Epigenes and Berosus
“Like Aristarchus, Berosus was interested in sundials. His dial is said to have been semicircular, hollowed out of a square block, and cut under to correspond to the polar altitude. The Babylonian was also interested in astrology, for Vitruvius (Vitruvius, The Ten Books on Architecture, 9.8.1) declares that Berosus founded an astrological school in Cos, and a remark by Pliny (Natural History, 7.160) confirms that he had a knowledge of technical astrology. According to Pliny, Epigenes held that a man could not live as long as 112 years, but Berosus claimed that a man could not live more than 116.
We have here an allusion to the astrological doctrine that the number of years in a human life can never exceed the maximal possible number of degrees which is necessary for one quarter of the ecliptic to rise.
As Neugebauer has shown, Epigenes’s remark applies to the latitude of Alexandria, but Berosus is speaking of Babylon. It is just, I think, to regard Berosus as an astrologer who brought his doctrines to Cos, but there is no sign that he helped to advance the study of astronomy amongst the Greeks.
He belongs rather to the genethlialogists at Babylon, whom, Strabo reports, the geniune astronomers did not admit to their number. Yet there may still be some truth in the statement of Josephus that Berosus introduced astronomical doctrines of the Chaldaeans to the Greeks, as well as their philosophical doctrines; just as there is perhaps a sound basis for the remark of Moses of Chorene that Ptolemy II Philadelphus (in whose empire Cos lay) incited Berosus to translate Chaldaean records into Greek.
By Georgios Synkellos also the same Ptolemy, who reigned from 283 to 247 B.C., is said to have had Chaldaean works collected for his library and to have had them translated.
If Berosus was not the bringer of Chaldaean astronomical knowledge to Aristarchus, then a possible intermediary is Epigenes. This scholar, who came from Byzantium, is almost certainly a near contemporary of Aristarchus and Berosus, though various views about his date have been held.
His views are twice mentioned next to those of Berosus, once on the antiquity of Babylonian astronomical records and once on the greatest length of human life. His remark that a man could not live more than 112 years applies to the latitude of Alexandria, and shows that Epigenes had worked there.
From Seneca we learn also that he and Apollonius of Myndus had studied amongst the Chaldaeans, in Babylon itself presumably, as Epigenes’s reference to astronomical cuneiform texts–observationes siderum coctilibus laterculis inscriptas–suggests.
His statement that the astronomical records went back 720 years, not 480, looks like an attempt to correct Berosus. When we add that Epigenes believed that children could be born in the seventh month, a view also held by Strata, Aristarchus’s teacher; and find that Epigenes was, like Strata, interested in comets, the case for dating him early in the third century looks strong, if not conclusive.
But it is pointless to speculate about any ties he may have had with Aristarchus.”
George Huxley, Aristarchus of Samos and Graeco-Babylonian Astronomy, Greek, Roman and Byzantine Studies, Duke University, Vol 5, No 2 (1964), pp. 127-9.
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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