### Recalculating the Antediluvian Reigns of Sumerian Kings

#### by Estéban Trujillo de Gutiérrez

“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.

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:

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:

where 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:

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.

[…] 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 […]

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If the Sumerians were using a base-10 numeric structure, why wouldn’t they divide the day into 10 hours? If they did so, a year is roughly 3600 hours long. Maybe they aren’t writing in years ruled, but in hours?

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