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Re: Ariadne's thread
Posted:
Nov 18, 2011 3:08 AM
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In the southwestern corner of the central court of
the palace at Mallia is a round stone called kernos,
along the rim are 33 cup marks plus a bigger one.
If each of the smaller cup marks represents one
day, all of them may represent a month of 33 days,
or 3 long weeks of 11 days. A year would have
33 long weeks or 11 months plus 2 and occasionally
3 more days, accounting for a regular year of 365 days
and an occasional leap year of 366 days, the additional
days represented by the bigger cup mark.
You may remember the number sequence I dubbed
Ariadne's thread (not to be confounded with the logical
strategy of this name):
136/11 (plus 235/19) 371/30 ... 4131/334
371 lunar years or lunations or synodic months
correspond to 30 solar years or simply years. How
many days are 30 years or 371 lunations? The ancient
way of counting lunations was 30 29 30 29 30 29 30
29 30 ... days for 1 2 3 4 5 6 7 ... lunations. 13 and 19
lunations counted that way yield 384 and 561 days
respectively, together 945 days for 32 lunations:
561/19 (plus 945/32) 403/51 ... 10956/371
30 years correspond to 371 lunations or 10956 days,
revealing a fine ceremonial calendar. A long week has
11 days, a month 33 days, a year has 33 weeks or 11
months plus 2 or 3 more days, while 30 years equal
371 lunations or 10956 days or 996 weeks.
Let us check on the relation of years and days.
One year is a little more than 365 days, 2 years
are more than 730 days, 4 years are slightly less
than 1461 days:
730/2 (plus 1461/4) 2101/6 3452/10 5113/14
6574/18 8035/22 9496/26 10957/30
Now we get 10957 days for 30 years, one day more
than before. The mistake in the above calendar is
one day (plus six hours), tolerable in a ceremonial
calendar.
365/1 (plus 1461/4) 1826/5 3287/9 4748/18
6209/17 7670/21 9131/25 10592/29 12053/33
33 years are 12053 days (exactly 12052.992... days).
33 regular years of 365 days are 12045 days, 8 days
less than the above number, suggesting this rule for
leap years: 33 years are composed of 25 regular
years of 365 days and 8 leap years of 366 days.
Next time: Minoan bull leapers
Milo, thank you for the hint at a 405 lunation period
used by the Maya, will have a look at the numerical
possibilities. You are right, calendars offer a window
on the past. Regarding very early calendars we have
not many written records, however, I believe, we have
many records in visual language. Regards, Franz
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