The Ishango bone

The find

The Belgian geologist Jean de Heinzelin found the bone in 1950 at Ishango, a site on the shore of Lake Edward, near one of the sources of the Nile, in what was then the Belgian Congo (today the Democratic Republic of the Congo). It is a slender, dark bone tool cut with three columns of notches. It is kept at the Royal Belgian Institute of Natural Sciences in Brussels.

The bone was first thought to date from about 9000 to 6500 BCE. Later work on the site pushed its age back to more than 20,000 years.

What the notches show

The notches are not random scratches. They are cut in groups, and the groups in each column can be counted:

• One column holds groups of 11, 13, 17 and 19 notches, the four prime numbers between 10 and 20.
• Another holds 11, 21, 19 and 9, which can be read as 10 + 1, 20 + 1, 20 − 1 and 10 − 1.
• The third holds smaller groups, among them 3 and 6, and 4 and 8, which look like doubling.

The counts themselves are documented. What they mean is where scholars part ways.

Four readings

An arithmetic game. De Heinzelin, writing in Scientific American in 1962, saw the groups as evidence of a number system and simple arithmetic, perhaps based on ten.

A lunar calendar. The researcher Alexander Marshack examined the notches under a microscope and found that the cuts differ in angle and depth, which he took as a sign that they were made at different times. He proposed that the bone records the phases of the moon over about six months.

Base 12. The physicist Vladimir Pletser and the mathematician Dirk Huylebrouck argue that the column totals point to counting in twelves, and they note that some African counting systems recorded in the 20th century also use base 12. Pletser's 2012 paper proposes that the bone worked like a simple "slide rule".

A tally or a grip. Skeptics note that the "primes" could be coincidence, since a second bone from the same layer has marks that suggest no mathematics, and that some notches may simply have improved the grip. A blog in Communications of the ACM concludes that advanced mathematics behind the marks seems unlikely.

Why it is labeled Debated

Everyone agrees the Ishango bone is very old, carefully made and shows deliberate grouping. Whether it records the moon, practises arithmetic or simply counts something is not settled, and popular claims that it is "the first calendar" or "the oldest mathematical tool" go beyond what can be shown. It is still one of the earliest objects anywhere that may show people counting, and it comes from Central Africa.