前文 世界末日與曆法循環 發表之後，有個老友和我在Facebook上討論中國二十四節氣的問題。所謂「二十四節氣」，其中有些大家都很熟，如「立春」、「清明」，今年剛剛過的「立冬」等等。這方面我不是專家，為了增加談助資料，也逼著做一點探索。寫博文拋磚引玉，開卷有益，自己也得到進步。
一般以為二十四節氣是傳統農曆(陰曆，即是根據月亮運行的曆法)的元素，不過有人指出並非如此：
「它是根據陽曆劃定的，即根據太陽在黃道上的位置，把一年劃分為 24個彼此相等的段落。也就是把黃道分成 24個等份，每等份各佔黃經 15℃。由於太陽通過每等份所需的時間幾乎相等，二十四節氣的西曆日期每年大致相同。(http://ihouse.hkedcity.net/~hm1203/atmosphere/climate-china-24.htm)
我與老友的對話如下：
Franz：各位知否今日中國傳統曆法，是明末東來傳教的德國天文學家湯約望將陽曆和陰曆 (原稱夏曆，即夏朝的曆法) 結合的產品麼？湯約望還當過康熙皇帝的欽天監呢！
Chris：我查了漢朝的「淮南子」一書，已分二十四節氣，包括春分、夏至、秋分和冬至了。
Franz：春分、夏至、秋分和冬至本來是陽曆的節令，立春、立夏、立秋和立冬才是陰曆的節令啊！北半球的冬至在南半球就是夏至，澳洲人今天正過夏至呢！春分、夏至、秋分和冬至是因為地球會自轉及圍繞太陽公轉的結果，這是一位中國古代歷史學家向我解釋的。
難道漢代人已知道地球是圓的麼？歐洲人到中世紀才發現並證實地球是圓的啊！
Chris：你的學者朋友，如果識中文的，請他去看看「淮南子」卷三「天文訓」。
其實在 2000 多年前，希臘的學者已經猜到地球是圓的。有一個希臘天才更在正午時間，觀察到太陽光在A地是直射，在B地是微斜，利用三角函數比例，配合角度差異、A 地和B地的距離，計算到地球的直徑和圓周！
Franz：陰曆的春分、夏至、秋分、冬至日期每年都不同，陽曆則年年如是，每個閏年(例如2012、2008、2004等)。請作思考。
Chris：阿媽都教落「冬過三日老番東(聖誕)」。中國二十四節氣怎樣算出來的，請看淮南子卷三「天文訓」，特別是第11段（http://ctext.org/huainanzi/tian-wen-xun/zh ）：
「斗指子，則冬至，音比黃鍾。加十五日指癸，則小寒，音比應鍾。加十五日指丑，則大寒，音比無射。加十五日指報德之維，則越陰在地，故曰距日冬至四十六日而立春，陽氣凍解，音比南呂。加十五日指寅，則雨水，音比夷則。加十五日指甲，則雷驚蟄，音比林鍾。加十五日指卯中繩，故曰春分則雷行，音比蕤賓。加十五日指乙，則清明風至，音比仲呂。加十日指辰，則穀雨，音比姑洗。加十五日指常羊之維，則春分盡，故曰有四十六日而立夏，大風濟，音比夾鍾。加十五日指巳，則小滿，音比太蔟。加十五日指丙，則芒種，音比大呂。加十五日指午，則陽氣極， 故曰有四十六日而夏至，音比黃鍾。加十五指丁，則小暑，音比大呂。加十五日指未，則大暑，音比太蔟。加十五日指背陽之維，則夏分盡，故曰有四十六日而立 秋，涼風至，音比夾鍾。加十五日指申，則處暑，音比姑洗。加十五日指庚，則白露降，音比仲呂。加十五日指酉中繩，故曰秋分雷臧，蟄蟲北向，音比蕤賓。加十五日指辛，則寒露，音比林鍾。加十五日指戌，則霜降，音比夷則。加十五日指蹄通之維，則秋分盡，故曰有四十六日而立冬，草木畢死，音比南呂。加十五日指亥，則小雪，音比無射。加十五日指壬，則大雪，音比應鍾。加十五日指子。故曰：陽生於子，陰生於午。陽生於子，故十一月日冬至，鵲始加巢，人氣鍾首。陰生於午，故五月為小刑，薺麥亭曆枯，冬生草木必死。」
這段一開始，「斗指子」三個字，已表明計算法是根據北斗星的移動，不是月亮，所以不關「陰曆」事。
(文章允許轉貼，請具作者名字：梁煥松)
............
you have talked about this similar time last year, man. so, just recycling some topics. not bad though, reporting on new developments or pointing out implications is what we readers need, man.
回覆刪除加料，亦逼著我讀找一下古書。
刪除溫故知新，有何不可？
刪除Redideal
Some 2500 years ago Chinese astronomers already knew the exact length of the solar year: they had 7 lunar leap years every 19 lunar years. It is very simple then to divide 365.25 days by 24 to arrive at the 24 subdivisions. The 4 divisions, vernal equinox, etc. were also well known to Chinese astronomers long ago, and they act as anchors for the 24 subdivisions.
回覆刪除是的，古人很聰明，但我不肯定當時的人是否知道地球繞日而行。
刪除提起「十九年」的問題，提醒一下各位，任何人19、38、57、66、85歲的生日(19的倍數)，當天的陽曆X月X日和陰曆的「X月初X」，與你出生那一年相同。
My kid just did a small 5th grade project on Eratosthenes a few weeks ago. Eratosthenes was the one who calculated the radius and circumference of the Earth.
回覆刪除If one is observant about that 冬至 is the same one or the next calendar day (西曆) every year, one should be able to figure out it isn't lunar.
I don't know about 根據北斗星, but one doesn't need it to fix what days are summer solstice, winter solstice, spring equinox, and autumn equinox. For example, winter solstice is the shortest day of the year. On doesn't really need to observe 北斗星.
From a website (I can't verify the info, sorry): "As early as 2,500 years ago, about the Spring and Autumn Period (770-476 BC), China had determined the point of Winter Solstice by observing movements of the sun with a sundial."
In ancient time, after the Chinese excelled in farming technology, it went on to do well in other sciences and technology, including astronomy. There are volumes of astronomy records left by ancient Chinese. Nowadays astronomers at times check their data against those records. No other nations or cultures have such volume and detailed records covering such a long period of time.
By reading something about ancient Chinese technology one will find that Chinese were no dummies. In many areas of science and technology we were the leader. We had many inventions. (Many Chinese people today think otherwise. Sad.) Today we (the whole world) still use some of those inventions, though in a better or more advanced form.
--zpdrmn
Eratosthenes，謝謝提供名字。
刪除我是憑幾十年前看的科普書的記憶道出的。
任何人19、38、57、66、85歲的生日(19的倍數)，當天的陽曆X月X日和陰曆的「X月初X」，與你出生那一年相同。
回覆刪除以上對我不合用,1942年10月30日農曆九月廿一日,用萬年曆查過。如你手上有本萬年曆請代查一下。
幫你查過，
刪除1923, 1942, 1961年的10月30日都是農曆九月廿一。
1980, 1999, 2018年的10月30日都是農曆九月廿二。
我若干年前`查過,以為弄錯,1942出生,至今中西曆同日只一次,謝謝代查.
刪除Try to make myself clearer: The position relative to the Sun the Earth is at in its orbit determines when summer solstice, winter solstice, spring equinox, or autumn equinox is. To fix these days, observing the movement of the Sun in the sky and the shadows it casts is more direct than observing 北斗星. Even if one could do it with 北斗星, it would be much more difficult. Why bother? I am not even sure if one can really do it with 北斗星 (using star positions??). That's why I doubt it. --zpdrmn
回覆刪除要待高明指點了。
刪除我想起老殘遊記第12回的一段
「北斗七星開陽搖光，像幾個淡白點子一樣，還看得清楚。那北斗正斜倚在紫微垣的西邊上面，杓在上，魁在下。心裡想道：「歲月如流，眼見斗杓又 將東指了，人又要添一歲了....」
是古人用北斗星移動以計算一年之中的日子的方法。
It makes me dig deeper about Big Dipper.
刪除The result leads to my guess: The Big Dipper may have been used in determining winter solstices, but it was probably not very accurate, given the technology back then. It was, if so used, probably replaced later by more accurate methods by observing the Sun. But I'm no astronomer or science historian. So, it's just a guess.
What lead to my guess are the info you've provided and the following.
One can use the big dipper to determine the season, because its orientation is different in different seasons. (http://www.synapticsystems.com/sky/learnsky.html)
Whether the accuracy, using it to determine a certain day, is within a day or not is another question.
What time of the evening one observes it may affect the result in fixing a certain day, because its orientation keeps changing during the night.
"Go out tonight ( unless its cloudy ) and look for the Big Dipper. Make a mental note of where it is. Now go back out a few hours later and look for it again. You will see that it has moved." (http://www.synapticsystems.com/sky/learnsky.html)
An extreme case:
"(An important note: This stellar method of tracking the seasons has been designed to apply to the sky in the evening when most people are observing. If you are looking after midnight or in the wee hours of the morning, the Big Dipper will be in a position that doesn’t relate to the current season with this method because the Earth continues to spin all night, changing the location of the stars around Polaris.)"
Source: http://connect.sierraclub.org/post/OnTrack/the_big_dipper_tells_the_seasons.html?cons_id=&ts=1357203955&signature=66b6b53013eff93572b2ec835a39343e
To fix the day of winter solstice, one needs an accurate enough measurement. From Wiki: "...to be precise to a single day one must be able to observe a change in azimuth or elevation less than or equal to about 1/60 of the angular diameter of the sun. Observing that it occurred within a two day period is easier, requiring an observation precision of only about 1/16 of the angular diameter of the sun... This is often done by watching the sunrise and sunset or vice versa or using an astronomically aligned instrument that allows a ray of light to cast on a certain point around that time."
--zpdrmn
老兄研究比我深，要跟你學嘢。
刪除I learn from you too. Your info is interesting and makes me dig deeper a little. I wonder if back then laymen used the Big Dipper to make estimates while the court scientists used a more accurate method. That could be the case. Again, I don't really know.
刪除I always question stuffs, especially if they are about science. It's a die hard habit from my college days. --zpdrmn
我完全不懂, 但能做一下文抄公, 來自王力主編的中國古代文化常識, 第一章天文:
刪除古人很重視北斗, 因為可以利用它來辨方向, 定季節. 把天璇, 天樞連成直線並延長五倍的距離, 就可以找到北極星, 而北極星是北方的標誌. 北斗星在不同的季節和夜晚不同的時間, 出現於天空不同的方位, 人們看起來它在圍繞着北極星轉動, 所以古人又根據初昏時斗抦所指的方向來決定季節: 斗柄指東, 天下皆春; 斗柄指南, 天下皆夏; 斗柄指西, 天下皆秋; 斗柄指北, 天下皆冬.
這本書內容頗硬, 也因內容包括太多主題, 內容並不十分完全, 但卻蠻有一看價值, 尤其是有興趣諗古書的話.
姑且借此列一下十四章主題:
天文, 曆法, 樂律, 地理, 職官, 科舉, 姓名, 禮俗, 宗法, 宮室, 車馬, 飲食, 衣飾, 什物.
P.S. 我不是在商務印書館工作
謝資料！
刪除蝮,
刪除//把天璇, 天樞連成直線並延長五倍的距離, 就可以找到北極星// the same for Westerners: Polaris, the North Star, is found by imagining a line from Merak (β) to Dubhe (α) and then extending it for five times the distance between the two Pointers. (Wiki)
Interesting trivia: take a look at the design of Alaska State flag: http://en.wikipedia.org/wiki/Alaska
--zpdrmn
北極星比其他的星略大一點.
刪除阿拉斯加又是在美國最北的一個洲.
又聽說那裏的人很擅長外交.
有趣.
廿四節氣是跟太陽年， 因為用月亮的話， 由於月亮年比大陽年少， 因此只用月亮年， 不能估計到耕作時間，
回覆刪除所以中國會用陰陽曆， 加入節氣和19年7潤。
中國節氣計法， 用冬至， 夏至， 春分， 秋分， 定位後， 再平均分配。
潤月的定法， 由於廿四節氣， 理論上一個月有2個節氣， 因此， 如該陰曆月無中氣， 就潤那個月，
那就可令到同一個月有2個節氣。
而中國早於周朝已知一年有365又4份1日， 所以中國所用的天球度數， 一個圓是365又4份1度， 和西方360度不同， 看古代天文誌要知這一點。
何解中國天球一個圓是365又4份1度？ 是因為在太陽在天球黃道行， 一日行一度， 一個圓剛好一年。
至於地球是否圓的問題， 中國古代司天監有討論過蓋天說和渾天說的問題， 但因傳統看法天圓地方所限， 所以只討論天是否球體， 因為司天監發現不同司天台測量數據有出入。
最後在唐朝時期做了個官方實驗（幾時就忘記了， 畢竟是十年前做的學校PROJECT）， 分別在北方和南方在同一日（忘了冬至日還是夏至日）正午用圭表度影長， 最後是渾天說勝， 證明天球是球體。
Thank you for pointing it out. I have read similar description before, but I don't have any sources off hand, so I haven't said anything. Once again, it shows how advanced ancient Chinese technology was. --zpdrmn
刪除謝謝，獲益良多。
刪除今年双春,年花會早開,明年冇立春,又俗稱盲年.
回覆刪除以前看過介紹中國古代天文學的書籍，最驚奇的地方是：中國古代天文學的理論基礎是錯誤的，但錯誤的理論卻能解釋和推演很多真實的天文現象。這就好似中醫的經絡理論，拿本質上不存在的東西作為立論依據來治病救人，功效神奇。這是很值得玩味的地方。
回覆刪除古代中國人似乎從未意識到地球是個球體。即便渾天說認為天如雞子，地如卵黃，其本意也絕不是說地球像蛋黃一樣是個球體，只是形容天包裹着地而已。大可以把渾天說里的地，理解成一個扁平的盤子，只有朝上的一面才有山川草木人畜。日月星辰散布在天球上，圍著“地盤子”转，當日月星辰轉到“地盤子”下面时，就在天空中看不到了。
古人不知道萬有引力能吸著人不至掉出太空，不能想象「地球」，所以有「天圓地方」的想法。
刪除看過有些文章說，中世紀的教會也是以此為真理，美國現在有些教會，仍然信這套。
Science is empirical. Sometimes, even if the theory sucks but the empirical data guide you in a big way. And you can still get a lot of things right.
刪除On the other, even if the theory is very elegant and sophisticated but the empirical data don't support it, you need to rewrite or even throw away the theory. --zpdrmn
以前讀過皮毛的Philosophy of Science，記得有類似的說法。
刪除I don't know much about philosophy. I just see it as a working methodology learned from past mistakes by scientists as a whole. --zpdrmn
刪除FYI, an example of Ming Dynasty math and music research, equal temperament musical scale and the 12th root of 2 to 24 decimal places:
回覆刪除http://zh.wikipedia.org/wiki/%E6%9C%B1%E8%BC%89%E5%A0%89
http://zh.wikipedia.org/wiki/File:%E4%B9%90%E5%BE%8B%E5%85%A8%E4%B9%A6%E5%85%A8-123.jpg
--zpdrmn
非常厲害！
刪除"加十五日指醜，則大寒，音比無射。" 中的 "醜", 應是 "丑".
回覆刪除是的。謝！
刪除