Ishango bones

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Ishango bones

The Ishango bone is a Stone Age artefact that was discovered by the Belgian archaeologist and geologist Jean de Heinzelin de Braucourt (1920–1998) in 1950 in what was then the Belgian Congo, now the Democratic Republic of the Congo . It is about 10 cm long bone on which several groups of notches are arranged in three columns. The sense and purpose of the notches are unclear, according to speculations the bone was used as a kind of slide rule . A function as a calendar is also suggested.

The age of the artifact is now estimated to be around 20,000 years. It is located in the Belgian Museum of Natural Sciences in Brussels.

Site and dating

The Ishango site is located near the Congolese- Ugandan border on the northwest bank of Lake Eduard . In the hilly area at the outflow of the Semliki , Jean de Heinzelin carried out excavations in the 1950s of a Stone Age residential area that had been destroyed by a volcanic eruption. Mainly human and animal remains, stone tools and harpoon tips were found. The increased by the volcanic eruption concentration of the carbon - isotope 12 C in the ambient prevented an accurate age determination of the findings by means of the C-14 method . On the basis of archaeological and geological evidence, de Heinzelin arranged Ishango as a Mesolithic dwelling from the time between 9000 BC. BC and 6500 BC A.

In 1985 excavations took place again in Ishango and the surrounding area, during which, among other things, further shells of molluscs were found. The analysis of these shells using the amino acid racemization method showed that the settlement was at least 20,000 years old. Even taking into account the warm African climate, an age of less than 10,000 years is extremely unlikely, so that Ishango is now attributed to the Upper Paleolithic .

description

The division of the notches into groups. The quartz tip is in the picture above.

The ishango bone is a curved baboon bone approximately 10 cm long with an oval cross-section. A piece of quartz is attached to its narrower end so that it could have served as a kind of stylus .

Almost the entire surface of the bone is provided with fine, transverse notches of different lengths. The notches can be grouped into 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 ) notches, the left column 11, 13, 17, 19 and the right column 11, 21, 19, 9 notches.

Interpretations

The beginnings of actual counting and arithmetic - detached from the pure notation of concrete objects - are generally believed to be from the time of settling in the course of the Neolithic revolution . Earlier artefacts with ornaments or notches are regarded as evidence of a preliminary stage of counting, since the existence of an abstract number concept cannot be assumed before the Neolithic. The arrangement of the notches of the Ishango bone suggests that the pattern is not purely random, and offers room for interpretations, which, however, must be considered speculative according to current research.

Arithmetic game

Jean de Heinzelin admitted the possibility of a random pattern, but even considered the bone to be an "arithmetic game", simple calculations or notations based on the decimal system . The basis for his theory were the following observations:

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

Lunar calendar

Marshack's interpretation of the bone as a lunar calendar.

Another approach comes from the American journalist Alexander Marshack, who wrote a book on the history of natural sciences on behalf of NASA and was able to examine the Ishango bone microscopically in this context. He noticed differences in the depth, shape and orientation of the notches and was able to align the notches with the phases of the moon . In his view, the artifact is clearly a lunar calendar. Marshack's theory is supported by the fact that the number of notches in the two outer columns add up to 60, i.e. almost exactly the number of days in two lunar months, and that parallels can be drawn with the calendars of modern hunter-gatherer cultures.

Marshack's work is controversial; the Italian anthropologist Francesco D'Errico, for example, rejects the methodology as "unscientific". Marshack's thesis, however, was supported by the American pedagogue and ethnomathematist Claudia Zaslavsky, who cited the menstrual cycle of women as one reason for measuring time in the rhythm of the moon phases .

Slide rule

Pletser's addition table
M.   L. R.
3 + 6   + 2         =   11
1 + 6 + 4           = 11  
    4th + 6 + 3       = 13
    4th + 8 + 9       =   21st
      8th + 9       = 17th  
        9 + 5 + 5   =   19th
+ 2         + 7 + 5 + 5 = 19th  
            2 + 7 =     9
6th 12 12 24 30th 12 12 12   60 60
The missing entries for completeness are crossed out.

Vladimir Pletser, scientist at ESA , took up de Heinzelin's interpretation of the Ishango bone as a mathematical object in 1999. He noticed that the numbers in the outer columns can be obtained by adding consecutive numbers in the middle column. If you read the uncertain number of the fifth middle group as 9 instead of 10, for example, the middle groups three to five add up to 21, the groups five to seven add up to 19, both values ​​that are found at approximately the same level in the right column. Pletser concluded from this that the bone had served as a slide rule on which one could read the sum of certain numbers by simply turning it. The addition table resulting from this hypothesis has gaps, however. Pletser had to add additional numbers for some calculations in order to be able to display all values ​​in the two outer columns.

In contrast to de Heinzelin, Pletser assumes a mixed number system in his interpretation, which is based on bases 3, 4 and - derived from this - base 12. Base 10 may have been used in parallel. The advantage of this assumption is that to explain the numbers 11, 13, 17 and 19 in the left column, the term prime number does not have to be used, but that it is combined with the last two numbers 5 and 7 in the middle column, which for de Heinzelin appear isolated as ½ • 12 ± 1, 1 • 12 ± 1 and 1½ • 12 ± 1.

Origin of the duodecimal system

The Belgian mathematician Dirk Huylebrouck, who supports the slide rule hypothesis together with Pletser, is of the opinion that the origin of the duodecimal and the related hexagesimal system can be seen in the Ishango bone .

The bases twelve and sixty can be found with the Sumerians , Assyrians and Babylonians , later in ancient Greece. The exact origin of these counting methods is still unclear.

Huylebrouck refers to research by the British anthropologist Northcote Whitridge Thomas , who in 1920 reported the use of base twelve in numerals in various plateau languages in West Africa. In his report Thomas had raised the question of how - if one does not want to assume an independent origin of the counting methods - this use in West Africa could be related to the Mesopotamian high cultures. Huylebrouck believes he has found the answer in de Heinzelin's work. By comparing the finds of harpoon tips, he had followed the temporal and geographical spread of the Ishango culture and determined essentially two directions: One branch led to West Africa, the other down the Nile to Egypt. The duodecimal system could have come from Ishango on the one hand to West Africa and on the other hand via Egypt to Mesopotamia, in which case the Ishango bone would be the link Thomas was looking for.

Literature and Sources

Individual evidence

  1. ↑ a b De Heinzelin (1962).
  2. ^ Alison S. Brooks, Catherine C. Smith: Ishango revisited: new age determinations and cultural interpretations. In: The African Archaeological Review 5 (1987), pp. 65-78.
  3. ^ Jeff Suzuki: Mathematics in Historical Context. The Mathematical Association of America, Washington, DC 2009, ISBN 978-0-88385-570-6 , p. 1.
  4. ^ Hans Wußing: 6000 years of mathematics. Springer, Berlin et al. 2008, ISBN 978-3-540-77189-0 , p. 6 ff.
  5. ↑ a b Huylebrouck (1996).
  6. ↑ Alexander Marshack: The Roots of Civilization. MacGraw-Hill, New York 1972, ISBN 0-07-040535-2 .
  7. ↑ James Elkins: Impossibility of Close Reading: The Case of Alexander Marshack. In: Current Anthropology 37 (1996), pp. 185-226.
  8. ↑ Francesco D'Errico: Palaeolithic Lunar Calendars: A Case of Wishful Thinking? In: Current Anthropology 30 (1989), pp. 117-118.
  9. ↑ Alexander Marshack, Francesco D'Errico: On Wishful Thinking and Lunar "Calendars". In: Current Anthropology, 30 : 491-500 (1989).
  10. ^ Claudia Zaslavsky: Women as the First Mathematicians . In: International Study Group on Ethnomathematics Newsletter 7 , No. 1 (1992).
  11. ↑ a b Pletser, Huylebrouck (1999).
  12. ↑ Pletser, Huylebrouck (1999), see also Huylebrouck (no year).
  13. ↑ See for example Georges Ifrah: Universal history of numbers. Campus, Frankfurt am Main 1993, pp. 74 f., 90 ff.
  14. ↑ Northcote Whitridge Thomas: Duodecimal Base of Numeration . In: Man, Nos. 13-14 (1920), pp. 25-29.