Re: hypothetical Yangshao calendar (early China)

From: Comm (tjsrno_at_spampost.com)
Date: 03/06/05 

Date: Sun, 06 Mar 2005 21:21:27 GMT

PUBLISH!!

"Franz Gnaedinger" <frgn@bluemail.ch> wrote in message
news:1110007522.862821.293190@l41g2000cwc.googlegroups.com...
>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
>>
>>
>> > My hypothetical Horus / Yangshao / Liangzhu calendar
>> > is based on a month of 30 days, a year of 12 months
>> > plus 5 and occasionally 6 days, and a cycle of 64
>> > lunations that equal 63 continual months = 1890 days.
>> > One lunation is obtained by multiplying a month of 30
>> > days by the famous Egyptian series of the Horus Eye:
>> >
>> > 1 lunation = 30 days x '2 '4 '8 '16 '32 '64
>> >
>> > = 29 '2 '32 days (mistake only 58 seconds)
>> >
>> > The Chinese Bi, from around 3400 till 2000 BC, are flat
>> > jade disks, diameters between 10 and 30 cm, with round
>> > perforations of a largely variable size in the center.
>> > The Bi is considered a symbol of the sky. I came across
>> > five Bi, measured them, and found numbers that may refer
>> > to crucial numbers of my calendar, especially 30 and 64.
>> > So a Bi could actually be a symbol of the sun and moon,
>> > the month of 30 days and the cycle of 64 lunations.
>> >
>> > FIRST BI: radius perforation / radius disk = 1/15
>> > ring perforation ring = 14 1+1 14 or 7 1 7
>> > diameter disk = 30 or 15; small grid 7 1 7 by 7 1 7
>> > rotating square 7 1 by 7 1 = 8 x 8 = 64
>> >
>> > SECOND BI: radius hole / radius disk = 1/5 or 3/15
>> > ring perforation ring = 4 1+1 4 or 12 3+3 12
>> > diameter disk = 10 or 30; small grid 4 2 4 by 4 2 4
>> > four corner squares of small grid = 4 x 4 x 4 = 64
>> >
>> > THIRD BI: radius perforation / radius disk = 1/4
>> > ring perforation ring = 3 1+1 3
>> > diameter 8, square 8 x 8 = 64
>> >
>> > FOURTH BI: radius perforation / radius hole = 1/3
>> > ring hole ring = 2 1+1 2 or 4 2+2 4 or 10 5+5 10
>> > diameter = 6 or 12 or 30; medium grid 4 4 4 by 4 4 4
>> > four corner squares of medium grid = 4 x 4 x 4 = 64
>> >
>> > FIFTH BI: radius perforation / radius hole = 7/8
>> > ring perforation ring = 8 7+7 8 or 4 7 4
>> > diameter disk 30 or 15; small grid 4 7 4 by 4 7 4
>> > four corner squares of small grid = 4 x 4 x 4 = 64
>> >
>> > The idea of a square grid going along with a BI
>> > seems justified by the early Chinese sign of heaven:
>> > a man with a square for a head.
>> >
>> > Next time: answering Paul's question
>> > -
>> > Regards Franz Gnaedinger www.seshat.ch
>

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