[neil]

Determination of the Founding Year of Zhou Dynasty and the Western Zhou Chronology by Coupling Ganzhi to the Western Calendar and the Basic Rules of Interpreting the Western Zhou Lunar Terminology

Lin, Ershen
First Draft: August 29-September 4, 2006
(posted: Sept. 5, 2006 on Chronology Research)

Introduction
Since the beginning of the Xia Shang Zhou Chronology Project in the 1990's, especially since the publication of the project report, much interest has been created among the scholars in China and overseas alike, which could be regarded as a major achievement of the project regardless of the correctness of the conclusions, and is responsible for this article as well.
The basic anchor point of the project is the founding year of Zhou Dynasty. The project has mobilized means and resources from archeology to astronomy and arrived at three candidate years: 1046 BC, 1044 BC, and 1027 BC, and gave its favor to 1046 BC. Discussion on the achievements and defects of the project is beyond the scale of this article. In particular, 14C-dating of the critical Fengxi samples has been extensively discussed by relevant papers. Hence, merely a brief discussion is attempted here regarding the methodology applied to the final choice of the founding year.
The choice itself was primarily based on the description of the astrological observation by Lingzhoujiu in the book Guoyu. Obviously, interpretation of ancient records could never be completely reliable. Therefore, it is dictated by the laws of statistics. If the reliability of the final conclusion is dependent on the individual deductions, it is the product of the individual deductions. With increased number of individual deductions, the reliability of the final conclusion drops exponentially. There are five descriptions of the observation by Lingzhoujiu, which is a large number. Assuming individual deduction is 90% reliable, the final conclusion is merely 59% reliable, totally unacceptable; assuming individual deduction is 95% reliable, the final conclusion is merely 77% reliable, still unacceptable; assuming individual deduction is 98% reliable, the final conclusion is merely 90% reliable, barely acceptable. But 98% requirement in reliability of any deductions of ancient records is an insurmountable obstacle considering the current state of art in archaeology, which naturally turns into an insurmountable obstacle for reaching a reliable final conclusion. This explains why the project merely used two of the five observations, namely those regarding the positions of the sun and Jupiter, in their deduction, and ended up with only one "precise" solution. From this perspective, the solution of 1046 BC is not the true solution based on the five observations of Lingzhoujiu; were all five observation be used, no solution would have been found in the probable time range for the founding year. This reflects an important point that has been made repeatedly by many researchers: the descriptions by Lingzhoujiu were not based on facts. Another important factor in their final choice was the "Wu-Cheng" document, which is also of dubious value, which will be further discussed later. As far as the solution of 1044 BC proposed by the project, it was based on seven astronomical observations, an unthinkable task that would have resulted in even lower reliability than the solution of 1046 BC.
Despite the fact that the project use numerous methods to check on each other, the final solution of the chronology solely depends on the deduction of the ancient articles and the inscription of the bronze vessels, as well as the understanding of the lunar phase terminology. The project ran into trouble precisely at this crucial point. First of all, the complexity and uncertainty of the early Zhou calendar especially the leap months cannot be resolved overnight. In addition, the calendars used by the ancient authors are hard to determine regardless of the official standard at the time. Finally, the interpretation of the lunar phase terminology has remained controversial while the project adopted more flexible interpretation and even went as far as changing numerous descriptions on the bronze vessels in order to match the framework of the proposed Zhou chronology.
Changing the descriptions on the bronze vessels is nothing unusual these days. But in the feudal time, mistakes on such important matter with symbolic meaning involving the kings was unthinkable, and any mistakes would have been corrected. As matter of fact, descriptions without solution usually indicate the necessity to change the interpretation or the chronological framework.
Overall speaking, the project suffers from the defects in its methodology and robustness. Hence, it is not surprising that the conclusions have been questioned by experts in the fields of archaeology, ancient calendar, astronomy, military strategy, etc. Unfortunately, many alternative chronological frameworks proposed thus far are even less convincing than that of the project, and no further comment is warranted here.
The brief analyses above show the need to establish a simpler, more reliable, and more general method for the purpose of determining the Zhou chronology. The ganzhi coupled to the western calendar is the first systematic attempt at this direction, and hopefully the conclusion will stands the test of time. For deduction of the lunar phase terminology, more strict interpretation will be used as much as possible, and a summary of three rules will be empirically formulated at the end of this article.

Methods
A. Determination of the Authenticity of the Historical Records.
Historical records on the military events leading up to the founding of Zhou Dynasty is inconsistent. Yi-Zhou-Shu (Ch. Shifu) mentioned on Bingwu day of the first month was Pang-sheng-ba; on the next day Dingwei, the Martial King (Wu King) left the capital to the battle ground. On Jiazi, which was "five days" later (actually four days later), he arrived at the destination. However, Zhou-Shu (Ch. Wu-Cheng) gave the departing dates as Guisi, the day after Pang-si-ba Renchen.
Was the correct day of departure then? Shang-Shu (Ch. Taishi) described that on the eleventh year, the Martial King battle the Ying. On the Wuwu day of the firth month, the army crossed the Yellow River at Mengjin. Shi-Ji (Ch. Zhou Benji) described that on the Wuwu day of the twelfth month, the army completed crossing the Yellow River at Mengjin, which confirms the day but not the month on Shang-Shu. "The twelfth month" does not comply with the calendar of either Xia, Ying, or Zhou, and appears to be unreliable. Similarly, Shi-Ji described the battle date as the Jiazi, five days after Ji-si-ba of the second month, confirming the day but not the month. So far, there is no controversy regarding the ganzhi of the day.
The march from the Zhou capital to Mengjin could be either from Dingwei till Wuwu (i.e., 12 days) or from Guisi till Wuwu (i.e., 26 days). On the other hand, from Mengjin to the capital of Ying lasted from Wuwu till Guihai (the day before Jiazi), or 5-6 days. Since the distance from the Zhou capital near Xi'an to Mengjin was only slightly longer than the distance from Mengjin to the Ying capital near Snyang, the march before Mengjin could not last as long as 26 days while the march after Mengjin lasted merely 5-6 days. Obviously, the 12-day option is more reasonable, which also includes the time required to cross the river; otherwise it could be as short as 7 days. Based on this analysis, Yi-Zhou-Shu (Ch. Shifu) is considered as the correct version of the history.
B. Method of Deduction.
The uncertainty of the early Zhou calendar pertaining the leap month is an obstacle and attracted many questions. In comparison, the western calendar is far more certain, as the uncertainty of the leap day of the early Julian calendar has been overcome by the uniform standard adopted by NASA for its pre-historical database. Furthermore, the ganzhi system for the day has been continuously and consistently adopted from the prehistory with very few exceptions in limited regions. Based on these considerations, combining the western calendar and the Chinese ganzhi system will produce a cyclical table, to which information on the lunar phases (Chinese Academy of Science database) was added to enable resolution of historical/archaeological records of the ancient dates based on ganzhi of the day and the lunar phase. This system bypasses the uncertainty of the ancient Chinese calendar. The information of the month of the lunar calendar, if available, are assigned based on the commonly known rule and generally is not an issue.
C. The BC and the Astronomical System.
The BC (Before Christ) system adopted by historians and the astronomical system adopted by the astronomers are both used here. It should be noted that the latter has Year Zero, or year 0 (1 BC); year -1 means 2 BC, etc. To avoid confusion, all the important results are described with both system, the rest with the BC system only.

The Date the Martial King Conquering the Shang Was March 10, 1044 BC/-1043, or the 5th Day in the Second Month on the Xia Calendar.
The historical event is assumed to fall into the 11th century BC. Using Dec. 31, 2000 (Guihai) as the starting point, Jan. 1, 1100 BC (Renxu) was 1,132,262 days or 18,871 ganzhi cycles plus 2 days back. Using Jan. 1, 1050 BC (Jiashen) was also calculated and used as the anchor point, we obtained the ganzhi-lunar phase table for 1071-1000 BC. Table 1 is a part of it spanning 1044-1042 BC, to be read by columns from left to right. The first and the last columns list the ganzhi combinations used to denote the day (1). The gray background denotes the days of the new moon; the yellow background denotes the days of the full moon; the orange background denotes the days referred to in the historical records (the days of departing, crossing the river, the battle day, and the day of casting the first Zhou bronze vessel); the bold font denotes the eclipses. The leap year and eclipses were checked with the NASA database to ensure the validity of the table. Similar table was created for the 9th and the 8th centuries BC.
The screening covers 1071-986 BC to ensure 90% coverage of the probability range based on the 14C-dating of the Fengxi samples, because the screening range (1050-1000 BC) used by the official project merely covers 68.4% probability range.
The ancient text proves by itself that the lunar phase terminologies used by Yi-Zhou-Shu and Shi-Ji are to be deduced in the narrow sense. Pang-sheng-ba indicates the asymmetrical feature of the phase on the day after the full moon; "ruo-yi-ri" means the day after pang-sheng-ba. Any broad sense interpretations would render the two-step reference system redundant. Similarly, Ji-si-ba is also to be deduced likewise. Considering the fact that Bingwu of the first month (pang-sheng-ba) is 15 days ahead of Gengshen of the second month (ji-si-ba), Pang-sheng-ba should refer to the day after the full moon whereas ji-si-ba should refer to the day of the new moon.
Within the range of 1071-986 BC, 1044 BC was the exclusive solution to match the records mentioned above with the restrain of the lunar New Year, which turns out to be the Xia calendar instead of the Ying calendar officially adopted during the period. Two probable explanations could be forwarded here: (1) the historical record was converted by later copyist to the Xia calendar; (2) The original author used the Xia calendar because it was still in use by the general populace although not in the official documents. The explanation is more probable as it could explain why the Han Dynasty eventually restored the Xia calendar.
Table 2 is a summary of the events. The 1st column shows the date on the lunar calendar starting from the New Year (1.1) of the Xia calendar (Feb. 4, 1044 BC) leading up to the battle day and ends in the vessel casting. The second column shows ganzhi of the day; the third column, the historical references; the fourth column, the source of the reference; the fifth column, the corresponding date on the western calendar.
The following is the selected translation of the table:
Month 1, day 1, Gengyin, (Lunar New Year or month 1, day 1, Feb. 4, 1044 BC)
Month 1, day 16, Yisi, full moon (Feb. 19, 1044 BC);
Month 1, day 17, Bingwu, month 1 Bingwu, pang-sheng-ba (the reference day), source: Yi-Zhou-Shu (Ch. Shifu) (Feb. 20, 1044 BC);
Month 1, day 18, Dingwei, yi-ri Dingwei (the departing day), source: Yi-Zhou-Shu (Ch. Shifu) (Feb. 21, 1044 BC);
Month 1, day 29, Wuwu, month 1 Wuwu (month 12 Wuwu on Shi-Ji), (the day of crossing the Yellow River at Mengjin), sources: Shang-Shu (Taishi)/Shi-Ji (Zhou Benji) (March 4, 1044 BC) (error on the month of the Shi-Ji record);
Month 2, day 1, Gengshen, ji-si-ba (the reference day), source: Yi-Zhou-Shu (Ch. Shifu) (Mar. 6, 1044 BC);
Month 2, day 5, Jiazi, five days after ji-si-ba (actually 4 days after) (month 1 Jiazi on Shi-Ji), (the battle day, the day Zhou Dynasty was considered founded), sources: Yi-Zhou-Shu (Ch. Shifu)/Li Gui (a bronze vessel)/Shi-Ji (Ch. Qi-Shijia) (Mar. 10, 1044 BC) (error on the month in Shi-Ji record);
Month 2, day 12, Xinwei, (the day of casting bronze vessel Li Gui), source: Li Gui (Mar. 17, 1044 BC).
What should be noted is that Jizhong Jinian mentioned the total duration of 257 years for western Zhou Dynasty. Starting from 770 BC (the end of western Zhou, as commonly acknowledged), the founding year should be 1027 BC. The issue has to be addressed.
If we assume the founding year of Zhou Dynasty to be 1027 BC, the year when Cheng King assumed power has to be 1018 BC (or later), taking into account of (no less than) 2 years of reign of the Martial King and 7 years of regency under Duke Zhou. The conclusion is contradicted by the independent conclusion derived from a bronze vessel made when Cheng King conducted his grand ceremony of assumption in 1035 BC (see below).
Furthermore, Zhu-Shu recorded forty years of peaceful time under Cheng King and Kang King, which was essentially consistent with the record on Shu-Ji of forty-plus years of peace under the same. Since the regency of Duke Zhou was marked by major rebellions and civil wars, the forty years of peace must be counted from the year of assumption of Cheng King. Taking into account of the year one of Zhao King in 996 BC that will be independently derived (see below), there are only 22 years left should we start from 1018 BC.
Taken together, the record of 257 years of duration is to be considered erroneous. Alternatively, from 1044 BC till 770 BC there are 274 years, or 275 years by the ancient way of counting, which has been demonstrated by the way of counting days ("5 days after" means "4 days after", see above). For this reason, the record of 257 years could have been caused by the error by the copyist who mistaken 275 years as 257 years (2). From 1044 BC till 1035 BC (9 years after) would be the year of assumption of Cheng King, and from 1035 BC till 996 BC there are 40 years (ancient way of counting), all fit into the records.
From the above analyses, the founding year of Zhou Dynasty was determined as 1044 BC/-1043, and the battle date was March 10, or month 2, day 5 on the Xia calendar.
It should also be pointed out that one of the candidate battle date obtained by the project was January 9, 1044 BC, which fall into the same year but different date, and was based on different starting records. The date of March 10 is more plausible as it addressed the question by military expert Mr. Wei Xiaoming that a major battle could not have been fought in the coldest time (at dawn) of the day in the coldest month (January) of the year, which follows a long forced march.

The Year One of Cheng King Was 1042 BC/-1041 (the Last Year of the Martial King), His Year of the Grand Ceremony Was 1035 BC/-1034, and His Last Year Was 1029 BC/-1028.

A. Literature analyses.
The year one of Cheng King was deduced from Zhou-Shu (Ch. Zhao-gao, Ch. Luo-gao). The two chapters describe the same historical event, namely, the foundation of Luo (today's Luoyang, Henan Provinece). The deduction was carried out with the ganzhi-lunar phase table as above. The deductions are attached to the record in parentheses.
Zhu-Shu, Ch. Zhao-gao:
Month 2, ji-wang (Nov. 24, 1037 BC). Six days thereafter on Yiwei (Nov. 29), the king came from Zhou, to Feng. Taibao carried out a survey of the location before Duke Zhou. Month 3, Bingwu, chu (Jan. 9, 1036 BC). Three days thereafter, Wushen (Jan. 11), Taibao arrived in the morning, determined the location by divination. … Three days thereafter, Gengwu (Jan. 13), Taibao and others surveyed the site on the band of Luo River. Five days thereafter, Jiayin (Jan. 17), the location was fully surveyed. The day after, Yimao (Jan. 18), Duke Zhou arrived at Luo in the morning, inspected the site of the new city. Three days thereafter, Dingsi (Jan. 20), a worshipping (of the Heaven) ceremony was conducted in the suburb (of Luo), and two bulls were sacrificed. The day after, Wuwu, worshipped (the Earth god) in the city. …
Zhou-Shu, Ch. Luo-gao:
Duke Zhao had completed his survey, and Duke Zhou departed to found Chengzhou … Wuchen (Sept. 28, 1036), the king conducted the annual worshipping in the new city. … The king decreed to Duke Zhou to record the event in the book on month 12 (the first of which was Sept. 29). Duke Zhou protects the heavenly mandate received by the Literate King and the Martial King, the year seven.
The word "gongwei" is interpreted as surveying of the city wall and the palace building. After the ceremony under Duke Zhou, the construction started in the late January till the royal annual worshipping in the late September, eight months had passed. This was the year seven of Duke Zhou's regency, or 1036 BC/-1035. Therefore, the year one of Cheng King (Duke Zhou's Regioncy) was 1042 BC/-1041, which was the last year of the Martial King.
It should be noted that Cheng King ascended the throne in 1042 BC, which was merely two years after the founding of Zhou Dynasty by the Martial King. Zhou-Shu (Ch. Jinteng) recorded the death of the Martial King "two years after the conquest of Shang", which is 1042 BC, indeed. Zhou-Shu (Ch. Tai-shi) recorded the conquest in "the eleventh year" of the Martial King (3) whereas Zhou-Shu (Ch. Hongfan) recorded king visiting Qizi in his "thirteenth year". All the evidences indicate that the Martial King lived at least until 1042 BC. As the last year of the Martial King and the year one of Cheng King are the same, the calendar conversion here took place immediately after the death of the Martial King.
The last year of Cheng King was deduced from Zhou-Shu (Ch. Gu-ming), the conclusion being attached to the record in parentheses.
Zhou-Shu, Ch. Gu-ming:
Cheng King was about to pass away … On month 4, zai-sheng-ba (Guihai, feb. 19, 1029), the king was ill. Jiazi (Feb. 20, 1029 BC), the king was cleansed in the river. The following day, Yichou (Feb. 21, 1029), the king died.

B. Analyses of the inscriptions on the bronze vessels.
The conclusion above was further supported by the inscription on Bao-You and he-Zun.
Bao-You:
Yimao, the king decreed to Bao and the five vessel kings in the east … to inform all parties to meet in the Grand Ceremony … on ji-wang of month 2.
Ji-wang is assumed to be 2 days after the full moon.
Yimao is Jan. 13, 1035 BC/-1034. Obviously, this year was the year of the Grand Ceremony, the year one of Cheng King in the true sense. The Grand Ceremony of 1035 BC should also be distinguished from the annual ceremony of 1036 BC as recorded in the document above.
He-Zun:
The king had recently moved to Chengzhou (Luo), … on month 4, Bingxu. The king decreed to Zong-Xiaozi in the chamber of Jing … the ceremony five (4) of the king.
Month 4, Bingxu was March 24, 1031 BC/-1030the date fits into the chronology.

The Year One of Kang King (the Grand King) Was 1028 BC/-1027

As the last year of Cheng King was 1029 BC, the year one of Kang King should be 1028 BC if the calendar was converted in the following year, as usually practiced. This conclusion is supported by the inscriptions on Zuoce-Da-Ding, Zhe-Zun, Xiao-Yu-Ding, and Ling-Zun. The deduction was carried out with the ganzhi-lunar phase table as above.
Zuoce-Da-Ding:
The Duke arrived for casting the ceremonial vessels of the Martial King and Cheng King. Month 4, Ji-sheng-ba, Yichou …
Ji-wang was assumed to be one day after the full moon.
The exclusive solution by narrow sense deduction during the reign of Kang King was February 23, 1023 BC/-1022.
Ze-Zun:
Month 5, the king at Xu. Xuzi, (the king) decreed to Zuoce Da … the ceremony nineteen of the king.
Month 5 is deduced as month 5, day 1; the date was April 5, 1010 BC/-1009.
Xiao-Yu-Ding: Month 8, Ji-wang, day of Jiashen … The following day Yiyou … the ceremony twenty-five of the king.
Ji-wang is assumed to be 5 days after the full moon (broad sense).
The date was August 27, 1004 BC/-1003.
Ling-Zun:
Month 8, day of Jiashen (Sept.19, 997 BC/-996), the king decreed to Mingbao, the son of Duke Zhou … Dinghai (Sept. 22), Chang-Ling-Shi prayed in the Temple of Duke Zhou. … Month 10, yue-ji, Guiwei (Nov. 17), Duke Ming arrived at Chengzhou …. Jiashen (Nov. 18), Duke Ming sacrificed the cattle in Jing Palace. Yiyou (Nov. 19), sacrificed in the Kang Palace (the Grand Palace). Thereafter, sacrificed to the king. …
Month 8, day of Jiashen and month 10, yue-ji are both assumed to be the day of new moon. The deduction shown is the last solution and provide the best fit and narrow sense deduction. At the time, Kang King was of senior age, and therefore, sent the son of Duke Zhou for administrative purposes.

The Year One of Zhao King Was 996 BC/-995 (the Last Year of Kang King), the Last Year was 977 BC/-976.

The year one of Zhao King was deduced from the inscription on Jing-Fang-Ding with the ganzhi-lunar phase table as above.
Jing-Fang-Ding:
Month 10, Jiazi (Spet. 25, 979 BC), the king was at Zongzhou, and decreed to Shizhong (and) Jing to inspect the south … Month 8, chu-ji, Gengshen (July 18, 978 BC), arrived, prayed in Chengzhou. The month, ji-wang, Dingchou (Oct. 3, 978 BC), the king was at the Grand Hall, Chengzhou …
Chu-ji Gengshen was assumed to be 4 days before the new moon (broad sense); ji-wang Dingchou, on the day of the full moon.
As the historians consider the vessel to be made in the year nineteen, and the record spans two years, the first date belongs to the year eighteen (979 BC/-978), whereas the second date, the year nineteen (978 BC/-977). Therefore, the year one of Zhao King was determined as 996 BC/-995. As mentioned earlier, this gives the so-called "forty years of peace" under Cheng King and Kang King (1035 BC-996 BC, 39 years in total, or 40 years by the ancient way of counting). As the last year of Kang King was also 996 BC, the calendar conversion must have taken place immediately after the death of Kang King.
In addition, Jing-Yi should also be assigned to the reign of Zhao King.
Jing-Yi:
Month 4, chu-ji, Bingyin (Feb. 20, 983 BC), the king was at Jing. The king bestowed the knife to Jing. … Month 13 (the first day was Nov. 12, 983 BC), the king was at Jing …
Chu-ji was assumed to be on the day of the new moon. There are multiple solutions; the one immediately before Jing-Fang-Ding was considered most likely and selected.
Zhu-Shu Jinian mentioned the following: "the year nineteen of Zhao King, the sky darken, the animals shocked, lost Army Six in Han River." And thereafter, another entrance mentioned "the last year of Zhao King, colorful light observed at Ziwei at night. This year, the king was in the south and never returned." These records suggest that Zhao King reigned for 20 years (996 BC/-995 till 977 BC/-976), as the last year is interpreted as the year after the year nineteen.

The Year One of Mu King Was 977 BC/-976(the Last Year of Zhao King).

The year one of Mu King was deduced from the inscriptions on Hu-Gui and Xian-Gui with the ganzhi-lunar phase table as above.
Hu-Gui (cover):
The year thirty, month 4, chu-ji, Jiaxu, the king was in the New Palace of Zhou, and resided in the Grand Hall …
Chu-ji was assumed to be one day after the new moon. Two alternative candidate dates include Feb. 24, 948 BC or Mar. 30, 943 BC.
Xian-Gui:
The ceremony thirty-four, month 5, ji-wang, Wuwu, the king was in Fengjing, conducted memorial ceremony of Zhao King.
Ji-wang was assumed to be the day of the full moon or the day after.
The ceremony thirty-four was interpreted as the year thirty-five (see below), otherwise the date on Xian-Gui and Hu-Gui are incompatible regardless of the chronology adopted. Two alternative candidate dates include May 13, 943 BC or April 17, 938 BC.
The results of Hu-Gui and Xian-Gui give two identical alternative candidates for the year one of Mu King: 977 BC and 972 BC. Since the year one of Zhao King has been determined as 996 BC, the year one of Mu King can only be 977 BC/-976. Two alternative candidate dates include, which is 19 years after the year one of the Zhao King (the year twenty of the Zao King), and calendar conversion took place immediately after the death of the Zhao King. This explains why ceremony thirty-four matches the year thirty-five.
The conclusions above is supported by the deduction of the inscriptions on Yao-Ding, Lu-Gui, Qiu-Wei-Gui, and Bokui-Fu-Xu.
Yao-Ding:
The king's year one, month 6, ji-wang, Yihai (May 28, 977 BC/-976), the king was in the Grand Hall of Mu King. … The month 4, ji-sheng-ba, Dingyou (April 15, 976 BC/-975)…
Ji-wang is assumed to be the day of the full moon, ji-sheng-ba Dingyou, 13 days after the new moon (broad sense). Also assumed is an advanced leap month in 975 BC, without which Yao-Ding would find no solution before Xuan King, an unlikely scenario. If the vessel were to be placed under the reign of Yi King ,it would make the two dates incompatible. Hence, it become necessary to place it under Mu King.
Lu-Gui:
The year twenty-nine, month 9, ji-wang, Gengyin (Aug. 11, 954 BC/-953), the king was at Zhou, residing in the Grand Hall …
Ji-wang is assumed to be the day after the full moon.
Qiu-Wei-Gui:
The year twenty-seven, month 3, ji-sheng-ba, Wuxu (Feb. 4, 951 BC/-950), the king was at Zhou, residing in the Grand Hall …
Bokui-Fu-Xu:
The year thirty-three, month 8, ji-si-ba, Xinmao (June 25, 945 BC/944 BC), the king was at Zhou …
Ji-si-ba Xinmao is assumed to be 8 days after the new moon (broad sense).

The Year One of Gong King Was 922 BC/-921.

The year one of the Gong King was deduced from the inscription on Cuocao-Ding of Year Fifteen with the ganzhi-lunar phase table as above.
Cuocao-Ding of Year Fifteen:
Year fifteen, month 5, ji-sheng-ba, Wuwu (April 3, 908 BC/-907), Gong King was at the New Palace of Zhou, shooting …
Ji-sheng-ba Wuwu is assumed to be 3 days after the new moon (broad sense). The date was the exclusive solution in the period from 925 BC till 900 BC, and the year one could then be determined to be 922 BC/-921(5).
The conclusion above is supported by the inscriptions on Cai-Gui, Wei-He of the year three, Wei-Ding of the year five, Shi-Cai-Gui, Wei-Ding of the year nine, Guai-Bo-Gui, Taishi-Yu-Gui, Xing-Hu of the year thirteen, and Xiu-Pan.
Cai-Gui:
The year one, ji-wang, Dinghai (Dec. 23, 923 BC/-922), the king was at Yu. …
Ji-wang was assumed to be the day of the full moon. The "year one, ji-wang" is interpreted as the year one, month 1, ji-wang".
Wei-He of the year three:
The year three, month 3, ji-sheng-ba, Renyin (Feb. 25, 920 BC/-919), the king raised the flag at Feng …
Ji-sheng-ba Renyin was assumed to be 12 days after the new moon (broad sense).
Wei-Ding of the year five:
Month 1, chu-ji, Gengyin (Dec. 25, 919 bC/-918), Wei reported to Jing-Bo … the ceremony five.
Chu-ji was assumed to be the day after the new moon, and an advanced leap month was assumed in 919 BC.
Shi-Cai-Gui:
The ceremony eight of the king, month 1, day of Dingmao (Dec. 26, 916 BC/-915) …
Wei-Ding of the year nine:
The year nine, month 1, ji-si-ba, Gengchen (Jan. 3, 914 BC/-913), the king was in the Ju-Palace of Zhou …
Ji-si-ba Gengchen is assumed to be 6 days before the new moon (broad sense).
Guai-Bo-Gui:
the year nine, month 9, Jiayin (Aug. 5, 914 BC/-913), the king decreed to Duke Yi to start an expedition against Mei-Ao … Month 2, Mei-Ao arrived … Yiwei (Jan. 13, 913 BC/912 BC), the king decreed Zhong to award Guai-Bo …
Month 9 Jiayin was 2 days after the new moon, month 9 Yiwei was on the day of the full moon.
Taishi-Yu-Gui:
The month 1, ji-wang, Jiawu (Jan. 1, 911 BC/-910), the king was in Shi-Liang Palace of Zhou, … the year twelve.
Ji-wang Jiawu is assumed to be 10 days after the full moon (broad sense).
Xing-Hu of the year thirteen:
The year thirteen, month 9, chu-ji, Wuyin (Aug. 20, 910 BC/-909), the king was in Si-Tu-Hu Palace of Zhou …
Chu-ji was assumed to be the day after the new moon.
Xiu-Pan:
The year twenty, month 1, ji-wang, Jiaxu (Dec. 30, 904 BC/-903), the king was in the Grand Palace of Zhou …
Ji-wang Jiaxu is assumed to be 12 days after the full moon (broad sense).

The Year One of the Yi King (the Virtues King) Was 899 BC/-898.

The year one of Yi King has been deduced by Fang from Zhu-Shu record of the solar eclipse on April 21, 899 BC/-898. This conclusion is supported by the deduction of the inscriptions of Shi-Li-Gui, Shi-Hu-Gui, and Bian-Dun with the ganzhi-lunar phase table as above.
Shi-Li-Gui:
The year one of the king, month 1, chu-ji, Dinghai (Dec. 22, 900 BC/-899), Bai-He-Fu said: …
Chu-ji Dinghai is assumed to be 2 days ahead of the new moon.
Shi-Hu-Gui:
The year one, month 6, ji-wang, Jiaxu (June 7, 899 BC/-898), the king was at Du residence …
Ji-wang Jiaxu is assumed to be 3 days after the full moon (broad sense).
Bian-Dun:
The year two, month 1, chu-ji (Dec. 14, 899 BC/-898), the king was in the shao Palace if Zhou. Dinghai (Dec. 17, 899 BC/-898), the king was at Xuanxie …
Ch-ji is assumed to be the day after the new moon, and Dinghai, 4 days after.

The Year One of Xiao King (The Filial King) Was 894 BC/-893.

The Year One of Xiao King is deduced from Shi-Dan-Ding and Dou-Bi-Gui with the ganzhi-lunar phase table as above.
Shi-Dan-Ding:
The year one, month 8, Dinghai (July 23, 894 BC/-893), Shi-Dan accepted the decree of casting the ceremonial Yi of Da-Ni of Zhou king. …
The main difficulty for determination of the year one of Xiao King has been caused by lack of "high-number year" vessels. The issue was resolved by Shi-Dan-Ding, which has no other solution before Xuan King. Since it is not considered to be as late as Xuan King, it is naturally assigned to the reign of Xiao King. The inscription has solutions in every year from 894 BC till 891 BC. The optimal solution is 894 BC as it is a narrow sense interpretation on the day of new moon, consistent with the bias of the Zhou tradition. Here, month 8 Dinghai is interpreted as month 8, chu-ji, Dinghai.
Dou-Bi-Gui:
The month 2 of the king, Ji-sheng-ba, Wuyin (Jan. 5, 892 BC/-891), the king occupied the Grand Hall of Shi-Xi …
Ji-sheng-ba is assumed to be the day of the new moon. The date is the exclusive solution of the middle period of the Western Zhou, which proves the correctness of the interpretation of the inscription on Shi-Dan-Ding.
The conclusion above is also compatible with the deduction of the inscriptions on Shi-Yu-Gui, Xing-Xu, and Mu-Gui of the year seven.
Shi-Yu-Gui:
The year three, month 3, chu-ji, Jaixu (Mar. 2, 892 BC/-891), the king was in Shi-Lu Palace of Zhou …
Chu-ji Jiaxu is assumed to be 3 days ahead of the new moon (broad sense).
Xing-Xu:
The year four, month 2, ji-sheng-ba Wuxu (Jan. 20, 891 BC/-890), the king was in Shi-Lu Palace of Zhou …
Ji-sheng-ba Wuxu is assumed to be 4 days ahead of the new moon (broad sense).
Mu-Gui of the year seven:
The year seven of the king, month 13, ji-sheng-ba, Jiayin (Nov. 16, 888 BC/-887), the king was at Zhou …
Ji-sheng-ba Jiayin is assumed to be 4 days after the new moon.

The Year One of Y'i King Was 887 BC/-886

The Year One of Y'i King is deduced from the inscriptions on Jian-Gui and yang-Gui with the ganzhi-lunar phase table as above.
Jian-Gui: The year five, month 3, chu-ji, Gengyin (Jan. 30, 883 BC/-882), the king was in Shi-Lu Palace of Zhou …
Chu-ji Gengyin is assumed to be 5 days after the new moon (broad sense).
Yang-Gui: the month 9 of the king, ji-sheng-ba, Gengyin (July 29, 883 BC/-882), the king was in the Grand Palace of Zhou …
Ji-sheng-ba Gengyin is assumed to be 7 days after the new moon (broad sense). There are multiple solutions; the one closest to Jian-Gui was selected due to linkage via Neishi Xian.

The Year One of La King (6) (the Spirited King) Was 879 BC/-878.

The Year One of La King was deduced from the inscription on Ni-Zhong with the ganzhi-lunar phase table as above.
Ni-Zhong: The year one of the king, month 3, ji-sheng-ba, Gengshen (Feb. 8, 879 BC/-878), Shu-Shi was in the Grand Temple …
Ji-sheng-ba was assumed to be 2 days ahead of the new moon. This is the exclusive solution after the reign of Kang King.
The conclusion above is compatible with the inscriptions on Hao-Ji-Zi-Bai-Pan, Bo-Ke-Zun, Wu-Hu-Ding, and Geyoubi-Ding.
Hao-Ji-Zi-Bai-Pan:
The year twelve, month 1, chu-ji, Dinghai (Jan. 8, 868 BC/-867), Hao-Ji-Zi conducted casting of the ceremonial plate …
Chu-ji is assumed to be 2 days ahead of the new moon.
Bo-Ke-Zun:
The year sixteen, month 10, ji-sheng-ba, Yiwei (Aug. 23, 864 BC/-863), Grand Master Bo bestowed Bo-Ke …
Ji-sheng-ba Yiwei is assumed to be 3 days after the new moon (broad sense).
Wu-Hu-Ding:
The year eighteen, month 13, ji-sheng-ba, Bingxu (Oct. 3, 862 BC/-861), the king was in Eastern Hall, the Grand Palace of Zhou …
Ji-sheng-ba Bingxu is assumed to be 6 days after the new moon (broad sense).
Geyoubi-Ding:
The year thirty-one, month 3, chu-ji, Renchen (Feb. 3, 849 BC/-848), the king was in the Grand Hall of the Grand Palace of Zhou. …
Chu-ji Renchen is assumed to be 6 days after the new moon (broad sense).

The Year One of Gonghe Regency Was 844 BC/-843 (the Last Year of La-King).

Shi-Ji:
The year thirty-four, the king was harsher, the people were too afraid to talk … Three years thereafter, they gathered and attacked the Li King. The king fled to Zhi.
Here, the counting is again by the ancient way: the year 34 as one year, then the year 36 was considered three years, as it has been shown before. Therefore, La King's calendar only counted to 36 years, not 37 years as commonly believed. From the year one of La King at 879 BC/-878, the year thirty-six is 844 BC/-843.
Shi-Ji:
The year fourteen of Gonghe, Li King died at Zhi. … Xuan King ascended the throne. …
If Gonghe converted the calendar immediately after the king fled, the year one of Gonghe regency would be 844 BC/-843, and the year fourteen would be 831 BC/-830, which matches the year one of Xuan King, provided the next conversion of the calendar was also of immediate nature (7).

The Year One of Xuan King Was 831 BC/-830 (the Last Year of Gonghe Regency).

The year one of Xuan King was deduced from Qiu-Dings of the year forty-two and the year forty-three with the ganzhi-lunar phase table.
Qiu-Ding of the year forty-two:
The year forty-two, month 5, ji-sheng-ba, Yimao (April 17, 790 BC/-789), the king was in the Mu Hall of the Grand Palace. …
Ji-sheng-ba is assumed to be the day after the new moon.
Qiu-Ding of the year forty-three:
The year forty-three, month 6, ji-sheng-ba, Dinghai (May 13, 789 BC/-788), the king was in the Mu Hall of the Grand Palace. …
Ji-sheng-ba is assumed to be 9 days after the new moon. This conclusion is compatible with that from Qiu-Ding of the year forty-two.
By traditional, the year one of Xuan King is considered to be 827 BC, which would render the Qiu-Ding of the year forty-two without a solution at 786 BC. A search in the range of 791-781 BC revealed two potential solutions: 790 BC and 785 BC, which give two candidates for the years one: 831 BC and 826 BC. These candidates would put Qiu-Ding of the year forty-three at 789 BC and 784 BC, respectively. A solution was found at 789 BC by a broad sense interpretation of the lunar phase terminology, but none was found at 784 BC. Hence, the year one of Xuan King is set at 831 BC/-830. Another candidate for the year one could be found at 836 BC, which would require introduction of certain advanced leap months, whereas later solutions (826 BC and 821 BC) would cause the reigns of the Xuan King and You King to overlap.
The above conclusion is compatible with the deduction of the inscriptions on Shi-Dui-Gui's, Wu-Zhuan-Ding, Wu-Yi, Ci-Ding, Ke-Xu, Huan-Ding, Da-Zhu-Zhui-Ding, Jinhou-Su-Zhong, and Shanfu-Shan-Ding.
Shi-Dui-Gui of the year one:
The year one, month 5, chu-ji, Jiayin (Mar. 22, 831 BC/-830), the king was in the Grang Temple, Zhou …
Chu-ji is assumed to be the day after the new moon.
Wu-Zhuan-Ding:
Month 9, ji-wang, Jiaxu (Aug. 9, 831 BC/830 CE), the king was in the Zhou Temple …
Ji-wang Jiaxu is assumed to be 9 days after the full moon (broad sense). There are multiple solutions in the reign of Xuan King. The first one was chosen as the awarding ceremony was conducted in the "Zhou Temple" only in the first two years of his reign; it was moved to the palace thereafter.
Wu-Yi:
Month 2, chu-ji, Dinghai (Dec. 20, 831 BC/-830), the king was in the Grand Hall of Zhou …
Chu-ji Dinghai is assumed to be 9 days after the new moon (broad sense).
Shi-Dui-Gui of the year two:
The year three (two), month 2, chu-ji, Dinghai (Dec. 20, 831 BC/-830), the king was in the Grand Hall of Zhou …
Chu-ji Dinghai is assumed to be 9 days after the new moon (broad sense).
This vessel has been called Shi-Dui-Gui of the year three since the text is supposed to have mentioned "the year three". Unfortunately, the date is incompatible with Shi-Dui-Gui of the year one regardless of the chronology adopted. In addition, the year-one vessel is compatible with the other vessels. Thus, the mistake must be in the text of the year three vessel, which is difficult to interpret due to the eroded state. This forms the internal evidence for correcting the text. Actually, the year-three vessel has a solution in the year two, everything else remains the same, and the solution is in the date of Wu-Yi. Interestingly, the inscriptions on the two vessels not only have the same lunar phase (chu-ji), ganzhi (Dinghai), but also the same location (the Grand Hall of Zhou), similar items of awards arranged in the same order, and similar style of writing. This suggests that the two award ceremonies were conducted in the same day at the same location, which serves as the external evidence for correcting the text. Everything considered, the text of "the year three" was corrected to "the year two", and the vessel was renamed.
Ci-Ding:
The year seventeen, month 12, ji-sheng-ba, Yimao (Oct. 25, 815 BC/-814), the king was in Yang Hall of the Grand Palace of Zhou. …
Ji-sheng-ba Yimao is assumed to be 9 days after the new moon (broad sense).
Ke-Xu:
The year eighteen, month 12, chu-ji, Gengyin (Nov. 24, 814 BC/-813), the king was in Mu Hall of the Grand Palace of Zhou …
Chu-ji Gengyin is assumed to be 10 days before the new moon (broad sense).
Huan-Ding/Huan-Pan:
The year twenty-eight, month 5, ji-wang, Gengyin (April 5, 804 BC/-803), the king was in Mu Hall of the Grand Palace of Zhou …
Ji-wang is assumed to be one day before the full moon.
Da-Zhu-Zhui-Ding: The year thirty-two, month 8, chu-ji, Xinzi (Xinhai, Aug. 3, 800 BC/-799), Bo-Da-Zhu-Zhui conducted casting of the ceremonial vessel …
Xinzi is not a valid ganzhi combination, and must be corrected. Assuming chu-ji as the day of the new moon, the correct ganzhi should be Xinhai (8).
Jinhou-Su-Zhong:
The year thirty-three of the king, the king personally inspected the east and the south. Month 1, ji-sheng-ba, Wuwu (Dec. 8, 800 BC/-799), the king departed from Zongzhou. Month 2, ji-wang, Guimao (Jan. 22, 799 BC/-798), the king entered Chengzhou. Month 2, ji-si-ba, Renyin (Jan. 16, 798 BC/-797), the king (marched) towards the east. Month 3, fang-sheng-ba (Jan. 18), the king arrived at … The king returned to Gongzu Zhengshi Palace of Zhou. Month 6, chu-ji, Wuyin (April 22), in the morning, the king entered the Grand Hall … Dinghai (May 1), in the morning …. Gengyin (May 4), in the morning, the king was in the grand Hall …
Ji-sheng-ba Wuwu is assumed to be 9 days after the new moon (broad sense); ji-wang Guimao, 10 days after the full moon (broad sense); Ji-si-ba, the day before the new moon, fang-sheng-ba, the day after the new moon; chu-ji Wuyin, 7 days after the new moon (broad sense).
Shanfu-Shan-Ding:
The year thirty-seven, month 1, chu-ji, Gengwu (Jan. 8, 795 BC/-794), the king was at Zhou …
Chu-ji Gengyin is assumed to be 5 days after the new moon.
The Grand Ke-Ding and the little Ke-Ding (809 BC), as well as Bi-Xu (807 BC) also belong to the reign of Xuan King but cannot be precisely dated due to lack of ganzhi and the lunar phase records.

The Year One of You King Was 785 BC/-784.

The Year One of You King was deduced from Song-Ding/Song-Hu with the ganzhi-lunar phase table.
Song-Ding/Song-Hu: The year three, month 5, ji-si-ba, Jiaxu (Mar. 30, 783 BC/-782), the king was in the Zhao Hall of the Grand Palace of Zhou. …
Ji-si-ba is assumed to be the day of the new moon.
The date on 783 BC is the exclusive solution of the narrow interpretation. Therefore, the year one of You King was 785 BC/-784. Based on this conclusion, Xuan King reigned for 46 years (831-786 BC), consistent with the record of Shi-ji, whereas You King reign for 15 years (785-771 BC).
The record on Shi-Ji regarding the king's decision to depose the crown prince in favour of a younger son in the year three is of dubious nature. Shou-Shen-Ji mentioned that You King was born in the year thirty-three of Xuan King. You King was only 16 years old in the year three, and is unlikely to have several sons. Zhu-Shu mentioned the king's decision in his year eight, when he should be 21 years old, somewhat more convincing. As far as the record on Guoyu about the death of You King in the year eleven, it was not quoted by Sima Qian in Shi-Ji, possibly due to his doubt on the reliability of the record.

The Rules of Interpreting the Lunar Phase Terminologies

The lunar phase terminologies interpreted in this paper is summarized in Table 3. Most of the records from the literature and the bronze vessels could find their solutions by narrow sense interpretations. The broad sense interpretations could be considered as the abbreviated expressions. For example, "month 4, ji-wang, Yiyou" of Geng-Yin-Ding could be interpreted as "month 4, after ji-wang, Yiyou", "month 1, ji-si-ba, Gengchen" of Wei-Ding of the year nine could be interpreted as "month 1, after ji-si-ba, Gengchen". This kind of broad interpretation is different from the old method of dividing the month into four quarters, the demand for which is to suit the need of erroneous interpretations. Theoretically speaking, all the lunar phase terminologies are to be interpreted in narrow sense, from the Martial King till You King; what really changed was nothing more than the expression. The above is the first rule of interpretation.
Secondly, many of the terminologies are synonymous. For example, Chu, fang-sheng-ba, ji-sheng-ba are synonymous, indicating the appearance of the crescent moon the day after the day of new moon; ji-wang and pang-sheng-ba are synonymous, indicating the lunar phase the day after the full moon; chu-ji, ji-si-ba, zai-sheng-ba are synonymous, indicating the dark face on the day of the new moon. The above is the second rule of interpretation.
There are several ways of expressing the the date. The most ancient and classical way is a two-step system: the previous lunar phase with ganzhi of the day (as the reference day), plus the number of the interval days (by the ancient way of counting) and the ganzhi of the day in concern. An example of this kind is the record in Yi-Zhou-Shu (Ch. Shifu): "month 1, Bingwu, pang-sheng-ba, the day after, Dingwei". Xiao-Yu-Ding provides another example of this kind: "month 8, ji-wang, day of Jiashen … the day after, Yiyou". The second way of expression is similar to the first except it omits the first ganzhi of the reference day. For example, Yi-Zhou-Shu (Ch. Shifu): "month 2, ji-si-ba, five days thereafter, Jiazi" belongs to this kind of expression. The third way is the abbreviated way of expression: the lunar phase terminology of the reference day plus the ganzhi of the day in concern, such as "month 4, ji-wang, Yiyou" of Geng-Yin-Ding, "ji-sheng-ba, Wuxu" of Qiu-Wei-Gui. Any deviation of more than two days from the proper lunar phase in the narrow sense should be viewed as the third way of expression, although such deviations could be caused by observation difficulties such as bad weather. The above is the third rule of interpretation.

Discussion

A. The significance of the ganzhi-lunar phase table.
The ganzhi-lunar phase table coupled to the western calendar is specifically designed for the chronological studies of the Chinese prehistory with the advantage of simplicity and ease of use. With the ganzhi cycle of 60, each ganzhi combination form a row, while the lunar phase form diagonal lines. The cross points of any combination with the diagonal lines with show all the solutions in any number of years. Usually it takes no more than a minute or two to resolve a proper record once the range of the era is known. This table can be used not only for resolving a recorded date within a chronological framework, but for identifying all potential solutions if the chronological framework is unavailable. For example, search of the founding year of Zhou Dynasty reveal not only the solution at 1044 BC by the Xia calendar, but also indicates another potential solution at 982 BC by the Ying calendar, which was eliminated due to the difficulty of compressing all the reign years from all the kings to a much shorter timeframe. From this perspective, any solutions in the tenth century BC are meaningless. Consistent application of this table to the entire research ensures the logical consistency, and proves the general applicability of this method. This is an important step towards establishment of the simple, reliable and general method.

B. The issues in the late chronology of Western Zhou
The year one of La King was fixed at 879 BC, and Xuan King, at 831 BC. Should we further fix the year one of Gonghe regency at 842 BC as usual, the regency will count only till eleven years and contradicts the record in Shi-Ji. Any change on the part of the year one of La King and that of Xuan King would mandate change of the ganzhi records; that was the way the official Chinese project took. Alternatively, combining the regency with the reign of La King (or even with Xuan King) does not help to resolve the issue. This has been a major obstacle in the late chronology of Western Zhou. However, careful analysis of the Shi-Ji record show that the so-called thirty-seven years of reign of Xuan King was based on modern way of counting. Once we adopt the ancient way of counting, the actual reign was 36 years (34 + 3 – 1 = 36). This suggests the year one of the regency was 844 BC. From 844 BC until the year one of Xuan King at 831 BC, there are fourteen years (again, by the ancient way of counting), consistent with the record. The resolution of this persistent issue further proves the validity of the late chronology proposed here. As far as the rule for the calendar conversion in the early Western Zhou, there no direct evidence to prove it either way due to the lack of the last-year vessel and historical record. Based on the chronology in this paper, only Gong King and You King in the entire Western Zhou converted the calendar in the year after the last year of the previous king, whereas Cheng King, Zhao King, Mu King, Gonghe regency and Xuan King converted the calendar as soon as the previous king died/departed. The cases with Cheng King, Zhao King and Mu King suggest that the calendar conversion in the early period was by instant conversion, different from the middle and the late periods. This hypothesis merely requires a prove of a instant conversion by Kang King to be established, and it is also consistent with the well-known cultural shift after Mu King ascended the throne, which could be proved with studies on the style and the inscriptions of the bronze vessels. So far, this chronology is the only one consistent with both Shi-Ji and Zhu-Shu records and without unjustified changes on the vessel inscriptions, which better preserves the overall theoretical integrity.

C. The debate between the official Chinese project and the Nivison school.
Dr. David Nivison of Stanford University has strongly questioned the results of the official Chinese project and triggered a prolonged debate with nationalistic characters. It is true that the official project suffers from obvious deficiencies in methodology and deduction (especially in the way historical records were treated and vessels inscriptions were changed). On the other hand, the theory of the Nivison school is not much better. Numerous reversals in the late years of Nivison suggest a weak theoretical basis, which could be statistically proved.
The theory of Nivison is nicknamed the theory of the double chronology, which is based on extrapolation of the three-year mourning period from the time of Confucius to the legendary king of Zhongkang in pre-historical Xia. This constitutes a violation of basic rule in scientific methodology. As matter of fact, there is no evidence for observation of the three-year mourning period by any kings of Western Zhou, not to mention those of Shang and the legendary Xia. The second fatal defect of his theory is, of course, to place the anchor point of his chronology in the legendary king of Xia based on a dubious record of "solar eclipse" and another legendary king Kongjia of Xia. Hence, the entire chronological framework is built on a sandy beach. The third problem is his interpretation of the "ganzhi name" as the ascension name of the kings. Obviously, he is unaware of similar names used by the commoners (shown in vessel inscriptions). The fourth issue is his cavalier attitude towards historical records, including his negation of the Mu King's reign, shifting of the planetary alignment, use of hypothetical rules for interpretation of the ganzhi of the day of the ascension year, shortening of the morning year from three years to two year for the Xia Dynasty kings, elimination of Jie, the infamous last king of Xia from history, etc. Of course, this is not a single issue but a category of issues. The fifth issue is his adoption of the old and obsolete way of interpreting the lunar terminology. last, but not least, his cumulative deduction of the chronology means accumulation of error; the correct way should be independent deduction of each time point from the inscription of the bronze vessel, a basic rule observed in the study of this paper.
The Nivison school will not surrender their territory to any challengers. The debate between the project and the Nivison school is of academic nature and should not be politicised. The Nivison school appears to have gained the upper hand in the debate, which is a natural outcome of the seniority system adopted in China and the lack of a critical tradition and proper training in scientific methodology.

Notes:
(1) The combination of tiangan (A-Jia, B-Yi, C-Bing, D-Ding, E-Wu, F-Ji, G-Geng, H-Xin, I-Ren, J-Gui) and dizhi (1-zi, 2-chou, 3-yin, 4-mao, 5-chen, 6-si, 7-wu, 8-wei, 9-shen, 10-you, 11-xu, 12-hai) form a ganzhi cycle of 60 in the following order: A1 (Jiazi), B2, C3, D4, E5, F6, G7, H8, I9, J10, A11, B12, C1, D2, E3, etc., until J12. These are listed from the top (A1 Jiazi) to the bottom (J12 Guihai) on both columns.
(2) Similar errors have been known with historical documents from the same period.
(3) The first year of the Martial King preceded the founding year of Zhou Dynasty by 11 years as the Zhou historians decided to start the count after the death of the father of the Martial King, who was posthumously recognized as "the Literate King" (Wen King).
(4) In this case, the ceremony number is different from the year number of the king since the first seven years belong to the regency of Duke Zhou. Because Ceremony One (the Grand Ceremony) took place in 1035 BC, Ceremony Five took place, naturally, in 1031 BC.
(5) This is the only "year one" determined by the official project in China that has been agreed upon by the conclusions in this article. The next "year one" of Yi King, of course, also agreed to that in the project report. But this date was initially proposed by Korean scientist Fang (1975) (see reference), and the project report made no mention about it, which, naturally, turned into a controversy.
(6) La King is commonly known as Li King by the literature tradition, but the bronze vessel inscription proves that La King was the throne name used during his reign.
(7) Calendar conversion typically took place in the year after the death of the previous king to show respect. But in this case, the overthrown king was certainly not respected either at the time of his departure (844 BC) or at his death (831 BC), which is plausible. No bronze vessel has been acknowledged as that of Gonghe regency, which makes it impossible to deduce the date from more reliable sources.
(8) The invalid ganzhi combinations were not caused by incidental mistakes, considering the peculiar bias of the "mistakes", which will be discussed in a separate article.

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This post has been edited by neil: 04 September 2007 - 11:27 PM

[fcharton]

Interesting, I'll have a few questions later, but I noticed these, which I think are mistakes

Quote

C. The BC and the BCE System.
The BC (Before Christ) system adopted by historians and the BCE (before Common Era) system adopted by the astronomers are both used here. It should be noted that the latter has Year Zero, or 0 BCE (1 BC); 1 BCE means 2 BC, etc. The Chinese scholar commonly refer to BC system as BCE. To avoid confusion, all the important results are described with BC/BCE dual system, the rest with the BC system only.

BC and BCE are strictly equivalent, the latter is just a secular name for the former (Common Era vs Christ), and none of those systems have year zero. What you call BCE, ie astronomical notation of years, use negative numbers.

1 BC/BCE is 0 in astronomical notation
1044 BC/BCE is -1043 in astronomical notation.

http://sunearth.gsfc...help/dates.html

also, I think these days are incorrect

Quote

Using Dec. 31, 2000 (Guihai) as the starting point, Jan. 1, 1100 BC (Yinxu) was 1,132,262 days or 18,871 ganzhi cycles plus 2 days back. Using Jan. 1, 1050 BC (Jiazi) was also calculated and used as the anchor point

Dec 31 2000 CE is Julian Day 2451909, it was a Guihai
Jan 1 1100 BCE, (-1099/1/1 in astronomical notation) is Julian Day 1318648, it was a Renxu, and 1132261 days before
Jan. 1, 1050 BCE is Julian Day 1337910, a Jiashen

As the rest of your days are correct, and as they are consistent with the confirmed eclipse records in the Chunqiu (eg July 17 709 BCE, duke Huan third year, Renchen), I suppose that these are typos.


Two additional questions (excuse me if they are silly, I am not certain I fully understood your method).

1- I have the impression that your system uses a combination of the lunar phases and the 60 day cycle to derive the year, as lunar phases follow a 29.53 day cycle, and the ganzhi follow a 60 day cycle, a quick calculation seems to show that they are pretty much in phase again (same phase = same day of the cycle) every 63 moon phases, which is just a little more than 5 years later, and is thus likely to fall in the same month of the year (whichever calendar is used, so long it doesn't drift...). Doesn't this pose a problem on the unicity of your solution? (ie by moving some series of events close in time 5 years around, you still get the right phases and cycle dates)
2- To which extent are the moon phase records correct. Eclipses always fall on the new moon (this is an astronomical law), yet records like the Chunqiu sometimes indicate it, and sometimes do not, which seems to show that the determination of the new moon, in the 7th century BC, was not quite precise. In fact, it is often considered that ancient chinese had practical system, which used alternating durations of 29 and 30 days, periodically ajusted to "catch up" with the real 29.53 duration. Now the new moon is probably the easiest phase to measure (with the full moon, probably), can't similar recording imprecisions exist in Western Zhou inscriptions? And wouldn't they have a strong impact on the method you use?

Francois

This post has been edited by fcharton: 05 April 2007 - 06:13 PM

[neil]

fcharton, on Apr 5 2007, 04:32 PM, said:

Interesting, I'll have a few questions later, but I noticed these, which I think are mistakes
BC and BCE are strictly equivalent, the latter is just a secular name for the former (Common Era vs Christ), and none of those systems have year zero. What you call BCE, ie astronomical notation of years, use negative numbers.

1 BC/BCE is 0 in astronomical notation
1044 BC/BCE is -1043 in astronomical notation.

http://sunearth.gsfc...help/dates.html

also, I think these days are incorrect
Dec 31 2000 CE is Julian Day 2451909, it was a Guihai
Jan 1 1100 BCE, (-1099/1/1 in astronomical notation) is Julian Day 1318648, it was a Renxu, and 1132261 days before
Jan. 1, 1050 BCE is Julian Day 1337910, a Jiashen

As the rest of your days are correct, and as they are consistent with the confirmed eclipse records in the Chunqiu (eg July 17 709 BCE, duke Huan third year, Renchen), I suppose that these are typos.
Two additional questions (excuse me if they are silly, I am not certain I fully understood your method).

1- I have the impression that your system uses a combination of the lunar phases and the 60 day cycle to derive the year, as lunar phases follow a 29.53 day cycle, and the ganzhi follow a 60 day cycle, a quick calculation seems to show that they are pretty much in phase again (same phase = same day of the cycle) every 63 moon phases, which is just a little more than 5 years later, and is thus likely to fall in the same month of the year (whichever calendar is used, so long it doesn't drift...). Doesn't this pose a problem on the unicity of your solution? (ie by moving some series of events close in time 5 years around, you still get the right phases and cycle dates)
2- To which extent are the moon phase records correct. Eclipses always fall on the new moon (this is an astronomical law), yet records like the Chunqiu sometimes indicate it, and sometimes do not, which seems to show that the determination of the new moon, in the 7th century BC, was not quite precise. In fact, it is often considered that ancient chinese had practical system, which used alternating durations of 29 and 30 days, periodically ajusted to "catch up" with the real 29.53 duration. Now the new moon is probably the easiest phase to measure (with the full moon, probably), can't similar recording imprecisions exist in Western Zhou inscriptions? And wouldn't they have a strong impact on the method you use?

Francois

1) Regarding the BC and BCE, I suggest that you go to the NASA web site since I cannot convince you.
2) Regarding the ganzhi, I use the one on the public calendar, I don't know your information source.
3) The5-year cycles has been noticed for a long time. But it is not strictly a 5-yr. cycle, so things do not simply repeat itself; otherwise there is no way of setting the date.
4) The last question will not be answered until my paper of statistical analyses is translated into English, so please wait. Or you could proceed to read the original on Chinese caligraphy on-line (Chinese version).

This post has been edited by neil: 04 September 2007 - 11:33 PM

[fcharton]

Hi Neil,

neil, on Apr 9 2007, 04:14 AM, said:

1) Regarding the BC and BCE, I suggest that you go to the NASA web site since I cannot convince you.

The link I posted in my previous comment is from the Nasa website: here is the passage I referred to...

Quote

In sixth century Europe, the concept of "zero" was still unknown. Thus, the year 1 BC was followed by the year AD 1. Furthermore, recent scholars have determined that Christ's birth was actually four years earlier than Exiguus thought. In spite of these deficiencies, the dating system established by Exiguus is now too deeply ensconced in the Western world to easily change.The Christian bias in Exiguus' dating terminology may be perceived as chauvinistic or insensitive to other religious belief systems. Fortunately, there is an alternative which preserves the year numbering established by Exiguus and now an unavoidable legacy of the historical record. The religiously neutral abbreviation BCE (for "Before Common Era") can be substituted for "BC." Similarly, the abbreviation "CE" (for "Common Era") can replace the nonsecular term "AD."

These modern terms are to be preferred because they do not impose a particular theology on the reader or writer. Futhermore, both "CE" and "BCE" are used as suffixes as opposed to the proper prefix and suffix usage, respectively, of "AD" and "BC". This has distinct advantages for computer generated lists and tables. This web site will strive to use the dating conventions of "CE" and "BCE" in place of "AD" and "BC" whenever the terminology is required.

Of course, Exiguus' dating system still lacks a "0" year which makes calendrical calculations awkward. The "astronomical" dating system refers to an alternative method of numbering years. It includes the year "0" and eliminates the need for any prefixes or suffixes by attributing the arithmetic sign to the date. Thus, the astronomical date for 2000 CE is simply +2000 or 2000. The astronomical year 0 corresponds to the year 1 BCE, while the astronomical year -1 corresponds to 2 BCE. In general, any given year "n BCE" becomes "-(n-1)" in the astronomical year numbering system. Historians should take care to note the numerical difference of one year between "BCE" dates and astronomical dates

neil, on Apr 9 2007, 04:14 AM, said:

2) Regarding the ganzhi, I use the one on the public calendar, I don't know your information source.

For ancient dates, ganzhi can be calculated. For ancient years, the idea is to calculate the Julian day (nr of days elapsed since a very old reference date) of the event, and then use one reference point (from a public calendar, or any know event) to adjust the beginning of the ganzhi cycle. I think you can find the method in this thread : http://www.chinahist...showtopic=15601. Now, this method confirms all your ganzhi dates except two, which is why I suggest they were typing errors.


Do you have a link to the chinese original or the text?

Francois

[neil]

You are right on BCE issue, thanks for the correction. "Yinxu" actually means Renxu, it was our southern pronounciation; "Jiashen" needs to be checked, I am not sure.
As for the last issue, I guess we don't need to wait (I am not sure when I will bother with the lengthy article). The historical literatures could have several potential problems: (1) counterfeit documents that were created by later astrologists or historians to promote their own ideologies, which has become one of the most hotly debated issues in modern China; (2) mistakes introduced by ancient copyists; (3) calendar conversions by ancient writers; (4) mistakes in the ancient calendars. By using bronze vessel inscriptions, we can eliminate the first three problems, and make the deduced conclusions far more reliable. The last problem is not nearly as common as the first three based on my experience. As for the so-called "mistakes" made in vessel casting, I have not positively identify any so far, and it must be extremely rare due to the semi-holy nature of such ancient ceremonies – we would only come to appreciate the care given by the ancients to such matters when we actually scrutinize the ancient records and compare them with those produced by the modern historians. Even those "invalid" combinations of ganzhi, which appear to have been caused by incidental mistakes, were actually used by design, as one of my more recent articles on statistical analyses has demonstrated. Those who pronounce ancient inscriptions "wrong" are usually wrong themselves, and yet they are not ready to admit it – that is why I am writing these papers. Statistical analysese will greatly help to resolve these issues, although this is again a complex issue. Of course, nothing can be absolutely sure, that is why there will always be historians.

[fcharton]

neil, on Apr 11 2007, 06:48 AM, said:

As for the so-called "mistakes" made in vessel casting, I have not positively identify any so far, and it must be extremely rare due to the semi-holy nature of such ancient ceremonies – we would only come to appreciate the care given by the ancients to such matters when we actually scrutinize the ancient records and compare them with those produced by the modern historians. Even those "invalid" combinations of ganzhi, which appear to have been caused by incidental mistakes, were actually used by design, as one of my more recent articles on statistical analyses has demonstrated. Those who pronounce ancient inscriptions "wrong" are usually wrong themselves, and yet they are not ready to admit it – that is why I am writing these papers. Statistical analysese will greatly help to resolve these issues, although this is again a complex issue. Of course, nothing can be absolutely sure, that is why there will always be historians.

I basically agree. Personally, I think days, indicated in the Ganzhi system, will always be correct, unless they have been edited, or added, at a much later date (note though, that this is not exceptional, the are evidences of late editions in the Zuozhuan, and many dates of the Zhushu Jinian were edited, for instance by adding the ganzhi for the year). Months, years and lunar phases are a different problem, because they rely on empirical observations, which can be either imprecise or unpractical. Just to give an example, the chinese month always began, in theory, on a new moon, and the beginning of the year was linked to the date of the winter solstice. Yet, establishing a calendar means being able to predict these dates, because observations are not always possible, and because you would want a calendar to be established in advance. As such, it seems that scholars from the springs and autumns used alternating months of 29 and 30 days, which amounted to a lunar month of 29.5 days, whereas the actual number is a little over 29.53. Of course, they would "adjust" the calendar at times, when it became clear it had drifted, but until such a correction was made, the calendar was slightly incorrect.

I think it all boils down to one problem: to which extent are the "astronomical components" of the recorded dates (solstices and lunar phases) the result of direct observation, or the product of a simple model, calibrated from time to time through observations.

Another point which seems to pose a problem lies in the way we calculate the precise dates of ancient astronomical events. The movement of celestial bodies are quite complex and some things which we consider as "constants", like the time between two solstices, or the duration of a moon cycle, and more importantly the duration of one day, have varied over time. I think Espenak mentions this on his site (look up for delta T), and you might want to try Meeus for more. We have estimates for these variations, which are derived from ancient astronomical records. So, ancient chinese records of eclipses have been used to calibrate the models which we use to calculate ancient astronomical events. As such, there is something circular in applying the models to validate ancient records.

For this reason, I think an analysis of the stability, or sensitivity to model error and initial conditions, of any dating model is crucial.

This said, I do agree with you that scientific approaches which try to link "calculated" astronomical events are very promising. Just to give an example, a few decades ago, proposed dates for the founding of the Western Zhou varied by more than a century (depending on whom you followed). Nowadays, we've narrowed the possibilities to less than a decade, from 1040 (Nivison) to 1046.

So... please keep posting...

Francois

This post has been edited by fcharton: 11 April 2007 - 09:36 AM

[neil]

fcharton, on Apr 11 2007, 06:35 AM, said:

I basically agree. Personally, I think days, indicated in the Ganzhi system, will always be correct, unless they have been edited, or added, at a much later date (note though, that this is not exceptional, the are evidences of late editions in the Zuozhuan, and many dates of the Zhushu Jinian were edited, for instance by adding the ganzhi for the year). Months, years and lunar phases are a different problem, because they rely on empirical observations, which can be either imprecise or unpractical. Just to give an example, the chinese month always began, in theory, on a new moon, and the beginning of the year was linked to the date of the winter solstice. Yet, establishing a calendar means being able to predict these dates, because observations are not always possible, and because you would want a calendar to be established in advance. As such, it seems that scholars from the springs and autumns used alternating months of 29 and 30 days, which amounted to a lunar month of 29.5 days, whereas the actual number is a little over 29.53. Of course, they would "adjust" the calendar at times, when it became clear it had drifted, but until such a correction was made, the calendar was slightly incorrect.

I think it all boils down to one problem: to which extent are the "astronomical components" of the recorded dates (solstices and lunar phases) the result of direct observation, or the product of a simple model, calibrated from time to time through observations.

Another point which seems to pose a problem lies in the way we calculate the precise dates of ancient astronomical events. The movement of celestial bodies are quite complex and some things which we consider as "constants", like the time between two solstices, or the duration of a moon cycle, and more importantly the duration of one day, have varied over time. I think Espenak mentions this on his site (look up for delta T), and you might want to try Meeus for more. We have estimates for these variations, which are derived from ancient astronomical records. So, ancient chinese records of eclipses have been used to calibrate the models which we use to calculate ancient astronomical events. As such, there is something circular in applying the models to validate ancient records.

For this reason, I think an analysis of the stability, or sensitivity to model error and initial conditions, of any dating model is crucial.

This said, I do agree with you that scientific approaches which try to link "calculated" astronomical events are very promising. Just to give an example, a few decades ago, proposed dates for the founding of the Western Zhou varied by more than a century (depending on whom you followed). Nowadays, we've narrowed the possibilities to less than a decade, from 1040 (Nivison) to 1046.

So... please keep posting...

Francois

"to which extent are the "astronomical components" of the recorded dates (solstices and lunar phases) the result of direct observation, or the product of a simple model" is not an easy question to answer, and the situation certainly changed as the history progress, possibly from the former to the latter. I think that minor deviations are acceptable as statistics could tolerate such uncertainties or even mistakes.

regarding "applying the models to validate ancient records", I suppose you are referring to the Yi-Zhou-Shu records, since there is no other case as such in this paper. Here, the validation process depends on the ganzhi system, which requires no validation as it is accepted per definition. A definition can never be validated and does not require validation. The only thing that could be validated in theory is the starting point of the ganzhi cycle relative to the absolute calendar (Chinese or western), which plays no role in the process. The validation process concerns merely the number of days spent on the famous forced march; the question is whether it took 12 days or 26 days? Both number are deduced from the ganzhi records. The month and the year was not the issue here. Of course, the records did contain the month. Assuming there were no record of the month, you might theoretically speculate the march took 72 days, 86 days, 132 days, or 146 days, etc. But what are the probabilities of these numbers? Would the question then be any different? At this point, it becomes obvious that the assertion of a circular reasoning pertaining the validation of the Yi-Zhou-Shu records is unwarrented.
However, this issue could be discussed in a broader sense. Assuming the record R1 was used to calibrate the calendar C, which was in turned used to validate record R2, there is no circular reasoning unless R1 and R2 are identical or logically linked. I guess you believe that all records belong to the Chinese system, so they must be linked. I am afraid this is not applicable to the ancient calendar; otherwise there will be no confusion about the early calendar. Every substantial modification/mistake breaks the linkage, assuming the calendar was based on a theoretical modeling. However, I believe that the early Zhou calendar was more likely based on observation or a mix of both. "Month 14" that I mentioned earlier was just an example of this kind. Even "month 13" is not as simple a matter as it looks like, which I would like to investigate further if the time comes. When records R1 and/or R2 are used to validate the chronology H, it does not constitute a circular reasoning. I do assume that the records are correct in general. A few cases of exception such as incompatible records or invalid ganzhi combinations could be explained/interpreted regardless of the calendar standards (the incompatible records are incompatible regardless of the variation on the part of the astronomical parameters). The trickiest issue on the calibration with ancient records is the correct deduction of the records, which could produce some nasty surprises. In a recent paper I questioned the so-called "first record of solar eclipse" from Xia; I hope no one will use it to calibrate anything.
On the other hand, I do not consider the ancient inscriptions requires so much validation; what really need to be validated is the model for the prehistory - and that is also why the conflict of different models often becomes very personal matters. For example, there are someone in Chinese forums even goes so far as accusing me of stealling the result from the official Chinese project since the conclusion is also 1044 BC as one of the candidate date in the oficial report (Of course, he conveniently forget that the date are different and the material and methods are different).

"from 1040 (Nivison) to 1046", The range of the founding year (or more accurately, the founding date) is not necessarily narrowed down since the theories concerned are incompatible with each other. Since no more than one conclusion is valid, they do not constitute a statistical sample group, I believe. In addition, there are alternative ways to come up with the Shang-Zhou boundary that could extend down to the 12th century BC. I did not bother with that possibility merely because it is difficult to support such an early date with a reasonable chronology. Taking the chronology into account, I consider 1044 BC as the practical upper limit whereas the lower limit could be placed at 1070 BC. Anything below that would extend the total duration of the dynasty beyond 300 years, a very low probability. However, I am open-minded to any revolutionary ideas.
As far as the Nivison theory is concerned, there is no need to repeat what I mentioned in the paper except that the burden of proof for the three-year mourning period rests entirely on his side, without which the theory will collapse even if he gets everything else right. Some believe the period is one year. I think it is variable and could be less than a year during Western Zhou, although much hard work is needed before a conclusion could be reached.
The official project has been in a precarious status since the meeting in the US, when criticism including the alleged plagiarism was fielded against it. Those participated in the project have failed to come up with a meaningful answer to the challenges. The plagiarism refers to the fact that the conclusion on Year One of Yi King at 899 BC by a Korean scientist was incorporated into the project report without giving a proper reference. The explanation by Mr. Li, the principle scientist, that it was omitted due to the limited scale of the report is never convincing; his student Jiang has written a lengthy book (with Li himself as the "consultant") on the project with discussion on the 899 BC date and numerous references to the articles of his mentor but without a single word about the Korean scientist whose work became the anchor point for the entire chronology. Now, some of them (primarily Mr. Wu Bojun, according to himself) have sunken to a new low by engaging in a smear campaign on the forum against me, which merely serve to prove their own moral and academic bankruptcy. I am not disturbed by the campaign since they could not expect to win over anyone other than those whose IQ belongs to the bottom 5% – could anyone in his right mind believe that they have a right to monopolize 1044 BC simple because they had claimed one day (even that date was obtained with the wrong source, with the wrong methods) out of the 365 days? Maybe they also want to monopolize the entire century. Any way, they must be aware of the many mistakes they made, and yet they are denied a chance to correct it since this paper was posted last September – that explains why they regard me as their enemy. I feel sorry for these miserable guys. This is a page the future generation of Chinese scientists (if I could considered history as a branch of science) would rather forget about.

In any event, this is a mine field. I don't think te debate will die down any time soon or focused to a narrower range. There are a few issues that I cannot even start to handle in this paper. For example, the inscription of "month 14", how it will be interpreted and how it will affect the global situation? Of course, the official report did not take care of that either.

By the way, Jan. 1, 1050 BC is "Jianshen", not Jiazi (a typo, indeed). The first draft of the Chinese original of the text stated "甲申", which has never been modified (The original draft is still available in case it is needed). Anyway, I created a continuous annual table (for Jan. 1) from 1100-769 BC before creating the daily table. The annual table observes certain geometry patterns and any mistakes would be instantly spotted; it is much easier than doing individual calculations.

I truly appreciate your interest in this paper. You are welcome to post any more questions here. I will try to answer as soon as possible, although there might be delays due to the fact that I have started an unrelated theoretical project and active in 7 forums, besides writing for Wikipedia and other business and legal affairs, which means less time for this forum in the immediate future.

This post has been edited by neil: 19 April 2007 - 07:57 PM

[neil]

Disbussion ( has been modified, please take notice.

Table 3 cannot be uploaded. I add the list "Interpretation of the Western Zhou Records and Bronze Vessel Inscriptions" under a new topic, which is more complete than table 3.

[neil]

对于匿名先生《干支月相与甲子克商日》一文评述

LIN, ERSHEN
2007年8月21日国际标准时间3时30分-4时10分初稿
2007年8月21日国际标准时间5时20分-5时50分修改稿

前些天在北大偶尔看到某匿名作者的奇文一篇，下载了，直到今天才看，因为有几篇现代史与经济学方面的文章要写的缘故，不想打断思路. 不过，回复此文所花的时间比预期的要短得多. 对我来说，活人的事情总归比死人 (武王) 的来得重要. 不管怎么样，还是给读者们说一声“迟复为歉！”

---------------
Quote:
本文仅仅就“干支月相”这一点，推出“甲子克商日”的可能日期是“二月二十九日”。它所对应的公元日期有两组。
第一组，武王克商二月二十九日。对应前1050年2月10日（甲子）。
相应的 “周公行政七年”的《召诰》：“二月既望[庚寅]（二月十七）”，对应前1041年1月20日。“三月，惟丙午朏”（三月初五）（差1天半）。对应前1041年2月5日。
第二组，武王克商二月二十九日。对应前1045年3月15日（甲子）。
相应的《召诰》：“二月既望[庚寅]（二月十七）”，对应前1036年2月22日。“三月，惟丙午朏”（三月初三）。对应公元前1036年3月10日。
这二组对应的年月日不可能都对（但有可能都错）。假如《召诰》与《武成》、《世俘》干支月相记载可靠，其中应该有一组与史实相符。
---------------
两组解均不符合“时四月，既旁生魄，越六日，庚戌”的记载, 唯1044 BC 有解 (分别在6.19与6.24). 这是一个“五年周期”的解, 但五年前的1049 BC早一天, 无解, 而五年后的1039 BC 的解在7.23/7.28, 已不是四月了. 《世俘》的两解与作者提出的1050/1045 BC的解无法弥合. 这进一步证实了“武王克商日为1044 BC/-1043年3月10日即夏历二月初五”为唯一正确的解.

---------------
Quote: （旁生魄与既旁生魄是同一月相。）
---------------
这是没有根据的错误推理. “既”表示完成时态, “既旁生魄”比“旁生魄”晚一天, 就如同“既望”比“望”晚一天. 本人后来对于大量的金文分析证明了这一点.

---------------
Quote: “定点论”者把月相定在每月不变的日子，这与月相变化的客观实际不符。
---------------
月相虽然是定点的，但可以用于表达两点之间的任何日期，就如同现代人对于时间的表述一样：就象“两点”和“三点”都是定点的，但仍然可以用于表达其间的任何时刻：2:45可以说成两点三刻或者差一刻三点. 语言本来就是约定俗成的. 从表达方式的角度来说, 一个时间区间, 不管是在一个小时之内, 还是在一个月之内, 都不可能被刻板地、人为地分成几个板块. 要知道，周人并非科学家，不可能用科学的要求定义周人的月相表达方式，更不可能要求周人们为了断代工程师们的方便而采用两分法或四方法分割月相周期. 因此，我不得不重申本人文章的结尾部分：

以下对本文研究牵涉到的月相的解释归纳如表3。从表中不难发现，多数的古籍记载与铜器铭文可以通过狭义的解释合历。符合广义解析的记述可以看做是文字省略的结果。如庚赢鼎的“四月既望己酉”可以解作“四月既望后己酉”，九年卫鼎的“正月既死霸庚辰” 可以解作“正月既死霸前庚辰”。这种广义定义完全不同于四分术；对四分术的需求只不过是错误推理的结果。严格地来说，所有的西周月相术语均作狭义的解析，自武王至幽王贯穿始终，从未改变；所改变的只是纪日的写法而已。以上是本文关于西周月相术语的第一个主要结论。
其次，表3的解释栏显示许多月相术语都是同义语：朏、方生霸、既生霸是同义语，指新月初见即朔后一日的月相；既望指望后一日的月相；旁生魄指望之后的月相；初吉、既死魄、哉生魄均指朔的月相。以上是本文关于西周月相术语的第二个主要结论。
其它日期的表达法有多种。最古老、最经典的表达法是先记述该日期前一个月相的名称及干支，加上两个日期间的差距 (虚数)，再加上所指日期的干支。《逸周书•世俘》中“维一月丙午旁生魄，若翼日丁未”的文字便是一例；小盂鼎的“唯八月既望，辰才(在)甲申……若翌日乙酉”是另一例。第二种类似于第一种，只是省略了月相后的干支，如《逸周书•世俘》中“二月既死魄，越五日甲子” 便是。第三种便是省略法：该日期前一个月相的名称再加上所指日期的干支，如庚赢鼎的“四月既望己酉”、裘卫簋的“既生霸戊戌”之类。严格地说，象小盂鼎和师虎簋那些滞后月相3日的记载也可以算作第三种表达法。然而，这类小的偏差有可能是月相观测失误 (例如由阴雨天气造成的失测) 所致。以上是本文关于西周月相术语的第三个主要结论。

作者无法理解定点之后的灵活表述的可能性, 犯了与断代工程同样的错误, 属于传统机械论的影响的结果, 建议作者学一点辩证法.

其实，这个问题在国学和先秦史上有几位工程的代言人早已提出过(走出派的马甲真多)，有的还一题三问，属于无端发难的trouble makers之类. 看来月相“板块结构”理论在国内史学界的影响就像“走出疑古时代”一样，遗害不浅. 有些人整天侈谈辩证法，到了该用的时候又不会用，正所谓“不当而而而，当而而不而，而今而后，而已矣！”

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Quote: 月相中“既望”（十六或十七）和“朏”（承小月初三，承大月初二？）基本上没有分歧。
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这里也许指断代工程组内部没有分歧, 不等于学术界没有分歧, 本推理的出发点仍属于主观臆断. 该文作者既然不同意刘歆的定点论，却又要不加分析的使用刘歆对于朏的猜测性结论，实为自相矛盾. 在此，我不仿引用本人另一篇文章的“事件对于月相周期的分布规律”部分：

事件在月相周期中的分布有朔、望两个参考点，分布的参考点根据记载的参考点而定 (图2-4)。相关样本对于朔的分布均数为5.04，标准差为7.00；对于望的分布均数为1.36，标准差为1.91。事件频率在朔当日、朔后一日和望后一日相对于各自的正态分布而言均显著高于随机概率：在朔当日和朔后一日，α = 0.00170；在望后一日，α= 0.000517。因此，朔当日与朔后一日和望后一日是每个月的吉日的可信度分别为99.83%和99.948%。由于朔当日和朔后一日的频率远高于望后一日，朔当日和朔后一日应被认为每个月的主要吉日，而望后一日为次要吉日。这一事实说明周人重朔，而以中原文化为基点的中国传统则是重望：元宵、中秋以及乡村地区的“七月半”都是与望相关的节日，只有新年是朔。重望是使用太阴历 (或阴阳历) 的传统农业社会的特点。周人重朔应该与其民族的特定历史有关。
以上是总的分布的情形，其中初吉 (包括月吉和吉日)、既生霸 (包括哉生魄) 以及既望有足够大的样本可以作个别的分析 (图2-5)。初吉的均数是2.44，标准差是4.79；事件频率在朔当日显著高于随机概率 (α= 0.000104)，在朔后一日显著高于随机概率 (α= 0.01595)。既生霸的均数是1.28，标准差是1.84；事件频率在朔后一日显著高于随机概率 (α= 0.000027)。既望的均数是0.80，标准差是1.22；事件频率在望后一日显著高于随机概率 (α= 0.000060)。以上结果表明初吉指朔当日 (可信度为99.9896%) 及朔后一日 (可信度为98.40%)；既生霸指朔后一日 (可信度为99.9973%)；既望指望后一日 (可信度为99.9940%)。
以上对于初吉和既生霸两个术语的分布分析结果表明事件频率对于朔的分布在朔当日和朔后一日连续2日居高不下的原因是两种月相术语的相关事件迭加而产生的表象。因此，周人在西周时期的月相观测精度已经高于一日的水平，关于周人的月相观测精度低于2-3日的种种猜测是毫无根据的，五花八门的四分术存在的依据也已经彻底消亡。
以上统计结论以超过99.9%的可信度证实了《公历干支纪日确定武王克商年与西周诸王年谱及西周月相术语的解析法则》一文提出的第一月相解析法则 (所有的西周月相术语均作狭义的解析，狭义意味着月相观测精确度为一日或更高) 和第二月相解析法则 (现可以用统计数据精确定义的术语包括：初吉指朔当日及朔后一日的月相 (后者可信度为98.40%)；既生霸指新月初见即朔后一日；既望指望后一日)。

“朏”没有统计，因为样本数不够，但很难想象其它的术语均为事件当日和滞后一日而“朏”却滞后三日. 作者的此一假设无法成立. 作者抓住无法证明，也无法证伪的“朏”做文章，真可谓“各尽所能，各取所需”了.

类似这一类无法证伪的命题 (例如“处女受孕”，“将来总有一天会发现夏朝的文字”之类) 见过不少了. 从科学方法论的角度来看，无法证伪的命题均属于伪科学的命题.

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Quote: 以可靠文献中没有分歧的干支、月相为基础，可以推断其它月相对应的日期。
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不存在“没有分歧的月相”, 这也是极其武断的说法.

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Quote: 《召诰》可作“标准件”。
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《召诰》与克商年的关系不能确定 (武王在位年数仍有争议), 必须以克商年记录为起点; 以《召诰》为起点, 则本末倒置, 属于方法论的错误, 其结果焉能不错.

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Quote: 从“一月丙午，旁生魄”（一月上半月）到“二月既死魄（二月下半月），越五日，甲子”，应该有五十天左右。而从丙午到甲子只有19天（或79天）。“甲子日克商”不会错，那么“惟一月丙午，旁生魄，若翼日丁未”必然有错误或脱漏。
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该作者对于“旁生魄”推理错误, 没有证明“旁生魄”推理的情况下轻言“那么‘惟一月丙午，旁生魄，若翼日丁未’必然有错误或脱漏”过于武断.

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Quote: 此学者又说：“武王从镐都到孟津的行军时间要么是从丁未至戊午共12天，要么是从癸巳至戊午共26天。从西安附近的镐都到孟津路程只比孟津到安阳附近的殷都略长。既然从孟津到安阳只用5-6天，则从镐都到孟津绝不可能要26天。从逻辑上讲，12天是比较合理的选择，而且这12天里面还包括渡河的时间 (所谓‘师毕渡盟津’指渡河完成)，否则需时更短，估计7天左右。综上所述，任何基于《周书.武成》关于武王癸巳出发的推理结果都是不可信的，因此，采用《逸周书.世俘》的记载为准。”卷入牧野大战的，除了武王所率“戎车三百乘，虎贲三千人，甲士四万五千人”以外，还有很多诸侯(至少八个)的兵卒。武王从丰镐（今陕西长安沣西地区）出发的同时，要联络其他诸侯到孟津会师。在当时的情况下，分散在各地的诸侯，率领大队人马，要在26天内，先结集孟津之西，再经过统一号令、协调编队、实地演习……，形成一支有统一指挥、能协同作战、有战斗力的部队……再在戊午日誓师东征伐纣，其速度并不算慢。(或许从一月癸巳到二月丙午各地诸侯用14天完成结集。再在二月丁未到丁巳，武王用十来天时间率领包括众诸侯在内的全部人马进行演习操练……。) ——只计路程不顾其它的“12天”，是脱离行军打仗的实际，用“乌合之众赶庙会”的思考方式做出的不合情理的“选择”。
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武王出师属于出奇制胜, 属于众所周知的事实, 根本不存在“用14天完成结集…用十来天时间率领包括众诸侯在内的全部人马进行演习操练”的可能性, 这种毫无根据的说法属于强词夺理的歪曲, 读起来好像在编电视连续剧, 浪漫则浪漫矣, 与逻辑无干. 光是这一点就足以说明为什么作者需要匿名了.

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Quote: 若《世俘》就是《汉书•律历志》所引之《周书•武成》篇。那么，就可以用《律历志》所引的“惟一月壬辰，旁死霸，若翌日癸巳”，补充修正现《世俘》中的错乱、脱漏。——校正后的《世俘》（《武成》）为：“惟一月壬辰，旁死霸，若翌日癸巳，武王乃朝步自周，于征伐纣”。……“[二]月丙午，旁生魄，若翼日丁未”……“越若來二月既死魄，越五日，甲子朝，至接于商……”——也就是说“月丙午，旁生魄，若翼日丁未”前后有错乱、脱漏。
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由猜想出发改动古文是极度不严肃的做法, 看来当下流行的“改字学”阴魂不散.

至此，全文的理论基础已经不复存在，其余不足论矣！

[neil]

There are a few follow-up studies, which I do not have time to do English translation. For anyone who can read Chinese, you could find them in the following pages:
《逸周书·世俘解》公历日期推定
http://bbs.guoxue.co...4...1&frombbs=1
昭王南征与王姜诸器再探讨
http://bbs.guoxue.co...4...1&frombbs=1
□公簋断代与断代工程的遗产
http://bbs.guoxue.co...4...1&frombbs=1
从燹公盨的灸手可热看现代考古研究的隐忧
http://bbs.guoxue.co...4...1&frombbs=1