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Tag: Xisouthros

Is the šãru the Solution to the Impossibly Long Antediluvian Reigns?

“Regardless of the names, however, it is apparent that when the formula for calculating the actual length of reigns is applied, the figures on Berossos’ list of ancient Sumerian kings are amenable to precisely the same treatment as the original Sumerian King List.

Among all the extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum cuneiform collection represents the most extensive version as well as the most complete copy of the King List.  In this depiction, all four sides of the Sumerian King List prism are portrayed.  http://cdli.ox.ac.uk/wiki/doku.php?id=the_sumerian_king_list_sklid=the_sumerian_king_list_skl

Among all the extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum cuneiform collection represents the most extensive version as well as the most complete copy of the King List.
In this depiction, all four sides of the Sumerian King List prism are portrayed.
http://cdli.ox.ac.uk/wiki/doku.php?id=the_sumerian_king_list_sklid=the_sumerian_king_list_skl

This indicates that Berossos was thoroughly familiar with the Sumerian system of computing lengths of reigns, as expressed on the Weld-Blundell prism, and that he was representing the priestly tradition many centuries later in his own configurations.

The revised king list of Berossos is as follows:

Revised King List of Berossus 1Revised King List of Berossos 2

Berossos’ figures constitute a remarkable tribute to the tenacity of ancient priestly traditions, since the Babylonians had normally used base-10 in their mathematical calculations for many centuries. Berossos, however, felt a commitment to honor the ancient heroes whom he was listing in the age-old Sumerian manner.

In attempting to provide a “rational” solution to the problem of large numbers in the antediluvian King List, I have said nothing as to precisely why base-60 squared was employed in the listing.

Scholars who have checked the numbers are satisfied that they have been transcribed accurately, with the result that the issue must now turn on mathematical considerations, as Young has suggested. From a prima facie standpoint it is no longer legitimate to question the numbers themselves, but instead to recognize the possibility that base-60 squared was actually functioning as a mathematical constant.

So little insight has been gained into the theoretical dynamics of Sumerian mathematics that it is impossible to say with certainty what the reason was for employing base-60 squared as a constant, assuming that this was its actual function in the King List, as seems eminently probable.

Calculation of the surface area of terrain at Umma, Mesopotamia (Iraq). Ur III Clay tablet (2100 BCE) 7 x 5.8 cm AO 5677, Louvre Museum. http://www.lessingimages.com/viewimage.asp?i=08020612+&cr=328&cl=1

Calculation of the surface area of terrain at Umma, Mesopotamia (Iraq). Ur III Clay tablet (2100 BCE) 7 x 5.8 cm AO 5677, Louvre Museum.
http://www.lessingimages.com/viewimage.asp?i=08020612+&cr=328&cl=1

It was certainly integral to the structure of the various recorded reigns, unlike some constants in modern mathematics that grace an equation but are not indispensable entities. Why base-60 should have been squared in order to perform its function satisfactorily is also problematical. Perhaps, after all, base-60 squared was intended to serve as a symbol of relative power and importance, which the compilers of the ancient Sumerian King List associated with those men whose reigns they recorded.

Regardless of the immediate answers to these queries, it seems clear that base-60 squared should be recognized as an “ideal” constant, which, however, must be factored out once it has been isolated so that it is not reckoned as part of the overall calculation.

In any event, we know that the ancient Sumero-Babylonian sexagesimal system employed at least the following mathematical bases as units: 60° (= 1), which in Akkadian was called ištēn; 60 (to the first power) 1 (= 60), which was called šūšu; 60 (to the second power) 2 (= 3600), which was called šãru; and 60 (to the third power) 3 (= 216,000), which was called šuššārū. The word šãru had a Sumerian antecedent (šár) that means not only “3600” but also “universe.” (See footnote 17 below).

In later times the Greeks put the sexagesimal system to full use, “both in the familiar division of the circumference of the circle into 360 “degrees’ of 60 minutes or 3600 seconds each, and in the division of the radius into units of consecutive sixtieths.” By employing the šãru as the key to unlocking the antediluvian numbers in the Sumerian King List as well as in Berossos, we find ourselves not only discerning “rational” numbers depicting the length of royal reigns in those ancient chronological tables but also walking in the footsteps of noble mathematical tradentes.”

Footnote 17:

O. Neugebauer, The Exact Sciences in Antiquity (2d ed.; New York: Harper, 1957) p. 141. U. Cassuto, A Commentary on the Book of Genesis. Part I: From Adam to Noah (Genesis I-VI 8) (Jerusalem: Magnes, 1961) p. 258, has observed that the 241,200 of the antediluvian Sumerian King List equals one great šãru (šuššārū—i.e., 216,000—plus seven šãru—i.e., 7 χ 3600 or 25,200) and that the 432,000 of Berossos equals 120 šãru (i.e., 120 χ 3600) or two great šãru (= two šuššārū—i.e., 2 χ 216,000).

Footnote 19:

I am deeply indebted to my daughters, C. Felicity Harrison and H. Judith Virta, for reviewing this paper critically, to my son, Graham K. Harrison, for technical advice involving the mathematical analysis, and to Ronald Youngblood for the Sumero-Akkadian and Greek information in the final paragraph and for the references in nn. 17 and 18 (footnote 18 omitted here).

R.K. Harrison, “Reinvestigating the Antediluvian Sumerian King List,” Journal of the Evangelical Theological Society (JETS) 36 / 1 (March 1993), pp. 6-8.

Recalculating the Antediluvian Reigns of Sumerian Kings

“At one time the present writer tended to interpret the large numbers associated with the Hebrew exodus from Egypt and also with the census lists in Numbers as “symbols of relative power, triumph, importance, and the like,” a position that can be sustained to a degree from ancient Near Eastern literature but does not account satisfactorily for all the Biblical data involved.

Sensing that there might, after all, be a rationale underlying the very large figures, a few scholars adopted cautious positions reflecting that possibility.

Among all extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum contains the most extensive version as well as the most complete copy of the King List. The prism contains four sides with two columns on each side. Perforated, the prism had a wooden spindle so that it might be rotated and read on all four sides. http://cdli.ox.ac.uk/wiki/doku.php?id=the_sumerian_king_list_sklid=the_sumerian_king_list_skl

Among all extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum contains the most extensive version as well as the most complete copy of the King List.
The prism contains four sides with two columns on each side. Perforated, the prism had a wooden spindle so that it might be rotated and read on all four sides.
http://cdli.ox.ac.uk/wiki/doku.php?id=the_sumerian_king_list_sklid=the_sumerian_king_list_skl

A serious mathematical investigation of the postdiluvian portions of the Sumerian King List was undertaken by D. W. Young (Dwight W. Young, “A Mathematical Approach to Certain Dynastic Spans in the Sumerian King List,” JNES 47 (1988), pp. 123-9), in which he suggested that the total years for certain dynasties utilized squares or higher powers of numbers, perhaps in combinations.

Thereafter his interests shifted to the problem of large numbers in the accounts of the Hebrew patriarchs (Dwight W. Young, “The Influence of Babylonian Algebra on Longevity Among the Antediluvians,” ZAW 102 (1990), pp. 321-5), but his studies in that area are not strictly relevant to the present problem.

His great contribution was to take seriously the numbers of the ancient writings with which he dealt and to attempt to interpret them mathematically.

The ancient Sumerians were innovators in the areas of astronomy and mathematics as well as in other unrelated fields of investigation. It is now known that their arithmetical calculations were based upon the sexagesimal system, and thus when they considered the mathematics of time it was natural to divide the hour up into sixty units, and then to reduce each one of those units to a further sixty components or, in our language, minutes and seconds.

There is still very much to be learned about Sumerian mathematics, but from what is known of the pragmatic nature of the subject it appears increasingly clear that their numerical exercises were organized on the basis of rationality rather than mythology.

Having regard to this situation, scholarship now has the responsibility of investigating the numerical problems of Sumerian times against such a background.

To the present writer it now seems evident that the solution to the large numbers found in the antediluvian Sumerian King List is disarmingly simple. It is obvious that, proceeding rationally, base-60 must be involved in numbers of the magnitude contained on the prism. The list of rulers and regnal years is as follows:

Cf. J. Finegan, Light From the Ancient Past (Princeton: Princeton University, 1946), p. 25.

Cf. J. Finegan, Light From the Ancient Past (Princeton: Princeton University, 1946), p. 25.

An inspection of this table shows two kings credited with reigns of 36,000 years each and three others recorded as having reigned for 28,800 years each. In the case of Alalgar and the divine Dumuzi, the numbers assigned to them contain two factors—namely, 3600 (the square of base 60) and 10 — which when multiplied furnish the large number under investigation.

In the case of the triad comprising Alulim, Enmengal-Anna, and Ensipazi-Anna, the factors involved are the square of base-60 multiplied by 8. When the base is isolated from the calculation, the remaining factor constitutes the actual length of the king’s reign.

This process can be expressed by a formula, as follows:

Formula for Calculating Actual Reignwhere Pr is the prism’s record, B is base-60 raised to the power of 2 to give base-60 squared, and At is the actual length of the king’s tenure. By employing this means of calculation, the above table can be rewritten as follows:

Recalculated Actual Reign of Years and Months

Notice may now be taken of the third century BC list compiled by Berossos. As observed earlier, the names are Greek and the total has been extended to ten rulers by the addition of two names.

Xisouthros, the legendary hero who survived the flood, is one of these. It has also been suggested that Amelon and Ammenon may be corrupt forms of the name Enmenlu-Anna, but this cannot be demonstrated.”

R.K. Harrison, “Reinvestigating the Antediluvian Sumerian King List,” Journal of the Evangelical Theological Society (JETS) 36 / 1 (March 1993), pp. 4-6.

On the Date of The Flood

“I now turn to Berossos’ account of the Flood as the central narrative of book 2. The extant fragments contain the following elements:

  • – Kronos reveals the destruction of mankind in a dream
  • Xisouthros is told he must bury the tablets in Sippar
  • – He must build a boat and embark together with family, friends, and animals
  • – The coming and receding of the deluge (mentioned in only one sentence)
  • – Bird scene
  • – Disembarking
  • – Worship and ritual offering
  • – Disappearance of Xisouthros, who will henceforth live with the gods
  • Xisouthros’ friends and relatives are told (not by Kronos, but a ‘voice’) to go to Sippar and dig up the tablets, and to hand them over to mankind.
  • – Landing place in Armenia, in the Korduaian mountains. The remains of the ark are still there, and people scrape off bitumen for magic purposes.

In Mesopotamian accounts of the deluge the Flood marks a break between a mythic prehis­tory and a history closer to the world as it is today. According to Manfried Dietrich, many mythical texts from Mesopotamia reflect this view of history, whereby an embryonic phase in the development of the world (‘embryonaler Status’) is followed by what he calls the ‘Jetzt-Zeit’, i.e. the present time.

The extant fragments of Berossos follow the same overall scheme. For Berossos too, the time before the Flood is a period of revelation, when the basis for all later knowledge was laid. Writings originating in this period would accordingly have a special authority and ‘the history which follows is the time when this revelation is transmitted and unfolded.’

Berossos was not the first to connect an antediluvian king list with the Flood story: al­ready the Sumerian version of the Flood story mentions five primeval cities known also from copies of the Sumerian King List.

Among all the extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum cuneiform collection represents the most extensive version as well as the most complete copy of the King List.  In this depiction, all four sides of the Sumerian King List prism are portrayed.  It lists rulers from the antediluvian dynasties to Suen-magir, the fourteenth ruler of the Isin dynasty (ca. 1763–1753 B.C.).   The prism contains four sides with two columns on each side. Perforated, the prism must originally have a wooden spindle going through its centre so that it might be rotated and read on all four sides. http://cdli.ox.ac.uk/wiki/doku.php?id=the_sumerian_king_list_sklid=the_sumerian_king_list_skl

Among all the extant exemplars of the Sumerian King List, the Weld-Blundell prism in the Ashmolean Museum cuneiform collection represents the most extensive version as well as the most complete copy of the King List.
In this depiction, all four sides of the Sumerian King List prism are portrayed.
It lists rulers from the antediluvian dynasties to Suen-magir, the fourteenth ruler of the Isin dynasty (ca. 1763–1753 B.C.).
The prism contains four sides with two columns on each side. Perforated, the prism must originally have a wooden spindle going through its centre so that it might be rotated and read on all four sides.
http://cdli.ox.ac.uk/wiki/doku.php?id=the_sumerian_king_list_sklid=the_sumerian_king_list_skl

Berossos’ own knowledge of primordial kings probably goes back to sources that were available in Hellenistic times. The Sumerian King List itself was still known in the Seleucid era, or rather versions of king lists that echo, structurally and stylistically, their ancient forerunners from the early second millenium.

In matching up the primordial kings with the seven sages, the apkallu, Berossos once again works in the vein of contemporary scholars, who demonstrably constructed lists with kings and apkallu in order to advertise their own importance, and the primordial roots of their knowledge, as Alan Lenzi has recently shown (Editorial note: this link is to Alan Lenzi, “The Uruk List of Kings and Sages and Late Mesopotamian Scholarship,” JANER 8.2, 2008, which will be serialized in its own posts shortly).

Detail, Apkallu head, from a frieze in Nimrud.  http://non-aliencreatures.wikia.com/wiki/Apkallu

Detail, apkallu head, from a frieze in Nimrud.
http://non-aliencreatures.wikia.com/wiki/Apkallu

Yet, Berossos does not merely translate ancient documents, but rather selects and reframes what he finds, thus constructing his own version of the past. For a start, he locates the beginnings of kingship in Babylon and not in Eridu as the first city of Mesopotamian tradition.

Moreover, he reckons the overall duration of pre-flood history at 432,000 years (120 saroi = 120 x 3600 years), a sum that reflects the sexagesimal count­ing system of ancient Mesopotamia but which, as far as we know, is unique in Mesoptamian tradition.

432,000, however, is no arbitrary accumulation of individual reigns, but rather represents an astronomical ‘great year’, or an exact fraction of it. A great year is the period of time it takes for all heavenly bodies to return to their original place in the sky.

Berossos evidently had at least some astronomical knowledge, and moreover was keen to display his knowledge. Indeed, another peculiarity of Babyloniaca 2, beside the exorbitant reigns of the pre-flood kings, is Berossos’ unusual and very specific reference to a date for the Flood:

Kronos stood over him in his sleep and said that on the 15th of the month of Daisios mankind would be destroyed by a flood.

The Armenian version (F4a) supplies some explanatory glosses inserted at a later stage (in italics):

He says that Kronos, whom they call the father of Aramazd and others call Time, revealed to him in his sleep that on the 15th of the month of De(s)ios, which is Mareri, mankind was to be destroyed by the Flood.

There is no mention of a specific date in cuneiform texts about the Flood, yet Berossos puts it on ‘the fifteenth of the month Daisios’. According to the Macedonian calendar introduced by the Seleucids, Daisios is the 8th month of the year, and comes in spring (April/May, Babylonian Ayyaru).

Perhaps Berossos inserted a Macedonian dating in order to make it more relevant to his readers who were familiar with Greek Flood narratives. The choice of date may not be entirely accidental, as the Tigris and the Euphrates burst their banks in spring.

However, extant cuneiform sources link the deluge with rains and a cosmic storm rather than natural inundations, and we may have to look elsewhere for an explanation.”

Martin Lang, “Book Two: Mesopotamian Early History and the Flood Story,” from Johannes Haubold, Giovanni B. Lanfranchi, Robert Rollinger, John Steele (eds.), The World of Berossos, Proceedings of the 4th International Colloquium on the Ancient Near East Between Classical and Ancient Oriental Traditions, Harrassowitz Verlag, Wiesbaden, 2013, pp. 49-51.

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