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 Age
Europe = 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. okan
2. eji
3. eta
4. erin
5. arun
Etc.
Numbers higher than 10 are represented
using addition and subtraction terms
For example:
11, 12, 13 and 14 would be represented as:
10 + 1
10 + 2
10 + 3
10 + 4
or
or
ookan laa
eeji laa
Then the numbers 15 to 20 are represented
using subtraction:
20 – 5
20 – 4
20 – 3
20 – 2
20 – 1
or
or
eedogan
eerin din logan
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.