Ishango bone

The Ishango bone is a Stone Age artifact that was by the Belgian archaeologist Jean de Heinzelin de Brau Court in 1950 in what was then the Belgian Congo, now the Democratic Republic of the Congo, discovered. Is an approximately 10 cm long bones, on the plurality of sets of notches are disposed in three columns. The purpose of the notches are unclear, There is speculation that the bone was used as a kind of slide rule. A function as a calendar is also proposed.

The age of the artifact is determined today at about 20,000 years. It is located in the Belgian Museum of Natural Sciences in Brussels.

  • 4.1 Notes and references

Location and date

The site Ishango is located near the Congolese- Ugandan border on the northwestern shore of Lake Edward. In the hilly terrain at the outflow of the Semliki Jean de Heinzelin led in the 1950s by excavation of a Stone Age living space, which had been destroyed by a volcanic eruption. Found mainly human and animal remains, stone tools and spear tips. The increased by the volcanic eruption concentration of the carbon isotope 12C in the area prevented a precise age determination of the finds by means of the C- 14 method. Based on archaeological and geological evidence associated de Heinzelin Ishango as Mesolithic dwelling-place one from the period between 9,000 BC and 6,500 BC.

1985 were again held in excavations Ishango and the surrounding area, where among other more shells were found molluscs. The analysis of these shells using the amino acid Razemisierungs method yielded an age of settlement of at least 20,000 years. Even taking into account the warm African climate is an age of less than 10,000 years is extremely unlikely, so Ishango is now attributed to the Upper Paleolithic.

Description

The Ishango bone is about 10 cm long, curved bones of animals of oval cross section. At its narrower end of a piece of quartz is mounted so that it could have served as a kind of stylus. The assignment of the bone to a specific species is still pending; are unconfirmed suspicions, he comes of the phalanx of a lion.

Almost the entire surface of the bone is provided with fine transverse grooves of different length. The notches can be summarized in 16 groups, which in turn are arranged in three columns. The middle column contains ( viewed from the quartz tip ) 3, 6, 4, 8, 10 ( or 9), 5, 5, 7 ( sequence A100000 in OEIS ) scores, the left column 11, 13, 17, 19 and the right column 11, 21, 19, 9 notches.

Interpretations

The beginnings of the actual counting and calculating - detached from the pure notation of concrete objects - are generally considered to be found from sedentation during the Neolithic revolution. Earlier provided with ornaments or notches artifacts be considered as evidence of a precursor of counting, since the presence of an abstract concept of number is not likely before the Neolithic. The arrangement of the notches of the Ishango bone leads to the conclusion that it is in the pattern is not purely random, and provides space for interpretations, but according to the current state of research must be considered speculative.

Arithmetic game

Although Jean de Heinzelin conceded the possibility of a random pattern, but stopped himself the bone for an " arithmetic game," simple calculations or notations that are based on the decimal system. Basis for his theory were the following observations:

  • The pairs (3,6 ), ( 4,8 ) and ( 10.5 ) the middle column are formed of a number and its double. The last two numbers 5 and 7, however, do not fit into this scheme.
  • The groups in the right column form exactly the numbers 10 ± 1 and 20 ± 1
  • The left column contains exactly the prime numbers 10 to 20

Moon Calendar

Another approach comes from the American journalist Alexander Marshack, who wrote a book on the history of science on behalf of NASA and in this context could examine the Ishango bone microscopically. He noted differences in the depth, shape and orientation of the notches and saw himself in a position to bring the scores in accordance with the lunar phases. In his view, it is in the artifact clearly a lunar calendar. For Marshack's theory is that the number of notches of the two outer columns will each have a 60, so add up almost exactly the number of days between two lunar months and that parallels can be drawn to calendars of modern hunter- gatherer cultures.

Marshack's work is controversial, the Italian anthropologist Francesco D' Errico has about the methodology as " unscientific " back. Marshack's thesis was supported, however, by the American educator and mathematician Claudia Zaslavsky Ethno, which led as a reason for the timing in the rhythm of the moon phases to the menstrual cycle of women.

Rechenstab

Vladimir Pletser, scientists at ESA, reached in 1999, Heinzelins interpretation of Ishango bone as a mathematical object on again. He noted that can be the numbers of the outer columns gain by adding consecutive numbers of the middle column. If one reads the uncertain number of fifth middle group as 9 instead of 10, for example, the middle groups of three to five add up to 21 groups of five to seven to 19, both values ​​that are found to be approximately the same in the right column. Pletser concluded that the bone was used as a slide rule, on which one can read off the sum of certain numbers by simply turning. The addition table, the results from this hypothesis, however, has gaps. Pletser had to add some additional invoices numbers to represent all the values ​​of the two outer columns.

In contrast to de Heinzelin Pletser assumed in its interpretation of a mixed number system on the bases 3, 4 and - based base 12 - derived from it. The base 10 may have been used in parallel. Advantage of this assumption is that to explain the numbers 11, 13, 17 and 19 of the left column of the concept of prime number must not be troubled, but that they, together with the isolated for de Heinzelin appearing last two numbers 5 and 7, the middle column ½ • 12 ± 1 arise as ½ • 12 ± 1, 12 ± 1 • 1 and 1.

Origin of the duodecimal

The Belgian mathematician Dirk Huylebrouck, which together represents the slide rule hypothesis with Pletser, is of the view that in Ishango bones of the origin of the duodecimal and Related Hexagesimalsystems can be seen.

The bases of twelve and sixty are found among the Sumerians, Assyrians, Babylonians and Egyptians, and later in ancient Greece. The exact origin of these scoring systems is considered as yet unexplained.

Huylebrouck refers to studies of British anthropologist Northcote Whitridge Thomas, who had reported in 1920 on the use of base twelve in the number of different words Plateau languages ​​in West Africa. Thomas had raised the question in his report, as - if you assume no independent origin of the counting methods - this use in West Africa could be related to the Mesopotamian civilizations. Huylebrouck believes to have found the answer in de Heinzelins work. This had followed the temporal and geographical spread of Ishango culture by comparing the findings of harpoon points and essentially it found two directions: One branch led to West Africa, the other down the Nile to Egypt. The duodecimal system could be reached on these paths of Ishango from one hand to West Africa, and partly via Egypt to Mesopotamia, the Ishango bone would be in this case the searched Thomas link.

Reproductive cycle of cicadas

Cicadas mate in prime years ( 11,13,17,19 ), which corresponds mainly indicated on the bone primes.

Literature and sources

  • Jean de Heinzelin: Ishango. In: Scientific American 206 (1962), pp. 105-116.
  • Dirk Huylebrouck: The Bone did Began the Space Odyssey. In: The Mathematical Intelligencer 18 (1996 ), pp. 56-60.
  • Dirk Huylebrouck: L' os Ishango, l' objet mathématique le plus ancien. ( o.J. ) PDF; 0.4 MB
  • Vladimir Pletser, Dirk Huylebrouck: The Ishango artifact: the missing base 12 link. In: Forma 14 (1999 ), pp. 339-346. PDF; 1.6 MB
Semliki River Ethnomathematics European Space Agency History of the Assyrian people
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