Category: Numbers

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

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.

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.

A Missing or Defective Letter, a 23 Character Alphabet, and Seven Books of the Torah

“Hence the author of the Book Temunah transfers his interest from the redemption at the end of the current shemittah (about which he has little to say anyway) to the vision of the following one. The vision of the end of the present shemittah, of the gradual extinction of humanity, and of the slowing down of the rhythm of life in the entire creation—of which older Jewish messianism knew nothing—already forms part of this newly erupting sense of utopia.

In this  conception of redemption, the Messiah himself no longer plays a visible role; interest is completely focused on the cosmic processes.

For the historian of religion, the most striking aspect of the doctrine of shemittoth resides in the close link between a rigorous Jewish piety that maintains the revelatory character of the Torah and the vision of a change in the manifestation of the Torah in the other shemittoth. We have a clear case of Utopian antinomianism.

The assertion of the Temunah that “what is forbidden below is permitted above” (fol. 62a) entails the logical inference that what is forbidden according to the reading of the Torah in our present aeon might be permitted and even required in other aeons, when some other divine quality—Mercy, for example, instead of Stern Judgment—governs the world.

In fact, in both the Book Temunah itself and writings that follow in its footsteps we find astonishing statements regarding the Torah that imply a virtual antinomianism.

Two ideas should be stressed at this point. Several passages suggest that in the current shemittah one of the letters of the Torah is missing. This lack can be understood in two ways. It could signify that one of the letters has a defective form, contrary to its past perfection, that would of course be restored in a future shemittah.

However, as the book indefatigably asserts, since each letter represents a divine potency, the imperfection of its form could mean that the sefirah of Stern Judgment that predominates today effectively restricts the efficacy of the divine lights, which are therefore unable to reveal themselves perfectly.

According to this view, one such “defective” or incomplete letter of the alphabet is shin, which in its perfect form should have four heads, but which is written at present with three:  But the statement also could signify that today one of the letters of the alphabet is missing completely: it has become invisible in our aeon but will reappear and become legible once again in the future aeon.

Such a view evidently implies a thoroughly changed attitude toward the received Torah. In fact, it can (and did) lead to the supposition that all the prohibitions we read in the present text of the Torah are due to this absent letter.

The alphabet, and with it the complete Torah, are actually based upon a series of twenty-three letters; if we find in the Torah positive and negative commandments, it is only because this letter has dropped out of the present text. Everything negative is connected with the missing letter of the original alphabet.

According to another and no less audacious idea, the complete Torah contained in reality seven books, corresponding to the seven sefiroth and shemittoth. It is only in the current shemittah that, through the restrictive power of Stern Judgment, two of these books have shrunk to the point that only a bare hint of their existence remains.

The proof text of this assertion was a passage in the Talmud (Shabbath 116a), according to which the book of Numbers actually consists of three books. A tradition from the school of Nahmanides specifies that the power inherent in the Torah will manifest itself in the future aeon in such manner that we shall again perceive seven books.

The Book Temunah itself (fol. 31a) avers that the first chapter of Genesis is merely the vestige of a fuller Torah revealed to the shemittah of Grace, but which has become invisible in our shemittah, as the light of this earlier book has disappeared.”

Gershom Scholem, Origins of the Kabbalah, 1962, pp. 471-3.

Revelation of Elijah

“Already in the case of the first Spanish kabbalists, among the disciples of Isaac the Blind, the magical elements in their doctrine of the kawwanah occasionally come to the fore, as we have seen. Similar elements are discernible in the “mysteries of the prayer” of the German Hasidim, in that he who prays must think of the various names of angels as they relate—in respect to the mysticism of words and numbers—to the words of the traditional prayer. But in the earliest kabbalist circles, as far as our information extends, this magical element is missing; at least it does not manifest itself openly.

The teaching of the mystical kawwanah in prayer corresponds perfectly, it seems to me, to the objective and psychological conditions surrounding a doctrine born into an exclusive circle of men who possess the gift of meditation. With it, a new layer is added to the old gnostic elements that were contained in the tradition of the Bahir, elements that these men continued to develop in greater detail.

The creation of this doctrine bears the seal of the vita contemplativa. No element of the old Kabbalah better corresponds to the tradition of a revelation of Elijah, and we may regard this tradition as testimony that in this circle something really new had burst forth from the depths. An indication, if not an absolute proof, of this connection may be found in the fact that the remarks concerning the revelation Elijah is supposed to have vouchsafed to Isaac the Blind or his teachers are found precisely in texts in which the kawwanoth of prayer were collected by the Spanish kabbalists at the end of the thirteenth century.

No other specific doctrine among the kabbalists expressly relates to this revelation and this, perhaps, provides us with a key to our problem. A notion analogous to that of gilluy ‘Eliyahu can be found in Sufi mysticism in the accounts of revelations of Khidr (the Muslim metamorphosis of Elijah). Reports or testimonies concerning such revelations exist with regard to Muhi al-din ibn Arabi (1165-1240) of Andalusia, who shortly before 1200 —the time of Rabad and Isaac the Blind—was still wandering about in Spain (cf. G. Husaini, The Pantheism of Ibn Arabi, 28.).”

Gershom Scholem, Origins of the Kabbalah, pp. 245-6.

Malkhuth, Mystery of All Mysteries

“Most significant in this regard is a passage of his Sefer ha-Hokhmah, a commentary on the mystical forty-two-letter name of God. In a text on the tefillin of God, which are composed of the prayers (tefilloth) of Israel, it is said of the crown (‘atarah), which by these prayers ascends from below to rest upon God’s head then to be called Aktariel, in thoroughly kabbalistic language:

“For the tefillah sits at God’s left like a bride by a bridegroom, and she is called the king’s daughter, sometimes she is also called, according to her mission [to those here below] daughter of the voice [the talmudic expression for the celestial voice that mortals sometimes hear]. Of this Solomon said [reinterpreting Proverbs 8:30]: And I was Shekhinah by him, and the name of the Shekhinah is ‘ehyeh [I was] and the word next to it [in the verse] can also be explained, according to the Targum, as “she became great.”

For she is called the king’s daughter because the Shekhinah is with him in his house and it is to this that reference is made [in Ps. 91:1] to the dwelling in the shadow of shaddai [sel, “shadow,” being taken here in the sense of ‘esel, “by”] which means: He has a shadow which is called “by him” and this is the tenth kingdom, malkhuth, and it is the mystery of all mysteries. And we know that the word sod, mystery, can be interpreted [by the method of letter-mysticism] as the word malkhuth.

On every side of the Shekhinah are the crowns of royalty. And she herself is 236,000 myriads of parasangs long [that is, she is the theophany of God upon his throne, as described in the Shi’ur Qomah]. . . . And she directs the world and is named angel of God by virtue [of this her] mission, but with her no separation [from God] takes place.

And of this the verse [Exod. 23:20] said: I am sending an angel before you. This is the Shekhinah. And it is in this sense that the sages explain the verse [Num. 16:4]: Moses fell on his face, that is, because the Shekhinah was [there], he prostrated himself before God. That is why the prophets saw the Shekhinah, which is emanated, as it is said in Sefer Hekhaloth that the Shekhinah dwells beneath the cherub, and [originally] angels and men saw it.

But when the generation of Enoch sinned, the Shekhinah ascended heavenward. As for the Creator and Master of the Shekhinah, he is hidden from all and has neither measure [as in the Shi’ur Qomah] nor likeness, and no eye saw him. . . . And this is the mystery of the crown and the mystery of the Shekhinah, and whoever has this knowledge has a part in the world to come, inherits both worlds, and is saved from the judgment of Gehenna and he is beloved above and cherished below.”

Gershom Scholem, Origins of the Kabbalah, pp. 184-5.