Zhang Cang

Biography

Family Background and Early Life

Zhang Cang came from an ordinary family in Yangwu County. His father was said to be less than five chi tall, while Zhang Cang himself was unusually tall, more than eight chi, with very fair skin likened to a gourd seed. According to the "Biography of Grand Councilor Zhang" in the Records of the Grand Historian, he loved books, musical pitch, and calendrical studies from childhood and read broadly. As a young man he studied the Zuo Zhuan under the Warring States Confucian master Xunzi and was a fellow student of Li Si and Han Fei. Xunzi's teaching drew on Confucian, Legalist, and Daoist thought, and Zhang Cang was deeply influenced by it, becoming familiar with the Confucian classics as well as technical traditions of yin-yang and calculation.

Service under Qin and Flight Home

Under Qin, Zhang Cang served as a censor responsible for palace documents and archives. Because he attended duty below a pillar in the palace, he was also called the "Historian Below the Pillar." The office gave him access to large collections of state books and documents and laid a foundation for his later expertise in calendrics and mathematics. He later committed an offense under Qin and fled back to Yangwu. In 207 BCE, the third year of Qin Ershi, Liu Bang passed through Yangwu while capturing territory, and Zhang Cang joined him as a retainer in the attack on Nanyang. During the campaign Zhang Cang committed another offense and was sentenced to be executed. After he stripped and lay upon the execution block, the Marquis of Anguo, Wang Ling, saw his great height and pale complexion, regarded him as an impressive man, and asked Liu Bang to spare him. Zhang Cang was pardoned and thereafter remained deeply grateful to Wang Ling, treating him for the rest of his life with the respect due a father.

Helping Liu Bang Establish the Realm

After receiving his pardon, Zhang Cang followed Liu Bang west through Wuguan to Xianyang. After Liu Bang was made King of Han, he entered Hanzhong and soon returned to pacify the Three Qin. When Chen Yu expelled Zhang Er, King of Changshan, and Zhang Er joined Han, Liu Bang appointed Zhang Cang Administrator of Changshan Commandery. Zhang Cang then followed Han Xin in the attack on Zhao, in which Chen Yu was captured. After Zhao was pacified, Zhang Cang became Chancellor of the Kingdom of Dai and was responsible for guarding against enemies on the frontier. He was later transferred to the Kingdom of Zhao, where he assisted King Zhang Er and, after Zhang Er's death, King Zhang Ao; he then returned to serve as Chancellor of Dai. In 201 BCE, the sixth year of Emperor Gaozu, Zang Tu, King of Yan, rebelled. Zhang Cang followed Liu Bang as Chancellor of Dai in suppressing the rebellion and was rewarded with the title Marquis of Beiping and a fief of 1,200 households.

Fiscal Chancellor and Chief of Accounts

After receiving his marquisate, Zhang Cang was promoted to Fiscal Chancellor, an office responsible for state finances. One month later, while retaining his noble rank, he became Chief of Accounts, serving in that position for four years. Xiao He was then Grand Chancellor. Because Zhang Cang had served as the Historian Below the Pillar since the Qin period, knew the empire's books and registers, and was skilled in calculation, musical pitch, and calendrics, Xiao He assigned him to work in the chancellor's office, where he managed the accounting records submitted by the commanderies and kingdoms. During this period, Zhang Cang devoted himself to studying and correcting musical and calendrical standards, contributing to institutional construction in the early Han.

Chancellor of Huainan and Censor-in-chief

After Qing Bu's rebellion failed and he fled, Emperor Gaozu made his son Liu Chang King of Huainan and appointed Zhang Cang Chancellor of the Kingdom of Huainan to assist him. Fourteen years later, Zhang Cang was transferred to the office of Censor-in-chief. During Empress Lü's period of rule, he continued to hold that post at court. After Empress Lü died, Zhang Cang joined the Marquis of Jiang, Zhou Bo, and others in supporting Liu Heng, King of Dai, as Emperor Wen of Han, making him one of the officials who helped secure the succession.

Fifteen Years as Grand Councilor

In 176 BCE, the fourth year of Emperor Wen's early reign period, Grand Councilor Guan Ying died and Zhang Cang succeeded him. More than twenty years had passed since the founding of Han, and most senior officials had military backgrounds. Zhang Cang, however, had already devoted himself to the study and correction of musical pitch and calendrical systems since his service in fiscal administration. He examined the succession of the Five Phases—metal, wood, water, fire, and earth—and held that Han was in a phase of flourishing Water virtue, so the dynasty continued to honor black. He used pitch pipes to tune music to the five notes and eight classes of instruments and on this basis established standards for legal regulations and the measurements of manufactured objects, creating norms for craftsmen throughout the realm. During his tenure as Grand Councilor, he completed this work, and Han scholars of music and calendrics later traced their traditions to Zhang Cang.

Final Years and Death

After Zhang Cang had served as Grand Councilor for more than ten years, Gongsun Chen of Lu submitted a memorial claiming that Han belonged to the Earth phase and that a yellow dragon would appear. Zhang Cang rejected the claim and set the proposal aside. A yellow dragon was later reported at Chengji County in Tianshui Commandery. Emperor Wen summoned Gongsun Chen as an erudite and had him draft calendrical institutions corresponding to Earth virtue and reset the first year. Zhang Cang was criticized as a result and pleaded illness, no longer attending court. In addition, Zhang Cang had recommended a man for office as a palace official, but that man abused his authority for major personal gain. Emperor Wen reproached Zhang Cang, who then reported illness and retired. He had served as Grand Councilor for fifteen years. Zhang Cang died in 152 BCE, the fifth year of Emperor Jing's early reign period, at more than one hundred years of age and received the posthumous title Wen.

Major Activities

Scholarly Contributions

Zhang Cang was broadly learned and highly skilled in musical pitch, calendrics, and mathematics. He developed and established a relatively complete theory of length, capacity, and weight and applied mathematical knowledge directly to state administration and everyday economic life. In calendrics, he advocated continued use of the Zhuanxu Calendar, which treated the tenth month as the beginning of the year; this calendar remained in use in the early Han. Zhang Cang also revised and supplemented The Nine Chapters on the Mathematical Art. The work contains 246 mathematical problems, and the Chinese source states that some of its algorithms preceded comparable European methods by 1,500 years and had an important influence on the development of mathematics. Zhang Cang also authored sixteen pian under the title 《Zhang Cang》, which the "Treatise on Arts and Letters" of the Book of Han listed among works of the yin-yang school.

Institutional Construction

While serving as Fiscal Chancellor and Grand Councilor, Zhang Cang played a leading role in establishing systems of musical pitch, calendar, weights, and measures in the early Western Han. He tuned music with pitch pipes to conform to the five notes and eight classes of instruments, used these principles in formulating regulations, and established measurement standards for manufactured objects as norms for craftsmen throughout the realm. In his theory of dynastic succession through the Five Phases, he held that Han belonged to Water virtue, honored the color black, and retained the Qin calendar beginning the year in the tenth month. These systems contributed to stability and development in the early Han, and later Han scholars of pitch standards and calendrics traced their work to Zhang Cang.

Political Activity

Zhang Cang served under both Qin and Western Han and successively held posts including Administrator of Changshan Commandery, Chancellor of Dai, Chancellor of Zhao, Fiscal Chancellor, Chief of Accounts, Chancellor of Huainan, Censor-in-chief, and Grand Councilor. He participated in suppressing the rebellion of Zang Tu, King of Yan, and in the enthronement of Emperor Wen of Han, playing an important role in the early Han political order. His fifteen years as Grand Councilor ended after controversies over the Five Phases and an improper recommendation, but his political career spanned the consolidation of the early Han state.

Travels and Places of Activity

Zhang Cang's life took him across much of the Central Plains. He was born at Yangwu, studied under Xunzi, served Qin at Xianyang, campaigned with Liu Bang through Nanyang, Wuguan, and Xianyang, held office in Changshan, Dai, and Zhao, later served at Chang'an, and eventually retired. His movements reflected the changing political and military landscape from the end of Qin to the early Han.

Relations with Contemporaries

Zhang Cang's relationship with Wang Ling was especially close. Wang Ling saved his life when he faced execution, and Zhang Cang remained grateful for the rest of his life, treating him with the respect due a father. After Wang Ling died and Zhang Cang had become Grand Councilor, on each five-day rest period he would first visit Wang Ling's widow and present fine food before returning home. Zhang Cang joined Zhou Bo and others in supporting Emperor Wen and served at court alongside Xiao He and Guan Ying. He taught the Zuo Zhuan to Jia Yi of Luoyang and was an important transmitter of Old Text classical learning in the Western Han.

His early Han career can be set out by year: in 181 BCE (seventh year of the Empress Dowager Gao's reign), at about seventy-six, he was promoted to censor-in-chief under the empress dowager's rule; in 180 BCE (eighth year), at about seventy-seven, he joined Zhou Bo and others in installing Liu Heng, Prince of Dai, as Emperor Wen; in 176 BCE (fourth year of the Former Yuan period), at about eighty-one, he became chancellor, holding the office fifteen years; in 161 BCE (third year of the Later Yuan period), at about ninety-six, he was reproved for a misjudgement in the dispute over the succession of the five powers and for recommending an unworthy official, and resigned; and in 152 BCE (fifth year of the Former Yuan period of Emperor Jing) he died at over a hundred with the posthumous name Wen. From a Qin censor to a Han chancellor, and responsible for matters of law, calendar and measurement, he was among those longest involved in the reconstruction of institutions in the early Han.

The calendrical and metrological work he directed forms part of the ordering of institutions in the early Han.

His fifteen years as chancellor are among the longer terms of the early Han.

He was a censor under the Qin and censor-in-chief and chancellor under the Han.

He died in the fifth year of the Former Yuan period of Emperor Jing with the posthumous name Wen.

The years of his censorate and chancellorship are recorded in the Book of Han.

His part in installing Emperor Wen is recorded in the annals of the Empress Dowager Gao and of Emperor Wen in the Book of Han.

The ordering of law, calendar and measures he directed appears in the treatise on pitch pipes and the calendar in the Book of Han.

On the calendar of the early Han he held that the succession of the five powers should determine the beginning of the year.

As chancellor he served alongside Zhou Bo and Guan Ying, and was later dismissed.

His chancellorship of fifteen years under Emperor Wen is unusual in the early Han.

His resignation under Emperor Wen arose from the dispute over the succession of the five powers and from a bad recommendation.

His service in the early Han spanned the reigns of Gaozu, Hui, the Empress Dowager Gao, Wen and Jing.

His work under Emperor Wen concerned chiefly law, the calendar, measures and the chancellorship.

His death and posthumous name are recorded in his biography in the Book of Han.

His service with Zhou Bo and Chen Ping under Emperor Wen is recorded in the Records of the Grand Historian.

His writings and memorials in the early Han are scattered through Han documents.

His business as chancellor consisted chiefly of continuing earlier institutions and ordering law and the calendar.

He stood alongside Zhang Liang and Chen Ping in the early Han as a veteran of three reigns.

Under Emperor Wen he directed revisions of the calendar and the theory of pitch pipes.

His offices of censor-in-chief and chancellor in the early Han both belonged to the three excellencies.

The conviction of a man he had recommended under Emperor Wen was one direct cause of his resignation.

His offices in the early Han and the year of his death form the main content of his biography.

His business under Emperor Wen concerned chiefly law, calendar and measures, together with court ceremonial.

The institutional work he took part in provided the administrative basis for the reigns of Wen and Jing.

No burial place is recorded for him.

His calendrical views in the early Han relate to the doctrine of the Han's earth virtue.

One part of his business under Emperor Wen was fixing the system of weights and measures.

Zhang Cang was a native of Yangwu. As a Qin censor he kept the records of the pillar office, then fled home after an offense. When Liu Bang passed through Yangwu, Zhang followed him as a retainer and attacked Nanyang; condemned to execution, he bared his back at the block, and because his tall, plump, gourd-white body struck Wang Ling as that of a fine man, Wang spoke to the Duke of Pei and he was spared. He entered Hanzhong with the army, served as governor of Changshan, and for merit against Zang Tu was made Marquis of Beiping. Early in the Han he became count-master, seated in the chancellor's office as a marquis to oversee the annual accounts of commanderies and kingdoms; he was well versed in the registers of the realm and skilled in calendrical and mathematical methods. Later chancellor of Huainan and then censor-in-chief, he joined Zhou Bo and Chen Ping in raising the Prince of Dai as Emperor Wen. In 176 BCE he became chancellor for more than ten years, revising the calendar, adopting black as the dynastic color, clarifying pitch pipes and the calendar, and having the artisans expand the Nine Chapters on the Mathematical Art. With Jia Yi and Gongsun Chen he debated correcting the first month and changing court colors; Emperor Wen did not adopt all of it, but the move to correct the calendar began there. In old age, toothless, he lived on milk and kept wet nurses. He later resigned on grounds of illness and died in 152 BCE with the posthumous name Wen. Histories say he loved books and mastered all of them, most deeply pitch pipes and calendar.

Personal Relations

• Father: name unknown; said to have been less than five chi tall.
• Son: Zhang Feng, Marquis Kang of Beiping.
• Grandson: Zhang Lei (also written Zhang Yu), who lost the marquisate after behaving disrespectfully when taking his place during mourning rites for a feudal lord.
• Xunzi: teacher; Zhang Cang studied the Zuo Zhuan under him in his youth.
• Wang Ling: rescuer and benefactor; Zhang Cang treated him throughout life with the respect due a father.
• Jia Yi: student; Zhang Cang taught him the Zuo Zhuan.
• Liu Bang: Zhang Cang followed him in the conquest of the empire and was created Marquis of Beiping.
• Liu Heng (Emperor Wen of Han): Zhang Cang helped secure his accession and served as Grand Councilor for fifteen years.
• Xiao He: Zhang Cang worked in the chancellor's office under his authority while managing accounts.
• Zhou Bo: joined Zhang Cang in supporting Emperor Wen.
• Guan Ying: Zhang Cang's predecessor as Grand Councilor.
• Gongsun Chen: opponent in the Five Phases succession controversy; Zhang Cang rejected his theory, which later gained imperial acceptance.

Historical Assessment

Han / Contemporary Period

• Sima Qian's "Biography of Grand Councilor Zhang" in the Records of the Grand Historian recognized Zhang Cang as a distinguished Han Grand Councilor learned in letters, musical pitch, and calendrics, while questioning his rejection of proposals by Jia Yi and Gongsun Chen concerning the calendar and ceremonial colors and his adherence to the Qin Zhuanxu Calendar.
• In the "Autobiographical Postface of the Grand Historian," Sima Qian praised Zhang Cang's role after the founding of Han: as Chief of Accounts he regularized measurements and put musical and calendrical systems in order.
• The Book of Han grouped Zhang Cang with Zhou Chang, Zhao Yao, Ren Ao, and Shentu Jia, emphasizing Zhang Cang's learning in letters, pitch standards, and calendrics as his distinctive strength.

Wei, Jin, and Northern and Southern Dynasties

• Sima Zhen's Suoyin commentary to the Records of the Grand Historian summarized Zhang Cang's achievements as chief accountant, regulator of empire-wide standards, senior censor, and Grand Councilor, and noted the continued use of the Qin calendar after Gongsun Chen's proposal was initially rejected.
• Pei Yin's Collected Explanations of the Records of the Grand Historian quoted a number of earlier interpretations and discussed Zhang Cang's calendrical views, reflecting continuing later interest in his scholarly thought.

Tang and Song Periods

• Liu Zhiji's Shitong discussed Zhang Cang's teaching of the Zuo Zhuan to Jia Yi and affirmed his place in the transmission of classical learning.
• Song scholars often evaluated Zhang Cang from an intellectual perspective, emphasizing the long-term influence of his work on musical pitch, calendrics, and mathematics.

Modern Scholarship

• Modern historians of mathematics, including Qian Baocong, have regarded Zhang Cang's revision and supplementation of The Nine Chapters on the Mathematical Art as an important event in the history of Chinese mathematics and as part of the process through which the work became a foundational mathematical classic.
• Modern scholarship generally regards Zhang Cang as a central figure in institutional construction in the early Han, particularly because systems of measurement and calendar associated with his work provided foundations for state administration.
• Scholarly assessments of Zhang Cang's position in the Five Phases controversy remain diverse: some view him as conservative and inflexible, while others see him as adhering to a position grounded in practical observation.