Information about Ishango Bone

This image shows both the front and back of the Ishango bone.

The Ishango bone is a bone tool, dated to the Upper Paleolithic era, about 18000 to 20000 BC. It is a dark brown length of bone, the fibula of a baboon,^[1] with a sharp piece of quartz affixed to one end, perhaps for engraving or writing. It was first thought to be a tally stick, as it has a series of tally marks carved in three columns running the length of the tool, but some scientists have suggested that the groupings of notches indicate a mathematical understanding that goes beyond counting.

The Ishango bone was found in 1960 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo.^[2] It was discovered in the African area of Ishango, which was centered near the headwaters of the Nile River at Lake Edward (now on the border between modern-day Uganda and Congo). The lakeside Ishango population of 20000 years ago may have been one of the first counting societies, but it lasted only a few hundred years before being buried by a volcanic eruption.^[3]

The artifact was first estimated to originate between 9000 BC and 6500 BC.^[4] However, the dating of the site where it was discovered was re-evaluated, and is now believed to be more than 20,000 years old.^[5]^[6]

The Ishango bone is on permanent exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.^[7]

Meaning of the tally marks

Mathematical calculations?

Left column

Center column

Right column

The three columns of asymmetrically grouped notches imply that the implement was more functional than decorative. The Ishango grouping may have been used to construct a number system.

The central 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. These numbers then, are not purely random and instead suggests some understanding of the principle of multiplication and division by two. The bone may therefore have been used as a counting tool for simple mathematical procedures.

Furthermore, the number of notches on either side of the central column may indicate more counting prowess. The numbers on both the left and right column are all odd numbers (9, 11, 13, 17, 19 and 21). The numbers in the left column are all of the prime numbers between 10 and 20 (which form a prime quadruplet), while those in the right column consist of 10 + 1, 10 - 1, 20 + 1 and 20 - 1. 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.^[8]

Lunar calendar?

Alexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month lunar calendar.^[8] Claudia Zaslavsky has suggested that this may indicate that the creator of the tool was a woman, tracking the lunar phase in relation to the menstrual cycle.^[9]^[10]

Similar finds

Several tally sticks predate the Ishango bone, and cuts on sticks or bones have been found worldwide. The Lebombo bone, a 37000-year-old baboon fibula was found in Swaziland. A 32000-year-old wolf tibia with 57 notches, grouped in fives, was found in Czechoslovakia in 1937.

References

1. ^ A very brief history of pure mathematics: The Ishango Bone University of Western Australia School of Mathematics - accessed January 2007.
2. ^ de Heinzelin, Jean: "Ishango", Scientific American, 206:6 (June 1962) 105--116.
3. ^ Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.
4. ^ Gerdes, Paulus (1991): On The History of Mathematics in Africa South of the Sahara; African Mathematical Union, Commission on the History of Mathematics in Africa.
5. ^ Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
6. ^ Brooks, A.S. and Smith, C.C. (1987): "Ishango revisited: new age determinations and cultural interpretations", The African Archaeological Review, 5 : 65-78.
7. ^ Exhibition at the Royal Belgian Institute of Natural Sciences, Brussels, Belgium.
8. ^ Williams, Scott W.: "Mathematicians of the African Diaspora" The Mathematics Department of The State University of New York at Buffalo.[1]
9. ^ Zaslavsky, Claudia: Africa Counts: Number and Pattern in African Culture, L. Hill, 1979.
10. ^ Zaslavsky, Claudia: "Women as the First Mathematicians", International Study Group on Ethnomathematics Newsletter, Volume 7 Number 1, January 1992.

External links

Bone tools have been documented from the advent of Homo Sapiens and are also known from Homo Neanderthalis contexts. Bone is a ubiquitous material in hunter-gatherer societies even when other tool materials were scarce or unavailable.
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Upper Paleolithic (or Upper Palaeolithic) is the third and last subdivision of the Paleolithic or Old Stone Age as it is understood in Europe, Africa and Asia. Very broadly it dates to between 40,000 and 10,000 years ago, roughly coinciding with the appearance of "high"
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For other uses see fibula (disambiguation)

The fibula or calf bone is a bone located on the lateral side of the tibia, with which it is connected above and below.
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A tally (or tally stick) was an ancient memory aid device to record and document numbers, quantities, or even messages. While the origin of this technique is lost in prehistory, archaeological proof of the existence of such devices is ample.
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Tally marks are an implementation of the unary numeral system. They are a form of numeral used for counting. They allow updating written intermediate results without erasing or discarding anything written down.
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Jean de Heinzelin de Braucourt (6 August 1920 – 4 November 1998) was a Belgian geologist who worked mainly in Africa. He worked at the Universities of Ghent and Brussels. He gained international fame in 1960 when he discovered the Ishango Bone.
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The Belgian Congo was the formal title of present-day Democratic Republic of the Congo (DRC) between King Leopold II's formal relinquishment of personal control over the state to Belgium on 15 November 1908, to the dawn of Congolese independence on 30 June 1960.
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Africa is the world's second-largest and second most-populous continent, after Asia. At about 30,221,532 kmÂ² (11,668,545 sq mi) including adjacent islands, it covers 6% of the Earth's total surface area, and 20.4% of the total land area.
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Situated on the Northern Shores of Lake Edward in the Democratic Republic of the Congo, Ishango is a sub-station of Virunga National Park. The station was created in the 1950s and is famous for many reasons:

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Origin Africa
Mouth Mediterranean Sea
Basin countries Sudan, Burundi, Rwanda, DR Congo, Tanzania, Kenya, Uganda, Ethiopia, Egypt
Length 6,650 km (4,132 mi)
Source elevation 1,134 m (3,721 ft)

Avg.
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Coordinates Coordinates:

Primary sources Nyamugasani
Ishasha
Rutshuru
Rwindi

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Motto
"For God and My Country"
Anthem
Oh Uganda, Land of Beauty

Capital Kampala

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Motto
Justice – Paix – Travail (French)
"Justice – Peace – Work"
Anthem
Debout Congolais
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Royal Belgian Institute of Natural Sciences is a museum in the Belgian capital of Brussels dedicated to natural history. Its most important pieces are 30 fossilized Iguanodon skeletons, which were discovered in 1878 in Bernissart.
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Brussels
Bruxelles / Brussel
Grand Place / Grote Markt

Flag
Seal
Nickname: European Union capital, Comic City
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Motto
Eendracht maakt macht (Dutch)
L'union fait la force" (French)
Einigkeit macht stark
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Asymmetry is the absence of, or a violation of, a symmetry.

Asymmetry in organisms

Due to how cells divide in organisms, asymmetry in organisms is fairly usual in at least one dimension, with biological symmetry also being common in at least one dimension.
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number system is a set of numbers, (in the broadest sense of the word), together with one or more operations, such as addition or multiplication.

Examples of number systems include: natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex
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Multiplication is the mathematical operation of adding together multiple copies of the same number. For example, four multiplied by three is twelve, since three sets of four make twelve:

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In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication.

Specifically, if c times b equals a, written:

where b is not zero, then a
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In mathematics, the parity of an object refers to whether it is even or odd.

The formal definition of an odd number is an integer of the form n=2k +1, where k is an integer. The definition of an even number is n=2k where k is an integer.
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In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid in about 300 BC.
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A prime quadruplet (sometimes called prime quadruple) is four primes of the form .^[1] It is the closest four primes above 3 can be together, because one of the numbers is always divisible by 3.
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Alexander Marshack (April 4, 1918 – December 20, 2004) was an American independent scholar and Paleolithic archaeologist. He was born in The Bronx and earned a bachelor's degree in journalism from City College of New York, and worked for many years for Life (magazine).
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lunar calendar is a calendar in many cultures that is oriented at the moon phase.

This is normally done by having a month which corresponds to a lunation so that the day of month indicates the moon phase. If a calendar tracks the seasons, it is also a lunisolar calendar.
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Claudia Zaslavsky (January 12, 1917 – January 13, 2006) was an American educator and ethnomathematician. She advanced the study of the links between mathematics and world cultures, especially with her pioneering book Africa Counts
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Lunar phase refers to the appearance of the illuminated portion of the Moon as seen by an observer, usually on Earth. The lunar phases vary cyclically as the Moon orbits the Earth, according to the changing geometry of the Earth, Moon, and Sun.
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The menstrual cycle is a recurring cycle of physiologic changes that occurs in the females of several mammals, including human beings and other apes.^[1] Humans are the only species that has a menstrual cycle with concealed ovulation.
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The lebombo bone is the oldest known mathematical artifact.

It dates from 35000 BC and consists of 29 distinct notches that were deliberately cut into a baboon's fibula. It was discovered within a cave in the Lebombo mountains of Swaziland.
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