Download - The Ishango Bone
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The Ishango Bone
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When, where, who and what??
• The Ishango bone is a bone tool dating from about 18 000 to 20 000 B.C.
• Upper Paleolithic (a.k.a Late StoneAge), about 40 000 – 10 000 B.C.
• Homo Sapiens , hunter-gathers, bow and arrow, cave painting, and tool specialization
• Interesting note: Africa = Stone AgeEurope = Upper Paleolithic
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Background• It is the fibula of a baboon with a sharp piece
of quartz fixed at one end.
• It is 10cm long.
• Contains a series of notches carved in groups on three rows running the length of the bone.
• Was it a writing tool, a “primitive” mathematical tool, an astronomical tool, or something different?
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• Found in 1960 in the then Belgian Congo, now the border between Uganda and The Democratic Republic of the Congo.
• Believed to be used by the Lake Edward Ishango fishing population.
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Interestingly enough, the Ishango Bone currently sits in the Royal Belgium Institute
of Natural Science.
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• The markings on rows (a) and (b) each add to 60.
• Row (b) contains the prime numbers between 10 and 20.
• Row (a) is quite consistent with a numeration system based on 10, since the notches are grouped as 20 + 1, 20 - 1, 10 + 1, and 10 - 1.
• Finally, row (c) seems to illustrate for the method of duplication (multiplication by 2)
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BUT ...
Alexander Marshack (an American Paleolithic archaeologist) concluded the Ishango was used as a lunar calendar.
Claudia Zaslavsky (an American ethnomathematician) concluded the creator of the Ishango was in fact a woman, who used the bone to track her menstrual cycle.
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The Yoruba Counting System
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The Yoruba people currently number over 15-30 million.
According to their legends they came from Upper Egypt and settled what is now Nigeria, Togo, and the Republic of Benin between 600 and 1000A.D.
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One of the most peculiar number scales in existence.
It is a base 20 system, many examples of which are found in western Africa.
It is unusual because it relies on subtraction to a great degree.
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The numbers from one to ten are represented with specific terms:
1. okan2. eji3. eta4. erin5. arunEtc.
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Numbers higher than 10 are represented using addition and subtraction termsFor example: 11, 12, 13 and 14 would be represented as:
10 + 1 or ookan laa10 + 2 or eeji laa 10 + 3 10 + 4
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Then the numbers 15 to 20 are represented using subtraction: 20 – 5 or eedogan20 – 4 or eerin din logan20 – 320 – 220 – 1
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Basically, you can add up to 4 to make a number. Anything over 5 must be
subtracted. I.e.: 14 = 10 + 4 so you are adding. 15 = 20 – 5 so you are
subtracting.
Adding -------------------------- 5--------------------------- Subtracting
Let’s try this together:
22 = 36 =
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Answers:22 = 20 + 2
36 = (20 x 2) – 4
Can you do it? Try to represent the number on your table in the Yoruba
system.
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