Re: hypothetical Yangshao calendar (early China)
From: Franz Gnaedinger (frgn_at_bluemail.ch)
Date: 03/21/05
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Date: 20 Mar 2005 23:35:22 -0800
No electricity at home, a short-circuit somewhere,
so I couldn't print out my prepared message on Sumer
and China, and will have to improvise.
Let me tell you about two marvellous Babylonian values
for the lunation of 29 days 12 hours 44 minutes 2.9
seconds, or 29.53058912 days.
Naburi' Annu, by the end of the third millennium BC,
used the value 29.530641 days, mistake less than five
seconds. Kidinnu, in around 380 BC, used a value of
29.530594 days, mistake less than half a second!
How can we possibliy explain these very fine values?
Have a look at the following fractions and try to
find the generating rule before reading on:
59/2 443/15 502/17 945/32 1447/49 2392/81
2 lunations are about 59 days, 15 lunation about 443
days. Add the numbers and you obtain the next value:
2 plus 15 are 17 lunations, and they equal 59 plus 443
yielding 502 days. And so on. The value 1447/49 has
a mistake of only two seconds. The value by Naburi'
Annu lies in between that fraction and the next one,
closer to 1447/49 than to 2392/81.
Now let us go for another sequence. Begin with 502/17
and add repeatedly 1447 in the numerator, and 49 in
the denominator:
502/17 (plus 1447/49) 1949/66 3396/115 4843/164
and so on 32336/1095 33783/1144
The value of Kidinnu lies between the last fractions.
Add the numerators and demoninators and you obtain
66119/2239 or 29.53059402... days.
-
Regards Franz Gnaedinger www.seshat.ch
-
> Picture yourself as a Mesopotamian astronomer, over
> 7,000 years ago, living on Tell Arpachiyah, observing
> the sun as it rises from and sets on the flat horizon
> of the wide river plain. You will make a marvellous
> discovery. The directions North, rising midsummer sun,
> rising midwinter sun, South, setting midwinter sun and
> setting midsummer sun divide the circle of the horizon
> into 6 perfectly equal angles ... Now you may divide
> each angle into 60 fine angles and call them degrees.
> Thus you obtain a circle of 360 degrees, which goes
> along with a year of 360 days. Add 5 and occasionally
> 6 days and you obtain a whole year of 365 and sometimes
> 366 days. You will of course also observe the moon.
> One moon or lunar cycle or lunation or synodic month or
> lunar year is between 29 and 30 days; a little closer
> to 30 days, and so you call a period of 30 days a month.
> By observing the sky for years and years you notice
> that 64 moons equal 63 continual months or 1890 days,
> namely 9000 plus 131 days. From these relations you can
> get fine numerical values for the lunar and solar year.
>
> The famous tiles from the House of Tiles at Lerna in
> the Argolis, Early Helladic period of time, came from
> Asia Minor. The numbers provided by the decorative
> patterns evoke the above calendar: the numbers 5 10 15
> may perhaps indicate short weeks of 5 days; the numbers
> 6 12 24, as divisors of 360, may indicate a year; while
> the numbers 4 8 16, as divisors of 64, would indicate
> a cycle of 64 lunations.
>
> The gold signet ring from Tiryns divides the circle of
> the sun into six angles: www.seshat.ch/home/ring.gif
> while the front of a bull-head from a Mycenaean tomb
> is decorated with a flower of 16 long and narrow petals.
> The number 16, belonging to the sequence 2 4 8 16 32 64,
> may be a lunar number (the bull being a lunar symbol)
> and stay for a cycle of 32 lunations that equal 21 long
> months of 45 days or 945 days (assuming that the Middle
> Minoan calendar from the Mesara plain in southern Crete
> was also used in the Argolis from the Middle Helladic
> onward).
>
> Preview: Sumer - China / Maya calendar / brillant
> historical Babylonian values for the lunation /
> replying to Paul
> -
> Regards Franz Gnaedinger
> -
>
> > Walther Hinz deciphered Linear A tablet Hagia Triada 95
> > as a list of grains that are to be given to the priests
> > and priestesses of Adu (Baal) and his wife Dadumatha
> > (the one loved by Baal). Hinz read the following signs,
> > which also appear on other Linear A tablets, and on at
> > least one hieroglyphic seal, as Mi-nu-the or Minut or
> > Ebla in Syria, 40 km south of Aleppo, famous for its
> > fine wheat (if you read my message via Google beta
> > please install the opiton "fixed font"):
> >
> > o
> > o o o ooooooo
> > o o o o o
> > o o o o ooooooo
> > o o o oooooo o
> > o o o o o ooooooo
> > o o oooooo o
> > o o o o o
> > o o o o o o
> > o o o
> >
> > I identified these signs as the head of a bull; a bull
> > leaper in motion, a flip-flop figure standing on his
> > feet his hands his feet again; and as a tree of life.
> > Together they yield MI-NU-THE or - MINOS.
> >
> > The Minoans, then, would have come from Ebla, and so
> > they may well have used the general calendar I ascribe
> > to all of Mesopotamia and its neighbours. However, that
> > calendar would have been modified and given in a very
> > simple form as a rosette of either 8 or 10 petals.
> >
> > The rosette of 10 petals may symbolize ten months of
> > 36 days, yielding 360 days. 5 or 6 addiontional days
> > fill a year of 365 and occasionally 366 days, while
> > 105 continual months or 3780 days equal 128 lunations.
> >
> > The flower of 8 petals may symbolize eight months of
> > 45 days, yielding 360 days. 5 or 6 additional days
> > fill a year of 365 and occasionally 366 days, while
> > 21 continual months or 945 days equal 32 lunations.
> > One month has five weeks of 9 days (week in Homer's
> > Odyssey.
> >
> > Hoping that my ASCII drawing will be transmitted
> > undisturbed, Franz Gnaedinger, www.seshat.ch
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