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Xintianlun 昕天論 "Inclined-Heaven Theory" was a book on cosmology compiled during the Three-Empires period 三國 (220~280 CE) by Yao Xin 姚信, courtesy name Yuanzhi 元直 or Deyou 德佑, from Wukang 武康 (today's Deqing 德清, Zhejiang). He held the office of Chamberlain for Ceremonials (taichang qing 太常卿) and was an expert in astronomy and astrology, having written the commentary Zhouyi zhu 周易注 on the Yijing 易經 "Book of Changes".
Of his book, only fragments survive that are quoted in the treatise on astronomy (11-13 Tianwen zhi 天文志) in the history book Jinshu 晉書. A full collection of fragments can be found in Ma Guohan's 馬國翰 (1794-1857) series Yuhanshanfang jiyi shu 玉函山房輯佚書.
The book is listed with a length of 1 juan in the bibliographical chapter Jingji zhi 經籍志 in the Suishu 隋書, but it refers to a Liang-period 梁 (502-557) catalogue and says the Xintianlun was already lost at the time. It is, however, still listed in the catalogue of the Xintangshu 新舊唐, but with the remark "lost".
The name of the theory includes the word xin 昕, which actually means "dawn, morning", but the word xin is used as a loanword for the word xuan 軒, a designation of a type of carriage with boards that make it higher at the front than at the back (commentary of Kong Yingda 孔穎達, Yueling zhengyi 月令正義). This shape is a metaphor for the assumed shape of Heaven in Yao Xin's theory. The expression xuantian 軒天 "carriage-shaped heaven" is mentioned in the book Yisizhan 乙巳占.
| 人爲靈蟲，形最似天。今人頤前侈臨胸，而項不能覆背。近取諸身，故知天之體南低入地，北則偏高。 | Humans are sentient beings and have a form most similar to the heavens. Now, a person's chin can extend forward toward the chest, but the nape cannot bend backward to cover the back. By drawing an analogy from the human body, it can be inferred that the celestial sphere is lower in the south, dipping into the earth, while it is relatively higher in the north. |
| 又冬至極低，而天運近南，故日去人遠，而斗去人近，北天氣至，故冰寒也。夏至極起，而天運近北，故斗去人遠，日去人近，南天氣至，故蒸熱也。 | Furthermore, during the winter solstice, the sun reaches its lowest point, and the celestial motion is closer to the south. As a result, the sun is farther from humans, while the Big Dipper constellation is closer. The influence of the northern heavens prevails, bringing icy cold weather. During the summer solstice, the sun reaches its highest point, and the celestial motion shifts closer to the north. Consequently, the Big Dipper is farther from humans, while the sun is closer. The influence of the southern heavens dominates, resulting in intense heat. |
| 極之立時，日行地中淺，故夜短；天去地髙，故晝長也。極之低時，日行地中深，故夜長；天去地下，故晝短也 | When the celestial pole is at its highest position, the sun travels shallowly beneath the earth, making the nights short; at the same time, the heavens are higher above the earth, resulting in longer days. When the celestial pole is at its lowest position, the sun travels deeply beneath the earth, making the nights long; at the same time, the heavens are lower, causing shorter days. |
The Xintianlun argues that humans, as the most intelligent of all creatures, share the closest resemblance to the form of the heavens. Since the human body is asymmetrical from front to back it follows that the celestial sphere is also tilted, with the south lower and the north higher. During the winter solstice, the sun is far from the zenith, resulting in cold weather. Conversely, during the summer solstice, the sun is closer to the zenith, making the weather hot. In winter, the sun descends deeper below the earth, leading to shorter days and longer nights. In summer, the sun dips only slightly below the earth, causing longer days and shorter nights.
The primary purpose of the theory was to explain the reasons behind seasonal climate differences and variations in day and night length. However, by drawing a direct analogy between the human body and the celestial sphere, it was clearly influenced by the concept of correspondence between heaven and humanity (tianren ganying 天人感應). Moreover, modern science attributes seasonal temperature changes to the tilt of Earth's rotational axis, making the explanations in the Xintianlun unscientific. This theory is essentially a variation of the model of Heaven as a "tilted [canopy] of a cart" (tian ru yi che gai 天如欹車蓋), and thus still belongs to the "Canopy-Heaven Theory" (gaitian shuo 蓋天説) of ancient cosmology.