Wednesday, October 7, 2009

Moon & Rusalka

中秋節 of 2009 falls on October 3. The temperature hovered around 60 degree on the day & I haven’t seen the moon so bright, so round & so shining for some time. I checked the luner calendar, it said 已丑中秋節. I don’t know how many people still use or follow 天干地支 counting in China. It takes 60 years to reach a cycle & restart. So when someone says 一甲子, he means 60 years. I have no idea why our ancesters used this system. Perhaps people at that time in average only lived to 60 years of age. Otherwise it will be confusing when some one say 甲午年. It may be 1894 or 1834. Think about it, we are all over 60 years old. How about 壬午年, it may be 1942 or 2002. As a matter of fact, our history book lists all these terms: 戊戌政變, 甲午战争, 辛亥革命, 庚子賠款 etc. It is nice to know that the events occur in that year. But the problem is that you really don’t know how it relates to 公元 or how many years between those events. You have to do some conversion or cross reference. I do have an algorithm that converts BC or AD to 天干地支. It is as follows:

十 天干:甲乙丙丁戊已庚辛壬癸 (index 0-9)
十二 地支: 子丑寅卯辰巳午未申酉戌亥 (index 0-11)

For AD, use (Year –4) & the following calculation:
(1972 - 4) mod (10) ≡ 8,所以天干是“壬”;
(1972 - 4) mod (12) ≡ 0,所以地支是“子”。
So 1972 is (8,0) 壬子
Same conversion leads 1942: 壬午

For year from 1 to 4, it is:
4: 甲子
3: 癸亥
2: 壬戌
1: 辛酉

For BC, it is more complicate & I will reserve this for some other time. Let’s get back to a soft side of our life. Moon to most of us is romantic. It shines on us, no talking, no complain, no excuse. No wonder some poet like 李白 & others ran the imagination to the wild. Here are some examples:

暮從碧山下, 山月隨人歸.
举杯邀明月, 对影成三人.
我歌月俳佪, 我舞影零乱.
暫伴月將影, 行樂須及春.
星隨平野闊, 月湧大江流.
霧溼樓台, 月迷津渡.
明月如霜, 好風如水.
明月幾時有, 把酒问青天.
沙上珏禽池上暝, 雲破月來花弄影.
海上生明月, 天涯共此時.
露從今月白,月是故鄉明.
明月松間照,清泉石上流.
深林人不知,明月來相照.
月落烏啼箱霜滿天

But the most famous & appropriate to 中秋節 is:
人有悲欢離合, 月有陰晴圓缺, 此事古難全.
但願人長久, 千里共嬋娟.

梁弘志 wrote a song “但願人長久”using 苏東坡 的水調歌頭 as the lyrics. It becomes very popular since 1980’s. On the western front, Dvorak composed “Song to the Moon” in opera Rusalka. It is one of the most well-known song dedicated to the moon. 歌 詞 傷 感, 期 待 而 無 耐, 冷 艶 而 淒 婉. 最 後 一 句 是 近 乎 绝 望 的 呼 喊. Rusalka is a water sprite, who seeks love with human beings that proves to be tragic. Here is the lyric in Czech & its verbatim translation: (* is repeated verse)

Mesiku na nebi hlubokem--------------O moon up in the deep sky
Svetlo tvé daleko vidi,------------------Your light sees distant places
Po svete bloudis sirokém, --------------You travel round the wide world
Divas se v pribytky lidi. ----------------You look into people’s houses
--------------------------------------*You travel round the wide world
--------------------------------------*You look into people’s houses

Mesicku, postuj chvili------------------ O, moon, stay for a moment
Reckni mi, kde je muj mily------------- Tell me where is my love!
----------------------------------------*O, moon, stay for a moment
-------------------------------------*Tell me, oh, tell me where is my love!

Rekni mu, stribmy mesicku, --Tell him please, silver moon in the sky,
Me ze jej objima rame, -----------------That I embrace him,
Aby si alespon chvilicku----------That he should for at least a while …
Vzpomenul ve sneni na mne ------------… remember his dreams!
-----------------------------------*That he should for at least a while …
--------------------------------------*… remember his dreams!

Zasvet mu do daleka -------------------Light up his distant place,
Rekni mu, rekni m kdo tu nan ceka!---Tell him, who waits here!
----------------------------------------*Light up his distant place,
------------------------------------*Tell him, oh, tell him who waits here!

mneli duse lidska sni -------------------If he dreams of me, …
At'se tou vzpominkou vzbudi! ----------… may this memory waken him!
Mesicku, nezhasni, nezhasni!---O, moon, don’t disappear, don’t go!

Here we found some striking similarity between eastern & western version that shows human feeling is universal. If we look at the first stanza of the song, it is 轉 朱 閣, 低 綺 户, 照 無 眠. The second & third stanzas are sort of like 不 應 有 恨, 何 事 偏 向 別 時 圓.. The fourth stanza is 人 有 悲 欢 離 合, 月 有 陰 晴 圓 缺, 此 事 古 難 全. The last stanza is equivalent to 但 願 人 長 久, 千 里 共 嬋 娟..

The following video clip is Rusalka performed by Lucia Popp, a Slovak soprano. She is ideal for singing Czech opera.
http://www.youtube.com/watch?v=4qxi-sYUT9s

PS:
Dvorak (1841-1904) is a Czech composer. His most famous works are Symphony from the New World, Cello Concerto, “American” String Quartet & Slavonic Dances.

6 comments:

markyang said...

Very good conversion formula. I was puzzled why 十 天干, 十二 地支 ends with only 60 combinations. It takes 10x12=120 for the full cycle. With you formula, if x mod(10) is even then x mod(12) is also even and the same relation holds for odd remainders too. That's why it end with 60 years per cycle.

Why 60? It must have something to do with a 265.25 day year and the lunar cycles (29-30 days). A perfect match year by year is definitely not possibe, because every year does not start with the same day of the moon cycle. Apparently, after 60 years, the lunar cycles have a nearly perfect match with the solar calendar. This calendar has been used for thousands of years without noticeable discrepancy.

Mark Lin said...

The lunar calendar has to take into consideration of the same discrepancies of solar calendar & does the necessary minor corrections. As to whether 60 years fits the correction cycle is not clear. Judging from the correction of solar calendar, the algorithm is just too cumbersome for most people to understand. For example, every 4 years you got leap year. But every 100 years & 400 years, you got exceptions etc etc etc. As to why the whole thing behaves like this, perhaps the people who belive in "Intelligent Design" have a better answer. The logic of using 干支 probably comes from the fact that about 30 days the moon wax & wane & about 12 moon cycles make a year. The least common multiplier (LCM) of 30 & 12 is 60. So a cycle of 60 sounds logical for convenience. In order to facilitate the notation, 10 is used instead of 30. And so (10,12) 干支 is adopted in our history.

For conversion of BC to 干支, the algorithm is 57 – Year mod 60, then calculate the index. For example,
57 BC the index is (0,0) 甲子
2 BC 55mod(10)=5, 55mod(12)=7, the index is (5,7) or 已未
1 BC 56mod(10)=6, 56mod(12)=8, the index is (6,8) or 庚申
For negative number, add 60 to it before the mod operation. For example,
58 BC –1+60=59, 59mod(10)=9, 59mod(12)=11, the index is (9,11) or 癸亥.
How about 0 BC? Ahha, it is non-existed. 0 is a fairly new concept. The next year of 1 BC is AD 1. So AD 1 must be 辛酉. That is what we got from our AD algorithm.
I am not sure how useful the conversion formula. The only info I got from is 地支. If you were born in 1942, it is 壬午 and 午’s index corresponds to Horse of 十二生肖. Even this info is not important to a lot of people. If you are interested, you probably can locate (ask your parents if they still alive) your 生辰八字, a piece of paper that showed your 年月曰時 of your birthday in lunar calendar format.

PS: Once in a while, someone wants to know your age but are afraid to ask. Instead they ask you 你數什麼? If you say 馬, you reveal your age right away. Here is the advice I got from my sister-in-law: 我數魚! (very clever).

陳哲俊 said...

I don't feel very comfortable with
index starting from 0. Normally, it starts from 1. If we do that, the equation for AD, we just use (
Year-3)Mod(10) and (Year-3)Mod(12). They still work.

Mark Lin said...

The reason for index from 0 is consistency. If we do index from 1, for example, (1973-3)mod(10) is 0, not 10. For AJ's algorithm, you have to convert 0 to 10. If we do index from 0, (1973-4)mod(10)=9. There is no conversion at all. In the digital world, it is logical & more convenient to start from 0 for indexing since there will be no two digit index 10. Number 0 is a fairly modern concept. This is the reason why there is no AD 0 or 0 BC in our calendar. If you work on computer programming, you will always find the indexing from 0 much more convenient. As a matter of fact, we got screwed up for a lot of things for so long. 1492 is 15th century & 1984 is 20th century. The one number difference throws us off since sometime we don't know whether we should add 1 or subtract one. If we just say 1492 is 14th century & 0076 is 0th (I just create a new English word) century, we don't have any confusion & the world will be a lot better place to live.

陳哲俊 said...

If we keep on arguing the issue, we'll touch a very controversal arguement about the natural number,which should include zero or not.
A very simple example is that any natural number can be devied by any natural number in natural number set without zero while the natural number with zero simply can't do that.I don't believe that
the world will be a lot of better place to live with natural number
without zero. As Ah-Ban puts it,
" Is that so serious?"

I am always very optimistic. If you believe that the world will be better, it will. Cheers!

陳哲俊 said...

I am sorry that I screwed up a very critical word just before " As Ah-
Ban puts it ". "without zero " should be " with zero "