Title

Numbers and Mathematics in the Zhouyi shilun hebian, tuxiang jibiao: A Preliminary Study of the “Jishu gai”

Author

Lee Chung-ta

Genre

Article

Pages

399-436

DOI

10.6503/THJCS.201909_49(3).0001

Download

PDF

Language

Chinese

Key words

Zhouyi shilun hebian周易時論合編, Tuxiang jibiao圖象幾表, mathematics, image-number symbolism, inner calculation and outer calculation

Abstract

The Zhouyi shilun hebian 周易時論合編, compiled in the mid-seventeenth century, collected together large amounts of earlier research on astronomy, musicology, medicine, physics and mathematics. The text not only reveals the Chinese interest in natural science, but also the belief among Chinese mathematicians and scientists that the Zhouyi 周易 had perfectly rendered visible Nature’s truth. The study of numbers in China was perceived to have had two functions: an inner-calculation (neisuan 內算), which concerned both the ability to be numinous and illuminating (shenming 神明) and to comply with one’s Nature and Destiny (xingming 性命); and an outer-calculation (waisuan 外算), which dealt with practical problems involving the application of certain mathematical methods. The idea that both inner and outer calculations, two subsets of numerical learning, originated with the Zhouyi inspired Chinese mathematicians to study the metaphysics of the Zhouyi and its numerology, which since antiquity was thought to have held the keys to predicting the future. In depicting and interpreting Zhouyi images, the Tuxiang jibiao圖象幾表, found at the beginning of the Zhouyi shilun hebian, made use of traditional mathematical knowledge and the image-number symbolism of the Zhouyi to express a combined worldview that did not treat natural sciences and numerology as distinct systems of thought.