Nippur cubit

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A nippur cubit is understood to mean two different things, either a tangible measure or a unit of length.

The real standard

Nippur cubit in the Istanbul Archaeological Museum

During excavations in Temple E in Nippur , Mesopotamia , a scale was found that has the greatly enlarged shape of a pen. It consists of a previously unanalysed copper alloy (quite pure copper in appearance) and is now in the Ancient Near Eastern Museum of the Archaeological Museums in Istanbul . There are obviously notches cast into it. The technique used means that the notches do not sit very precisely. The rule weighs around 45.5 kg and was probably not removed when the temple was sacked because of its weight. Its exact total length is 110.35 cm. Taking radiocarbon dating (C14 method) into account, it dates back to the first half of the 3rd millennium BC. To date.

Unit of length

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Classification of the nippur cubit

Eckhard Unger recognized that the notches are marks of a measurement system. In his publications he explains why the distances between them result in a cubit of 51.80 cm divided into 30 parts ( finger widths = Ubanu, Ninda , Digitus) . The nippur cubit is therefore the oldest standard that has come down to us. If you use the sections given by Unger to calculate an average of six distances, you get 518.6 mm. In the course of decades of research, it has been found that all other pre-metric units of length can be derived from this oldest unit of length . The conversions are known.

The project group Measures - Music - Mathematics (MMM) collected 872 real measures (scales) worldwide. If you calculate them back to the nippur cubit, you get a length of 518.30 mm +/- 0.87 mm with a coefficient of variation of 0.168%. The statistical confidence interval (expectation interval) is +/- 0.042%. Of course, antiquity did not know these numbers. They can be calculated today because the historical development of the Nippur cubit is complete and 872 scales represent a sufficiently large sample for all pre-metric scales.

At all times the "normal" foot has been 16 digiti long. "(There are 'feet' of 18 digiti. This is the so-called pygme , actually the length of the forearm to the wrist, which in German is often also called 'foot'.)" The length of a digitus can be calculated from the above information: 518.30 mm: 30 = 17.277 mm (five counting digits!). This results in the length of the foot of the nippur cubit 16 × 17.277 mm = 276.43 mm (five counting digits!). If you divide the total length of the ruler of 1103.5 mm by these 276.43 mm, you get 1103.5 mm: 276.43 mm = 3.992, rounded 4. In other words: The intended length of the real nippur cubit should be four feet be. The deviation (the "Error") is 0.1995%. (In general, ancient standards differ by around +/- 0.2% from the target.)

It is noticeable that there is no notch of 16 digiti anywhere on the scale, although the scale is long enough for this. The foot is made up of 12 and 4 digiti. In contrast, there is a distance of 12 digiti twice. Therefore the 12 digiti distance should be particularly important. (In Roman times it was called dodrans) Its length is 12 × 17.277 mm = 207.32 mm. Four times this (the ancient world thought in doubling steps) is 4 × 207.32 mm = 829.30 mm. For the megalithic yard, A. Thom found the mean value of approx. 220 megalithic stone settings 829.056 mm, coefficient of variation 0.110%. The difference is 0.029% and is irrelevant. The megalithic yard (MY) is therefore four times the 12-digit measure of the nippur cubit and it is a single system of measures. In purely mathematical terms, a third of the MY is exactly the same length as the foot of the nippur cubit, but nowhere is there any indication that the MY would have been divided into thirds. The MY is 48 digiti long and the foot 16 digiti, and this results in equality. On the Nippur cubit, however, the distance of 18 digiti, formed from 14 and 4 digiti, can be tapped. It has already been said that there are 18 digiti feet, such as the Drusian foot.

The system of the Nippur-Elle / MY was known in all fully Neolithic cultures, therefore also in predynastic and early dynastic Egypt. There, however, the cubit was divided into only 28 digiti, because this is easier to calculate with the foot of 16 digiti: The digitus is then 518.30 mm: 28 = 18.511 mm; 18.511 mm × 16 = 296.17 mm. This is the well-known Roman foot (pes Romanus). The mean value from 58 found rulers with a Roman scale is 296.13 mm +/- 0.5 mm.

The 4-digit distance is plotted twice on the Nippur cubit. That must also have a special meaning. This distance is the palma (also palmus). Twelve palmae are 4 × 12 digiti or one megalithic yard . The twelve was a particularly important number in ancient Mesopotamia because it belonged to the sexagesimal system . We still use the number 12 as a dozen measure and divide the year into 12 months.

For some years now, many specialists have preferred an arbitrarily defined definition value for the Nippur cubit size: 518 616 µm. This value has the double advantage of being clearly within the confidence range of the research work described here, and on the other hand this well-defined value is the product of only three simple prime numbers : 7⁴ × 3³ × 2³ (see even number ). For the many other ancient measures derived from the nippur cubit, this also results in simple values, e.g. B. the Garde-cubit 15/14 NE, the Arabian Nile-cubit 25/24 NE, the Pechys basilikos 36/35 NE, the Egyptian royal cubit 50/49 NE, the Salamis-cubit 14/15 NE, the Roman cubit, which is 6/7 nippur cubits; for the Roman foot the value is exactly 296.352 mm.

literature

  • E. Unger: Die Nippur-Elle, publications of the quays. Osman. Museums, Constantinople 1916 ders. Eberts Reallexikon, keyword Nippur - Elle, Vol. VIII, p. 58, (1927)
  • KW Beinhauer (Ed.), RCA Rottländer: The matter with hand and foot. Exhibition catalog Mannheim 1994
  • A. Thom: Megalithic sites in Britain. Oxford, Clarendon press 1967, p. 43
  • RCA Rottländer: On the current status of historical metrology. In: Ordo et mensura VIII pp. 1-8, Fl. Huber and R. Rottländer Eds., 2004

Web links

Commons : Nippur-Elle  - Collection of images, videos and audio files