Hesiod, the Great Year, and the Phoenix
“In the discussion of the Classical conception of the Great Year it was mentioned that Plato was the first author to make a clear statement about this cosmic period. He referred to an almost inconceivably long time, which he could characterize only by saying that at the completion of such a cosmic revolution the perfect number of time comprises the perfect year. It remains possible, however, that in another connection he assigned a specific duration to the Great Year.
In the eighth book of Politeia, Plato discusses the question of how an aristocracy can become degraded into a timocracy, i.e. a form of government in which ambition is the dominant principle of the rulers. (Plato, Politeia, VIII, 3, 544d-547c).
This occurs, he says, because the Guardians will not be able, by calculation and observation, to determine the appropriate times for birth. In an extremely difficult passage which has given rise to many commentaries he then gives the computation of what is incorrectly called the “nuptial number.” (A. Diès, Le nombre de Platon, essai d’exégèse et d’histoire, Académie des Inscriptions et Belles-Lettres, XIV, Paris, 1936, and others).
Plato begins by remarking that for the divine creature there is a period embraced by a perfect number. (Plato, Politeia, VIII, 3, 546b). This is reminiscent of his statement that the duration of the Great Year can be expressed in a perfect number.
The zodiac is a planisphere or map of the stars on a plane projection, showing the 12 constellations of the zodiacal band forming 36 decans of ten days each, and the planets. These decans are groups of first-magnitude stars. These were used in the ancient Egyptian calendar, which was based on lunar cycles of around 30 days and on the heliacal rising of the star Sothis (Sirius).
The celestial arch is represented by a disc held up by four pillars of the sky in the form of women, between which are inserted falcon-headed spirits. On the first ring 36 spirits symbolize the 360 days of the Egyptian year.
On an inner circle, one finds constellations, showing the signs of the zodiac. Some of these are represented in the same Greco-Roman iconographic forms as their familiar counterparts (e.g. the Ram, Taurus, Scorpio, and Capricorn, albeit most in odd orientations in comparison to the conventions of ancient Greece and later Arabic-Western developments), whilst others are shown in a more Egyptian form: Aquarius is represented as the flood god Hapy, holding two vases which gush water. Rogers noted the similarities of unfamiliar iconology with the three surviving tablets of a “Seleucid zodiac” and both relating to kudurru, “boundary-stone” representations: in short, Rogers sees the Dendera zodiac as “a complete copy of the Mesopotamian zodiac”.
http://en.wikipedia.org/wiki/Dendera_zodiac
For the elucidation of “the divine creature,” reference can be made to the statement in the Timaeus that the Demiurge himself was only the creator of the fixed stars, the planets, and the earth. (Plato, Timaeus, 39e-40b.)
It is therefore probable that the reference in the Politeia to a period comprising a perfect number as belonging to that which the deity generates, should be seen as the duration of the complete cosmic revolution of the Great Year.
But for human creatures, says Plato, there is a geometric number, and this is the one for which he supplies the complex computation already mentioned. Especially since the research done by Diès there has been general agreement that this geometric number, which can be computed in several different ways, is 12,960,000.
To provide the long-sought harmony between the various components of this passage, it has been assumed that the perfect number of the divine creature is the same as the whole geometric number holding for human procreation, the component factors of the geometrical number having special relevance for the latter. (Ahlvers, 19-20, basing himself on 12,960,000 days = 36,000 years).
If this is valid, it may be concluded that in the Politeia Plato assumed a duration of 12,960,000 years for the Great Year.
Even if Plato did not mean that the perfect number of the rotation of that which the deity generates is equal to the geometric number, it would nevertheless have to be taken as probable that the number 12,960,000 originally pertained to the duration of the Great Year and that there is a relationship to the concept underlying Hesiod, frg. 304, since this fragment assumes a cycle of four successive world eras forming together a Great Year of 1,296,000 years. The Platonic number—which, incidentally, is a Babylonian sar squared—is thus ten times Hesiod’s value.”
R. van den Broek, The Myth of the Phoenix: According to Classical and Early Christian Traditions, Brill Archive, 1972, pp. 98-9.)
June 18, 2015
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
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:
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
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.
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