Advertisement

Same Rods, Same Calculation? Contextualizing Computations in Early Eighteenth-Century Korea

  • Young Sook OhEmail author
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 11)

Abstract

The early eighteenth-century Korean mathematical sources testify that there were two types of authorship, the mathematical officials in the lower class and the literati in the upper class. This paper aims to show how each authorship, from dissimilar educational background, affected and transformed the algorithms and grounds of the computation differently in spite of the usage of the same computational tool, based on the analysis of two early eighteenth-century mathematical texts, the Writings of Nine and One (Kuiljip 九一集) by a skilled mathematical official, Hong Chǒng-ha 洪正夏 (1684–?), and the Summary of Nine Numbers (Kusuryak 九數略) by a renowned member of the literati, Ch’oe Sǒk-chǒng 崔錫鼎 (1646–1715). In their texts on the computational techniques using counting rods, Hong appraised the adeptness in handling counting rods and expanded the existing algorithms based on the real practice, while Ch’oe approved the algorithms in which he could find the meaning close to that conveyed by texts and images of Confucian philosophical tradition.

Keywords

Counting rods Early eighteenth-century Korea Mathematical officials Literati 

References

Primary Sources

  1. Cho Tae-gu 趙泰耈. [1718] 1985. Chusǒ kwan’gyǒn 籌書管見 (Narrow view of mathematical text). Reprint. In vol 2. of Hankuk kwahakkisulsa charyo taeye: Suhakpyǒn 韓國科學技術史資料大系: 數學篇 (Source Materials of the Korean science and technology: Mathematics). Seoul: Yǒgang ch’ulp’ansa 驪江出版社. 1–199.Google Scholar
  2. Ch’oe Sǒk-chǒng 崔錫鼎. [ca. 1700] 1985. Kusuryak 九數略 (Summary of nine numbers). Reprint. In vol 1. of Hankuk kwahakkisulsa charyo taeye: Suhakpyǒn 韓國科學技術史資料大系: 數學篇 (Source Materials of the Korean science and technology: Mathematics). Seoul: Yǒgang ch’ulp’ansa 驪江出版社. 369–704.Google Scholar
  3. Hong Chǒng-ha 洪正夏. [ca. 1724] 1985. Kuiljip 九一集 (Writings of nine and one). Reprint. In vol 2. of Hankuk kwahakkisulsa charyo taeye: Suhakpyǒn 韓國科學技術史資料大系: 數學篇 (Source Materials of the Korean science and technology: Mathematics). Seoul: Yǒgang ch’ulp’ansa 驪江出版社. 201–693.Google Scholar
  4. Kim Si-jin 金始振. [1660] 1993. “Chunggan sanhak kyemong sǒ” 重刊算學啓蒙序 (Preface to the reprint of Suanxue qimeng). In vol. 1 of Zhongguo kexue jishu dianji tonghui : Shuxue juan 中國科學技術典籍通彙: 數學卷 (Source Materials of ancient Chinese science and technology: Mathematics section), ed. Guo Shuchun 郭書春, 5 vols. Zhengzhou: Henan jiaoyu chunbanshe 河南敎育出版社.Google Scholar
  5. Kyǒng Sǒn-jing 慶善徵. 1985. Muksachip sanbǒp. 默思集算法 (Mathematical methods of Muksa). Reprint. In vol 1. of Hankuk kwahakkisulsa charyo taeye: Suhakpyǒn 韓國科學技術史資料大系: 數學篇 (Source Materials of the Korean science and technology: Mathematics). Seoul: Yǒgang ch’ulp’ansa 驪江出版社. 1–368.Google Scholar
  6. Zhu Xi 朱熹. 1985. Zhouyi benyi 周易本義. In vol. 201 of Wenyuange Siku quanshu 文淵閣四庫全書. Taipei 臺北: Shangwu yinshu guan 商務印書館.Google Scholar

Secondary Sources

  1. Bréard, Andrea. 2002. Problems of pursuit: Recreational mathematics or astronomy? In From China to Paris: 2000 years transmission of mathematical ideas, ed. Yvonne Dold-Samplonius, Joseph W. Dauben, Menso Folkerts, and Benno van Dalen, 57–86. Stuttgart: Franz Steiner Verlag.Google Scholar
  2. Chemla, Karine, and Guo Shuchun. 2004. Les Neuf chapitres: le classique mathématique de la Chine ancienne et ses commentaris. Paris: Dunod.Google Scholar
  3. Chemla, Karine. 2010. Mathematics, nature and cosmological inquiry in traditional China. In Concepts of nature: A Chinese–European cross-cultural perspective, ed. Hans Ulrich Vogel and Günter Dux, 255–284. Leiden: Brill.Google Scholar
  4. Chemla, Karine. 2012. Reading proofs in Chinese commentaries. In The history of mathematical proof in ancient traditions, ed. Karine Chemla, 423–486. Cambridge: Cambridge University Press.Google Scholar
  5. Chǒng Ok-ja. 1993. Chosǒn sahoe-ǔi byǒnhwa-wa chunginkyech’ǔng-ǔi sǒngjang (The change of Chosǒn society and the development of chungin class). In Chosǒn huki yǒksa-ǔi ihae (The understanding of history of late Chosǒn), 165–172. Seoul: Ilchisa.Google Scholar
  6. Guo Shuchun, Joseph W. Dauben, and Xu Yibao (eds.). 2013. Nine chapters on the art of mathematics. Shenyang, China: Liaoning Education Press.Google Scholar
  7. Guo Shirong. 2009. Zhongguo Shuxue Dianji Zaichaoxian bandaode Liuchuan Yingxiang (Chinese mathematical texts that circulated in the Korean Peninsula and their influence). Shandong jiaoyu chubanshe. 2009.Google Scholar
  8. Han Yǒng-u. 1997. Chosǒn sitae chungin-ǔi sinbun, kyekǔp-chǒk sǒnggyǒk (The social status and class of chungin in Chosǒn period). In Chosǒn sitae sinbunsa yǒn’gu (History of Social Status in Chosǒn Period), 63-95. Seoul: Chimmundang.Google Scholar
  9. Ho Peng Yoke. 1995. Li, Qi and Shu: An introduction to science and civilization in China. Seattle and London: University of Washington Press.Google Scholar
  10. Horng Wann-Sheng. 2002a. Sino-Korean transmission of mathematical texts in the 19th century. Historia Scientiarum 12: 87–99.Google Scholar
  11. Horng Wann-Sheng. 2002b. Shiba shiji dongsuan yu zhongsuan de yi duan duihua: Hong Zhengxia vs. He Guozhu (The eighteenth century dialogue of Eastern (Korean) mathematics and Chinese mathematics: Hong Chǒng-ha vs. He Guozhu). Hanxue yanjiu 20, no. 2: 57–80.Google Scholar
  12. Hwang Chǒng-ha. 1988. Chosǒn Yǒngjo, Chǒngjo sitaeǔi sanwǒn yǒn’gu: Chuhakipkyǒkan-ǔi punsǒkǔl chungsimǔro (A study of mathematical officials in King Yongjo, King Chǒngjo period in Chosǒn: An analysis of Chuhakipkyǒkan). Paeksanhakpo 35: 219–258.Google Scholar
  13. Hwang Chǒng-ha. 1994. Chosǒn huki sanwǒnjiban-ǔi hwaltong yǒn’gu: Kyǒngju Yisi ch’anggakyelǔl chungsimǔro (A study of activities of a family of mathematical officials: A case study of Kyǒngju Yi Family). Chǒngjusarim 6: 80–110.Google Scholar
  14. Jami, Catherine. 2012. The emperor’s new mathematics: Western learning and imperial authority during the Kangxi Reign (1662–1722). Oxford: Oxford University Press.Google Scholar
  15. Jun Yong Hoon. 2006. Mathematics in context: A case in early nineteenth-century Korea. Science in Context 19 (4): 475–512.CrossRefGoogle Scholar
  16. Kang Myǒng-gwan. 1997. Chosǒn hugi yǒhang muhak yǒgu (A study of Yǒhang literature in late Chosǒn). Seoul: Ch’angjakkwa bip’yǒngsa.Google Scholar
  17. Kawahara Hideki. 1996. Kusuryak: Sangaku to sisyō (Kusuryak: Arithmetics of four images). Chōsen bunka kenkyū 3: 77–93.Google Scholar
  18. Kawahara Hideki. 1998. Tōzan to Tengenjutsu: 17seikichūki-18seikishoki no Chōsensūgaku (The eastern mathematics and the method of the celestial element). Chōsengakuhō 169: 35–71.Google Scholar
  19. Kawahara Hideki. 2010. Chōsen sūgakushi: Shushigakuteki na tenkai to sono shūen (History of mathematics in Chosǒn: Development and ending under the studies of Zhu Xi). Tokyo: University of Tokyo Press.Google Scholar
  20. Kim Yong-un and Kim Yong-guk. 1977. Han’guk suhaksa (History of mathematics in Korea). Seoul: Kwanhak-kwa In’gansa. [Revised ed.: Yeolhwadang, 1982].Google Scholar
  21. Koo Mhan-ock. 2010. Matteo Ricci ihu sǒyang suhak-e daehan Chosǒn chisigin-ūi banūng (The Chosǒn literati’s response to the Western mathematics after the import of Matteo Ricci’s mathematics). Han’guk silhakyǒn’gu 20: 301–355.Google Scholar
  22. Koo Mhan-ock. 2012. How did a Confucian scholar in late Joseon Korea study mathematics? Hwang Yunseok 黃胤錫 and the mathematicians of late eighteenth-century Seoul (1729–1791). The Korean Journal of the History of Science 34: 227–256.Google Scholar
  23. Libbrecht, Ulrich. 1973. Chinese mathematics in the thirteenth century: The Shu-shu chiu-chang of Ch’in Chiu-shao. Cambridge, Mass.: MIT Press.Google Scholar
  24. Li Yan and Du Shiran. 1987. Chinese mathematics, A concise history. Trans. John. N. Crossley and Anthony W. C. Lun. Oxford: Clarendon Press.Google Scholar
  25. Lim Jongtae. 2009. Emergence of literati mathematicians and the new culture of mathematics in late eighteenth-century Korea. Hankuk-ǔi kirok munhwa-wa bǒpko-ch’angsin (The Sourcebook of the 2nd international symposium of Kyujanggak Korean Studies).Google Scholar
  26. Martzloff, Jean-Claude. 1997. A history of Chinese mathematics. Trans. Sthephen S. Wilson. Berlin: Springer.CrossRefGoogle Scholar
  27. Moon Joong-Yang. 2001. 18seki huban Chosǒn kwahakgisul ǔi Ch’ui wa Sǒnggykǔk (The scientific or ideological nature of royal astronomical projects and politics in the late eighteenth-century Korea). Yǒksawa hyǔnsil 39: 199–231.Google Scholar
  28. Needham, Joseph. 1959. Science and civilisation in China, vol. 3. Cambridge: Cambridge University Press.Google Scholar
  29. Netz, Reviel. 2002. Counter culture: Towards a history of Greek numeracy. History of Science 40: 321–352.CrossRefGoogle Scholar
  30. Shapin, Steven, and Simon Schaffer. 1985. Leviathan and the air pump. Princeton: Princeton University Press.Google Scholar
  31. Taub, Lisa. 2011. Reengaging with instruments. ISIS 102: 689–696.CrossRefGoogle Scholar
  32. Wagner, Edward Willett. 1987a. The three hundred year history of the Haeju Kim Chapkwa-Chungin lineage. In Song Chun-ho kyosu chǒngnyǒn kinyǒm nonch’ong pyǒlswae [Essays in commemoration of Professor Song Chun-ho’s retirement, offprint], Chǒnju, 1–22.Google Scholar
  33. Wagner, Edward Willett. 1987b. An inquiry into the origin, development and fate of Chapwa-Chungin lineage. Kuknaeoe e issǔsǒ Hangukhak ǔi hyǒnjae wa mirae.Google Scholar
  34. Yi Sǒng-mu. 1997. Hankuk kwakǒ chedosa (History of civil service examination of Korea). Seoul: Minǔmsa.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Program of History and Philosophy of ScienceSeoul National UniversitySeoulSouth Korea

Personalised recommendations