twin primes, as are 11 & 13, 17 &19 on the left column).
The values on the right column are 11, 21, 19, and 9, and the difference between them are 10, -2 and 10 respectively.
The total of values for the columns are 60 (left and right) and 48 (middle).
Its true purpose has been a matter of debate, with some scientists originally dismissing the notches as markings designed to improve the grip so that the bone could be used for some other non-mathematical purpose.
Some other researchers suggest that it could have been used to track a six month lunar cycle, while others contend it was developed by a woman keeping track of her periods.
Given that the bone contains all the odd prime numbers under 20, other researchers suggest that it was a table of prime numbers.
Whatever its true purpose, it is clear that it was used to keep some sort of count, millennia before Ancient Egypt and Babylon started engaging in basic Mathematics.
By Matengo Chwanya
Sources: Math.buffalo/ PSU/ Numberwarrior/
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