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Re: Prime numbers and pi
Posted:
Apr 26, 2009 4:18 AM
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Milo, there are no exact numbers in astronomy. A lunar
year has in between 29 and 30 days, a solar year in
between 12 and 13 lunar years or lunations, and in
between 365 and 366 days. The oldest way of counting
lunations - Lebombo, Central Equatorial Africa, 35,000
years ago, Lascaux, 18,000 years ago - was 30 29 30 29
30 29 30 29 30 29 30 ... days for 1 2 3 4 5 6 7 8 9 10
11 ... lunations. The people of the Göbekli Tepe culture,
12,000 years ago, used this algorithm for a fixed value:
17 lunations are 502 days
15 lunations are 443 days
17 lunations are 502 days
15 lunations are 443 days
64 lunations are 1,890 days
A year had 12 months of 30 days, plus 5 and occasionally
six more days, while 63 continuous periods of 30 days,
or 270 weeks of 7 days, are 1,890 days and correspond
to 64 lunations.
The Egyptians inherited the Göbekli Tepe calendar. An
Egpyptian year had 12 months of 30 days, corresponding
to the 36 dekans of the sky, while 63/64 or '2 '4 '8 '16
'32 '64 of a month was a lunation of 29 days 12 hours
45 minutes, mistake less than one minute per lunation,
or half a day in a lifetime.
Doubling and halving was important in Egyptian
mathematics and came handy with the abacus, but I
can't believe that the Egyptians of the Old Kingdom
used only Horus eye fractions. Giving 63/64 as "3 '6
'12 '24 '48 '192 or as '3 '5 '6 '10 '20 '36 '40 '80
'144 '288 '320 makes no sense, '2 '4 '8 '16 '32 '64
of a month of 30 days is much simpler, but concluding
from the Horus eye series that the mathematicians of
the Old Kingdom had no third, no fifth, and so on,
is certainly wrong.
We may assume a very ancient myth of a former cosmic
balance, an early time when a lunar year had 30 days,
and a solar year 12 lunations or 360 days. Then an
evil-doer must have destroyed the primeval harmony.
In the Nile Valley this evil-doer was Seth who
destroyed the lunar eye of the Horus falcon. Wise
Thoth restored the lunar eye, he added up '2 and '4
and '8 and '16 and '32 and '64 and obtained a lunation.
The primeval lunar eye was then a month of 30 days,
and the restored lunar eye one lunation, 63/64 of
a month, the best Thoth was able to achieve once
the primeval order had been overthrown.
Regards, Franz Gnaedinger
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