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The Ishango Bone – Is This
The World’s Oldest Mathematical Artefact?
Most people think that the study of
mathematics has its origins in Ancient Egypt and Babylonia,
but this view was dramatically challenged in the 1950’s with
the discovery of a small animal bone, inscribed
with markings that appear to represent numbers.
This artefact was discovered in the small African
fishing village of Ishango, on the border of Zaire and Uganda
by the Belgian geologist Jean de Heinzelin.
The Ishango Bone now lies at the Museum of Natural Sciences in Brussels, and
has been dated to around 20,000 BC. It is thought to be the
oldest mathematical artefact ever discovered.
The
Bone
At first glance the bone appears to
be a simple writing tool. It is 10 cm long, and at one
end is embedded with a piece of quartz thought to be for
engraving and tattooing. Closer examination reveals a series
of notches running up the side of the bone, in three
columns.
The notches are clustered together
as shown below: |
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The middle column begins with 3
notches, and then doubles to 6 notches. The process is
repeated for the number 4, which doubles to 8 notches, and
then reversed for the number 10, which is halved to 5 notches.
This suggests that the layout of numbers is not purely random
and instead suggests some understanding of the principle of
multiplication and division by 2. The bone may therefore have
been used as a counting tool for simple mathematical
procedures.
This view is further supported by
looking at the number of notches on either side of the central
column. The numbers on both the left and right column are all
odd numbers (9, 11, 13, 17, 19 and 21). Furthermore, the
numbers on the left column are all prime numbers, suggesting
some mathematical knowledge. The numbers on each side column
add up to 60, with the numbers in the central column adding up
to 48. Both of these numbers are multiples of 12, again
suggesting an understanding of multiplication and division.
Is this proof of
mathematical insight?
There are several critics who feel
that the mathematical claims for the Ishango bone are
exaggerated. They suggest that, as there are only 4 numbers on
the left hand column of the bone, it may be just a simple
coincidence that all of these are prime numbers. The most
compelling aspect of their argument is the fact that there is
no evidence of the knowledge of prime numbers before the
Classical Greek period, at least 10,000 years later.
It was suggested that the Ishango
bone, instead of being a counting device, may instead be some
sort of calendar, and there is some circumstantial evidence to
suggest this may be the case.
One of the oldest known calendars
was discovered in 1940 in caves in Lascaux, France, and are
consists of drawings representing the various phases of the
moon. They indicate the awareness of the 29 day cycle of the
moon and are the earliest known examples of a lunar calendar.
These drawings were painted at around 18,000 BC, making them
of a similar age to the Ishango Bone.
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13 dots and an empty
square. The dots represent
a lunar cycle, up until the
14th day when the moon
disappears from view,
represented by the
empty
square. |
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A horse, and a
series
of 29 dots. The dots
represent the 29
days
of the lunar cycle. |
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Lunar calendars represent one of
the earliest uses of numbers by mankind, and both the Isturitz
Baton (an antler bone found in Isturitz, France engraved with
markings) and the Blanchard Bone shown below (found in Abri
Blanchard, France) provide examples of the use of bones as
possible lunar calendars. Both of these findings can be dated
to around the time of the Ishango Bone. They contain markings
that coincide with 2, 4 and 5 month lunar phases, and
suggestions have been made that the notches on the Ishango
Bone correlate to a 6-month lunar calendar.
The suggestion is further
substantiated by the present day use of bones, strings and
other objects as lunar calendars in African civilizations. If
the Ishango Bone is indeed a lunar calendar, it would be one
of the earliest examples to be unearthed outside of Europe.
But most scholars do not consider recording dates to be proper
mathematics.
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The
Blanchard Bone
Plaque, discovered
in Abri Blanchard,
France.
This bone has been
dated back to around
25,000 - 32,000 BCE. |
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Calendar or
Calculator?
The Ishango Bone is clearly open to
interpretation and there is evidence both for and against it
being a calendar or some kind of mathematical device. The
puzzle will only be solved if other similar items can be
unearthed. Only then will we know if these notches represent
dates, calculations or coincidences.
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