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1. I have shown that the dimensions of the Ark reported in the Epic of Gilgamesh were extremely important to the people of Mesopotamia, since they constituted the link between their system of measures and the structure of the cosmos. Because of their importance they were used as the dimensions of the ziggurat of Babylon, the biblical Tower of Babel, the tallest building of Mesopotamia. But scholars have treated these dimensions casually on the assumption that they did not have any specific meaning. It is assumed that the writers of the accounts of the Deluge chose these figures in a free flight of fantasy and that they could have chosen different ones. This view is supported by the belief that there was in Mesopotamia a tradition that assigned to the Ark absolutely different and discrepant dimensions. This second set of dimensions would be that reported by Berossos.

Berossos was the priest of the temple of Bel who, after Alexander the Great conquered the Near East and imposed Greek culture on it, tried to explain the essential points of Babylonian culture to the new rulers of his country. To this purpose he wrote in Greek a book entitled Babyloniaka, which is now lost, but is known through extensive quotations by Greek authors. The sections of Berossos' book that dealt with the Deluge and the Ark happened to be quoted by Alexander Polyhistor, a Greek scholar who was taken prisoner in war and brought as a slave to Rome, where he was employed as a tutor by some major political figures of the last period of the Roman Republic. For the benefit of his Roman masters, Alexander wrote several compilations of curious information about the areas of the eastern Mediterranean on which the Romans were at the moment in the process of imposing their rule. As one empire succeeded another, the Greek Alexander Polyhistor was in a situation in relation to the Romans similar to that of the Babylonian Berossos in relation to the Greeks. Hence Alexander included exerpts from the Babyloniaka of Berossos in his works. The writings of Alexander are now lost too, but the section in which he reported Berossos' account of the Deluge and the Ark was quoted again when there was a further convulsion in the cultural development of the ancient world.

When in the age of Constantine the Great the Roman Empire became Christian, scholars applied themselves to the problem of reconciling the traditions of the Christian Church with those of the Roman state. At this juncture, Eusebios, one of the great scholars of the time, produced a comprehensive survey of historical chronology in which he tried to combine biblical dates with Greek and Roman ones. In dealing with the date of the Deluge he quoted what Alexander Polyhistor had quoted from Berossos.

2. The first part of the text of Eusebios dealing with the announcement of the Deluge and the construction of the Ark, reads as follows:

After the death of Ardates, his son Xisuthros reigned for 18 x 3600 years; under him a great deluge took place. The story has been recorded as follows. Kronos appeared to him in his sleep and revealed that on the fifteenth of the month Daisios mankind would be destroyed by a deluge. He therefore commanded him to set down in writing the beginning, middle, and end of all knowledge, and to bury [this knowledge] in Sippar, the city of the Sun; to build a boat and to go aboard it with his family and retinue; to store in it food and drink, to put into it also living creatures, winged and four-footed, and, when all was ready, to set sail. If asked whither he was sailing, he should say, "to the gods, in order to pray that it may be well with mankind." He obeyed and built a boat, 15 stadia in length and 2 stadia in width. He carried out all these orders and embarked with wife, children, and retinue.

Berossos states that the Deluge began on the 15th day of the month Daisios. The month Daisios is a month of the Macedonian calendar which was introduced by the followers of Alexander the Great into the Near East; hence, we are left wondering which month of the Babylonian calendar was referred to by Berossos.

It could be inferred that the version reported by Berossos intended to give to the episode of the Deluge the length of a lunar month of 29 days: the water began to come on the 15th and the hero came out on the 29th, which was occupied by the sacrifice to the gods (described at great length in the Epic of Gilgamesh). Hence, according to the version of Berossos, the preparation for the Deluge and Deluge may have taken 14 + 14 days.

It has to be noted that the Sumerian King Gudea, received in a dream from a god the plan of a temple to be built according to a specitic measurius ruler. But it is more important to notice that the construction of the Ark is mentioned by Berossos together with the problem of the preservation of the fundamentals of knowledge. A parallel to this association is the tradition conveyed by early Arab historians that the great Pyramid of Gizah was built by a king in order to preserve the fundaments of all arts and sciences because a deluge was impending.

The dimensions of the Ark were conceived as linked with the preservation of knowledge, and in this spirit Berossos tried to preserve the knowledge of these dimensions when the Greeks threatened to obliterate Babylonian culture. Alexander Polyhistor tried to preserve them when the Romans swept through the Greek world, and Eusebios preserved them when imperial decrees outlawed pagan cults and beliefs in the Roman Empire. But in spite of these pious efforts to preserve a precious inheritance of mankind, modern scholars have done their best to wash it away. They treat the figures of Berossos as if he, or somebody before him, had contrived figures more or less at random, guided only by the spirit of the marvellous. The only use that scholars make of Berossos' figures is to infer that the people of Mesopotamia gave discrepant data about the size of the Ark, so that the figures of the Epic of Gilgamesh should not be taken earnestly. The truth of the matter is that Berossos, living during the last gasp of Mesopotamian culture, carefully reported the figures that had been incorporated into the Epic of Gilgamesh about two millennia earlier.

3. Berossos transmitted what was essential on the subject of the Ark, its volume. The explanation of his figures is most simple. In Mesopotamia there was a method of expressing volumes which consisted in using the units of surface and assuming that the surfaces are given the height of the cubit. The existence of this procedure was noticed by the earliest Sumerologists of the last century and more recently has been emphasized by Otto Neugebauer, who has carried this fact to the absurd inference that the people of Mesopotamia did not calculate volume as cubes. The procedure of expressing volumes as units of surface was of practical advantage in construction works, such as canals, embankments, and houses, in which huge volumes may be involved, but the height of the constructions is usually only a few cubits. Furthermore, mathematically this procedure permits to reduce calculations by cubes and cubic roots to calculation by squares and square roots. It achieves a purpose of the same nature of that which the people of Mesopotamia achieved by the invention of logarithms, namely, it lowers the level of mathematical operations. In spite of all current assertions that the Mesopotamians were primitive in their science and mathematics, no responsible scholar denies the fact that they used logarithms. In our culture logarithms were rediscovered by John Napier in 1614 A.D., and anyone would easily agree that modern science could not have been possible without them. As Novalis puts it, "what logarithms are to mathematics, that mathematics are to sciences."

Whereas the Epic of Gilgamesh had expressed the volume of the Ark as a cube, 1203., Berossos, in the mathematical spirit which I have just mentioned, reduced the same calculation to the level of a mere multiplication of two numbers.

4. At this point it is necessary to shift from a mathematical issue to a philological one. Since Eusebios' survey of chronology is full of figures, these were badly garbled by amanuenses as one manuscript was successively copied into another. Fortunately, there is an Armenian translation of the Greek original in which the figures have been reproduced more carefully; for this reason scholars consult the Armenian translation.

In the Greek manuscripts the dimensions of the Ark read as 2 stadia by 5 stadia, but in the Armenian translation the length is given as 15 stadia. All recent biblical scholars quote only the figures of the Greek manuscript, because in 1927 Paul Haupt, who established Mesopotamian studies in the United States, rejected the figures in the Armenian translation as preposterous.(109)

It is true that a ship of the length of 15 stadia is inconceivable, but so would be a ship of the length of 5 stadia. It did not occur to Haupt to draw the evident inference that Berossos was not talking about the dimensions of a ship. That the notion of an entity intended to navigate must be dismissed should have occurred to scholars merely on the basis of the statement of the Epic of Gilgamesh according to which the Ark is a cube with sides of 120 cubits, with each face having the surface of an iku. But modern scholars are committed on principle to exclude that the statements about the Ark refer to mathematical entities, because they want to eliminate as much as possible mathematical thought from the spirit of ancient cultures. Haupt's interpretation received acceptance because he was so bent in the direction of excluding mathematical and geometric concepts from ancient thought, that he went further than conceiving the Mesopotamian Ark as an actual ship. He realized that the Ark is connected with the ziggurats and that the ziggurats of Mesopotamia are related to the pyramids of Egypt. Concerning the relation between Ark and ziqqurat, Lehmann Haupt concluded that the ziqqurats represented ships turned upside down and were a reminder of "the vessel that brought the Sumerian invaders to the northern shore of the Persian Gulf."(110)

But the Egyptian pyramids, too, represent inverted ships. Ark, ziqqurat, pyramid, would be instances of a universal symbolism of the ship, of which the ship of the Argonauts, the solar ship of the Egyptians, and the carrus navalis of Carnival would be further instances.

That ziggurats and pyramids have to be understood in terms of mathematics and geometry is obvious to anyone who is not blinded by ideological commitments. Haupt at least was consistent in his line of reasoning, since he argued that Mesopotamian ziggurats and Egyptian pyramids have the shape of a ship, that is, of a ship turned upside down. He carried prevailing scholarly assumption to the point of a reductio ad absurdum.

5. I shall limit myself to commenting on that part of Berossos' account that deals with the dimensions of the Ark, but I must observe that other details of his account reveal that he drew from the earliest layer of the story of the Flood, the Sumerian version. This indicates that Berossos, far from being a decadent latecomer, did derive information from the most ancient records of Mesopotamia. But modern scholars treat Berossos as a vapid storyteller who gave the length and width of the Ark, but forgot to mention its height.

Since Berossos mentions a width of 2 stadia and a length of 15 stadia, it is assumed that he wanted to impress the reader by describing a ship of a size beyond any reasonable imagination. However, the very enormous extentions of the Ark according to Berossos should have forced modern commentators not to take his figures according to their most literal meaning and to pay some attention to the style of Mesopotamian mathematical texts.

The only possible difficulty in interpreting the dimensions reported by Berossos may be that of establishing the value of the stadion of which he is speaking. In dealing with Herodotos' description of the city of Babylon, I have stated that the only difficulty in interpreting his text results from the cirumstance that he counted by stadia corresponding to a minute of march, whereas Greek authors by stadion usually mean a double minute of march. Herodotos reports that the sides of the ziggurat of Babylon are a stadion long, whereas from the Smith tablet and from actual excavation we know that the length was 120 "great cubits" = 180 natural barley cubits. Since the Ark according to the Epic of Gilgamesh had sides of 120 "great cubits," we could expect Berossos to have applied the Greek name of stadion to this unit. But, writing for a Greek audience, he used the term stadion as indicating a double minute of march, which in this particular case is 240 "great cubits." According to Berossos the Ark measured 2 x 15 stadia = 480 x 3600 cubits, which means it had a volume of 480 x 3600 x 1 cubits = 1,728,000 cubic cubits. Hence, Berossos was stating in different form what had been stated in the Epic of Gilgamesh, according to which the Ark had a volume of 1203. = 1,728,000 cubic cubits.

My interpretation of the metric data concerning the Ark reduces to simplicity a question on which there has been spilled a great quantity of ink. In defense of the value of traditional metrology, I may quote the interpretation offered by Haupt who contributed to the establishment of the new school. The question of the Ark was his favorite topic, and his position is summed up in the essay, The Ship of the Babylonian Noah, published posthumously. He combines the figures of Berossos with those of Gilgamesh's Epic. The latter would merely have formulated the vertical section, whereas the length must be derived from Berossos: the Ark would be 120 cubits wide and 120 cubits high with a length of 15 stadia or 3600 cubits.

There is further reason why Berossos preferred the mentioned way to express the volume of the Ark. The volume of the Ark was related to the size of the Earth. The Mesopotamians calculated the equatorial radius as 12,600,000 natural barley cubits = 6,378,750 meters. They simplified the enormous figure of 12,600,000 cubits by expressing it as 3600 x 3600 or as 140 x 300 x 300. Calculating ammatu rabbtu, "by great cubits,"(111) the equatorial radius is 8,400,000, which could be expressed as 480 x 17,500 or as 240 x 35,000.

Hence, Berossos by using the stadion of 240 "great cubits" and implying that the Ark was 480 x 3600 cubits, was establishing a link with these figures.

109. "The Ship of the Babylonian Noah," Beitr. Assyr. X (1927), Heft 2, published posthumously.
110. Ibid.
111. The ratio of "great cubits" to natural barley cubits is 2:3.

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