The Ishango bone is a bone tool and possible mathematical object, dated to the Upper Paleolithic era. It is a dark brown length of bone, the fibula of a baboon, with a sharp piece of quartz affixed to one end, perhaps for engraving. It is thought by some to be a tally stick, as it has a series of what has been interpreted as tally marks carved in three columns running the length of the tool, though it has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason. It has also been argued that the marks on the object are non-random and that it was likely a kind of counting tool and used to perform simple mathematical procedures. The Ishango bone was found in 1960 by BelgianJean de Heinzelin de Braucourt while exploring what was then the Belgian Congo. It was discovered in the area of Ishango near the Semliki River. Lake Edward empties into the Semliki which forms part of the headwaters of the Nile River. The bone was found among the remains of a small community that fished and gathered in this area of Africa. The settlement had been buried in a volcanic eruption. The artifact was first estimated to have originated between 9,000 BC and 6,500 BC. However, the dating of the site where it was discovered was re-evaluated, and it is now believed to be more than 20,000 years old. The Ishango bone is on permanent exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
Mathematical interpretations
The etchings on the bone are in three columns with marks asymmetrically grouped into sets, leading to "various tantalizing hypotheses" such as that the implement indicates an understanding of decimals or prime numbers. Though these propositions are in doubt, it is considered likely by some scholars that the tool was used for simple mathematical procedures or to construct a numeral system. The third column has been interpreted as a "table of prime numbers", but it is more likely to be a coincidence. Historian of mathematics Peter S. Rudman argues that prime numbers were probably not understood until about 500 BC, and were dependent on the concept of division, which he dates to no earlier than10,000 BC. Alexander Marshack speculated that the Ishango bone represents a six-month lunar calendar. This has led Claudia Zaslavsky to suggest that the creator of the tool may have been a woman, tracking the lunar phase in relation to the menstrual cycle. This is countered with the argument that Marshack overinterprets the data and that the evidence does not support lunar calendars. More recently Vladimir Pletser has proposed that the Ishango bone is a counting tool using the base 12 and sub-bases 3 and 4, and involving simple multiplication, somewhat comparable to a primitive slide rule." Caleb Everett has also stated of the object, that "the quantities evident in the groupings of marks are not random", and are likely evidence of prehistoric numerals. He suggests that the first column may reflect some "doubling pattern" and that the tool may have been used for counting and multiplication and also possibly as a "numeric reference table".
Second bone
During earlier excavations at the Ishango site in 1959, another bone was also found. It is lighter in color and was scraped, thinned, polished, and broken on one end, revealing it to be hollow. The artifact possibly held a piece of quartz like the more well-known bone or it could have been a tool handle. The 14-cm long bone has 90 notches on six sides, which are categorized as "major" or "minor" according to their length. Jean de Heinzelin interpreted the major notches as being units or multiples and the minor notches as fractions or subsidiary. He believed the bone to be an "interchange rule between bases 10 and 12."
