You are to say that the objects of knowledge not only receive from the presence of the good their being known, but their very existence and essence is derived to them from it, though the good itself is not essence but still transcends essence in dignity and surpassing power.
Plato, The Republic, Book VI1
Introduction
Many Koreans in the pre-modern period believed that the universe exists with China, the Middle Kingdom, at its center. Korean civilization was within the cultural orbit of China, with the spread of Chinese books and Korean efforts to learn Chinese inventions and technology. The concept of the Middle Kingdom, which signified a definite order of things as identified by sages in Chinese antiquity, was one of many paradigms that Koreans relied on for knowledge production. As Korean elites admired Chinese scholarship as the only right source to understand the world, their worldview naturally heavily depended on the Chinese order of things. In hindsight, the Korean Sino-centric epistemology may look irrational and unscientific, but we should note that classical Chinese was the only known literature that Koreans had for learning until and even for a time after the invention of the Korean alphabet. Though the new phonetic alphabet ended the monopoly of classical Chinese in the long run, the modification proceeded slowly and gradually, taking a few hundred years.
The earliest sign of such reformation in Korean intelligence can be found in elite society where the traditional concepts of human cognition and morality were updated as a result of Western influence. In this chapter, I will analyze a few math enthusiasts who deepened their interest in Euclidian geometry. Their search for accurate knowledge opened a way to European mathematics and eventually met a moment of enlightenment to reconsider the Sino-centric paradigm.2 Until then, ancient mathematics had developed from the early era in China, as evidenced in the He tu [C] (River Chart) and the Luo shu [C] (Inscription of Luo).3 The two diagrams from mysterious origin became symbolic marks of many different schools and religions. As the prehistoric number series inspired early mathematical imagination, the Chinese math tradition had acquired its own depth and color with the formation of classics such as the Zhou bi suan jing [C] (Arithmetic Classic of the Gnomon and the Circular Paths of Heaven) and the Jiu zhang suan shu [C] (Nine Chapters on the Mathematical Art). The ancient art of mathematics, however, did not receive as much interest as other classical texts when Chinese empires canonized the latter and used them as fundamental texts of the Confucian school. Except for specific practical needs, most notably the need for making an accurate calendar, arithmetic skills moved gradually to the possession of a few people who fell in love with the esoteric and mysterious elements of numbers. The Chinese classics, in this regard, provided an essential foundation of mathematical thinking and counting systems for Koreans.4 The advantage of Sino-classics was that Korean mathematicians could have a substantial and consistent textual basis. There were also disadvantages, the main one being that they could hardly imagine any systems of numbers beyond those of Chinese antiquity.5
The translation of Euclid’s Elements in classical Chinese was revolutionary as it eventually challenged the convention of Korean mathematical knowledge and its practice.6 It was not only an eye-opening experience of different mathematical thinking but also evidence that China-based knowledge could not be self-evident and would not suffice. In the Korean history of classical learning, it was believed that Chinese sages and scholars had accomplished so much that it could be considered an insult, if not a blasphemy, to imagine that there were any vital knowledge that they failed to ascertain. After the civil service exams canonized specific classics and commentaries, Chosŏn Korea saw the formation of the classical absolutism in the body of knowledge. Therefore, respectful knowledge was to come from Chinese texts and official interpretations. After European science and mathematics entered Korea, some began to doubt the infallibility of the Sino-classics from the seventeenth century. Korean math enthusiasts organized private and secretive societies in which they cultivated their shared interest in mathematics during the eighteenth century. Mathematics had an incredible power to attract followers, as it did the Pythagoreans in the ancient world.
As a first step in examining the epistemological transition in the late Chosŏn period, I will analyze how accuracy expressed in numbers and verified by operations attracted Korean intellectuals in the eighteenth century. Impressed by the Jesuits’ capability of precise calculation, these intellectuals realized that scientific knowledge could be produced by argumentation with physical evidence. In other words, it was the discovery of logos, that knowledge needs verification by the exercise of reason. In the view of Korean mathematicians, mathematical skills represented the power of inherent rationality in the human mind. The new math, therefore, created an anomalous condition where the old and new knowledge systems came into conflict and convergence. Though Korean scholars could not give up the preexisting premise on the rationality of the li, this historical episode illustrates complicated tensions and transitions in the Korean intellectual landscape.
The pursuit of encyclopedic knowledge
Our survey on new Korean mathematics can start from an eighteenth-century man named Yi Ik. He was born in 1681 into a prominent noble clan, Yŏju Yis. It was a rather depressing time because just one year prior to his birth, his father had been arrested and banished to a remote, cold, and barren northern town. His father died in exile shortly thereafter and never got to see his last son. The trauma of the early loss of his father seems to have haunted him his entire life and was also a sad foreshadowing of the court politics that would continue to take more loved ones from him. In his youth, he grew up under the care and teaching of his older brother Yi Cham (1660–1706). In 1706, when he turned twenty-five, his mentor and brother Yi Cham also perished in a political storm. Yi Cham was arrested and put in jail after petitioning the king and got tortured to the point of death. This additional traumatic loss transformed Yi Ik’s life forever. He decided never to sit for the civil service exam. He retreated into private life after moving to his family’s manor near the west coast.7
The country estate called Sŏngho became his lifetime workplace and a private academy for his reclusive intellectual circle. It was there that he devoted the entire life to satisfy nothing else but his intellectual curiosity until he died in 1763. Yi Ik’s magna opus Sŏngho sasŏl (Petty Words of Yi Ik), a thirty-volume compendium of his essays and notes on myriad things, was the result of twenty years of study in Sino-classics and natural objects. Even though he never took the civil service exams, his scholarly fame was well established in his lifetime. Many students traveled to his country home to study under him. A network of independent private scholars formed around Yi’s works and teaching. He built a private club that he taught to investigate the natural world in somewhat unconventional ways.
It was against convention when he chose to construct private communication networks with his students, acquaintances, and protégés based on their common interest in scholarly topics. In Korean society at that time, private networks lacked the solid institutional base of public ones as we can see from political factions, family lineages, and sŏwŏn (authorized local schools). To serve kong (the public), one was expected to acquire a degree and rank in the public realm. Under Confucian ethics, noblemen were born to serve the noble causes of family, society, and state. Their divine mission for public service was their raison d’être of being and learning. At the opposite end was sa (the private). This binary setting between public and private created an environment in which secret assembly for hobbies received no formal esteem in literati society. Yi’s circle was a new private academic community in the sense that the gathering was voluntary and autonomous from the state’s qualification.8
His group of dilettanti was bound by affection for their leader and respect for the mastery of Sino-classics. “Serious students of classical literature in the time all gathered under Master Yi [Ik],” his pupil An Chŏng-pok (1712–1791) recalled in a nostalgic tone.9 While others chased conventional state-authorized degrees, his group sought out their own scholarly reputation built on peer review through the exchange of letters. To be a member of this group required adopting the same ethos, that is, autonomy from the state, and literacy in classical Chinese. In particular, his group demanded an ability to read and understand Sino-classics and Chinese belles lettres. They studied and debated various topics and controversies about the Chinese classics and presented their own opinions by writing letters or essays in classical Chinese.10
What comprised their prevailing ethos was the pursuit of humanistic erudition in Chinese classics (Hanhak). Straying from the official curriculum of Neo-Confucianism, Yi Ik envisioned the ideal of respectful learning in much broader terms. He showed a keen interest in the actuality of the external world, keeping the belief in the mission of purifying the human mind. Well aware of the ferocious effects of Confucian literati politics driven by partisanship and dogmatism, he expanded the scope of his interests through philosophical and practical actions. Encyclopedias, more than any other genre, ably represented the virtue he sought. Before he pursued encyclopedic knowledge, an attribute of erudition had been a unique value of noncompliant intellectuals from the early seventeenth century. Two prominent encyclopedists, Yi Su-kwang (1563–1628) and Yu Hyŏng-wŏn (1622–1673), set the prototypes for producing encyclopedic knowledge. Yi’s Chipong yusŏl (Compendium of Yi Su-kwang) and Yu’s Pan’gye surok (Jottings of Yu Hyŏng-wŏn) denoted the age of new humanism in Chosŏn Korea.11 Yi Ik, as a Neo-Confucian moralist, reinterpreted the humanistic erudition in combination with Neo-Confucian moral knowledge.
The name Broad Learning aptly expressed the reinvigorated mood of the literati society in the eighteenth century. We can trace the origin of Broad Learning back to a Chinese writer and thinker, Wang Shizhen, of sixteenth-century Ming China. Wang’s idea of unlimited learning triggered powerful currents of skepticism, iconoclasm, and uncertainty in the intellectual world that had, for long, taken human knowledge as something self-evident. But, equally, Wang’s call for Broad Learning was deprived of a core discipline or scientific method.12 The meaning of Broad Learning was open to various interpretations in t...
