The Ishango bone, discovered at the "Fisherman Settlement" of Ishango in the Democratic Republic of Congo, is a

bone tool In archaeology, a bone tool is a tool created from bone. A bone tool can conceivably be created from almost any bone, and in a variety of methods. Bone tools have been documented from the advent of ''Homo sapiens'' and are also known from ''Hom ...

and possible mathematical device that dates to the

Upper Paleolithic The Upper Paleolithic (or Upper Palaeolithic) is the third and last subdivision of the Paleolithic or Old Stone Age. Very broadly, it dates to between 50,000 and 12,000 years ago (the beginning of the Holocene), according to some theories coin ...

era. The curved bone is dark brown in color, about 10 centimeters in length, and features a sharp piece of

quartz Quartz is a hard, crystalline mineral composed of silica ( silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall chemical f ...

affixed to one end, perhaps for engraving. Because the bone has been narrowed, scraped, polished, and engraved to a certain extent, it is no longer possible to determine what animal the bone belonged to, although it is assumed to belong to a mammal.Association pour la diffusion de l'information archéologique/Royal Belgian Institute of Natural Sciences, Brussels (n.d.). "Have You Heard of Ishango?" (PDF). ''Natural Sciences''. The ordered engravings have led many to speculate the meaning behind these marks, including interpretations like mathematical significance or astrological relevance. It is thought by some to be a

tally stick A tally stick (or simply tally) was an ancient memory aid device used to record and document numbers, quantities and messages. Tally sticks first appear as animal bones carved with notches during the Upper Palaeolithic; a notable example is the ...

, as it features a series of what has been interpreted as

tally marks Tally marks, also called hash marks, are a unary numeral system ( arguably). They are a form of numeral used for counting. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate ...

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. Others argue 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. Other speculations include the engravings on the bone serving as a lunar calendar. Dating to 20,000 years before present, it is regarded as the oldest mathematical tool to humankind, with the possible exception of the approximately 40,000-year-old

Lebombo bone The Lebombo bone is a bone tool made of a baboon fibula with incised markings discovered in the Lebombo Mountains located between South Africa and Eswatini. Changes in the section of the notches indicate the use of different cutting edges, which the ...

from southern Africa.

History

Archaeological discovery

The Ishango bone was found in 1950 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the

Belgian Congo The Belgian Congo (french: Congo belge, ; nl, Belgisch-Congo) was a Belgian colony in Central Africa from 1908 until independence in 1960. The former colony adopted its present name, the Democratic Republic of the Congo (DRC), in 1964. Colo ...

.de Heinzelin, Jean: "Ishango", ''

Scientific American ''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...

'', 206:6 (June 1962) 105--116. It was discovered in the area of Ishango near the Semliki River.

Lake Edward Lake Edward (locally Rwitanzigye or Rweru) is one of the smaller African Great Lakes. It is located in the Albertine Rift, the western branch of the East African Rift, on the border between the Democratic Republic of the Congo (DRC) and Uganda, ...

empties into the Semliki which forms part of the headwaters of the

Nile River The Nile, , Bohairic , lg, Kiira , Nobiin: Áman Dawū is a major north-flowing river in northeastern Africa. It flows into the Mediterranean Sea. The Nile is the longest river in Africa and has historically been considered the longest riv ...

(now on the border between modern-day

Uganda }), is a landlocked country in East Africa. The country is bordered to the east by Kenya, to the north by South Sudan, to the west by the Democratic Republic of the Congo, to the south-west by Rwanda, and to the south by Tanzania. The ...

and

D.R. Congo The Democratic Republic of the Congo (french: République démocratique du Congo (RDC), colloquially "La RDC" ), informally Congo-Kinshasa, DR Congo, the DRC, the DROC, or the Congo, and formerly and also colloquially Zaire, is a country in ...

). Some archaeologists believe the prior inhabitants of Ishango were a "pre-sapiens species". However, the most recent inhabitants, who gave the area its name, have no immediate connections with the primary settlement, which was "buried in a volcanic eruption". On an excavation, de Heinzelin discovered a bone about the "size of a pencil" amongst human remains and many stone tools in a small community that fished and gathered in this area of Africa. Professor de Heinzelin brought the Ishango bone to

Belgium Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to ...

, where it is now stored in the treasure room of the Royal Belgian Institute of Natural Sciences in Brussels. Several molds and copies were created from the petrified bone in order to preserve the delicate nature of the fragile artifact while being exported. A written request to the museum is required to see the artifact, as it is no longer on display for the public eye.

Dating

The artifact was first estimated to have originated between 9,000BC and 6,500BC, with numerous other analyses debating the bone to be as old as 44,000 years. However, the dating of the site where it was discovered was re-evaluated, and it is now believed to be about 20,000 years old (dating from between 18,000BC and 20,000BC).Davidson, I. (1993). The Roots of Civilization: The Cognitive Beginnings of Man's First Art, Symbol and Notation. Alexander Marshack. American Anthropologist. The dating of this bone is widely debated in the archaeological community as the ratio of Carbon-14 isotopes was upset by nearby volcanic activity.

Interpretations

Mathematical

The 168 etchings on the bone are ordered in three parallel columns along the length of the bone, each marking with a varying orientation and length. The first column, or central column along the most curved side of the bone, is referred to as the M column, from the French word (middle). The left and right columns are respectively referred to as G and D, or (left) and (right) in French. The parallel markings have led to various tantalizing hypotheses, such as that the implement indicates an understanding of decimals or prime numbers. Though these propositions have been questioned, it is considered likely by many scholars that the tool was used for mathematical purposes, perhaps including simple mathematical procedures or to construct a

numeral system A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbo ...

. Discoverer of the Ishango bone, de Heinzelin, suggested that the bone was evidence of knowledge of simple arithmetic, or at least that the markings were "deliberately planned". He based his interpretation on archaeological evidence, comparing "Ishango harpoon heads to those found in northern Sudan and ancient Egypt". This comparison led to the suggestion of a link between arithmetic processes conducted at Ishango with the "commencement of mathematics in ancient Egypt." The third column has been interpreted as a "table of prime numbers", as column G appears to illustrate prime numbers between 10 and 20, but this may be a coincidence. Historian of mathematics Peter S. Rudman argues that prime numbers were probably not understood until the early Greek period of about 500 BC, and were dependent on the concept of division, which he dates to no earlier than 10,000 BC. More recently, mathematicians Dirk Huylebrouck and Vladimir Pletser have 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. However, they have concluded that there is not sufficient evidence to confirm an understanding of prime numbers during this time period. Anthropologist Caleb Everett has also provided insight into interpretations of the bone, explaining that "the quantities evident in the groupings of marks are not random", and are likely evidence of prehistoric numerals. Everett 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".

Astronomical

Alexander Marshack, an archaeologist from Harvard University, speculated that the Ishango bone represents numeric notation of a six-month

lunar calendar A lunar calendar is a calendar based on the monthly cycles of the Moon's phases ( synodic months, lunations), in contrast to solar calendars, whose annual cycles are based only directly on the solar year. The most commonly used calendar, t ...

after conducting a "detailed microscopic examination" of the bone. This idea arose from the fact that the markings on the first two rows adds up to 60, corresponding with two lunar months, and the sum of the number of carvings on the last row being 48, or a month and a half. Marshack generated a diagram comparing the different sizes and phases of the moon with the notches of the Ishango bone. There is some circumstantial evidence to support this alternate hypothesis, being that present day African societies utilize bones, strings, and other devices as calendars. However, critics in the field of archaeology have concluded that Marshack's interpretation is flawed, describing that his analysis of the Ishango bone confines itself to a simple search for a pattern, rather than an actual test of his hypothesis. This has also led

Claudia Zaslavsky Claudia Zaslavsky (January 12, 1917 – January 13, 2006) was an American mathematics teacher and ethnomathematician. Life She was born Claudia Natoma Cohen (later changed to Cogan) on January 12, 1917, in Upper Manhattan in New York City an ...

to suggest that the creator of the tool may have been a woman, tracking the

lunar phase Concerning the lunar month of ~29.53 days as viewed from Earth, the lunar phase or Moon phase is the shape of the Moon's directly sunlit portion, which can be expressed quantitatively using areas or angles, or described qualitatively using the t ...

in relation to the

menstrual cycle The menstrual cycle is a series of natural changes in hormone production and the structures of the uterus and ovaries of the female reproductive system that make pregnancy possible. The ovarian cycle controls the production and release of eggs ...

Cautionary tales

While it is important to attempt to identify the potential meaning behind this piece of material culture, it is vital to not become wrapped up in dubious hypotheses. Mathematician Olivier Keller warns against the urge to project our modern culture of viewing numbers everywhere onto the Ishango bone. Keller exclaims that this practice encourages observers to negate and possibly ignore alternative symbolic materials, those which are present in a range of media (on human remains, stones and cave art) from the Upper Paleolithic era and beyond which also deserve equitable investigation. Dirk Huylebrouck, in a review of the research on the object, favors the idea that the Ishango bone had some advanced mathematical use, stating that "whatever the interpretation, the patterns surely show the bone was more than a simple tally stick." He also remarks that "to credit the computational and astronomical reading simultaneously would be far-fetched", quoting mathematician George Joseph, who stated that "a single bone may well collapse under the heavy weight of conjectures piled onto it." Similarly, George Joseph, in "The Crest of the Peacock: Non-European Roots of Mathematics" also stated that the Ishango bone was "more than a simple tally." Moreover, he states that "certain underlying numerical patterns may be observed within each of the rows marked." But, regarding various speculative theories of its exact mathematical use, concluded that several are plausible but uncertain.