Müller’s argument, however, is misleading and unsound. To begin with the
later period (second centuryCE), his probability calculation is only correct if
one posits that the alternative to a 19-year cycle was that intercalated and
ordinary years occurred purely at random. No one, however, has ever made a
claim of this kind. The whole purpose of intercalation was clearly to keep the
lunar calendar in line with the solar or seasonal year, and this would have
required the right number of intercalations to be made, and at the right
frequency. Even if intercalations were irregular (e.g. because decided on a
year-to-year basis, or on the basis of extraneous, political, or other considera-
tions), at times causing deviations from a well-regulated scheme, we cannot
expect them to have been completely random. The probability of agreement of
our eleven cases with a 19-year cycle would have been therefore considerably
higher than Müller allows (even if this probability would be difficult to
measure or calculate). Furthermore, as Müller himself points out, if only one
single‘contradictory’year were to be discovered andfirmly established, his
hypothesis would have to be abandoned. The risk of there being a‘contradic-
tory’year among the 66 (as yet) unattested years in the second centuryCE
(between 111/12 and 177/8) should be treated as high, especially as an irregu-
lar intercalation is attested at the‘outer limit’of 211/12CE. Müller’s probability
calculations create an illusion of mathematical certainty, but mask the fact that
the record for the second centuryCEremains too sporadic to infer anyfixed
pattern of intercalations.
On this basis, it is no longer possible to extrapolate to the intervening period
(between 95/4BCEand the second centuryCE), for which there is no evidence at
all.We are left only with the short period of 125/4 to 95/4BCE; and there again,
Müller’s inference is unconvincing. Although this period is reasonably well
furnished with evidence, the only sequence of years that is repeated after 19
years is 125/4–120/19, repeated in 106/5–101/0, thus only a six-year section of
Müller’s 19-year cycle.^60 There is no other evidence of cyclicity, except for a
single intercalation in 116/15 that is repeated, 19 years later, in 97/6. This is
clearly insufficient to confirm the existence of a recurring 19-year pattern.We
cannot even be sure that seven intercalations were made in any 19-year period,
because of the gap in the evidence between 115/14 and 109/8. Müller assumes
that two intercalations would have been made in 113/12 and 110/9 (years 14
and 17 of the cycle), but we cannot rule out the possibility that only one
intercalation was made.^61
(^60) Actually onlyfive years, since 123/2 (year 4 of Müller’s cycle) is not attested.
(^61) The possibility of three intercalations in these years is also possible but less likely, because
this means that two consecutive intercalations would have been necessary (since an ordinary year
is attested in 112/11), which is uncommon. For a brief refutation of Müller (1991), see also
Lehoux (2007) 92 n. 49.
Calendars of AncientGreece 41