[Retros] Kung Hei Fat Choy!

[andrew buchanan]

Happy Chinese New Year from Hong Kong!
www.janko.at/Retros/d.php?ff=k7/4b3/pP1N1P2/2P5/3K4/2P1P1P1/8/8after Bonsdorff, Väisänen & Stanleyser-h#21 How many solutions?
You may ask: why this number? What year is *2018 CE* by the Chinese calendar? The official calendar in China is the Gregorian calendar, but the traditional Chinese calendar still plays an important role. Historically, there has been no original "epoch date": years were differentiated using a cycle of 60 years, together with the name of the current Emperor. Curiously, in the historical period, there was only one Emperor who ruled for more than 60 years.
I consulted friends and colleagues in Hong Kong, Beijing & Taipei, what an absolute Chinese year number is, and all said there is no answer. Everyone only knows the 60 year cycle. Before the 1911 revolution, Sun Yat Sen wanted to establish a republican alternative to the imperial reign cycles. According to Chinese tradition, the first year of the reign of the legendary Yellow Emperor (Huangdi) was 2697 BCE but for some reason he introduced a counting system based on 2698 BCE - a one year discrepancy. Under this system, 2018 CE would be the Chinese year 4716 or 4715. The yellow emperor is attributed with many inventions including wheeled vehicles and football, but he would have been a small child in 2698, as he then reigned for over 100 years. 

An alternative system, which makes more sense to me, is to start with March 8, 2637 BCE, when the calendar was supposedly invented, and Huangdi was well established on the throne. So it is customary to number the 60-year cycles since then. In 2018 CE, we enter the 35th year of the 83rd cycle: i.e. 4655.

By the way, why 60 years in the cycle? This is a complicated business involving astronomy with reference inter alia to the orbit of Jupiter, but let me at least say how the 60 years are named.

It's well known in the West that there is a 12-year cycle of animals (known as the "Terrestrial Branch"):
1    zi (rat)        7    wu (horse)
2    chou (ox)        8    wei (sheep)
3    yin (tiger)        9    shen (monkey)
4    mao (hare, rabbit)    10    you (rooster)
5    chen (dragon)        11    xu (dog)
6    si (snake)        12    hai (pig) 

It's less well known by westerners that there is a parallel 10-year cycle called the "Celestial Stem": 
1    jia (wood)    6    ji (earth)
2    yi (wood)    7    geng (metal)
3    bing (fire)    8    xin (metal)
4    ding (fire)    9    ren (water)
5    wu (earth)    10    gui (water)

The combination of stem+branch gives the year name. So year 1 of the cycle is "jia-zi" (wood-rat), and year 35 (i.e. 2018) is "wu-xu" (earth-dog). 2019 will be "ji-hai" (earth-pig ~= Groundhog?) Year.

Since 10 & 12 have a common factor of 2, these two cycles between them generate a period of 60 years. But only half of the 120 theoretical combinations of Stem and Branch can be reached: "jia-chou" for example, can never happen. Not surprisingly, this parity issue is related to Yin-Yang. Stems and branches are alternately assigned to be "Yin" or "Yang". Yin stems go only with Yin branches, and Yang with Yang.

So if:
2637 BCE was the beginning of the 1st year, then:
1 BCE was the beginning of the 2637th and:
1 CE was the beginning of the 2638th, (there being no year 0 in the calendar) while
2018 is the beginning of the 4655th.
This is only skimming the surface of the complexities of the Chinese calendar, which are most apparent in the determination of months, as there is an ongoing reconciliation between lunar and solar orbits involving periodic "leap months".

What's so auspicious about 4655? Well, combinatorially it is the number of Young's tableaux of shape (17,4). This means it can appear in a chess queue problem, and 17 is *just* small enough to be accommodated without difficulty in a known matrix, which supported (17,17) although Richard Stanley points out that the matrix can be pushed to (18,7).

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