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A Study on the Punishment Day Calculation Method and Related Issues in the “Punishment Day” Section of the Mawangdui Manuscript Yinyang wuxing A

馬王堆帛書《陰陽五行》甲篇《刑日》章“刑日”推算方法及相關問題研究

In: Bamboo and Silk
Authors:
Ting Zhang Nanjing University, School of Literature, Nanjing, “Paleography and Chinese Civilization Inheritance and Development Program” Collaborative Innovation Platform (南京,南京大學文學院、“古文字與中華文明傳承發展工程”協同攻關創新平台)

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Shaoxuan Cheng Nanjing University, School of Literature, Nanjing, “Paleography and Chinese Civilization Inheritance and Development Program” Collaborative Innovation Platform (南京,南京大學文學院、“古文字與中華文明傳承發展工程”協同攻關創新平台)

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Abstract

First, through an analysis of the binary categorization of the heavenly stems and the earthly branches in calculations and arts (shushu 數術) literature in transmitted and excavated texts, this paper argues that the two characters meng 䖟(孟) and zhong 中(仲) next to the branches in the Punishment Day diagram do not connote substantive meaning, but constitute a set of binary categories in the same vein as the binarisms yin/yang, hard/soft, man/woman, female/male, heaven/earth, punishment/virtue, and so on. Next, this paper points out a mistake made in the previous calculation of punishment days in the Changsha Mawangdui Han mu jianbo jicheng before putting forward a new calculation method. Based on the new method, we find that the two columns of stem-branch binomes inscribed on the manuscript should be construed such that the stem-branch binomes in one column represent the punishment days resulting from the movements of a stem and a branch starting from contiguous branch positions, and those in the other column represent the punishment days resulting from the movements of a stem and a branch starting from branch positions six branches apart. The reason for the emphasis on the punishment days resulting from these two cases lies in the fact that the branches of these punishment days are the grave branches (muchen 墓辰) in the Three Unions Scheme of the Five Agents. The meaning of the grave branches as vanishing and decaying resonates with the activities of military display, battling, attacking, killing, imprisonment, and demolishing constructions that may be undertaken on punishment days. Therefore, particular attention is paid to the punishment days identified by the four grave branches. In the end, this paper argues against the view that correlates Punishment Day with Meeting Day. This paper maintains that despite their similarity on the surface, they are in fact two different types of calendar spirits and should not be confused.

摘要

首先,本文通過傳世和出土數術類文獻中常見的對天干地支進行的二元分類,認為刑日圖中四方地支後所書的“䖟”(孟)、“中(仲)”二字並非具有實在表意內涵,而是一組與陰陽、剛柔、男女、牝牡、天地、刑德等類似的用於表二元對立屬性的詞。其次,本文指出了原“刑日”推算方案在具體推導時所出現的失誤之處,然後提出新的刑日推算方法,據此方法,最後發現帛書所列的兩行干支實則一為相鄰辰位下日辰運行推算的刑日結果;一為日辰起始位置相隔六個辰位下推算出來的刑日結果,而之所以尤其重視這兩種情況下推算出來的刑日,則與其辰位為五行三合局中的墓辰有關,墓辰之消亡、衰老義正與刑日之“張軍、戰鬭、攻伐、殺戮、圄罪、毀築”等事項相契合,所以對這四辰所在的刑日尤為關注。最後,本文還對將“刑日”和“會日”聯繫起來的觀點予以辯駁,認為兩者雖然表面上存在相似之處,但實質上是兩種不同類型的神煞,不可混為一談。

The “Xingri” 刑日 (“Punishment Day”)1 section in the manuscript Yinyang wuxing A 陰陽五行甲 (Yinyang and Five Agents A), which has a parallel section in the manuscript Yinyang wuxing B 陰陽五行乙 (Yinyang and Five Agents B), consists of two subsections: a diagram and prognosticatory statements.2 The diagram follows the “cord-hook” pattern and features the two heavenly stems wu and ji in the center.3 Surrounding the extremities of the cords and hooks are inscribed two rings of texts. The inner ring is a list of the twelve earthly branches arranged in clockwise fashion. The outer ring is an alternation of the characters meng and zhong inscribed next to the twelve earthly branches. The two characters are written as meng and zhong in Yinyang wuxing B. In addition, the corners of the four right-angle hooks are inscribed, beginning from the northeast corner, chun shi 春始 (beginning of spring), xia shi 夏始 (beginning of summer), qiu shi 秋始 (beginning of autumn), and dong shi 冬始 (beginning of winter). See the following diagrams for more details:

Figure 1
Figure 1

Photographs of Punishment Day diagram (left: Yinyang wuxing A; right: Yinyang Wuxing B)

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

Figure 2
Figure 2

Punishment Day diagrams reconstructed by Cheng Shaoxuan (left: Yinyang wuxing A; right: Yinyang wuxing B)

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

1 Meng/Zhong Are Terms of the Same Type as Yin/Yang and Hard/Soft in Denoting Binarism

Not a few scholars have done research on the characters meng and zhong inscribed next to the twelve branches. Scholars such as Li Xueqin 李學勤 and Chen Songchang 陳松長 hold that meng and zhong should be read as meng and zhong as in mengyue 孟月 (initial month) and zhongyue 仲月 (median month) attested in the Yueling 月令 (Monthly ordinances).4 Ikeda Tomohisa 池田知久 and Sagawa Mayuko 佐川繭子 suggest that meng might be a signific loan of wang and, given its juxtaposition with zhong (middle) and shi (, beginning; the second character in chun shi, xia shi, qiu shi and dong shi), could mean wu (nothingness) or zhong (ending).5 Li Ruohui 李若暉 puts forward a different opinion and instead of reading meng and zhong as in mengyue and zhongyue, takes meng to mean the beginning of the sexagenary cycle and zhong to mean the middle of the sexagenary cycle.6 Huang Ruxuan 黃儒宣 thinks that meng and zhong should be separated from shi (in the phrases “a season + shi”), but she does not offer specific identifications of these characters.7

As regards the above opinions, first, we agree with Huang Ruxuan that meng and zhong should be separated from shi. The use of the four corners to signify the four seasons has been attested in early transmitted literature. The “Zhizhen yao dalun” 至真要大論 (“Great treatise on the essentials of the ultimate truth”) chapter of the Suwen 素問 (Plain questions) states that “The function of the flourishing and decaying of cold, heat, warmth, and coolness consists in the four conjunctions (siwei 四維),” the gloss of which in Zhang Zhicong’s 張志聰 collected annotations to the Huangdi neijing reads, “Wei refers to the intersections of spring and summer, summer and autumn, autumn and winter, and winter and spring. The four corners denote the four conjunctions.”8

In addition, there is no shortage of examples in excavated manuscripts and material objects. For example, the four corners of the Zidanku 子彈庫 silk manuscript are inscribed with drawings of four trees that, arranged clockwise starting from the northeast, are in the colors of green, red, white, and black. A text written on the manuscript reads, “the essence of the green tree, the red tree, the yellow tree, the white tree, and the black tree.” This also uses trees of different colors to correspond to the four seasons and four sectors with green representing spring and the east sector, red summer and the south sector, white autumn and the west sector, and black winter and the north sector. Its rationale resembles that of the “Punishment Day” diagram in that both correlate the four corners/four conjunctions with the four seasons. For another example, on the front of the cosmic board (shipan 式盤) discovered in 1977 at Fuyang 阜陽 in the tomb of the Lord of Ruyin 汝陰, the four corners are also inscribed li chun 立春 (establishment of spring), li xia 立夏 (establishment of summer), li qiu 立秋 (establishment of autumn), and li dong 立冬 (establishment of winter), which recalls the inscription of beginning of spring, beginning of summer, beginning of autumn, and beginning of winter in the “Punishment Day” diagram. Although the cosmic board – mimicking the movement of the Thearch star of the northern pole through the eight solar terms9 – operates on a rationale different from that of the “Punishment Day” diagram, the temporal-spatial notion it reflects is the same as that of the “Punishment Day” diagram. Therefore, we think that the inscriptions on the four corners and the inscriptions on the four sides belong to two different systems and that the inscriptions on the four corners should be excluded from our discussion of the meaning of meng and zhong .

Figure 3
Figure 3

Zidanku manuscript

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

photograph courtesy of The Arthur M. Sackler Gallery in 2012
Figure 4
Figure 4

Zidanku manuscript, Cai Xiuhuan’s 蔡修渙 reconstruction

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

Furthermore, in light of the parallel section in Yinyang and Five Agents B, we think that there is no problem in identifying meng and zhong as meng and zhong . However, their meanings are not as in mengyue and zhongyue, nor are they the beginning and middle of the sexagenary cycle. Here, meng and zhong should be taken as another pair of binary concepts corresponding to the binary categories such as yin/yang and hard/soft that are commonly seen in shushu 數術 (calculations and arts) literature.

Transmitted literature abounds with the binary categorization of the ten stems and the twelve branches. The “Qu li shang” 曲禮上 (“Trivial rites A”) chapter of the Liji 禮記 (Records of Ritual) states “[Undertake] external affairs on hard days and internal affairs on soft days.” Kong Yingda’s 孔穎達 sub-commentary to the passage offers the gloss that “Hard refers to odd days. A ten-day period consists of five odd and five even days. The five odd days jia , bing , wu , geng , and ren are hard. The five even days yi , ding , ji , xin , gui are soft.” The chapter “Tianwen xun” 天文訓 (“Celestial patterns”) of the Huainanzi 淮南子 (Master of Huainan) also states that “Speaking of days, jia is hard, yi is soft; bing is hard, ding is soft; and so on to ren and gui.” All these texts categorize days into hard days and soft days based on the heavenly stem value of a day, positing days of odd stems as hard and days of even stems as soft. By the same token, the earthly branches are classified into two categories. For instance, the chapter “Lun pei ganzhi” 論配干支 (“On the matching of stems and branches”) of the Wuxing dayi 五行大義 (Summation of the Five Agents) states that “Of the branches, yin , chen , wu , shen , xu , zi are yang, mao , si , wei , you , hai , chou are yin.” One can see that like the heavenly stems, the odd earthly branches are yang, and the even ones are yin.

Figure 5
Figure 5

Photograph and reconstruction of the cosmic board in the tomb of Lord of Ruyin

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

According to Wang Qiang 王強, the binary categorization is also often seen in excavated manuscripts, in which hard days are also called yang days, male days, and man days, and soft days are called yin days, female days, and women days.10 There is a slight difference between these designations regarding which of the stems and branches are subsumed by each of them, but it is unquestionable that these designations share the common binary categorization of the stems and branches and, by corollary, of days identified by the stems and branches. Differentiating between yin and yang and between hard and soft according to odd and even positions was the prototype. In its later development, the binary categorization obtained different associations. For instance, in the manuscript Caoshi Yinyang 曹氏陰陽 (Yinyang of the Cao clan) from the Yinqueshan 銀雀山 Han bamboo slips, the categorization of the earthly branches integrates further the elements of the Wuxing sanhe ju 五行三合局 (Three Unions Scheme of the Five Agents). As a result, the categorization can represent the attribute of the Five Agents inherent in the earthly branches, while simultaneously attending to the attributes of the Three Unions Scheme of the Five Agents.11 Based on our grasp of the nature of these binary categories and conceptions, we can then infer the attributes and meaning of meng / and zhong /.

We think that meng/zhong in the “Punishment Day” diagram should be taken as another pair of terms like that of yin/yang, hard/soft, man/woman, and female/male used to denote binarism. Similar binary conceptions can often be seen in calculations and arts literature: Punishment (xing ) and Virtue (de ) in the Xingde 刑德 (Punishment and Virtue) manuscripts; odd (qi ) and regular (zheng ) palaces in the “Xingde xiaoyou tu” 刑德小遊圖 (“Diagram of the short wandering of Punishment and Virtue”) of the Punishment and Virtue manuscripts;12 Heavenly One (tianyi 天一) and Earthly One (diyi 地一) in the “Chuansheng zhan” 傳勝占 (“Prognostication on transmitting victory”) of the manuscript Xingde C 刑德丙 (Punishment and Virtue C); Heaven and Earth in the “Tiandi” 天地 (“Heaven and earth”) section of the Yinyang and the Five Agents A; Heavenly Mainstay (tiangang 天罡), Heavenly Pattern (tianwen 天文), Earthly Force (diwu 地武), and Earthly Reinforcement (dimu 地楘) in the “Zhu B” 築二 (“Construction B”) section of Yinyang and the Five Agents A and in the Huxi shan 虎溪山 Han bamboo-slip manuscripts of the Zhu A & B 築甲乙篇 (Construction A & B); and the female spirit of the Northern Dipper (Beidou cishen 北斗雌神) and the male spirit of the Northern Dipper (Beidou xiongshen 北斗雄神), Establish and Oppress (jianyan 建厭), and great time (dashi 大時) and small time (xiaoshi 小時) in the chapter “Tianwen xun” of the Huainanzi. He Lulu 賀璐璐 holds that binary calendar spirits in the calculations and arts system are related to the ancient cosmological notion of “one giving birth to two” (yi sheng er 一生二) and reflect ancient cosmological and temporospatial perception.13

To tackle the question why meng /zhong can function as binary categories, we need to look at the basic meanings of these two words. In the Shuowen 說文, Xu Shen 許慎 states that “Meng means elder.” The Fangyan 方言 says that “Meng refers to an elder sister.” The Yupian 玉篇 states that “Meng refers to the beginning.” In his sub-commentary to the line “Lord Hui’s first wife is Meng Zi” in the Zuozhuan 左傳, Kong Yingda says that “Meng, zhong, shu , and ji are words to distinguish birth sequence among siblings. Meng and bo both refer to the elders.” The Pianhai leibian 篇海類編 states that “Zhong means secondary (ci ) [in birth sequence].” We can see that the ancient Chinese took meng to mean the elder and zhong to mean secondary. Since the elder contrasts with secondary just as yin contrasts with yang, hard with soft, man with woman, and female with male, meng and zhong can form another pair of binary categories. In addition, we need to note that binary conceptions in calculations and arts literature are characterized by a unity of opposites in that they are opposite to each other but also mutually dependent. It is because of the existence of one category that the other category exists. Their opposition is to be viewed against their unity – the Year star (suixing 歲星) and the Taisui 太歲 (Great Year) are illustrative: the existence of Taisui depends on the existence of the Year star, but they differ from each other in their directions of motion and prognostications for fortune and misfortune. That is to say that the opposition between binary conceptions is, as often as not, relative. For this reason, to form the binarism, meng needs not necessarily be contrasted with ji; rather, it is acceptable for meng to be contrasted with zhong. When the elder is contrasted with the secondary, the elder denotes yang and hard, whereas the secondary denotes yin and soft. The distribution of meng/zhong in the “Punishment Day” diagram accords with the distribution of yin/yang and hard/soft in transmitted literature in that like yang and hard, meng is placed in odd positions, and like yin and soft, zhong is placed in even positions.

The phenomenon of designating the same attribute or principle by different names can often be seen in calculations and arts literature. Wang Qiang has done research devoted to this phenomenon. He classifies the complicated signifier-signified relationships in calculations and arts into two types of “same name for different arts (tongming yishu 同名異術)” and “same arts by different names (tongshu yiming 同術異名).” The former refers to the phenomenon that “several calendar spirits have the same name, but their operative mechanisms are not entirely unified.” The latter refers to the phenomenon that “several calendar spirits have a unified operative mechanism, but their names are not the same.” The meng/zhong under discussion belongs to the type of “same arts by different names.” Regarding the phenomenon of “same arts by different names,” Qing dynasty scholars already had a clear awareness. In recording the reason for the composition of the Xieji bianfang shu 協紀辨方書 (Treatise on Harmonizing the Times and Distinguishing the Directions), the “Xiangwei kao” 象緯考 (“Examining images and weft texts”) part of the Qingchao wenxian tongkao 清朝文獻通考 (A Comprehensive Examination on Qing Literature) states,

In selecting auspicious days, the consideration in and before the three dynasties was only about the hardness and softness of the stems and branches, hardly about limitation and avoidance. Discussion and theory have become increasingly excessive in later generations. Specialists in arts built upon [the discussion and theory] to add and establish calendar spirits. [As a result,] concerning a single day, the identification as auspicious or inauspicious became utterly different; of a single star, names and designations were recklessly multiplied. Consequently, commoners were disoriented as to what to follow and what to avoid.

The statement that “of a single star, names and designations were recklessly multiplied” speaks to the phenomenon of “same arts by different names.” Moreover, the Xieji bianfang shu also comments on the phenomenon of “same arts by different names:”

Where calendar spirits of the year and months came from is indeed old. Specialists in arts loved the unusual and often engaged in fabrications. When they failed to invent [new calendar spirits], they fabricated different names for old calendar spirits, which were further altered and modified to cover up the tawdriness. Consequently, calendar spirits have proliferated … Of a same calendar spirit, names and designations are jumbled and confusing, which is indeed loathsome. Now fabrications, once verified, will be deleted, whereas the accepted ones will be listed on the left. One can extrapolate other similar phenomena that cannot be specified.14

We can see that not only were Qing scholars aware of such phenomena, but they also attempted to sort out fabrications in order to clear up the confusion.

There are also occasions where different divisions of the calculations and arts not only gave the same calendar spirits different names, but even different auspicious or inauspicious qualities as well. For instance, what is known as Yandui 厭對 (Oppress Paired [Branches]) in the arts of kanyu 堪輿 (Canopy and Chassis) is called Liuyi 六儀 (Six Companions) in the arts of congchen 叢辰 (Collected Branches). Although they both function as clashing oppressive day branches, days identified by Yandui are judged by the kanyu specialists as “prohibited for marrying off a daughter or taking a wife,” whereas days identified by Liuyi are judged by the congchen specialists as “appropriate for betrothals and giving betrothal gifts.”15

In addition to transmitted literature, similar phenomena can also often be seen in excavated manuscripts. For instance, Bakui 八魁 (Eight Heads) is also called Bamu 八楘 (Eight Reinforcements) and Bagui 八鬼 (Eight Ghosts). For another instance, Furi 復日 (Return Day) is also called Baori 報日 (Repay Day) and Chongri 重日 (Repeat Day). Moreover, the twelve day qualifiers of both the jianchu 建除 (Establish-Remove) and the congchen systems contained in Qin and Han daybook manuscripts also have a few different sets of names.16 According to Wang Qiang, there are several reasons accounting for the phenomenon of “same arts by different names.” First, specialists of arts created different names, which are often seen in transmitted literature. The second contributing factor is the use of Chinese characters, such as phonetic and signific loans, variant characters, the interchange of synonyms and near-synonyms, and less often, erroneous characters and the avoidance of taboo characters. The third contributing factor is the indiscriminate use of full names and their abbreviations. The use of meng/zhong is explained by the second factor whereby terms of the same meaning are used interchangeably.17

Terms denoting binarism that we knew already include yin/yang, hard/soft, man/woman, female/male, punishment/virtue, and odd/regular. After understanding the meaning of meng/zhong in the “Punishment Day” section, we can add to the above list a new pair of binary categories. The chapter “Lun pei zhigan” 論配支干 (“On matching branches and stems”) of the Summation of the Five Agents states that “Yang can be hard, lords, husbands, above, external, exterior, motion, advancing, erecting, looking up, front, left, virtues, giving, and opening. Yin can be soft, subjects, wives, concubines, properties, below, internal, interior, stillness, retreating, hiding, in attitudes, behind, right, punishments, withdrawing, and closing. There are more phenomena that yin/yang signify but these are omitted here.”18 One can see that yin/yang symbolizes a profusion of phenomena. It is hoped that more terms denoting binarism will be found in future excavated manuscripts to allow us a glimpse into the duality of calculations and arts literature that is variegated and dynamic, on the one hand, and yet forms a unified system, on the other.

There is yet one more, profounder reason for the phenomenon of “same arts by different names.” Wang Qiang notes that calendar spirits serve as an intermediary connecting the rationale behind calculations and arts with hemerological activities (xuanze shixiang 選擇事項). In other words, calendar spirits provide a bridge between the calculations and arts rationale and hemerological activities. Since the calculations and arts rationale often remains constant, the variation in the designations of calendar spirits is largely a result of different hemerological activities. That is to say, the designations of calendar spirits vary due to different hemerological circumstances and objectives. We suspect that the choice of the unprecedented categories of meng/zhong in the “Punishment Day” section over the commonplace categories of yin/yang, hard/soft, man/woman, punishment/virtue is likely due to the use of the four corners to represent the four seasons. In this light, although here meng/zhong cannot be directly understood along the lines of mengyue and zhongyue, the use of meng/zhong as binary categories is doubtlessly influenced by the calendar year context. Therefore, on the one hand, we need to recognize that meng/zhong are distinguished from beginning of spring, beginning of summer, beginning of autumn, and beginning of winter. On the other hand, we also need to acknowledge the correlation between the two sets of terms.

2 The “Punishment Day” Calculation Method and Principle

The second part of this article deals with the prognosticatory statements in the “Punishment Day” section. According to the prognosticatory statements, the calculation method is that “When a stem (ri ) is born, it begins from a meng day to move in the regular direction (shunxing 順行). When a branch (chen ) is born, it begins from a zhong day to move in the opposite direction (nixing 逆行). When a stem and a branch encounter for the first time, it is Great Punishment (daxing 大刑). When they encounter afterwards, it is Small Punishment (xiaoxing 小刑).” Ri stands for the heavenly stems, and chen for the earthly branches. The line that “When a stem is born, it begins from a meng day to move in the regular direction” means that a stem begins from a position in the “Punishment Day” diagram marked by meng to move clockwise or leftwards. The line that “When a branch is born, it begins from a zhong day to move in the opposite direction” means that a branch begins from a position in the diagram marked by zhong to move counterclockwise or rightwards.

Regarding the leftward movement of heaven and the rightward movement of the earth, there are abundant records in transmitted literature. Kong Yingda’s sub-commentary on the Monthly Ordinances says that “the twenty-eight stellar lodges and various stars follow heaven to move leftwards … the sun, moon, and five planets move rightwards.” The “Riyue” 日月 (“Sun and moon”) chapter of the Baihu tongyi 白虎通義 (Comprehensive Discussions in the White Tiger Hall) says that “heaven rotates leftwards. How about the sun, moon, and five planets? In comparison with heaven, the sun, moon, and five planets are yin, and therefore, move rightwards.”19 The Chuxue ji 初學記 (Notes to First Learning) cites the Chunqiu yuanming bao 春秋元命苞 (Inclusive Primary Mandate of the Chunqiu) to say that “heaven rotates leftwards, and the earth rotates rightwards,” that “the earth is deficient in the southeast. Yin moves rightwards and eventually enters the numinous gate,” and that “the reason why the earth rotates rightwards is that it is constituted by turbid qi and is short of refined [qi], it contains yin and commences late. Consequently, it rotates rightwards to welcome heaven and assist the heavenly way.” The Yi qian zaodu 易乾鑿度 (Changes: Chiseling open the Regularity of Qian) says that “the way of heaven rotates leftwards. The way of the earth moves rightwards.”20 The Taixuan jing 太玄經 (Classic of Supreme Mystery) records that “the sun moves eastward. Heaven moves westward. Heaven and the sun move in opposite directions. Yin and yang tour alternately.”21 The “Shuo ri” 說日 (“Explaining the sun”) chapter of the Lunheng 論衡 (Assay of Arguments) states that “heaven moves leftwards. The sun and moon move rightwards to meet with heaven.” Because heaven rotates leftwards, stars such as the Northern Dipper and the twenty-eight stellar lodges follow heaven to move leftwards, whereas the sun, moon, and five planets move rightwards.

Among excavated texts, the “Chuansheng zhan” 傳勝占 (Prognostications of Transmitted Victories) section in the manuscript Xingde C also says that “Heavenly One is male and moves leftwards. Earthly One is female and moves rightwards.” The “Tiandi” 天地 (“Heaven and earth”) section in Yinyang and the Five Agents B also contains a text on the directions of motion of heaven and earth. In consultation with Yinyang and the Five Agents A, the text can be reconstructed as saying that “The earth moves rightwards beginning from the west … Heaven moves leftwards beginning from the west …”22

One can see that the modality that heaven moves leftwards and the earth rightwards is related to the yin or yang attribute of heaven and earth. In other words, what is male moves leftwards, whereas what is female moves rightwards, to which a passage in the “Tianwen xun” of the Huainanzi is a testimony:

The spirits of the Northern Dipper have a female spirit and a male spirit. In the eleventh month, the Northern Dipper is established at zi and shifts to the next branch every month. The male spirit moves leftwards, while the female spirit moves rightwards. In the fifth month, they unite at wu to plan for punishments. In the eleventh month, they unite at zi to plan for virtues. The branches where Taiyin 太陰 (Great Yin) dwells are “oppressive days” (yanri 厭日) when all activities may not be taken. On the Canopy and Chassis, the male is slowly moved, thereby perceiving the female.23 Thus, [the branches of oppressive days] are odd branches.24

Now we can understand why it is stated in the prognosticatory statements that ri moves in a clockwise direction, while chen in a counterclockwise direction. This is because ri stands for the heavenly stems that are yang and male, while chen stands for the earthly branches that are yin and female. Furthermore, the yin/yang opposition corresponds precisely to the opposition between meng and zhong branch positions from which the heavenly stems and the earthly branches begin to move. The heavenly stems belong to yang and begin from a meng position to move clockwise, whereas the earthly branches belong to yin and begin from a zhong position to move counterclockwise.

In the line “When a stem and a branch encounter for the first time, it is Great Punishment (daxing 大刑). When they encounter afterwards, it is Small Punishment (xiaoxing 小刑),” “encounter” (hui ) refers to the conjunction between the heavenly stems and the earthly branches. For example, if the heavenly stems – counting from jia – move from the meng position of yin in a clockwise direction, and if the earthly branches – counting from zi – move from the zhong position of mao in a counterclockwise direction, the first encounter occurs when the heavenly stems count to yi and the earthly branches count to chou . The stem-branch binome yichou 乙丑 then identifies a punishment day. By corollary, the second encounter occurs at the stem-branch binome xinwei 辛未, which then also identifies a punishment day. The former encounter at yichou identifies a Great Punishment day, and the later encounter at xinwei identifies a Small Punishment day. Based on this calculative algebra, every six days can be seen as a cycle.

In our earlier editing of the manuscript, we understood correctly the Punishment Day calculation method recorded in the prognosticatory statements, but when we put the method into practice, we made a mistake that led us to draw the wrong conclusion, to wit: of the two columns of the stem-branch binomes inscribed on the manuscript, five chou days and five wei days in the first column “are the most likely to be punishment days,” whereas five chen days and five xu days in the second column “are the least likely to be punishment days.”25 But when we tried to verify our earlier account based on the new calculation method, we found that chen days and xu days are also likely to be punishment days. Let us corroborate this observation in more detail below.

First, let us reexamine our previous thought about the calculation. In our annotations, we illustrated the calculation method by positing that the heavenly stems begin from the yin , chen , or wu positions in the diagram, and the earthly branches from the mao , si , or wei positions. We presented the results in the following table.26

In the notes to the table, we wrote that “The table enumerates the positions in the diagram where the heavenly stems and the earthly branches dwell in a twelve-day cycle. The movement of each of the three stems is then paired with the movement of each of the three branches. Where a stem and a branch encounter are highlighted in color. The cells in color represent the distribution of punishment days.” Although even then we were already aware that our explanation was unclear, we did not come up with a better illustration due to limitations of time and our capability and ended up with nothing more than the table and the simple notes.

Now we will first explain our previous thought in greater detail and with more straightforward tables before proceeding to modify it. First, the above table posits the cycle of twelve branch positions and enumerates the encounters between a stem and a branch in nine scenarios in which the heavenly stems move clockwise through the twelve branch positions and the earthly branches move counterclockwise through the twelve branch positions. The results of the above table can be summarized in the table below.

Table 1
Table 1

Original calculation method for punishment days

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

Table 2
Table 2

Summary of punishment days

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

Based on this table, the frequency of punishment days is three times in chou and wei days, two times in zi and wu or yin and shen days, and once in mao and you or si and hai days. This led us to draw the conclusion that “chou and wei days have the highest probability to be punishment days, whereas in no case will chen and xu days be punishment days.” But instead of listing exhaustively all the combinatory possibilities, the fact is that we considered only the nine scenarios in which the heavenly stems begin from yin, chen, or wu, and the earthly branches begin from mao, si, or wei. This led to our wrong conclusion. Taking into account all the combinatory possibilities, there should be a total of thirty-six scenarios. We now expand our earlier table into the more complete one below.

Table 3
Table 3

Revised calculation method for punishment days

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

The calculation results can be presented in the following table:

Table 4
Table 4

Revised summary of punishment days

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

One can see that any earthly branch can be identified as an encounter day with the equal probability of 1/6. For this reason, we can be sure that our previous calculation was problematic. What, then, is the relationship between the five chou and five wei days, on one hand, and the five wu and five chen days, on the other hand, inscribed on the manuscript? We think that the relationship has something to do with the branch positions from which the heavenly stems and the earthly branches begin to move.

The way our previous calculation was marked allows one to see the encounter days (i.e., two punishment days, one Great Punishment day and one Small Punishment day) of only one cycle and did not present clearly all punishment days. Its presentation was not straightforward enough in that it presented only branches instead of stem-branch binomes. Given these considerations, we have made the following modifications to our previous calculation.

First, since the heavenly stems and the earthly branches rotate in the cycle of the twelve branch positions, we use numbers 1 to 12 to represent the twelve branch positions, which can be visualized as forming a dial-like disc.

Table 5
Table 5

The twelve branch positions

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

Furthermore, in the illustration below, we use the format of “the heavenly stems / the earthly branches + numbers” to represent the location of a stem and a branch on the twelve branch positions. For instance, “jia 1” represents the location of the stem jia on the zi branch position that is also a meng position. “Zi 2” represents the location of the branch zi on the chou branch position that is also a zhong position. We display the entire process of the movements of the heavenly stems beginning from the zi branch position and the earthly branches beginning from the chou branch position in the following table.

Table 6
Table 6

Location of stems and branches on the twelve branch positions

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

We can see that a complete cycle comprises five rotations through the twelve branch positions, namely, the completion of a sexagenary cycle. The highlighted cells in the above table represent the encounter days between the heavenly stems and the earthly branches. The five chou days yichou 乙丑, dingchou 丁丑, jichou 己丑, xinchou 辛丑, and guichou 癸丑 are Great Punishment days, and the five wei days xinwei 辛未, guiwei 癸未, yiwei 乙未, dingwei 丁未, and jiwei 己未 are Small Punishment days. We have used the same method to calculate all the combinatory possibilities of the movements of the heavenly stems beginning from a meng position and the earthly branches beginning from a zhong position. The results are presented in the following table (the number of intervening branches between the beginning position of a stem and that of a branch is counted clockwise).

Table 7
Table 7
Table 7
Table 7

Combinatory possibilities of the movements of the heavenly stems beginning from a meng position and the earthly branches beginning from a zhong position

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

In the end, we find that if the heavenly stems and the earthly branches begin from positions next to each other, the resulting punishment days will always be chou and wei days, of which there are six possible scenarios:

  1. the heavenly stems begin from zi, and the earthly branches from chou;

  2. the heavenly stems begin from yin, and the earthly branches from mao;

  3. the heavenly stems begin from chen, and the earthly branches from si;

  4. the heavenly stems begin from wu, and the earthly branches from wei;

  5. the heavenly stems begin from shen, and the earthly branches from you;

  6. the heavenly stems begin from xu, and the earthly branches from hai.

Of the punishment days in these scenarios, the five chou days yichou, dingchou, jichou, xinchou, and guichou are Great Punishment days, and the five wei days xinwei, guiwei, yiwei, dingwei, and jiwei are Small Punishment days. If the heavenly stems and the earthly branches begin from positions six branches apart, then the resulting punishment days will be chen and xu days, of which there are also six possible scenarios:

  1. the heavenly stems begin from zi, and the earthly branches from wei;

  2. the heavenly stems begin from yin, and the earthly branches from you;

  3. the heavenly stems begin from chen, and the earthly branches from hai;

  4. the heavenly stems begin from wu, and the earthly branches from chou;

  5. the heavenly stems begin from shen, and the earthly branches from mao;

  6. the heavenly stems begin from xu, and the earthly branches from si;

Of the punishment days in these scenarios, the five chen days wuchen, gengchen, renchen, jiachen, and bingchen are Great Punishment days, and the five xu days jiaxu, bingxu, wuxu, gengxu, and renxu are Small Punishment days.

Now note that the two columns of stem-branch binomes inscribed in the manuscript precisely contain these chou, wei, chen, and xu days:

乙未、辛丑、丁未、癸丑、己未、乙丑、辛未、丁丑、癸未、己丑。9

戊戌、甲辰、庚戌、丙辰、壬戌、戊辰、甲戌、庚辰、丙戌、壬辰。10

In other words, the binomes in the first column are the punishment days when the heavenly stems and the earthly branches begin from positions next to each other. The binomes in the second column are the punishment days when the heavenly stems and the earthly branches begin from positions six branches apart.

Moreover, the “Ji yi” 祭一 (“sacrifice one”) section contains contents related to punishment days:

【□、□、□】、辰、丑、辰、〖□〗、辰、未、戌、未、戌,直辰;以祭有死之,女得㓝(刑)日閟(閉)。1–5

【□、□、□】, chen, chou, chen, 〖□〗, chen, wei, xu, wei, xu, straight branches. To perform sacrifice will entail death. You should refrain [from performing sacrifice] on punishment days.

In this passage, days identified by the four branches chen, xu, chou, and wei are to be avoided. One can see that regarding punishment days, the days identified by these four branches require particular attention. Judging from this, our previous conclusions that “in no case will chen and xu days be punishment days” and that “five chen and five xu days are the least likely to be punishment days” appear even more invalid.

The reason why the punishment days resulting from the movements of the heavenly stems and the earthly branches beginning from positions next to each other and from positions six branches apart – the punishment days being the five chou and five wei days when the beginning positions are next to each other and the five chen and five xu days when the beginning positions are six branches apart – has something to do with the special attribute of the four branches chou, wei, chen, and xu. They turn out to be the grave branches (muchen 墓辰) in the Three Unions Scheme of the Five Agents. Records of the Three Unions Scheme of the Five Agents can be seen in transmitted literature, such as the “Tianwen xun” chapter of the Huainanzi and the officially sponsored Qing compendiums on calculations and arts: the Xieji bianfangshu and the Xingli kaoyuan 星曆考原 (Investigations into Stars and the Calendar).27 In the Shuowen, Xu Shen also says that “regarding the Five Agents, Wood ages at wei .” The theory of the Three Unions Scheme of the Five Agents deems the three stages of birth, maturity, and death as forming a scheme. The three branches shen , zi , and chen form the Water scheme in which Water is born at shen, reaches maturity at zi, and dies at chen. The three branches hai , mao , and wei form the Wood scheme in which Wood is born at hai, reaches maturity at mao, and dies at wei. The three branches yin , wu , and xu form the Fire scheme in which Fire is born at yin, reaches maturity at wu, and dies at xu. The three branches si , you , and chou form the Metal scheme in which Metal is born at si, reaches maturity at you, and dies at chou.

Texts related to the Three Unions Scheme of the Five Agents can also be seen in excavated manuscripts, including the “Wusheng” 五勝 (“Five Conquests”) section of the Shuihudi 睡虎地 Qin bamboo-slip Rishu 日書 (Daybook) manuscript,28 the “Wuxing” 五行 (“Five Agents”) section of the Fangmatan 放馬灘 Qin bamboo-slip Rishu manuscript,29 and the “sheng” (“birth”) section of the Kongjiapo 孔家坡 Rishu manuscript.30 The stages of birth, maturity, and death are written in the Shuihudi manuscript with different characters and in slightly different order: “grave (mu ), birth, flourishing (wang ).” The other two manuscripts arrange the stages of birth, maturity, and death in exactly the same order as the Three Unions Scheme of the Five Agents, which testifies to the existence of a systematic theory of the Three Unions Scheme of the Five Agents as early as the pre-Qin period. Jao Tsung-I 饒宗頤 and Liu Lexian 劉樂賢 have done thorough research on this. Although the three stages are written in different characters – either “birth , maturity , and death ,” “birth , maturity , and old age ,” or “birth , flourishing , and grave ,” they denote the same life cycle that Water, Wood, Fire, and Metal undergo: birth to prime and then to vanishment. The four branches chen, wei, xu and chou are correlated with the vanishment stage denoted by death , old age , and grave . We know that punishment days are inauspicious from the lines that “to perform sacrifice might entail death” and that “the hundred of activities may not be undertaken; to perform sacrifice is very inauspicious and will certainly end in death” contained in the prognosticatory statements of the “Punishment Day” section. However, it is precisely by virtue of their inauspicious attribute that punishment days are appropriate for activities such as “military display, battles, attacking, killing, imprisoning criminals, and demolishing constructions.” In other words, inauspicious days are unfavorable for festive undertakings, but very favorable for destructive activities. The destructive activities accord with the connotation of the grave branches.

Furthermore, under the entry “Days for officials, magistrates, and people” 王官守相民日, the Xieji bianfang shu states that “beyond the five days, calendrical specialists further regard wei, xu, chou, and chen as four successive prison days … xu, chou, chen, and wei as four successive bereavement days … chou, chen, wei, and xu as four successive crime and punishment days, also called punishment and imprisonment days. This is probably because imprisonment days are identified by the four successive grave branches, while the rest of the twelve branches are indicators of retirement, confinement, and death.”31 This text points out even more clearly that the four branches chen, wei, xu, and chou are closely related to crime, imprisonment, punishment, and bereavement. It is for this reason that the Mawangdui manuscript lists the punishment days identified by the four branches and foregrounds them as days favorable for military and war activities. In addition, under the punishment days yichou and xinwei are inscribed, respectively, “twenty-fifth year” 廿五年 and “twenty-six year” 廿六年. Li Xueqin 李學勤 pointed out that they refer to the twenty-fifth and twenty-six years of the reign of King Zheng of Qin (later known as Qin Shihuang 秦始皇).32 The Shi ji 史記 tells us that King Zheng of Qin vanquished the state of Yan and the state of Qi successively in the twenty-fifth and twenty-sixth years of his reign.33 This provides further evidence that chou and wei days are related to war, killing, and attacking. It is likely that the notes “twenty-fifth year” and “twenty-sixth year” were added under yichou and xinwei after the actual warfare had taken place in the twenty-fifth and -six years of King Zheng’s reign. The appended notes thus serve to reaffirm that chou and wei days are indeed favorable for military activities, thereby enhancing the credibility of the Punishment Day prognostication. One can say that the very designation Punishment Day is based on such activities. Additionally, the “Punishment Day” section provides us with more information to study the theory of the Three Unions Scheme of the Five Agents. It enables us to realize that the application of the Three Unions Scheme of the Five Agents does not stop at a merely theoretical formation of the three stages of birth, maturity and death; rather, by virtue of their connotations, birth, maturity, and death can be combined with practical and specific prognostications to become the basis for selecting auspicious or inauspicious days. The “Punishment Day” section thus enriches our understanding of the theory of the Three Unions Scheme of the Five Agents.

Figure 6
Figure 6

Graphic representation of the Three Unions Scheme of the Five Agents

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

3 “Punishment Day” Is Not the Same as “Meeting Day” (Huiri 會日) That Is Attested in Transmitted Literature

Regarding the specific meanings of Punishment Day, Great Punishment, and Small Punishment, Tao Lei 陶磊 thinks that punishment days are related to days of Eight Meetings (Bahui 八會) or Eight Unions (Bahe 八合) in transmitted literature and that Great Punishment and Small Punishment correspond to Great Meeting (Dahui 大會) and Small Meeting (Xiaohui 小會).34 We consider this view problematic. Since these two types of calendar spirits of Punishment Day and Meeting Day are very similar in terms of names, movement, and stem-branch binomes identified by them, they are easily confused. For this reason, it is necessary to elaborate on the two types of calendar spirits in order to distinguish one from the other.

Meeting , is also called Eight Unions, Eight Meetings and Great Meeting between Yin and Yang (Yinyang Dahui 陰陽大會), and so on. It is a calendar spirit related to the female and male spirits of the Northern Dipper. Relevant sources about it are mainly seen in the Zhouli 周禮 (Rites of Zhou), the Huainanzi, the ancient lost book Kanyu jing 堪輿經 (Classic of Canopy and Chassis), and the Kanyu 揕輿 text from the Peking University Han bamboo-slip manuscripts. Let us quote the relevant passages below.

  1. The “Tianwen xun” chapter of the Huainanzi:

    The spirits of the Northern Dipper have a female spirit and a male spirit. In the eleventh month, the Northern Dipper is established at zi and shifts to the next branch every month. The male spirit moves leftwards, while the female spirit moves rightwards. In the fifth month, they unite at wu to plan for punishments. In the eleventh month, they unite at zi to plan for virtues. The branches where Taiyin 太陰 (Great Yin) dwells are “oppressive days” (yanri 厭日) when all activities may not be taken. On the Canopy and Chassis, the male is slowly moved, thereby perceiving the female. Thus, [the branches of oppressive days] are odd branches. Starting with jia and zi. The son and mother seek each other, and where they unite is a union. Ten stems and twelve branches form a sexagenary cycle, and there are in total eight unions. Uniting in front of the Year entails death. Uniting in the back of the Year entails no calamity. Jiaxu, the state of Yan; yiyou, the state of Qi; bingwu, the state of Yue; dingsi, the state of Chu; gengchen,35 the state of Qin; xinmao, the state of Rong; renzi, the state of Dai; guihai, the state of Hu. Wuxu and jihai, the state of Han; jiyou and jimao, the state of Wei. Wuwu, wuzi. Eight unions, all under Heaven.36

  2. A passage of the Kanyu jing as quoted in the Lishi mingyuan 曆事明原 (Elucidating the Origin of Calendrical Matters) under the entry “Great Meeting between Yin and Yang”:

    In the first month, the Great Meeting appears on jiaxu. The two types of qi of yin and yang begin from zi and shift to the next branch every month. Yang qi moves leftwards from zi to chou. Yin qi moves rightwards from zi to hai. The branch where yang qi arrives is called Month Establisher (Yue jian 月建), or Yang Establisher (Yang jian 陽建). The branch where yin qi arrives is called Month Oppressor (Yue yan 月厭), or Yin Establisher (Yin jian 陰建). Suppose that in the first month, Yang Establisher is at yin, and Yin Establisher is at xu. Yang guides the stems, and Yin guides the branches. Yang Establisher is at yin and close to jia. To have jia call on xu is for a yang stem to call on a yin branch. The yang stem jia and the yin branch xu unite. Accordingly, jiaxu identifies the Great Meeting in the first month. The Great Meeting in the second month is on yiyou … The Great Meeting in the fifth month is on bingwu … The Great Meeting in the sixth month is on dingsi … The Great Meeting in the seventh month is on gengchen … The Great Meeting in the eighth month is on xinmao … The Great Meeting in the eleventh month is on renzi … The Great Meeting in the twelfth month is on guihai

    Another passage of the Kanyu jing is quoted in the Lishi mingyuan under the entry “Small Meeting between Yin and Yang”:

    The Small Meeting day in the second month is jiyou. Yang Establisher is at mao, and Yin Establisher is at you. Yin and yang clash. It coincides with the spring equinox (chun fen 春分) for growth and birth. Establisher and Oppressor are in separate positions. To connect yin and yang, ji is employed to pair with you where Yin Establisher dwells. Accordingly, jiyou identifies the Small Meeting in the second month. The Small Meeting in the third month is on wuchen … The Small Meeting in the fourth month is on jisi … The Small Meeting in the fifth month is on wuwu … The Small Meeting in the eighth month is on jimao … The Small Meeting in the ninth month is on wuxu … The Small Meeting in the tenth month is on jihai … The Small Meeting in the eleventh month is on wuzi. When Yin Establisher is at zi, it is also the case that yin and yang conjoin, and wu is paired with the zi branch where it is established. Accordingly, wuzi in the eleventh month identifies the Small Meeting.37

  3. The entry “Month Oppressor” in the Xieji bianfang shu:

    Month Establisher is what the dipper handle establishes. Its image appears in the sky and can be seen by looking at the sky … from Establisher, Oppressor can be inferred.

    The entry “Yin and yang do not accommodate each other” 陰陽不將 in the Xieji bianfang shu quotes the Tianbao li 天寶曆 (Tianbao Calendar) to say:

    That yin and yang do not accommodate each other means this: Month Establisher is taken as yang and called Yang Establisher; it begins from yin in the first month and shifts through the twelve branches in the regular (clockwise) direction; Month Oppressor is yin and called Yin Establisher; it begins from xu in the first month and shifts through the twelve branches in the opposite (counterclockwise) direction.38

  4. The Kanyu text from the Peking University bamboo-slip manuscripts:

    The Year’s (sui ) positions: of the Year’s positions, jia and xu meet in the first month; yi and you meet in the second month; shen meets in the third month; wei meets in the fourth month; bing and wu meet in the fifth month; ding and si meet in the sixth month; geng and chen meet in the seventh month; xin and mao meet in the eighth month; yin meets in the ninth month; chou meets in the tenth month; ren and zi meet in the eleventh month; gui and hai meet in the twelfth month.39

Several points can be seen from the above passages. First, the “Tianwen xun” chapter of the Huainanzi shows that Meeting Day is a calendar spirit related to the spirits of the Northern Dipper, and the stem-branch binome of the days when it occurs can be known by observing when the female spirit and the male spirit of Northern Dipper conjoin. Second, the movements of the female spirit and the male spirit of the Northern Dipper exhibit the following patterns: the male spirit moves leftwards, commences at yin in the first month, defines the branch at which the dipper handle points as Month/Yang Establisher, and shifts to the next branch every month, whereas the female spirit moves rightwards, commences at xu in the first month, defines the established branch as Yin Establisher and the dwelling branch as Oppressor, and shifts to the next branch every month. Finally, meeting days calculated from the movement pattern are slightly different between the above passages. We find that the Eight Meetings system can be classified into two types. On the surface the difference between the two types is that meeting days occur in different months, but in fact the difference is a result of different calculation methods.40 The first type comprises the meeting days deduced from Jia Gongyan’s 賈公彥 sub-commentary to the Zhouli and from the Huainanzi by scholars such as Qian Daxin 錢大昕, Qian Tang 錢塘, Wang Niansun 王念孫, and so on. The second type is found in the quoted passages of the lost book Kanyu jing. Through setting out the passages in transmitted literature and the Kanyu text in Peking University bamboo-slip manuscripts as above, we have come to think that the Eight Meetings system in the Kanyu jing should be favored. According to the second quote above, its calculation method is to form a meeting day by combining the heavenly stem near Yang Establisher with the earthly branch where Yin Establisher dwells. The distribution of Great Meeting days and Small Meeting days in each month is illustrated in the following table.

Table 8
Table 8

Distribution of Great Meeting days and Small Meeting days by month

Citation: Bamboo and Silk 7, 1 (2024) ; 10.1163/24689246-20240004

One can see that meeting days occur in all months except the third, fourth, ninth, and tenth months. But the “Suiwei” 歲立(位) (“Year’s positions”) section of the Kanyu text lists meeting days in the months that are without Great Meeting days; i.e., “shen meets in the third month; wei meets in the fourth month … yin meets in the ninth month; chou meets in the tenth month.” The meeting days of these four months are apparently different from that of other months for they contain only the earthly branches where Yin Establisher dwells. The Kanyu jing explains the absence of meeting days in the third, fourth, ninth, and tenth months by saying that “yin and yang are not matched and cannot be paired.” Qian Tang also notes that “there are twenty-four squares in the Canopy and Chassis. There are eight stems and twelve branches. Consequently, four branches are left without a match.”41 One can see that the reason why there are only eight meeting days is because there are only eight heavenly stems in the four sectors, which are insufficient to be paired with the twelve earthly branches, necessarily leaving four branches unpaired. For this reason, the meeting days in the third, fourth, ninth, and tenth months listed in the Kanyu text in the Peking University Han bamboo-slip manuscripts contain only the earthly branches without corresponding heavenly stems. It remains dubious whether they can be called meeting days. But it is clear that the meeting days in these four months and the meeting days in the rest of the months do not belong to the same system. This suggests that, in fact, the meeting days recorded in the Kanyu text still accord with those recorded in the Kanyu jing.

It follows from the above discussion that Punishment Day clearly differs from Meeting Day in several respects:

  1. Meeting Day is a calendar spirit deriving from the spirits of the Northern Dipper, whereas Punishment Day is a calendar spirit whose formation is based on the yin/yang binary categorization of the twelve branches.

  2. The occurrence of Meeting Day is deduced from the movement patterns of the female and male spirits of the Northern Dipper, whereas the occurrence of Punishment Day is deduced from the movement patterns of the heavenly stems and the earthly branches. They are based on different calculation rules. For Meeting Day, the female and the male spirits begin from fixed branches, move through corresponding branches (Yang Establisher at yin and Yin Establisher at xu in the first month, Yang Establisher at mao and Yin Establisher at you in the second month, Yang Establisher at chen and Yin Establisher at shen), and eventually coincide at zi or wu. For Punishment Day, by virtue of the yin/yang binary categorization, the heavenly stems begin at odd positions, whereas the earthly branches begin at even positions. This means that the heavenly stems and the earthly branches will never coincide at the same branch. Moreover, the calculation for the occurrence of Meeting Day is complicated in that the identification of a meeting day is through the combination of the heavenly stem contiguous to Yang Establisher with the earthly branch of Yin Establisher, whereas a punishment day is identified by simply combining the heavenly stem and the earthly branch that encounter.

  3. The two also differ in the way of determining the auspicious or inauspicious qualities of a day. Meeting Day determines the auspicious or inauspicious qualities of a day by its spatial relation with the Year. The “Tianwen xun” chapter of the Huainanzi says that “Uniting in front of the Year entails death. Uniting in the back of the Year entails no calamity.” The Kanyu text from the Peking University manuscripts states that “if the meeting takes place in front of the Year, there will be misfortune in the month of the meeting. If the meeting takes place in the back of the Year, there will be great fortune in the month of the meeting. If the meeting takes place opposite the Year, there will be small fortune in the month of the meeting.” It is particularly complicated in practical applications that involve the concept of “days overseen by Meeting Day.”42 In contrast, Punishment Day directly determines the day of its occurrence as inauspicious. All punishment days are taboo days except for military activities. The application of the Punishment Day system is more easily accessible.

  4. The two diverge further in the way of distinguishing great from small. Small Meeting of yin and yang comes about by combining the central heavenly stems of wu and ji with the earthly branches associated with months in which yin and yang are not paired (chen, xu, si, and hai), yin and yang conjoin at the same positions (zi and wu), and yin and yang occupy separate positions (mao and you). In contrast, Great Punishment and Small Punishment are simply distinguished by sequence: “When a stem and a branch encounter for the first time, it is Great Punishment. When they encounter afterwards, it is Small Punishment.”

  5. Based on the calculated days identified by the stem-branch binomes, there are normally eight Meeting days, whereas there are ten Punishment days in each stem and branch combination.

In the final analysis, the two are at variance with each other in terms of both inner logic and practical applications. All in all, Meeting Day belongs to the ancient Kanyu system and is more complicated and systematic, whereas, given the scant record of Punishment Day in both transmitted and excavated texts, which of the calculations and arts divisions it belongs to remains a mystery and awaits further research. Nevertheless, what we can say with certainty is that there is no relationship whatsoever between the two, and accordingly, they should not be confused in our research and discussions.

4 Concluding Remarks

By reexamining the “Punishment Day” section in the Mawangdui manuscript Yinyang and the Five Agents A, this paper contends that the two characters meng and zhong inscribed next to the twelve branches in the Punishment Day diagram do not have substantive meaning; rather, they constitute binary categories in the same vein as the binarisms yin/yang, hard/soft, man/woman, female/male, and so on. The reason why meng/zhong can assume such a function is because the meaning of meng (elder) and that of zhong (secondary) pose a contrast between strong and weak on one hand, and primary and secondary, on the other hand. As such, meng/zhong can be used to replace other sets of binary conceptions such as yin/yang. We also think that this special usage of meng/zhong may be related to the use of the four corners to represent the four seasons in the Punishment Day diagram.

This paper proceeds to point out a mistake made in our previous calculation of punishment days in the Changsha Mawangdui Han mu jianbo jicheng before putting forward a new calculation method. Based on the new method, we find that the two columns of stem-branch binomes inscribed on the manuscript should not be construed such that the stem-branch binomes in one column represent days that are the most likely to be punishment days, whereas the stem-branch binomes in the other column represent days that are the least likely to be punishment days. Instead, the stem-branch binomes with the branches wei and chou in the first column represent the punishment days resulting from the movements of a stem and a branch starting from contiguous branch positions, and the stem-branch binomes with the branches xu and chen in the second column represent the punishment days resulting from the movements of a stem and a branch starting from branch positions six branches apart. The emphasis on the four branches chou, wei, chen, and xu in the calculation of punishment days is related to the special attributes of the four branches in the Three Unions Scheme of the Five Agents. As the four branches are classified into the grave branches in the Three Unions Scheme of the Five Agents, they are associated with the punishment days that are related to punishments, imprisonment, war, battling, killing, and attacking, activities for which these punishment days are stressed as favorable.

Finally, we argue against the view that Punishment Day and Meeting Day are related. We maintain that despite their similarity on the surface, they are in fact two different types of calendar spirits and should be differentiated.

Acknowledgements

Translated by Zhu Ronghu. This article is a preliminary result of the National Social Science Fund Understudied Fields Program “Study of Image and Text Transformation in Bamboo and Silk Calculations and Arts Manuscripts and Related Issues” 國家社科基金冷門絶學項目「簡帛數術文獻圖文轉换及相關問題研究」(20VJXG043) and the National Social Science Fund Major Project “Compilation and Comprehensive Study of Bamboo and Silk Yinyang Wuxing Materials” 國家社科基金重大項目「簡帛陰陽五行類文獻集成及綜合研究」 (20&ZD272).

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1

Transl. Translations of calculations and arts related terms in this article follow Donald Harper and Marc Kalinowski eds., Books of Fate and Popular Culture in Early China: The Daybook Manuscripts of the Warring States, Qin, and Han (Leiden: Brill, 2017).

2

Qiu Xigui 裘錫圭 ed., Changsha Mawangdui Han mu jianbo jicheng 長沙馬王堆漢墓簡帛集成, (Beijing: Zhonghua, 2014), vol. 1, 101 (photograph of Yinyang wuxing A); vol. 5, 99–101 (annotated transcription of Yinyang wuxing A); vol. 2, 11 (photograph of Yinyang wuxing B); vol. 5, 138–139 (annotated transcription of Yinyang wuxing B).

3

For detailed discussion of the cord-hook pattern, see Marc Kalinowski, “The Understanding and Uses of the ‘Day Court Diagram’ in Qin-Han Hemerology and Calendrical Astrology,” Bamboo and Silk 3.2 (2020), 294–343.

4

Li Xueqin 李學勤, “Mawangdui Han mu boshu shifa shiwen zhaiyao” 馬王堆漢墓帛書式法釋文摘要, Wenwu 文物2000.7, 85–94. Chen Songchang 陳松長, “Mawangdui shifa chulun” 馬王堆式法初論, in Ai Lan 艾蘭 (Sarah Allan) and Xing Wen 郉文 eds., Xinchu jianbo yanjiu 新出簡帛研究 (Beijing: Wenwu, 2004), 172.

5

Cf., Li Ruohui 李若暉, “Mawangdui boshu shifa xingri shitu chutan” 馬王堆帛書式法刑日式圖初探, in Ai Lan and Xing Wen eds., Xinchu jianbo yanjiu, 195.

6

Li Ruohui, “Mawangdui boshu shifa xingri shitu chutan” 馬王堆帛書式法刑日式圖初探, 195.

7

Huang Ruxuan 黃儒宣, Rishu tuxiang yanjiu 日書圖像研究 (Shanghai: Zhongxi, 2013), 43–44.

8

Zhang Zhicong 張志聰, Huangdi neijing jizhu 黃帝內經集註 (Hangzhou: Zhejiang guji, 2002), 632.

9

For detailed discussion, see Cheng Shaoxuan 程少軒, “Ruyinhou mu erhao shipan taiyi jiugong yunxing fuyuan” 汝陰侯墓二號式盤太一九宮運行復原, Chutu wenxian 出土文獻2020.4, 72–100.

10

The “Nanri nüri pian” 男日女日篇 of the Shuihudi 睡虎地 Qin bamboo-slip manuscript Rishu 日書 (Daybook) mentions man day (nanri 男日), woman day (nüri 女日), female day (pinri 牝日) and male day (muri 牡日). The “Renri pian” 人日篇 of the Shuihudi manuscript mentions boy day (nanziri 男子日) and girl day (nüzi ri 女子日). The Fangmatan A 放馬灘 manuscript Rishu contains man day (nanri 男日) and woman day (nüri 女日) on slip 1. The Fangmantan B manuscript Rishu contains female month (pinyue 牝月) on slip 194 and male month (muyue 牡月) on slip 195.

11

Wang Qiang 王強, “Yinqueshan Hanjian dizhi yinyang xiaokao” 銀雀山漢簡地支陰陽小考, in Di si jie guwenzi yu chutu wenxian yuyan yanjiu xueshu yantaohui ji chutu wenxian yuyan wenzi yanjiu qingnian xuezhe luntan lunwen ji 第四屆古文字與出土文獻語言研究學術研討會暨出土文獻語言文字研究青年學者論壇論文集 (Changchun, 2021), 177–181.

12

The manuscript Xingde A 刑德甲 (Punishment and Virtue A) states that “Punishment wanders at odd [palaces] at zi, unites with Virtue at four regular [palaces] at wu, and moves leftwards. Punishment wanders at odd [palaces] … dwells.” The manuscript Xingde B 刑德乙 (Punishment and Virtue B) states that “Punishment wanders at odd [palaces] at zi and unites with Virtue at regular [palaces] at wu. Accordingly, at wu they unite; at zi they separate.” Furthermore, the arrangement of the small wandering diagram exhibits an alternation between the odd palace and the regular palace, whose yin and yang distribution is very similar to that of meng/zhong in the Punishment Day diagram. However, it should be noted that the yin or yang attributes of odd and regular palaces are more likely influenced by the four cardinal directions and the four corners (to wit, the four cardinal directions are regular, whereas the four corners are odd) rather than, as in the binarisms hard/soft, man/woman, female/male, and meng/zhong, by the quality of the stems and branches.

13

He Lulu 賀璐璐 has done thorough research on the binary calendar spirits in bamboo-slip and silk manuscript calculations and arts texts. See He Lulu, “Jianbo shushu wenxian zhong eryuan duili shensha yanjiu: yi mawangdui boshu wei zhongxin” 簡帛數術文獻中二元對立神煞研究:以馬王堆帛書為中心, PhD dissertation, Hunan University, 2021.

14

Yunlu 允祿 et al. ed., Qinding xieji bianfang shu 欽定協紀辨方書, in Bao Yunlong 鮑雲龍 et al. ed., Siku shushulei congshu 四庫數術類叢書 (Shanghai: Shanghai guji, 1991), 1008.

15

“It is evident that Yandui is the same as Liuyi. In hemerological books, Yandui is said to be prohibited for marrying off a daughter and taking a wife, but Liuyi is said to be appropriate for betrothals and giving betrothal gifts, which are diametrically opposite.” Qinding xieji bianfang shu, 260.

16

Li Ling 李零, Zhongguo fangshukao 中國方術考 (Taibei: Dongfang, 2001), 123–125. Liu Lexian 劉樂賢, “Chu Qin xuanzeshu de yitong ji yingxiang: yi chutu wenxian wei zhongxin” 楚秦選擇術的異同及影響:以出土文獻為中心, Lishi yanjiu 歷史研究2006.6, 19–31.

17

Wang Qiang 王强, “You tongshu yiming xianxiang tan shensha de mingming” 由同術異名現象談神煞的命名, in Di yi jie chutu wenxian yu zhongguo gudaishi xueshu luntan ji qingnian xuezhe gongzuofang huiyi lunwen ji 第一屆出土文獻與中國古代史學術論壇暨青年學者工作坊會議論文集 (Shanghai, 2019), 278–286.

18

Shōhachi Nakamura 中村璋八, Nihon on’yōdōsho no kenkyū 日本陰陽道書の研究 (Tokyo: Kyūko, 1985), 56–57.

19

Chen Li 陳立, Baihu tong shuzheng 白虎通疏證 (Beijing: Zhonghua, 1997), 423.

20

Zhao Zaihan 趙在翰, Qiwei 七緯 (Beijing: Zhonghua, 2012), 46.

21

Sima guang 司馬光 ed., Taixuan jing jizhu 太玄經集注, edited by (Beijing: Zhonghua, 1998), 185.

22

Changshu Mawangdui Han mu jianbo jicheng, vol. 5, 135.

23

堪輿徐行,雄以音知雄. The line is slightly different in a Wenxuan quote that reads 堪輿行雄以知雌. The translation of this line is modified from Donald Harper’s rendering. Donald Harper, “The Han Cosmic board (shih ),” in Early China 4 (1978–79), 9, note 53.

24

Liu Wendian 劉文典 ed., Huainan honglie jijie 淮南鴻烈集解 (Beijing: Zhonghua, 2013), 124–125.

25

Changsha Mawangdui Han mu jianbo jicheng, vol. 5, 101.

26

Changsha Mawangdui Han mu jianbo jicheng, vol. 5, 100–101. The table was originally marked in different colors, but the Changsha Mawangdui Han mu jianbo jicheng is printed in black and white and marks different sets of branches by grey in varying degrees. The original table in colors is quoted here.

27

The “Tianwen xun” chapter of the Huainanzi uses sheng , zhuang , si in the main text and sheng , zhuang , lao in the attached diagram to represent the three stages. Huainan honglie jijie, 144 & 153. The Xingli kaoyuan speaks of sheng , wang , mu , cited by the Xieji bianfangshu under the entry “Sanhe” 三合. Yunlu et al. ed., Yuding xingli kaoyuan 御定星曆考原, in Bao Yunlong 鮑雲龍 et al. ed., Siku shushulei congshu 四庫數術類叢書 (Shanghai: Shanghai guji, 1991), 24. Xieji bianfang shu, 153.

28

The original text reads:

丑巳【酉】金,金勝木83;未亥【卯木,木】勝土85;辰申子水,水勝火87;【戌寅午火,火勝金】.

The supplemented text is based on Jao Tsung-I 饒宗頤, “Qinjian zhong de wuxing shuo yu nayin shuo” 秦簡中的五行說與納音說, Zhongguo yuwen yanjiu 中國語文研究 1984.7, 37–50.

29

The original text reads:

火生寅,壯午,老戌73。金生巳,壯酉,老丑74。水生申,壯子,老辰75。木生亥,壯卯,老未76

The transcription follows Liu Lexian 劉樂賢, “Wuxing sanheju yu nayin shuo: du Jao Tsung-I xiansheng qinjian zhong de wuxing shuo yu nayin shuo” 五行三合局與納音說——讀饒宗頤先生《秦簡中的五行說與納音說》, Jianghan kaoku 江漢考古1992.1, 89–91.

30

The original text reads:

水:生申,壯子,老辰;木:生亥,壯卯,老未103;火:生寅,壯午,老戌;金:生巳,壯酉,老丑。104

See Wang Qiang, “Kongjiapo hanmu jiandu jiaoshi” 孔家坡漢墓簡牘校釋, MA thesis, Jilin University, 2014, 43.

31

Xieji bianfangshu, in Siku shushulei congshu, 288.

32

Li Xueqin 李學勤, “Preface,” in Chen Songchang 陳松長 ed., Mawangdui jianbo wenzibian 馬王堆簡帛文字編 (Beijing: Wenwu, 2001), 3.

33

Sima Qian 司馬遷, Shi ji 史記 (Beijing: Zhonghua, 1982), 234.

34

Tao Lei 陶磊, Huainanzi tianwen yanjiu: cong shushu shi de jiaodu 淮南子天文研究: 從數術史的角度 (Jinan: Qilu, 2003), 160–161.

35

Qian Tang 錢塘 recognizes gengshen 庚申 as erroneous and changes it to gengchen 庚辰 in his Huainan tianwen xun buzhu 淮南天文訓補註. See Huainan honglie jijie, 887.

36

Qian Daxin 錢大昕 has edited this passage, saying that “the list from jiaxu to guihai in the Huainanzi should be Great Meeting days” and that the stem-branch binomes after guihai, i.e., wuxu, jihai, jiyou, jimao, wuwu, and wuzi, should be Small Meeting days. Qian thinks that two Small Meeting days are left out and by extension, are wuchen and jisi. Qian Daxin 錢大昕, Qianyantang ji 潛研堂集 (Shanghai: Shanghai guji, 2009), 217–219. Wang Niansun 王念孫 agrees with Qian and thinks that wuchen should precede wuxu, and jisi should precede jihai. Wang Niansun 王念孫, Dushu zazhi 讀書