Re: hypothetical Yangshao calendar (early China)

From: Franz Gnaedinger (frgn_at_bluemail.ch)
Date: 03/07/05 

Date: 6 Mar 2005 23:51:56 -0800

Dylan and Paul: there are several good reasons for
assuming that 'my' calendar originated from northern
Mesopotamia in the Halaf period, as I shall explain
in a later message. - Good ideas spread. America got
the French constitution; Switzerland the American one;
Turkey the Swiss one. Same basis, different nations.
My calendar is another good idea that spread (Richard
Dawkins would speak of a good meme), and every region
made something special of it. Have a little patience.
>>From tomorrow on I shall show you that the Chinese
modified the Mesopotamian calendar into an appealing
and more precise calendar, which paved the way for
the Chang cycle (lunisolar calendar of 19 years). 

---
A month of 30 days; a year of 12 months plus 5 and
occasionally 6 days; 64 lunations equal 63 months or
1890 days - these are the basic numbers of a calendar
which I ascribe to Mesopotamia in the Halaf period,
and which may then have spread to Egypt, Persia,
India, and China.
The number 64 became part of the famous Egyptian series
of the Horus Eye, which, mutliplied by the 30 days of
a regular month, yields a lunation:
  1 'moon' = 30 days x '2 '4 '8 '16 '32 '64
  = 29 '2 '32 days (mistake only 58 seconds)
The number 64 = 2x2x2x2x2x2 is useful as it allows
an ever finer windrose: North and South / N E S W /
N NE E SE S SW W NW / and so on.
The numbers 2 4 8 16 32 64 became also important for
Chinese philosophy. Liang I: two principles, Yin and
Yang. Sz' Siang: four figures. Pa-kua: eight trigrams,
ascribed to the legendary first king Fuh-hi, and basis
of the 64 quasi-binary hexagrams in the later I-king.
In the 'begin' was the Wu Gi or Non-Begin, represented
by an empty circle. The Wu Gi was followed by the well
known figure of the Tai Gi: Yin and Yang in a circle,
meeting each other along an S-line, one drop of Yin
included in the Yang, one drop of Yang in the Yin.
We also find the number 3: Dao (sense, logos) produces
unity; unity produces duality; duality produces trinity;
and trinity produces all creatures ... From Saying 42
by Li, whose name as a young man was Erl or perhaps Er,
meaning Ear. His name as a scholar was Ye Bang, meaning
Earl Sun. His posthumous name of honor was Lao Dan,
meaning Old Long-Ear, Old Teacher. He is best known to
the world as Lao-tse, an appellativum meaning Old One.
Lao-tse may have known the two calendars (tomorrow),
and, I believe, he had a deep understanding of time
as wheel, vessel, house or shell of becoming (by
the end of this week or next week).
-
Regards   Franz Gnaedinger   www.seshat.ch
> I argued that 'my' calendar - a month of 30 days,
> a year of 12 months plus 5 and occasionally 6 days,
> 64 lunations equal 63 months or 1890 days - stems
> from Mesopotamia in the 6th millennium BC and spread
> from there to Egypt, Persia, India, and China.
>
> Horus, in ancient Egypt, was the Celestial Falcon.
> His one eye was the sun, his other eye was the moon.
> The moon eye was destroyed by Seth and restored by
> Thoth. However, a small part was missing, and that
> small part was the gap between 'moon' and month:
> '64 of 30 days.
>
> In mathematical terms, the Horus Eye was represented
> by a series of unit fractions: '2 '4 '8 '16 '32 '64.
> Multiply 30 days by that series and you obtain one
> 'moon': 30 days x '2 '4 '8 '16 '32 '64 = 29 '2 '32
> days (mistake only 58 seconds).
>
> The Horus Eye series can be developed as follows,
> and then carried on ad infinitum:
>
>   1 = '1
>   1 = '2 '2
>   1 = '2 '4 '4
>   1 = '2 '4 '8 '8
>   1 = '2 '4 '8 '16 '16
>   1 = '2 '4 '8 '16 '32 '32
>   1 = '2 '4 '8 '16 '32 '64 '64   and so on
>
> That principle was well known in the Old Kingdom,
> while the mathematician of the Middle Kingdom had,
> I believe, a second stairway:
>
>   1 = '1
>   1 = '1x2 '2
>   1 = '1x2 '2x3 '3
>   1 = '1x2 '2x3 '3x4 '4
>   1 = '1x2 '2x3 '3x4 '4x5 '5
>   1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6
>   1 = '1x2 '2x3 '3x4 '4x5 '5x6 '6x7 '7  etc.
>
> The resulting series contains a fascinating subseries:
>
>   '1x2 '2x3  '5x6 '6x7  '19x10 '10x11 ... = pi/4
>
> A transformation of that series approximates pi/4:
>
>   '1x3 ('16)
>   '1x3 '5x7 ('32)
>   '1x3 '5x7 '9x11 ('48)
>   '1x3 '5x7 '9x11 '13x15 ('64)
>   '1x3 '5x7 '9x11 '13x15 '17x19 ('80)  and so on
>
> A famous equivalent of the first pi-series was found by
> the Indian Madhavan (ca. 1340-1425 AD)
>
>   pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ...
>
> while the Indian Nilakantha, who flourished in the 15th
> century AD, found more than a dozen pi-series, among
> them a fast one:
>
>   pi = square root of twelve, multiplied by the series
>        1 - '3x3 + '5x3x3 - '7x3x3x3 + '9x3x3x3x3 ...
>
> For those who complain about eurocentrism in the
> humanities: the Indian pi-series are older than the
> ones from Europe, where the Madhavan series is named
> for Gregory, and the pyramid builders of ancient Egypt
> discovered a systematic method for calculating the
> circle on the basis of the Sacred Triangle 3-4-5:
>
>   www.seshat.ch/home/egypt2.htm
>
> Preview: The number 64 in China / A second calendar
> modifies the first one / More on the second calendar /
> Paving the way for the lunisolar calendar of 19 years,
> known as Chang cycle in China, and Metonic cycle in
> Europe. All messages ready, delivered on a daily basis,
> new ideas galore, and you get my work for free.
> -
> Regards   Franz Gnaedinger
>
>
> > Chinese yue = English moon/month = German Mond/Monat.
> >
> > A lunation, for example from one to the next full moon,
> > lasts 29.53058912 days. A calendar requires natural
> > numbers. 29.53... lies between 29 and 30, but a little
> > closer to 30, which number has the advantage of being
> > divisible by several smaller numbers apart from 1:
> > 2, 3, 5, 6, 10, and 15. So it makes sense to replace
> > a moon or lunation by a month of 30 days.
> >
> > 12 months yield 360 days. Add 5 and occasionally 6 days
> > and you obtain a year of 365 and sometimes 366 days.
> >
> > Add continual periods of 30 days and observe the moon
> > for years. If you are a good astronomer and make records
> > you may come across a fine relation: 64 moons equal 63
> > months or 1890 days (mistake only about one hour).
> >
> > >From this relation you may calculate a moon: 30 days
> > multiplied by a factor of 63/64. Now that factor equals
> > the famous Egyptian series of the Horus Eye. Hence
> >
> >   1 moon  =  30 days  times  '2 '4 8 '16 '32
> >
> >   =  29 '2 32 days  (mistake only 58 seconds)
> >
> > Horus was the Celestial Falcon. His one eye was the sun,
> > his other eye was the moon. Seth destroyed his moon eye,
> > whereupon Thoth restored it. However, a small part was
> > missing, and this small part turns out to be a duration,
> > namely the gap between moon and month: '64 of 30 days.
> >
> > Where and when did 'my' calendar originate? I plead for
> > Mesopotamia in the 6th millennium BC, from where it may
> > have spread to Egypt, Persia, China, and India.
> >
> > Have a look at a good reproduction of the famous plate
> > from the youngest Halaf level of Tell Arpadjije (near
> > Ninive) from around 5500 BC. The central rosette counts
> > 32 leaves: double the number and you obtain 64. On the
> > outmost rim are 36 white crosses: multiply them by a
> > long week of 10 days and you obtain 360 days or 12
> > months.
> >
> > Next time: the number 64 in Egypt
> > -
> > Regards   Franz Gnaedinger   www.seshat.ch

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