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THE EPIC OF GILGAMESH

According to the version of the Deluge story contained in the Epic of Gilgamesh (Tablet XI) the Ark is a cube with an edge of 120 cubits. The stark nakedness of this statement should have made clear to the interpreters that it is a matter of a mathematical entity. Like the ziggurat of Entemenaki, it has a base of 1202. square cubits, or one iku. The only one who has called attention to this fact is Alfred Schott in a footnote(114) in which he also observes that the Ark is divided into 7 decks like a ziqqurat and that each level is divided into 9 rooms, which correspond to the formulation of the Smith Tablet by which each side of the iku is composed of 3 segments of 60 cubits so that the entire area is divided into 9 squares. But Schott considered his association of the Ark and ziqqurat as a cube as too daring and ended his statement with a qualification that is obscure to me, but substantially means that what he said must not be understood literally. Two years later(115) he took a more conventional position by trying to interpret the text of Gilgamesh's epic so as to understand that the Ark has the shape of an inverted trunk of a pyramid and hence somehow resembles a ship.

The Ark in the story of the Flood has the shape of a cubic iku because the Flood is tantamount to a destruction and new creation of the world, and the Ark is the principle of measure that creates order out of chaos. For the Mesopotamians the draining of swampy lands by a grid of canals is the creation of the world, and this is the background of the story of the Flood. The ziggurat was a symbol of the typical embankment of land and represented the place of refuge in case of floods.

The division into 7 levels corresponds to the usual division of the earth and of the corresponding concentric vault of heaven into 7 zones from the equator to the pole. But the further division by 9 indicates that the Ark is divided into 63 parts.

The division of the Ark into 7 decks of 9 rooms each may have a connection with number magic. W. H. Roscher has written several studies on the mystical meaning of the coupling of the numbers 7 and 9 in Greece, and Father Franz Xaver Kugler has dealt with a similar symbolism in Mesopotamia. But these numbers may have a metrological explanation which I consider the original one. In metrics a cube is often divided into 64 parts by dividing each edge into 4 parts; this originates the discrepance diesis between the division of a cube into 64 parts and its division into 60 parts according to sexagesimal computation. The discrepancy is reduced to a leimma when the 60 parts brutto are calculated netto and become 62.5. The number 63 may be a compromise between the figure 62.5 indicated by metrics and the figure 64 indicated by geometry. That one aimed at dividing the Ark into 60 parts is suggested by the total volume of 6,000,000 cubic cubits netto.

A cube with an edge of 120 cubits has a volume of 1,728,000 cubic cubits. It is not specified whether these cubits are barley cubits or great cubits, but the calculation of the volume of the Ark by Berossos, discussed below, indicates that they were great cubits. 120 great cubits correspond to 180 barley cubits. In developing the reckoning, I shall calculate by barley cubits, in order to make the presentation simpler for the modern reader who is not used to sexagesimal reckonings. Converting 1,728,000 cubic great cubits into cubic natural barley cubits, the volume is 1803 = 5,832,000 cubic cubits.

The calculation of the Ark begins with the datum of 12,600,000 barley cubits (140 x 300 x 300) for the radius of the Earth = 8,400,000 great cubits = 17,500 US.

These figures mean that the radius is 6,378,750 meters. Even though it is a matter of round figures, they come quite close to absolute exactness, since the most recent modern calculations estimate the equatorial radius as only 350 meters less -- around 6,378,400 meters.

The Ark was intended to represent the northern hemisphere on a scale of 1:90,000. Hence, the calculation started from a sphere with a radius of 140 cubits, since 140 x 90,000 = 12,600,000. A hemisphere with a radius of 140 barley cubits has a volume equal to 1/90,000 of the volume of the Earth. The figure of 140 cubits was chosen because units of 70 were particularly significant in Mesopotamia.

Calculating by the exact value of p, a hemisphere with a radius of 140 cubits has a volume of 5,747,020 cubic cubits = 747,652 cubic meters.

In order to cube this volume in simple terms it was said to be equal to a cube with sides of 180 cubits, which means 5,832,000 cubic cubits = 756,496 cubic meters.

There is a slight excess in this conversion, ca. 1/83. This excess is taken care of by removing 1/63 from the total volume, that is, by removing one of the parallepiped-shaped "rooms" into which the Ark is subdivided:
62/63 x 5,832,000 = 5,739,427 cubic cubits.
In metric terms the volume becomes 746,669.4 cubic meters. If we multiply this figure by 2 x 90,0003 we would obtain a figure for the volume of the Earth of 1,085,727,972,660 cubic kilometers.

Calculating by the exact value of p, a volume of 5,739,427 cubic cubits is that of a hemisphere with a radius of 140.24 cubits. Or we could say that a hemisphere with a radius of 140 cubits has a volume of 5,739,427 cubic cubits, if 4/3 pi is taken as 4.18326. It is possible that in sexagesimal reckoning 4/3 p was computed as 4 11/60 = 4.18333, (assuming p = 3 11/80 = 3.1375). But probably 4/3 p was calculated as 4.2, (assuming p = 3.15; the exact figure is 4.1888). The result would be a volume of 5,762,400 cubic cubits = 747,650 cubic meters.

Let us repeat the procedure just described by removing one more parallelopiped from the cube with sides of 180 cubits which is the Ark. We obtain a volume of 61/63 x 5,832,000 = 5,646,857 cubic cubits. Assuming 4/3 pi = 4.1833, this volume equals the volume of a hemisphere with a radius of 139.3 natural barley cubits. Taking the scale of the Ark into account, this means that the radius of the Earth is 12,537,000 cubits, or 6,346,856 meters.

    114. ZA 40 (1931), 15 n.

    115. ZA 42 (1933), 140 n. 1.


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