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Encyclopedia of India–China Cultural Contacts v1.c6.s1.t1: Ancient Indian Mathematics and Astronomy

Encyclopedia of India–China Cultural Contacts v1.c6.s1.t1

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Ancient Indian Mathematics and Astronomy

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A kind of knowledge hierarchy which was applied to observing and describing astronomical phenomena, as well as to giving explanations and predictions via mathematical methods was developed in ancient India. According to the opinions of D. Pingree, Indian ancient astronomy can be divided into five periods orderly as Vedic Period (about 1000-400 BCE), Babylonian Period (about 400-200 BCE), Hellenistic Babylonian Period (about 200-400 CE), Greek Period (from 400-1600 CE) and Islamic Period (from 1600-1800 CE).

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The astronomical data of the Vedic Period is mainly preserved in Vedas such as Rig-Veda, thus constituting the most indigenous astronomy in India. During the Babylonian Period, a large

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Stone inscription in Gwalior, India from 9th century CE

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number of Mesopotamian astronomical contents were blended in Indian astronomy, including the method of describing day length changes, other parameters, mathematical models, time units, instruments etc derived from Babylon. Then, the astronomy of Babylonian Seleucid Period which was adapted by Greeks, was introduced into the Hellenistic Babylonian Period including the description of the planetary configuration, the geometric calculations etc concerned to eclipses, shadow length etc and meanwhile some contents were preserved in Pañcasiddhāntikā completed around 575 CE. Successively, a lot of astronomical talents came out in the Greek Period that the Indian astronomy lasted for more than one thousand years, many classic works were created and Pakṣa was also formed. Therein, Brāhmapakṣa was first established (400 CE) and lasted for the longest time (more than

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Ancient text books on Mathematics

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1,500 years) thus having a far-reaching influence and the rest are as follows: Āryapakṣa established in 500 CE, Ārdharātikapakṣa established in 500 CE, Saurapakṣa established in 800 CE and Gaṇeṣapakṣa established in 1500 CE. Along with the introduction of Islam into India, India experienced an Islamic Period between 1600 CE and 1800 CE, and after that the country came in direct contact with western modern astronomy.

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According to history, though foreign astronomy made inroads in India several times, Vedic astronomy as the indigeneous Indian astronomy was still preserved though various methods while blending with other external astronomy. Meanwhile, such Indian ancient astronomy blended with other external astronomy spread to China along with the eastern spread of Buddhism. Moreover, the detailed description of the spread of Indian ancient astronomy knowledge to China can be found in Chinese Buddhist Scriptures and various other historical records, and the contents thereof can be divided as follows: 1. Cosmology 2. Constellation system 3. Running of the sun and the moon, eclipses 4. Season and calendar 5. Running of planets and calendar thereof.

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The cosmology knowledge introduced along with Buddhism shall belong to early India mainly including the concept of Kalpa, cyclic destruction and creation of cosmos, size and measurement of cosmos etc. Buddhism world view believes that at the beginning of Kalpa, the cosmos with certain structure is constructed via wind while the whole world is destroyed completely at the end of Kalpa thus forming one cycle and then recreating the world. The Indian ancient cosmic structure is quantitatively described in Buddhist scriptures as follows: All things in the cosmos are located on a large wind wheel without edge, with the thickness thereof as 1,600,000 *yojanas*. A water wheel is set on the wind wheel, with the thickness as 1,120,000 *yojanas* and the surface of 320,000 *yojanas* is coagulated to form gold and land wheel. The

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New Delhi's Jantar Mantar observatory is located at Sansad Marg, New Delhi in India. It was built in 1724.

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Diagram of the four divisions of the twenty eight constellations, namely, Azure Dragon, White Tiger, Vermilion Bird, and Black Tortoise.

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diameter of the water wheel and the gold wheel are both 1,203,450 *yojanas* and the perimeters thereof are three times the diameters. Sumeru is located centrally on the gold wheel with the outflow height and the underwater penetration both as 84,000 *yojanas* and with seven gold hills orderly embracing externally; four great regions are located outside the seven gold hills while Cakkava is located outside the four great regions. The underwater penetration of the seven hills and Cakkava is the same with that of the Sumeru but the outflow height is orderly halved, and the widths of the hills are equal to the outflow height. Among the above nine hills, there are eight seas with the first seven seas as the inland seas, the width of the innermost sea is 80,000 *yojanas* and the perimeter thereof is 240,000 *yojanas*. The widths of the rest of the six seas are orderly halved and the eighth sea is open sea with the width as 321,000 *yojanas*. This Indian ancient cosmos model is similar with the Chinese ancient canopy heavens cosmos model but there is still no definite evidence to prove the correlation.

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We need to pay attention to the name translations, the Citrā issue, the constellation amount, the constellation width, the configuration etc of the Indian constellation system in Chinese Buddhist Scriptures. Before the Indian constellation system was introduced to China, a set of similar constellation system had already formed in China. The name translations of the Indian constellation in Chinese translation process have the following three conditions: 1. Most of the constellations are translated into Chinese existing constellations 2. Some of the constellations are translated into Chinese via transliteration according to Sanskrit pronunciations 3. Only one example which is translated into Chinese according to the literal meaning of the Sanskrit constellation name can be found in Chinese Buddhist Scriptures. The Citrā of Indian constellation system is different from that in ancient China and besides Spica, Kṛttikā and Asvini are also taken as Citrāin Chinese Buddhist scriptures. Obviously, Spica is taken as Citrā in order to remain the same with Chinese ancient constellation system. Moreover, Kṛttikā is taken as Citrā diagnostically in ancient India meaning the constellation where the spring equinox is located but taking Asvini as Citrā successively in Chinese Buddhist scriptures aims at reflecting the adjustment due to precession. There are two kinds of constellation amount, namely 28 and 27, in Chinese Buddhist scriptures. The 28 constellation system is consistent with ancient China on amount, however, the 27 constellation system excluding Abhijil is the Indian local constellation system which is the adjusted product aiming at matching with the signs of the zodiac. The most complete and clearest descriptions for the 27 constellation system in Chinese Buddhist scriptures first appeared in *Sutra on Taking Auspices by Celestial Constallations and Bodies* translated by Tang Bukong. However, the width of the constellations in Chinese Buddhist Scriptures division is mainly an uneven division and the unevenness is not ruleless as that in ancient China and can be roughly divided into wide, secondary wide and narrow. From *Sutra on Taking Auspices by Celestial Constellations and Bodies* and other Buddhist scriptures, we also can find a trend of unifying the widths of the constellations which shall be influenced by the introduction of signs of the zodiac into India. Additionally, in Buddhist Scriptures, the star numbers of the constellation systems are greatly different from that in ancient China and the star numbers of only five constellations are totally the same. Meanwhile, the names of the implements or the products used for describing the constellation configuration also have an Indian characteristic.

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Diagram on astronomy, Qing Xiao Yun Cong

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Indian Observatory at Jaipur, located in Rajasthan, India

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In regard to the running of the sun and the moon, several Chinese Buddhist Scriptures mention that the sun and the moon run around Sumeru while being supported and blown by the wind wheel and the running height is half height of Sumeru, namely 42,000 *yojanas*. The diameter of the sun is 51 *yojanas* while that of the moon is 50 *yojanas*. The four continents experience day and night alternative as well as seasonal variation along with the running of the sun around Sumeru. Volume V “Orbits of The Sun And The Moon 19th” in *Abhidharma Theory* mentions: the sun has 180 orbits while the moon has 15 orbits. The sun continuously transits from one sun orbit to another sun orbit every day in half-a-year and then returns to the innermost sun orbit from the outermost sun orbit orderly which can reasonably explain annual variation, such as Sunrise azimuth change, day and night length change etc. As for the orbits of the moon, one moon orbit is equivalent to 12 sun orbits, the sun and the moon repeatedly run between the most southern sun orbit and the most northern sun orbit between which the distance is 290 *yojanas*. Meanwhile, it also mentions that solar radiation shapes in a sphere with the diameter as 721,200 *yojanas*.

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According to Chinese Buddhist scriptures, eclipses were caused by Asurindaka Rahu with his hands covering the sun and meanwhile six eclipse periods were mentioned. From other document literatures except Chinese Buddhist scriptures, we can know that the Indian astronomy introduced in China featured the eclipse theory. Moreover, “Kasyapa Harvey Indian Method” which is an Indian method for calculating eclipses is attached to the article of Eclipse Theory in *Linde Calendar* of Volume 33 of *Old Book of Tang* (refer to article “Kasyapa Harvey” for details) and one paragraph of Indian eclipse method which is “Eclipse Cutting Method” spread by Indian Buddhist Kumāra is also attached to the article of Eclipse Theory in *Taien Calendar* of Volume 34 of *Old Book of Tang* (refer to article “*Kumāra*” for details). In addition, the Indian eclipse method translated by Gautama Siddha clearly introduces the Indian eclipse calculation method (refer to article ‘Jiuzhi Calendar’ for details).

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The contents related to the season and the calendar of ancient India are abundantly recorded in Chinese Buddhist scriptures mainly including season division, month name, concept of the white moon and black moon, arrangement of a solar month of 31 days and a solar month of 30 days, inserting of leap month, day and night length change, division and denomination of day and night etc. Four kinds of different definitions for the month are given in Volume 48 of *Great Treatise on the Perfection of Wisdom* namely “Solar Month”, “Karma Month”, “Lunation Month”, “Nakshatra Month”. Therein, “Solar Month” is one-twelfth the length of the tropical year, “Karma Month” is an ideal year (360 days as an ideal year), “Lunation Month” is namely the synodic month and “Nakshatra Month” is namely the sidereal month. And several sheets of the shadow length change during seasonal variation are also given in Buddhist Scriptures and *Time and Non-Time* has the most detailed data. Except Jiuzhi Calendar, Futian Calendar which originated from Indian astronomy and was popular among Chinese folks during the late Tang dynasty is a representative of the complete writings similar with Indian ancient siddhanta, but the main contents have been lost. In addition, Guangzhai Calendar written by Gautama Ambrosius is presumed to be a kind of astronomical table for calculating astronomical phenomena according to Indian astronomy.

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The following planet knowledge is mainly involved in Chinese Buddhist scriptures: planet name and order, planetary scale, travelling range, planetary calendar etc. Especially, Rahu and Ketu are also taken as planets. Sometimes Chinese ancient names are adopted as the names of the planets but sometimes the transliteration names are adopted. And the orders of the planets are sometimes determined by the order of Chinese ancient generation among five elements and sometimes determined by the brightness thereof, and meanwhile the orders “From Fast to Slow” are also given in *Sutra on Taking Auspices by Celestial Constellations and Bodies*. In addition, the travelling range of the planets and the calendar thereof are intensively described in *Expelling the Seven Planets’ Fated Calamities* (refer to *Expelling the Seven Planets’ Fated Calamities* for details).

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Since Indian astronomy was introduced in China in the early times and had a large time span (from 3^rd to 10^th centuries CE), thus the related materials are piecemeal preserved till now and it is also difficult to establish the correlation between the astronomical contents thereof and certain astronomical classics of Pakṣa in different Indian periods. However, we are still able to trace the impact of Indian astronomy on Chinese astronomy and such impact most seriously influenced Chinese astronomy in Tang dynasty. Li Qiao mentioned in *Shenlong Calendar Serial* that the Indian and Chinese astronomers were different from each other but they had the interlinked astronomy thoughts and fought for modifying the calendar together. The most classic works shall be *Taien calendar* as Japanese Buddhist Saicho who came to Tang for Buddha dharma described in *Dharma Blood Spectrum* that “Tang and Brahman Buddhists communicate and reach an agreement” thus completing the classic works in Chinese calendar history and becoming the model of later calendars.

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(*Chen Ming* & *Niu Weixing*)

Cites (6)