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One of the connections on which evidence of intellectual connections is plentiful is the impact of Buddhists in general, and of adherents of Tantric Buddhism in particular, on Chinese mathematics and astron­ omy in the seventh and eighth centuries, in the Tang period. Yi Jing, with whose rhetorical question this essay began, was one of many translators of Tantric texts from Sanskrit into Chinese. He was in India in the last quarter of the seventh century, at a time when Tantrism was beginning to generate a lot of interest in China. Tantrism became a major force in China in the seventh and eighth centuries, and had followers among Chinese intellectuals of the high­ est standing. Since many Tantric scholars had a deep interest in mathematics (perhaps connected, at least initially, with the Tantric

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fascination with numbers), Tantric mathematicians had a significant influence on Chinese mathematics as well.

Indeed, as Needham notes, 'the most important Tantrist was I-Hsing (+672 to +717), the greatest Chinese astronomer and math­ ematician of his time'. Needham goes on to remark that 'this fact alone should give us pause, since it offers a clue to the possible significance of this form of Buddhism for all kinds of observational and experi­ mental sciences'. 26 Though Tantrism is of Indian origin, the influences, as Needham points out, went in both directions. 27 Indeed, 'C1nadira' (or Chinese practice) figures prominently in parts of the Indian Tantric literature, as do Indian texts in Chinese Tantric writings.28

Yi Xing (or I-Hsing, to use Needham's spelling) was fluent in Sanskrit. As a Buddhist monk, he was familiar with Indian religious literature, but he had acquired a great expertise also on Indian writ­ ings on mathematics and astronomy. Despite his own religious con­ nection, it would be a mistake to assume that Yi Xing's mathematical or scientific work must have been motivated by religious concerns. As a general mathematician who happened to be also a Tantrist, Yi Xing dealt with a variety of analytical and computational problems, many of which had no particular connection with Tantrism or Buddhism at all. The combinatorial problems tackled by Yi Xing included such classic ones as 'calculating the total number of possible situations in chess' . Yi Xing was particularly concerned with calendrical cal­ culations, and even constructed, on imperial order, a new calendar for China.

Calendrical studies, in which Indian astronomers located in China in the eighth century, along with Yi Xing, were particularly involved, made good use of the progress of trigonometry that had already occurred in India by then (going much beyond the original Greek roots of Indian trigonometry) . The movement east of Indian trigonometry to China was part of a global exchange of ideas that also went west around that time. Indeed, this was also about the time when Indian trigonometry was having a major impact on the Arab world (with widely used Arabic translations of the works of Aryabhata, Varahamihira, Brahmagupta and others), which would later influence European mathematics as well, through the Arabs. Some verbal signposts to the global movement of ideas can be readily

CHINA AND IND IA

traced. A good example is the transformation of Aryabhata's Sanskrit term jya for what we now call sine: jya was translated, through prox­ imity of sound, into Arabic jiba (a meaningless word in Arabic) and later transformed into jaib (a bay or a cove in Arabic), and ultimately into the Latin word sinus (meaning a bay or a cove), from which the modern term 'sine' is derived. Aryabhata's jya was translated in Chinese as ming and was used in such tables as yue jianliang ming, literally 'sine of lunar intervals'. 29

There are detailed Chinese records of the fact that several Indian astronomers and mathematicians were employed in high positions in the Astronomical Bureau at the Chinese capital in this period. As was mentioned earlier, one of them, Gautama (Qutan Xida), became President of the Board of Astronomy in China. He produced the great Chinese compendium of astronomy Kaiyvan Zhanjing - an eighth­

century scientific classic.30 He was also engaged in adapting a number of Indian astronomical works into Chinese. For example, ]iuzhi li, which draws on a particular planetary calendar in India ('Navagraha' calendar), is clearly based on the classical Paiicasiddhantika, pro­ duced around 5 50 CE by Varahamihira. It is mainly an algorithmic guide to computation, estimating such things as the duration of eclipses based on the diameter of the moon and other relevant param­ eters. The techniques involved drew on methods that were established by Aryabhata and then further developed by his followers in India such as Varahamihira and Brahmagupta.

Yang Jingfeng, an eighth-century Chinese astronomer, described the mixed background of official Chinese astronomy thus:

Those who wish to know the positions of the five planets adopt Indian calendrical methods . . . . So we have three clans of Indian calendar experts, Chiayeb (Kasyapa), Chhiithan (Gautama), and Chiimolo (Kumara), all of whom hold office at the Bureau of Astronomy. But now most use is made of the calendrical methods of Master Chhiithan [Qutan], together with his 'Great Art', in the work which is carried out for the government. 31

In scrutinizing these Sino-Indian connections in science, which were evidently important, we have to assess the role of Budd.hism as a catalyst. Even though the Indian astronomers, such as Gautama, or

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Kasyapa or Kumara, would not have been in China but for the relations generated by Buddhism, their work can hardly be seen primarily as contributions to Buddhism.