Lingxian 靈憲

Lingxian 靈憲 "Numinous principles" was a book on astronomy from the Later Han period 後漢 (25-220 CE) written by Zhang Heng 張衡 (78-139 CE), courtesy name Pingzi 平子, from E 鄂 in the commandery of Nanyang 南陽 (in today's Henan province). Apart from his astronomical achievements, Zhang is known for his rhapsodies Liangjing fu 兩京賦 (Xijing fu 西京賦 and Dongjing fu 東京賦). For many years, he was Grand Astrologer (taishi ling 太史令) at the imperial court. He also wrote a book on a celestial sphere, Huntian yi zhu 渾天儀注 that was connected to a water clock. Other inventions of Zhang Heng are a cart with an embedded compass (zhinan che 指南車), an odometric cart (jiligu che 記里鼓車), an automatic flying bird (zifei mudiao 自飛木雕), a seismoscope (didongyi 地動儀), and a weather vane (houfengyi 候風儀). A book on mathematics, Suanwanglun 算罔論, is lost.

The Lingxian was lost early and only survives in fragments assembled in Wang Mo's 王謨 (c. 1731-1817) Chongding Han-Tang dili shuchao 重訂漢唐地理書鈔, Hong Yixuan's 洪頤煊 Wenjingtang congshu 問經堂叢書 (part Jingdian jilin 經典集林) and Ma Guohan's 馬國翰 (1794-1857) Yuhan Shanfang jiyi shu 玉函山房輯佚書.

The Lingxian is an important theoretical work on astronomy. It provides a comprehensive explanation of the origin and structure of the cosmos, describes the nature and movement of the Sun, Moon, and stars, and offers scientific explanations for moonlight and lunar eclipses. Moreover, Zhang Heng introduced an innovative theory linking the speeds of the Sun, Moon, and five visible planets to their distances from Earth.

Zhang Heng describes the origin and evolution of the universe in three stages: The first stage, mingzi 溟滓 "Dark Sediments", was boundless, bottomless, tranquil, obscure, and void, without any form or shape. However, within it existed a particular "spirit" (ling 靈), corresponding to the Daoist concept of Dao 道. After an unknown span of time, the universe entered the second stage, known as panghong 龐鴻 "Huge Vastness". At this point, vital energy or ether (qi 氣) arose, forming an undifferentiated, chaotic unity. This stage served as the direct precondition for forming a tangible universe and is called the Stem of the Dao (daogan 道干). After another immeasurable period, the universe transitioned into the third stage, taixuan 太玄 "Grand Mystery". At this stage, the primordial ether differentiated into clear and turbid, light and heavy components—the lighter, purer ether rises to form the heavens above or "outside" (wai cheng wei tian 外成爲天), while the denser, heavier matter settled to become the Earth (nei cheng wei di 內成爲地). Thereafter, Heaven and Earth moved and operated, and the two vital forces (Yin and Yang) refined and merged, thus giving birth to all things—this is the realisation of the Dao. This theory of the origin and evolution of the universe inherits many philosophical elements from the pre-Qin period while also incorporating new developments from the Han period. However, it possesses its unique characteristics. This becomes evident when comparing it with the theory of celestial formation and evolution in the astronomy chapter (3 Tianwen xun 天文訓) of the Huainanzi 淮南子.

The Lingxian gives the diameters of the celestial sphere and the Earth as 232,300 li (one li being about 0.5 km). The distance from the Earth's surface to the heavens is precisely half of this value (116,150 li), and the depth of the Earth is also the same. The angular diameter of the Sun and Moon is stated to be 1/736 of the whole celestial circumference, which corresponds to 29'24". This celestial model retains some aspects and influences of the Canopy-Heaven Theory (gaitian shuo 蓋天說), according to which the heavens cover the Earth like an umbrella. In this model, the Earth remains flat rather than spherical and is considered to fill the lower half of the celestial sphere. The idea from the Zhoubi suanjing 周髀算經 that "a north-south displacement of 1,000 li results in a difference of one inch in shadow length (of a gnomon)", is also directly adopted.

However, the book introduces a significant breakthrough through his theorem that the limits of space (yu 宇) were boundless and the ends of time (zhou 宙) infinite. This suggests that the cosmos was infinite and without boundaries. This idea originates from the book Mozi 墨子, part Jing 經).

On astronomical observations, the Lingxian explains that among the central and outer regions of the sky, 124 stars remained constantly visible (chang ming zhe 常明者), 320 "could be named" (ke ming zhe 可名者), and their total number was 2,500. The number of "faint stars" (weixing 微星) was approximately 11,520. Since this was recorded without the aid of telescopes, it is clear that these numbers were not obtained purely through direct observation.

According to historical accounts, Zhang Heng is said to have created China's first complete star chart. This suggests that his observations of fixed stars (hengxing 恒星) had already reached a remarkably high level of precision. He adopted the correct views of Jing Fang 京房 (77-37 BCE) and Wang Chong 王充 (27-97 CE), affirming that moonlight is the reflected light of the Sun and that lunar eclipses occur when the Earth blocks sunlight from reaching the Moon. His insights into the varying speeds of celestial bodies were groundbreaking. He proposed: "Near the heavens, motion appears slow; far from the heavens, motion appears fast." This means that the variation in distance explains the changing speeds of the Seven Luminaries (qiyao 七曜: the Sun, Moon, and the five visible planets). He reasoned that objects farther from the Earth appear to move slower, while those closer appear to move faster. The Moon, Mercury, and Venus move quicker and are classified as "Yin stars", but the Sun, Mars, Jupiter, and Saturn move slower and are classified as "Yang stars". Because the distances of the Seven Luminaries from the Earth vary, their speeds also change, leading to apparent variations such as prograde motion (shun 順), stationing (liu 留), and retrograde motion (ni 逆). This insight contains a degree of scientific validity and bears similarities to the Ptolemaic system.

Additionally, the Lingxian already includes terminology such as the equator (chidao 赤道), the ecliptic (huangdao 黄道), the South Pole, and the North Pole.