The 25-year cycle and the Ptolemaic Macedonian calendarAlthough there was thus no standard‘new’lunar calendar, the appearance of
various 25-year cycles and other fixed schemes in the Ptolemaic period
represents, atfirst sight, a considerable change in the way Egyptians reckoned
the lunar calendar, which perhaps demands to be explained.
The possibility of external influence has been explored in several different
ways. On the basis of Parker’s fourth-centuryBCEdating of the cycle of pap.
Carlsberg 9—which, as we have seen, as is actually quite uncertain—some
have suggested that the 25-year cycle may have been imported into Egypt by
its Persian Achaemenid rulers.^84 Although the Persians themselves are not
known for expertise in astronomy or calendars—in fact, as we shall see in
Chapter 4, calendrical influence between them and Egypt worked in the
opposite direction—they may have facilitated the spread of the Babylonian
calendar and, perhaps, of Babylonian mathematical astronomy. This sugges-
tion should be rejected, however, because the 25-year cycle cannot be related
to any aspect of the Babylonian calendar. The only known Babylonian cycle
was of 19 years, and this cycle only regulated the intercalations (see Chapter
2); the Babylonians are not known to have designed a cycle where—as in the
Egyptian 25-year scheme—the beginning of each month wasfixed. It should
also be said that the astronomical knowledge that was necessary to design the
25-year cycle would have been minimal: essentially, all that was required was
the knowledge that 25 civil years equal 309 months. This would certainly not
have necessitated any borrowing from Babylonian mathematical astronomy.^85
An alternative attempt has been made to relate the 25-year cycle—which, as
Pap. Rylands shows, was definitely in existence by the Ptolemaic period—to
the Macedonian lunar calendar. The Macedonian calendar was introduced
into Egypt by the Ptolemaic dynasty in the late fourth centuryBCE, and was
used by the Macedonian elite as a lunar calendar until the early or mid second
centuryBCE, after which it lost its lunar characteristics and became assimilated
to the Egyptian civil calendar.^86 Some have suggested that the 25-year cycle
(^84) Neugebauer (1975) ii. 563–4, but not without reservations (also Clagett 1989–99: ii. 137– 8
n. 31).
(^85) Depuydt (1998) shows that the scheme of pap. Carlsberg 9 was not based on mathematical
astronomy, but on simple arithmetic; the purpose of this scheme was simplicity, not astronomi-
cal accuracy. Although Depuydt is assuming his own reading of the text, whereas the theory of
Babylonian influence which we are now considering assumes Parker’s reading, it remains
uncontestable that the scheme is built on the simple alternation of 29- and 30-day months,
not on a sophisticated astronomical calculation of when new moons are actually likely to occur.
(^86) As convincingly demonstrated by Samuel (1962) 129–38, on the basis of double-dated
documents from this period and later where the same date is given for Macedonian and Egyptian
civil months, indicating that both calendars had become identical. Samuel dates this change to
the end of the 3rd c.; for the later, mid-2nd-c. date, see now Bennett (2008) 527 n. 9. But the
equivalence between Macedonian and Egyptian month-names did not remain consistent: until
154 Calendars in Antiquity