Abstract
This chapter offers an overview of the intimate relationship that tied together legal and mathematical manuscripts in early imperial China, whether these manuscripts were unearthed during regular archeological excavations or bought on the antiquities market. The author shows how the legal manuscripts display the way in which measurement and number were essential for the social and economic organization of the early Chinese empire, as well as for the working of its bureaucracy. Measurement values and numbers defined and brought together the social and administrative hierarchy. They served as a basis for diversifying the allotment of land and the determination of salaries. Measurement values and numbers also defined how tax was collected both on land and on goods moving from one jurisdiction to another across customs, and how corvée labor was organized. The significant use of measurement values and numbers in these administrative regulations, and the related requirement to compute with them to put regulations into practice, suggest that proficiency in mathematics was an asset for officials. The chapter analyzes the various pieces of evidence showing that the mathematical manuscripts from roughly-speaking the same time period mesh with the legal texts. They contain numerical data similar to those presented in legal texts, and even complement them in this respect. In other words, the data given by mathematical manuscripts appear to have been faithful to administrative practice. Mathematical manuscripts also detail procedures required to put the norms in practice. The chapter suggests that we can infer that the procedures given in these mathematical manuscripts were precisely those used by officials in charge of implementing regulations as we find them in legal texts. Finally, the author shows that the manuscripts and the received texts do not contradict each other in this respect, suggesting that all these documents display a certain coherence.
Translated by Daniel Patrick Morgan and Andrea Eberhard-Bréard. Prepared for publication by Karine Chemla
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC Grant agreement No. 269804.
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Notes
- 1.
Tr. (Cullen 2004: 60). (Zhangjiashan Han mu zhujian [ersiqi hao mu]) 2006: 141). Slips numbers for the Han manuscripts from Zhangjiashan are as per (Zhangjiashan Han mu zhujian [ersiqi hao mu] 2006). [Editorial note: The reader should bear in mind that for the expression of numbers and measurement values, the original documents contain only Chinese characters, and no symbols comparable to Arabic numerals. Given that there is no ambiguity, in this chapter these numbers and measurement values were translating using Arabic numerals. For explanations on measurement units, see Annex A2 ‘Numbers, Measurement Values and Measurement Units in Chinese Texts’ at the end of this volume].
- 2.
As to the date of Qin laws contained in the Shuihudi tomb 11 corpus, the majority of scholars consider them to be from the period of Ying Zheng’s 嬴政 (260–210 BCE) reign as king (246–222 BCE), preserved therein being parts of laws drafted during the time of Shang Yang’s 商鞅 legal reforms (356–338 BCE). See Shu Zhimei (1981). The terminus ante quem for the Qin manuscript Mathematics of the Yuelu Academy collection should be no later than the date of the ‘Zhi ri’ 質日 calendar slips recovered from the same tomb, i.e. 213 BCE. See Chen Songchang (2009).
- 3.
(Zhangjiashan Han mu zhujian [ersiqi hao mu] 2006: 2).
- 4.
收膳夫之秩 (Chunqiu Zuo zhuan zhengyi, Zhuang 19: 1773). All official and noble titles are rendered according to Hucker (1985).
- 5.
Specifically, the Hanfeizi 韓非子 records that ‘According to the Law of Lord Shang, “he who cuts off one head in war is promoted by one grade in rank, and, if he wants to become an official, is given a 50-dan office; he who cuts off two heads in war is promoted by two grades in rank, and, if he wants to become an official, is given a 100-dan office” ‘(‘商君之法曰: “斬一首者爵一級,欲為官者為五十石之官; 斬二首者爵二級, 欲為官者為百石之官”)’ (Hanfeizi jijie, 399, tr. modified from (Liao 1959, Vol. 2: 215)). The Book of Lord Shang records that ‘the 1 000-dan prefect has 100 swordsmen, the 800-dan prefect has 80 swordsmen, the 700-dan prefect has 70 swordsmen, and the 600-dan prefect has 60 swordsmen’ 千石之令,短兵百人。八百之令,短兵八十人。七百之令,短兵七十人。六百之令,短兵六十人 (Shangjun shu zhushi, 147), tr. modified from (Duyvendak 1928: 296–97).
- 6.
內史、郡二千石官 (Chen Songchang 2009: 87).
- 7.
See (Zhangjiashan Han mu zhujian [ersiqi hao mu] 2006: 69–82).
- 8.
See (Zhangjiashan Han mu zhujian [ersiqi hao mu] 2006: 50; Han shu, 19A: 742).
- 9.
See (Han shu, 19: 743 (comm.)). Note that the standards adduced in Yan Shigu’s commentary are probably quite late, differing from those of the Qin and early Western Han.
- 10.
The Qin dynasty jin was equal to approximately 253 grams; see Qiu Guangming et al. (2001: 190).
- 11.
Mozi jian gu, 15.626, specifies that the annual salary of a dou-eater came out to 36 dan.
- 12.
漢制, 三公號稱萬石, 其俸月各三百五十斛穀 (Han shu, 19A: 721 comm.).
- 13.
The ‘Sikong’ 司空 (Controller of Works) statutes of the Shuihudi Eighteen Qin Statutes, for example, stipulate that ‘It is permitted that office chiefs as well as officials use government carriages and oxen to draw their monthly rations as well as rations for government oxen and carriage horses’ 官長及吏以公車牛稟其月食及公牛乘馬之稟,可殹(也) (slip 128; tr. modified from Hulsewé (1985: 75)).
- 14.
臣朔長九尺餘, 亦奉一囊粟,錢二百四十 (Han shu, 65: 2843).
- 15.
凡諸受奉, 皆半錢半穀 (Hou Han shu, zhi 28: 3633).
- 16.
(Juyan xin jian: 205).
- 17.
(Juyan Han jian jia-yi bian, Vol. B: 107).
- 18.
(Shuihudi Qin mu zhujian: 31), tr. modified from Hulsewé (1985: 44).
- 19.
(Shuihudi Qin mu zhujian ‘Falü dawen shiwen zhushi 法律答問釋文注釋’: 129), tr. modified from Hulsewé (1985: 163).
- 20.
(Shuihudi Qin mu zhujian: 39–40), tr. modified from Hulsewé (1985: 50).
- 21.
See Xu Daosheng and Li Wei (2010).
- 22.
(Zhangjiashan Han mu zhujian [ersiqi hao mu] 2006: 52): 大夫五頃, 不更四頃, 簪裊三頃, 上造二頃, 公士一頃半, 公卒、士伍、庶人各一頃……大夫五宅, 不更四宅, 簪裊三宅, 上造二宅, 公士一宅半宅, 公卒、士伍、庶人各一宅。5 qing (measurement unit for the size of fields) for grandees of the fifth order, 4 qing for grandees of the fourth order, 3 qing for grandees of the third order, 2 qing for grandees of the second order, 1 qing and a half for grandees of the first order, and 1 qing each for government conscripts, rank-and-file servicemen, and subofficial functionaries... 5 zhai (measurement unit for the size of residences) for grandees of the fifth order, 4 zhai for grandees of the fourth order, 3 zhai for grandees of the third order, 2 zhai for grandees of the second order, 1 zhai and a half zhai for grandees of the first order, and 1 zhai each for government conscripts, rank-and-file servicemen, and subofficial functionaries.
- 23.
(Jiu zhang suan shu, 3: 24), tr. modified from Chemla and Guo (2004: 285).
- 24.
(Shuihudi Qin mu zhujian: 29–30), transcription modified according to Peng Hao (2006), cf. Hulsewé (1985: 42). Note that the Qin dan equals 120 jin. Note also that this statute converts (harvested) broomcorn millet and rice measured by weight into unhulled millet and rice, for which dan and dou are units of capacity.
- 25.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 144), tr. modified from Cullen (2004: 66–67).
- 26.
麻、麥、菽、荅……(而當粟十……麥三而當稻粟四, 禾粟五為稻粟四 (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 147), tr. modified from Cullen (2004: 73).
- 27.
(Shuihudi Qin mu zhujian: 60), tr. modified from Hulsewé (1985: 84–85). Note that the term ‘strategist’ (mou ren 謀人) in the original is an alternative appellation for zanniao 簪裊, a grandee of the third order in the Qin aristocracy.
- 28.
According to the ‘Statutes on Granaries’ (Shuihudi Qin mu zhujian: 29–30), tr. modified from Hulsewé (1985: 42):【禾黍一】石【為粟十】六斗大半斗, 舂之為
(糲)米一石;
(糲)米一石為鑿(糳)米九斗;【鑿(糳)米】九【斗】為毀(毇)米八斗。稻禾一石為粟廿斗, 舂為米十斗; 十斗粲〈毀(毇)〉, 毀〈粲〉米六斗大半斗。麥十斗, 為
三斗。【1】 dan 【harvested broomcorn millet (he shu)】【makes 1】6 dou and 2/3 dou 【unhulled grain (su)】; pounded, it makes 1 dan hulled grain (li mi); 1 dan hulled grain (li mi) makes 9 dou refined grain (zuo); 9 [dou refined grain] makes 8 dou polished grain (hui mi). 1 dan harvested rice (dao he) makes 20 dou unhulled grain (su); pounded, [it] makes 10 dou hulled rice (mi); 10 dou [hulled rice (mi)], when polished, [make] 6 dou and 2/3 dou polished rice (hui mi). 10 dou of barley (mai) make 3 dou barley flour (zhi). — GRANARIES (slips 41 and 43).
- 29.
Based on the meaning of the problem and the calculations of this section of the Writings on Mathematical Procedures, the mi 米 (‘hulled, comestible grain’) in ‘Refined and Polished Grain’ refers to hulled millet (li mi); see Peng Hao (2001: 84–85).
- 30.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 263), tr. modified from Cullen (2004: 74).
- 31.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 147), tr. modified from Cullen (2004: 73).
- 32.
(Shuihudi Qin mu zhujian: 31), tr. modified from Hulsewé (1985: 30).
- 33.
(Zhangjiashan Han mu zhujian [ersiqi hao mu] 2006: 66)
- 34.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 139), tr. modified from Cullen (2004: 54).
- 35.
芻新(薪)積廿八尺一石。稾卅一尺一石。茅卅六尺一石. See Xiao Can (2010a: 60).
- 36.
(Shuihudi Qin mu zhujian: 60), tr. modified from Hulsewé (1985: 83–85).
- 37.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 40).
- 38.
建平五年十二月官吏卒廩名籍 , see Xie Guihua (1994).
- 39.
Note that the capacity of the Qin sheng was 200 ml, see Qiu Guangming et al. (2001: 185).
- 40.
See (Jiu zhang suan shu, 6: 62), cf. Chemla and Guo (2004: 509).
- 41.
Writings on Mathematical Procedures, slips 76–77, in (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 142), cf. Cullen (2004: 62–63).
- 42.
- 43.
(Shuihudi Qin mu zhujian: 69–70), tr. modified from Hulsewé (1985: 93–94).
- 44.
爰積十六寸五分寸壹為升 (Zhongguo gudai du-liang-heng tuji: 44).
- 45.
See Qiu Guangming et al. (2001: 167–169).
- 46.
Zhangjiashan Han mu zhujian [ersiqi hao mu]: 138), tr. modified from Cullen (2004: 53).
- 47.
See Statutes and Ordinances of the Second Year, slips 253–254, in (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 43)
- 48.
See (Jiu zhang suan shu, 3: 25), cf. (Chemla and Guo 2004: 285–287).
- 49.
Huang Jinyan (2007) argues that the Shuihudi manuscripts show that the Qin dynasty levied taxes by ‘household’ according to the standard that a single household was to possess ‘one qing’ of fields. I am afraid, however, that this position is based on a misreading of the line ‘households, horses, and oxen in excess of one is a serious mistake’ 人戶、馬牛一以上為大誤 (‘Statutes on Checking’, slip 60). In the transcription of slip 60, however, the original editors explain that this means instead that ‘miscounting household members, horses, or oxen by more than one is a serious mistake’ (Shuihudi Qin mu zhujian: 76).
- 50.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 51–52). In the Qin and early-Western Han, there were 240 square bu to the mu, and 100 mu to the qing.
- 51.
頃入芻三石、稾二石 (Eighteen Qin Statutes, slip 9), in (Shuihudi Qin mu zhujian: 21), tr. modified from Hulsewé (1985: 23).
- 52.
See Statutes and Ordinances of the Second Year, slip 255, in (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 43).
- 53.
卿以上所自田戶田, 不租, 不出頃芻槀 (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 52).
- 54.
See slips 268 and 240, respectively, in (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 46, 41)
- 55.
芻一石當十五錢, 稾一石當五錢 (Statutes and Ordinances of the Second Year, slip 241), in (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 41).
- 56.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 136–137).
- 57.
See (Jiu zhang suan shu, 6: 65), cf. (Chemla and Guo 2004: 523).
- 58.
See slips 492 and 493 of the Statutes and Ordinances of the Second Year ‘Decrees on Fording Passes’ in (Er nian lü ling yu Zou yan shu: 307–309).
- 59.
(Shuihudi Qin mu zhujian: 42), tr. modified from Hulsewé (1985: 56).
- 60.
See Chen Songchang (2010: 18–20).
- 61.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 67).
- 62.
Er nian lü ling yu Zou yan shu: 256).
- 63.
See Qiu Xigui (1974).
- 64.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 57–58).
- 65.
See Qiu Xigui (1974).
- 66.
See Zang Zhifei (1987).
- 67.
(Jiu zhang suan shu, 3: 26), tr. modified from Chemla and Guo (2004: 289–291).
- 68.
- 69.
(Han shu, 28B: 1639–1640).
- 70.
提舉四封之內 (Han shu 65: 2847–2848).
- 71.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 157), tr. modified from Cullen (2004: 110).
- 72.
Xiao Can and Zhu Hanmin (2009: 11–14).
- 73.
See Xie Guihua (1997).
- 74.
See Qiu Xigui (1974).
- 75.
- 76.
Stipulations concerning early-Western Han field and residence grants are found in slips 310–316 of the Statutes and Ordinances of the Second Year, in (Zhangjiashan Han mu zhujian [ersiqi hao mu]: 52), see above, footnote 22. For stipulations concerning the archiving of field registration documents, see slips 331–334, in ibid.: 54.
- 77.
- 78.
租枲述(術)曰 : 置輿田數, 大枲也, 五之…. See Xiao Can (2010a: 25–26).
- 79.
(Yunmeng Longgang Qin jian: 24).
- 80.
Xu Daosheng and Li Wei (2010).
- 81.
Xiao Can (2010b).
- 82.
In the Qin and early-Western Han, there were 6 chi to a bu and 240 square bu to the mu. With the chi corresponding to 23.1 cm by today’s metrics, one mu corresponds to roughly 461 m2 (0.231 × 6 = 1.386 m ; 1.386 × 1.386 × 240 ≈ 461.04 m2).
- 83.
田一畝租之十步一斗, 凡租二石四斗。
- 84.
程田以為臧(贓)與同法 (Yunmeng Longgang Qin jian: 38, slip 190). Note that Yang Zhenhong (2008: 336) believes that cheng tian refers to the calculation of the amount of field tax due on a particular parcel of land.
- 85.
訾粟而稅 (Shangjun shu zhushi: 20), cf. (Duyvendak 1928: 176). Note that Gao Heng’s 高亨 commentary glosses zi 訾 as ‘measure’, i.e. calculate.
- 86.
On reading the xi 希 here as xi 稀 (‘thin’), see (Yunmeng Longgang Qin jian: 37).
- 87.
See (Yunmeng Longgang Qin jian: 38–39, slips 215, 226 and 240–241).
- 88.
Liu Xinfang and Liang Zhu believe that ‘three norms’ and the ‘two norms’ and ‘one norm’, etc. below should be interpreted as some quantity of field tax, see (Yunmeng Longgang Qin jian: 37).
- 89.
(Zhangjiashan Han mu zhujian [ersiqi hao mu]: 258), tr. modified from Cullen (2004: 60).
- 90.
(Yinqueshan Han mu zhujian, Vol. 1: 30).
- 91.
Note that the character dui 兌 (‘exchange’) has been emended to shui 稅 (‘tax’) according to Xiao Can (2010a: 31–32).
- 92.
(Han shu, 24A: 1125).
- 93.
Tr. modified from Hulsewé (1985: 23).
- 94.
See Li Hengquan and Zhu Degui (2003)
- 95.
See Xiao Can (2010b).
- 96.
(Juyan Han jian shiwen hejiao: 21).
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Peng 彭浩, H. (2020). Official Salaries and State Taxes as Seen in Qin-Han Manuscripts, with a Focus on Mathematical Texts. In: Michel, C., Chemla, K. (eds) Mathematics, Administrative and Economic Activities in Ancient Worlds. Why the Sciences of the Ancient World Matter, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48389-0_4
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