Zhang Heng (Chinese: 张衡; AD 78–139), also known as Pingzi, was a Chinese scientist and statesman who lived during the Eastern Han dynasty. He studied in the cities of Luoyang and Chang’an, which were important capitals of China at the time. He became well-known for his work as an astronomer, mathematician, seismologist, engineer, inventor, geographer, cartographer, ethnographer, artist, poet, philosopher, politician, and writer.

Zhang Heng started his career as a minor government worker in Nanyang. Later, he held important positions such as Chief Astronomer, Prefect of the Majors for Official Carriages, and Palace Attendant at the imperial court. His strong beliefs about history and calendars made him a controversial figure, which limited his ability to reach the highest rank of Grand Historian. His disagreements with powerful palace officials during the rule of Emperor Shun (125–144) led him to leave the central court and work as an administrator in Hejian Kingdom, now part of Hebei province. After returning briefly to Nanyang, he was asked to return to the capital in 138. He died there in 139.

Zhang Heng used his knowledge of mechanics and gears in many of his inventions. He created the first water-powered armillary sphere to help with astronomical observations. He improved the inflow water clock by adding another tank. He also invented the first seismoscope, a device that could show the direction of an earthquake 500 kilometers (310 miles) away. He made better calculations for the number pi. He recorded the positions of about 2,500 stars in his star catalog. He also wrote about the Moon, explaining that it is round, reflects sunlight on one side, and that the other side is not visible. He described how solar and lunar eclipses happen. His poetry, including fu and shi, was admired during his time and studied by later writers. After his death, he was honored for his contributions to science and knowledge. Some modern scholars compare his work in astronomy to that of Ptolemy, a scientist from the Greco-Roman world who lived from AD 86 to 161.

Life

Zhang Heng was born in the town of Xi'e, located in the Nanyang Commandery, which is north of modern Nanyang City in Henan Province. He came from a respected family that was not wealthy. His grandfather, Zhang Kan, had been a governor of a region and helped restore the Han dynasty under Emperor Guangwu after the rule of the Xin dynasty ended. When Zhang was ten years old, his father died, and he was raised by his mother and grandmother.

As a young man, Zhang was a skilled writer. In 95, he left his home to study in the capitals of Chang'an and Luoyang. During his journey to Luoyang, he passed by a hot spring near Mount Li and wrote a poem called "Fu on the Hot Springs" about it. This hot spring later became known as the Huaqing Hot Springs, a place visited by the imperial concubine Yang Guifei during the Tang dynasty. After studying at Luoyang's Taixue, Zhang became well-versed in ancient texts and formed friendships with notable figures, such as the mathematician Cui Yuan, the official Ma Rong, and the philosopher Wang Fu. Government officials offered him positions, including one as an Imperial Secretary, but he politely declined.

At age 23, Zhang returned home with the title "Officer of Merit in Nanyang," working under Governor Bao De. He wrote official documents and helped select candidates for government roles. He also composed poems about the capital cities. When Governor Bao De was recalled to the capital in 111, Zhang continued his literary work in Xi'e. At 30, Zhang began studying astronomy and published works on astronomy and mathematics.

In 112, Zhang was summoned to the court of Emperor An, who had heard of his mathematical skills. He was escorted to Luoyang by carriage, a sign of his official status, and became a court gentleman working for the Imperial Secretariat. He later served as Chief Astronomer, working under Emperor An from 115 to 120 and under the next emperor from 126 to 132. As Chief Astronomer, Zhang recorded celestial events, prepared calendars, and oversaw literacy tests for government officials. He also managed official carriages and received memorials from the throne.

In 123, Zhang opposed a proposal to reform the Chinese calendar using teachings he considered unreliable. Though others shared his view, his suggestion to ban these teachings was rejected. Zhang also disagreed with how the role of the Gengshi Emperor in restoring the Han dynasty was portrayed. Because of these views, he was unable to assist a committee compiling the dynastic history "Dongguan Hanji." After the deaths of his historian allies, Liu Zhen and Liu Taotu, Zhang had no further opportunities for promotion.

In 126, Zhang was reappointed as Chief Astronomer after Emperor Shun of Han took the throne. His work earned him a salary of 600 bushels of grain, which was the lowest rank the emperor could directly assign. In 132, Zhang introduced a complex seismoscope to detect the direction of distant earthquakes. When his device indicated an earthquake in the northwest, his political enemies doubted it until a messenger confirmed the event occurred 400 to 500 kilometers northwest of Luoyang in Gansu Province.

A year later, officials discussed recent earthquakes, which ancient Chinese believed were signs of punishment for wrongdoing by rulers. In a memorial, Zhang criticized a new recruitment system that set a fixed age for candidates and shifted oversight to the Three Excellencies. Though his memorial was rejected, Zhang was later promoted to Palace Attendant, a prestigious role that allowed him to advise Emperor Shun and earned him a salary of 2,000 bushels.

As Palace Attendant, Zhang warned Emperor Shun about the threat posed by court eunuchs, citing past scandals. When eunuchs tried to slander him, Zhang responded with a poem called "Fu on Pondering the Mystery," which expressed his frustration. This work used imagery similar to the famous poem "Li Sao" by Qu Yuan, exploring whether virtuous people should remain in a corrupt world or leave it.

Literature and poetry

Zhang Heng worked for the central court and had access to many written materials in the Archives of the Eastern Pavilion. He read many important historical works and noted ten places where the Records of the Grand Historian by Sima Qian and the Book of Han by Ban Gu disagreed with other ancient texts. His observations were recorded in the 5th-century Book of Later Han by Fan Ye. Zhang’s writings showed deep knowledge of classic texts, Chinese philosophy, and history. He also wrote a commentary on the Taixuan ("Great Mystery") by Yang Xiong, a Daoist author.

Xiao Tong, a prince of the Liang dynasty, included some of Zhang’s works in his anthology Selections of Refined Literature. Zhang’s fu rhapsodies included Western Metropolis Rhapsody, Eastern Metropolis Rhapsody, Southern Capital Rhapsody, Rhapsody on Contemplating the Mystery, and Return to the Field. The last combined Daoist ideas with Confucianism and influenced later Chinese poetry. A set of four short poems called Lyric Poems on Four Sorrows is also included, with Zhang’s introduction. These poems are among the earliest examples of seven-character shi poetry.

While in Luoyang, Zhang wrote Western Metropolis Rhapsody and Eastern Metropolis Rhapsody, inspired by Ban Gu’s Rhapsody on the Two Capitals. Zhang’s work was similar to Ban’s but warned that the Eastern Han could fall into moral decay, unlike Ban’s praise for the Eastern Han. These works criticized the luxury of the upper class. Zhang’s Southern Capital Rhapsody honored his hometown, Nanyang, where the Han dynasty was restored by Guangwu.

In Four Sorrows, Zhang wrote about being unable to reach a beloved woman because of mountains, snow, and rivers. Scholars Rafe de Crespigny and David R. Knechtges suggest this poem hinted at Zhang’s inability to communicate with the emperor due to rivals. This poem is one of the first in China with seven words per line. The poem reads:

*In Taishan stays my dear sweetheart,
But Liangfu keeps us long apart;
Looking east, I find tears start.
She gives me a sword to my delight;
A jade I give her as requite.
I’m at a loss as she is out of sight;
Why should I trouble myself all night?*

In Stabilizing the Passions, Zhang praised a virtuous woman, influencing later works by Cai Yong. The poem reads:

*Ah, the chaste beauty of this alluring woman!
She shines with flowery charms and blooming face.
She is unique among all her contemporaries.
She is without a peer among her comrades.*

Zhang’s long poems provided details about cities, geography, and daily life. His Sir Based-On-Nothing described Chang’an’s terrain, palaces, markets, and buildings. His Nanyang rhapsody mentioned gardens with spring garlic, summer bamboo shoots, autumn leeks, winter rape-turnips, perilla, evodia, and purple ginger. Zhang and Sima Xiangru listed animals in hunting parks, separated by their origins in northern or southern China. Zhang also described Western Han emperors enjoying boat rides, water plays, fishing, and archery on Kunming Lake. His focus on places, people, and customs showed early efforts at ethnographic study.

In Xijing fu, Zhang mentioned Buddhism, introduced via the Silk Road, and the legend of the Buddha’s birth with the vision of a white elephant. His Western Metropolis Rhapsody described court entertainments like juedi, a wrestling performance with music and bull-horn masks.

In Responding to Criticism, Zhang wrote in the shelun style, a genre of hypothetical dialogue. He criticized himself for not achieving high office but concluded that virtue, not power, defined a true gentleman. Scholars believe the character urging Zhang to advance his career represented corrupt officials or the Liang clan. Zhang rejected their influence, stating his pursuit of virtue over power.

Zhang also wrote about emperors seeking lovers outside the palace, criticizing the Eastern Han’s decadence and their failure to follow yin-yang beliefs. In a poem, he wrote:

*Those who won this territory were strong;
Those who depended on it endured.
When a stream is long, its water is not easily exhausted.
When roots are deep, they do not rot easily.
Therefore, as extravagance and ostentation were given free rein,
The odor became pungent and increasingly fulsome.*

Achievements in science and technology

For many years, the Chinese used the number 3 to estimate pi. Liu Xin, who lived around 23 CE, was the first known Chinese person to try a more accurate value of 3.154, but no records explain how he calculated this. Around 130 CE, Zhang Heng compared the size of the sky circle to the diameter of Earth, using the numbers 736 and 232, which gave pi a value of 3.1724. At that time, people believed the area of a square to the area of its inscribed circle and the volume of a cube to the volume of its inscribed sphere should be in a 4:3 ratio. Using the formula D:V = 16:9 or V = 9/16 D, Zhang noticed the diameter value was incorrect. He adjusted the formula by adding 1/16 D, making V = 5/8 D. This led to a ratio of 8:5 for the cube to the sphere, and a square to circle ratio of √8 : √5. From this, Zhang calculated pi as the square root of 10, approximately 3.162. In the 3rd century, Liu Hui improved accuracy with his π algorithm, achieving 3.14159. Later, Zu Chongzhi calculated pi as 355/113, or about 3.141592, the most precise value achieved by ancient Chinese mathematicians.

In his work "The Spiritual Constitution of the Universe" (Ling Xian), written in 120 CE, Zhang Heng described the universe as an egg-like shape with stars on its surface and Earth as the central yolk. This idea supported the geocentric model (Earth at the center) rather than the heliocentric model (Sun at the center). While earlier Chinese astronomers like Shi Shen and Gan De had created star catalogs, Zhang cataloged 2,500 stars, placing them in a "brightly shining" category (with an estimated total of 14,000 stars). He also identified 124 constellations. His catalog included more stars than those recorded by Greek astronomers Hipparchus (around 190–120 BCE) and Ptolemy (83–161 CE). Zhang explained solar and lunar eclipses using the "radiating influence" theory, which was later opposed by Wang Chong. In the Ling Xian, Zhang wrote:

— Zhang Heng (120 CE), Sublime Model (Joseph Needham, trans.)

Zhang also believed that events like comets, eclipses, and the movements of celestial bodies were signs from the heavens guiding human affairs. Other writers of his time discussed eclipses and the spherical shape of the Sun and Moon. Jing Fang (78–37 BCE) noted the spherical nature of the Sun and Moon in his writings about eclipses. This theory was later supported by Shen Kuo (1031–1095), who explained why the Sun and Moon are spherical. However, the idea that Earth is flat and square was later criticized by Yu Xi (fl. 307–345), who suggested Earth might be round like the heavens. This spherical Earth theory was fully accepted by Li Ye (1192–1279) but not widely adopted in China until European influence in the 17th century.

The outflow clepsydra, an ancient water clock, was used in China as early as the Shang dynasty (c. 1600–1050 BCE). By the Zhou dynasty (1122–256 BCE), the inflow clepsydra with a float and indicator rod became common. Zhang Heng, in 117 CE, solved the problem of decreasing water pressure in the inflow vessel by adding a compensating tank between the reservoir and the vessel. He also added two statues of a Chinese immortal and a heavenly guard on the clepsydra, which guided the indicator rod and pointed to graduations. This design may have inspired later clock jacks in mechanical clocks. Additional compensating tanks were added to later clepsydras following Zhang’s methods. In 610 CE, Sui dynasty engineers Geng Xun and Yuwen Kai created an unequal-armed balance to adjust the pressure head of the compensating tank for seasonal changes in water flow. Zhang Heng described a "jade dragon's neck," later understood as a siphon, and wrote about the floats and indicator rods of the inflow clepsydra.

Zhang Heng was the first known person to use hydraulic power (waterwheels and clepsydras) to rotate an armillary sphere, an instrument representing the celestial sphere. The Greek astronomer Eratosthenes (276–194 BCE) invented the first armillary sphere in 255 BCE. The Chinese version was fully developed by 52 BCE with Geng Shouchang’s addition of a fixed equatorial ring. In 84 CE, astronomers Fu An and Jia Kui added the ecliptic ring, and Zhang Heng added the horizon and meridian rings. His water-powered armillary sphere influenced later Chinese water clocks and led to the discovery of the escapement mechanism by the 8th century. Historian Joseph Needham (1900–1995) noted that Zhang did not start the Chinese tradition of hydraulic engineering, which began in the Zhou dynasty (c. 6th century BCE) with engineers like Sunshu Ao and Ximen Bao. Zhang’s contemporary, Du Shi (d. 38 CE), used waterwheels to power blast furnaces for iron production. Zhang described his water-powered armillary sphere in a 125 CE treatise, stating:

Zhang Heng’s water-powered armillary sphere had a lasting impact on Chinese astronomy and mechanical engineering. His model, with its complex gears, influenced later astronomers like Yi Xing (683–727), Zhang Sixun (10th century), Su Song (1020–1101), and others. Although the original armillary sphere was recovered in 418 CE after the

Legacy

Zhang Heng's mechanical inventions inspired later Chinese inventors, including Yi Xing, Zhang Sixun, Su Song, and Guo Shoujing. Su Song used Zhang Heng's water-powered armillary sphere as the inspiration for his 11th-century clock tower. The scholar-official Chen Hongmou (1696–1771) created a cosmic model with nine points in the sky matching nine areas on Earth, following the ideas in Zhang Heng's book Spiritual Constitution of the Universe. The seismologist John Milne, who helped create the modern seismograph in 1876 with Thomas Gray and James A. Ewing at the Imperial College of Engineering in Tokyo, praised Zhang Heng's contributions to seismology in 1886. The historian Joseph Needham highlighted Zhang Heng's role in pre-modern Chinese technology, noting that Zhang Heng was known for making three wheels move like one. Many scholars called Zhang Heng a polymath. However, some noted that Zhang Heng's writings did not include clear scientific theories. When comparing Zhang Heng to Ptolemy (83–161) of Roman Egypt, Jin Guantao, Fan Hongye, and Liu Qingfeng said:

Zhang Heng's poetry was widely read during his lifetime and after his death. The Eastern Wu official Xue Zong (d. 237) wrote commentary on Zhang Heng's poems Dongjing fu and Xijing fu. The influential poet Tao Qian admired Zhang Heng's poetry for its simple and clear language, which reflected calmness and honesty. Tao Qian noted that both Zhang Heng and Cai Yong avoided overly elaborate language and focused on simplicity. Their poems began with imaginative ideas but ended with quiet, balanced conclusions.

Zhang Heng received great honors during his life and after his death. The philosopher and poet Fu Xuan (217–278) of the Wei and Jin dynasties wrote that Zhang Heng was never placed in the Ministry of Works. He praised Zhang Heng and the 3rd-century engineer Ma Jun, stating that their talents were wasted because authorities ignored skilled people.

To honor Zhang Heng's achievements, his friend Cui Ziyu (Cui Yuan) wrote a memorial inscription on his burial stele, which is preserved in the Guwen yuan. Cui Ziyu wrote that Zhang Heng's math explained the mysteries of the universe and Earth, and his inventions were as remarkable as those of the Author of Change. The minor official Xiahou Zhan (243–291) of the Wei dynasty wrote an inscription for a commemorative stele at Zhang Heng's tomb. It read: "Since people began writing, no one has chosen words as skillfully as Zhang Heng. If the dead could rise, I would ask him to be my teacher."

In modern times, many things have been named after Zhang Heng, including the lunar crater Chang Heng, the asteroid 1802 Zhang Heng, and the mineral zhanghengite. In 2018, China launched a research satellite called the China Seismo-Electromagnetic Satellite (CSES), also named Zhangheng-1 (ZH-1).