The Ishango Bone

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

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?

• 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.

Interestingly enough, the Ishango Bone currently sits in the Royal Belgium Institute

of Natural Science.

• 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)

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.

The Yoruba Counting System

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.

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.

The numbers from one to ten are represented with specific terms:

1. okan2. eji3. eta4. erin5. arunEtc.

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

Then the numbers 15 to 20 are represented using subtraction: 20 – 5 or eedogan20 – 4 or eerin din logan20 – 320 – 220 – 1

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 =

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.