• Journal for History of Mathematics
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• v.24 no.3
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• pp.1-12
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• 2011

It is well known that the sexagesimal cycle(干支) has been playing very important role in ordinary human affairs including astrology and almanacs and the arts of divination(術數). Yin-Yang school related the cycle with the sixty four hexagrams and the system of five notes(五音) and twelve pitch-pipes(十二律), and the processes to relate them are called respectively NaJia(納甲) and NaYin(納音) and quoted in Shen Kuo's Meng qi bi tan(夢溪筆談, 1095). Yang Hui obtained the process NaYin in the context of mathematics. In this paper we show that Yang Hui introduced the concept and notion of functions and then using congruences and the composite of functions, he could succeed to describe perfectly the process in his Xu gu zhai qi suan fa(續古摘奇算法, 1275). We also note that his concept and notion of functions are the earliest ones in the history of mathematics.

• Journal of Korean Medical classics
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• v.35 no.2
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• pp.51-76
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• 2022

Objectives : To provide foundation for research on local medical examination of the Ming period, the contents on 'He who does not know Yi(易) cannot speak of medicine' in the Yixuetongzong(醫學統宗) written by He Jian was analyzed. Methods : Proofreading of the original texts, followed by interpretation of words and phrase and translation into Korean were done. The resulting contents were then analyzed from the perspective of the theory of Medical Yi(Yi-Yi). Results : In this medical exam paper for physicians, He answers himself on topics such as the Four Symbols[四象], Eight Symbols[八象], the Sixty-four hexagrams[Liushisigua], the combinations of the Organs and Bowels[Zangfu], Nine Orifices[Jiuqiao], and Five Body Parts[Wuti], the origin of the pulse, the reasoning behind calling the pulse 'the station for blood[xuezhifu]', what the 'Tianzhen Weihezhi Qi' stands for and the meaning of the Twelve Organs[shierguan]. He also supports the perspective of the 'Medicine and Yi having the same roots[Yi-yi tongyuan]', arguing that due to this, the body's physiology could be explained through the theories of Yi[易]. This shows that He understood the Yi-yi theory as a larger category. Conclusions :He's medical exam paper reflects his uniqueness in the field of the Yi-yi theory that precedes that of Zhao Xianke.

• Journal of the Daesoon Academy of Sciences
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• v.47
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• pp.65-103
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• 2023

In The Canonical Scripture (典經), the core scripture of Daesoon Thought, the Former World and the Later World are divided into the Era of Mutual Contention and the Era of Mutual Beneficence. This concept of the Former World and the Later World appears in diagrams on I-Ching Studies (易學) in the text titled, The Comprehensive Mirror of Taegeukdo (太極道通鑑). In I-Ching Studies, Anterior Heaven (先天) and Posterior Heaven (後天) are the main concepts in Song Dynasty diagram books on I-Ching Studies. Among the diagrams of I-Ching Studies, Fuxi's Diagram of the Sequence of the Eight Trigrams, Fuxi's Diagram of the Positions of the Eight Trigrams, Fuxi's Diagram of the Sequence of the 64 Hexagrams, and Fuxi's Diagram of the Positions of the 64 Hexagrams correspond to the Anterior Heaven, and King Wen's Diagram of the Sequence of the Eight Trigrams and King Wen's Diagram of the Positions of the Eight Trigrams correspond to Posterior Heaven. In The Comprehensive Mirror of Taegeukdo, the diagrams of I-Ching Studies are reinterpreted according to Daesoon Thought. The Diagram of the Eight Trigrams of King Wen's Era corresponds to King Wen's Diagram of the Eight Trigrams in I-Ching Studies. This diagram was drawn according to the text in Chapter Five of the Treatise of Remarks on the Trigrams. This diagram corresponds to "the Era of the Nobility of Earth (地尊時代)" centered on the trigram kun (坤 / ☷ ground). Fuxi's Diagram of the Positions of the Eight Trigrams in I-Ching Studies corresponds to The Diagram of the Positions of the Eight Trigrams of Fuxi's Era in Daesoon Thought. The most significant feature of this diagram is that the trigrams assigned to the directions of north and south match the hexagram indicating the obstruction of Heaven and Earth. This is hexagram 12 (否), meaning "obstruction," and it depicts no exchange or communication between Yin and Yang. Naturally, this symbolizes mutual destruction overtaking Yin and Yang. Daesoon Thought expresses this as "the Era of the Nobility of Heaven (天尊時代)." The most significant feature of The Diagram of the Eight Trigrams of the Corrected Book of Changes in The Comprehensive Mirror of Taegeukdo is that the trigrams assigned to the directions of south and north are indicative of hexagram 11, Peace on Earth and in Heaven (泰). This is a diagram in which mutual destruction is resolved through the Five Phases because the trigrams for water (坎 / ☵) and fire (離 / ☲) are in a corrected orientation. Therefore, this diagram symbolizes a world "free from Mutual Contention" and "the Era of Human Nobility (人尊時代)." According to the contents of The Canonical Scripture, the Supreme God performed the Reordering Works of the Three Realms to correct the Mutual Contention of the Former World, and as a result, the Mutual Contention of the Former World will give way to the implementation of the Dao of Mutual Beneficence. The Supreme God's Reordering Works of the Three Realms have been completed in the realm of divine beings, but in the Later World, they appear as an Earthly Paradise where the Dao of Mutual Beneficence is realized. The diagram depicting the Later World is The Diagram of the Eight Trigrams of the Era of the Corrected Book of Changes in The Comprehensive Mirror of Taegeukdo.

• Journal of architectural history
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• v.14 no.3 s.43
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• pp.39-52
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• 2005

This study relates to the architectural planning principle of Gyeonghoeru pavilion, one of the major buildings in Gyeongbokgung palace. The study is concentrated on The Book of Gyeonghoeru Pavilion written by Jeong Haksun in 1865 during the reconstruction of Gyeonghoeru pavilion. The architectural planning principle of Gyeonghoeru pavilion disclosed in The Book of Gyeonghoeru Pavilion appears to be 'the method of expanding with six by six system'. 'The method of expanding with six by six system' means a way of continuously extending the number related to 6 by addition, subtraction, multiplication and division, and reflecting to architecture, having number 6 as the basic number. Number 6 means a large amount of water in East Asian philosophy, Applying 'the method of expanding with six by six system' to the architecture of Gyeonghoeru includes an intention to prevent fire in a way of a type of incantation because Korean traditional wooden buildings are we to fire. Since Gyeonghoeru is surrounded by a pond and was constructed based on the number 6 having a strength of water, it was believed that it could be safe from fire. This study compares the contents disclosed in The Book of Gyeonghoeru Pavilion with the construction of Gyeonghoeru to find out how the number 6 was applied to the overall construction of Gyeonghoeru. From the fact that the total number of km of Gyeonghoeru is 36 ($6{\times}6$), the number of pillars is 42 ($6{\times}7$), and the number of windows and doors is multiples of 6, it has been found out that the number 6 is deeply related to the overall construction of Gyeonghoeru. In addition to the fact that the construction of Gyeonghoeru can be explained by 'the method of expanding with six by six system', The Book of Gyeonghoeru Pavilion also discloses parts where Diagram of Hotu, Later Heaven Arrangement and Arrangement of 64 Hexagrams are applied. Therefrom, it has been found out that Gyeonghoeru pavilion was constructed by applying the principles of East Asian philosophy based on The Book of Changes.

• Journal of Haehwa Medicine
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• v.26 no.1
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• pp.33-48
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• 2017

Objective : Ten heavenly stems and twelve earthly branches are the important means to understand the orders of changes in heaven and earth. Method : We have so far looked into detailed explanations about twelve earthly branches in Seolmunhaeja, annotations in Seolmun of four major people, and commentaries in Jeongyeokwonui. Result & Conclusion : This can be also applied to the explanations of twelve early branches, as follows. In the $11^{th}$ month of the lunar calendar, the yang energy is finally born amid full of the ying energy. In the $12^{th}$ month, the yang energy prepares to break through the knots of the ying energy and gets ready to come out of the ground. In the first month, three kinds of the yang energy start to become vigorous and active. In the second month, the yang energy gains more force, sprouting various plants on the ground. In the third month, the yang energy arouse further, strengthening and growing plants. In the fourth month, all the yang energy is released, while the ying energy is still hiding. In the fifth month, one ying energy is born amid full of the yang energy, and there are interchanges between the yang energy and the ying energy. In the sixth month, the yang energy is still strong and vigorous, ripening the fruits in the fields. In the seventh month, the yang energy starts to hurt all creation. In the eighth month, the ying energy starts to flourish, and the yang energy starts to decline, diminishing all creation and, however, still ripening grains to be harvested. In the ninth month, one yang energy starts to hide from sight, not working its duty, while five kinds of the ying energy start to annihilate all creation. Finally, in the tenth month, the small yang energy hides to be rebirthed amid the flux and reflux of the ying-yang energy. The creative and unique interpretation of Jeongyeokwonui about twelve earthly branches is worth to be referred. It is definitely beyond the other existing explanations, as it incorporates trigrams and hexagrams from I Ching (Book of Changes) and the five primary substances.

• Journal of Korean Philosophical Society
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• v.129
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• pp.1-22
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• 2014

Columns 12-18 record a conversation between an aged Confucius and his disciple Zi Gong concerning the Changes and especially the role of divination in its use. The last section, from the bottom of column 24, concerns the hexagrams Sun損, "Decrease," and Yi益, "Increase," which Confucius is here made to regard as the culmination of wisdom in the Zhouyi. The conversation between Confucius and Zi Gong, and especially Zi Gong's apparent misunderstanding of Confucius's interest in the text, has already attracted considerable scholarly interest. Zi Gong criticizes Confucius for changing his teaching about the importance of the Zhouyi and for performing divinations. Confucius responds that while he does indeed perform divinations. there is a major difference between his use of the text and that of others: he regards the I Ching as a repository of an ancient wisdom. This would seem to signal recognition of a dramatic change in the function and status of the text. Zi Gong said: "Does the Master also believe in milfoil divination?" The Master said: "I am right in only seventy out of one hundred prognostications. Even with the prognostications of Liangshan of Zhou one necessarily follows it most of the time and no more." The Master said: "As for the Changes, I do indeed put its prayers and divinations last, only observing its virtue and property. Intuiting the commendations to reach the number, and understanding the number to reach virtue, is to have humaneness and to put it into motion properly. If the commendation do not lead to the number, then merely acts as a magician; if the number does not lead to virtue, then one merely acts as a scribe. The divinations of scribes and magicians tend toward it but are not yet there; delight in it but are not correct. Perhaps it will be because of the Changes that sires of later generations will doubt me. I seek its virtue and nothing more. I am on the same road as the scribes and magicians but end up differently. The conduct of the gentleman's virtue is to seek blessings; that is why he sacrifices, but little; the righteousness of his humaneness is to seek auspiciousness; that is why he divines, but rarely. Do not the divinations of priest and magicians come last!" Although Confucius says two ways of the symbolic numbers and virtue-property, he emphasizes his way of virtue and property more important. In fact he who wrote in Yao 要, "essentials," Confucius's saying describes his own viewpoints of the Changes throughout the conversations between Confucius and his disciple Zi Gong, and is only to borrow the name of Confucius. Furthermore, quoting the original text in Yao 要, "essentials," in sequence, also comparing the materials of "the Analects of Confucius論語," with "the Shih chi史記," this thesis will be centered to a great extent on the relative similarity and differences between the Mawangdui Boshu Zhouyi Manuscript and the received text, and discussed the authencity of Yao 要, "essentials," of the contents shown in the chapter of 'Confucius became aged, and liked "The Book of Changes."' the relation of Confucius and the Changes will be clarified naturally through this progress.

• Journal of Korean Philosophical Society
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• v.131
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• pp.223-244
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• 2014

In this paper, the author interprets Juyeok (The Book of Changes) as a philosophical book on self-culture instead of a book on divination. Juyeok, originally, was a book on divination written to tell fortunes; however, it has been a rich source producing the discourse of the humanities. This is because it has a unique system of linguistic symbols. Gwae-Hyo (Hexagrams and Horizontal Lines) system of Juyeok has a number of symbolic features, and there is too much room for new philosophical, cultural interpretations. Thus, Juyeok can be applied to any information and events, and it can, accordingly, help solve the problems of life we are facing. Moreover, Juyeok's unique characteristics are revealed very well in active intervention of persons who read and interpret it. Carl Gustav Jung is the very person who argued that one should interpret Juyeok through this active intervention. In the foreword of Juyeok translated by Richard Wilhelm, he mentions a possibility of the interpretation of Juyeok applying 'synchronicity.' According to him, Juyeok is a material not to predict the future or tell the fate ordained, but to look back on oneself or find the solutions of problems oneself. It allows the inquirer to interpret Gwae-Hyo-Sa (Explanations) not simply through the result of fortune-telling but the act of telling one's fortune. He applies 'synchronicity' to the finding of answers to one's problems in the given Gwae-Hyo-Sa. Synchronicity refers to 'the principle of non-causal relationship explaining a phenomenon of meaningful coincidence.' Here, simultaneity, unlike contingency the principle of causality refers to, means 'meaningful coincidence.' He presents a theory that the divination signs derived from Gwae-Hyo-Sang (Images) through synchronicity is a reflection of the psychology of the unconscious the fortune-teller or a man who receives the results of the divination signs has under certain circumstances on the outside. This is because Jung interprets it like this because the way of communication of Juyeok using symbolic language is not direct but indirect. Juyeok's system of symbolic language aims not at delivering objective knowledge, but the reader's self-transformation. This point can be applied in clinical philosophy. People who suffer from agony and pain in their daily lives may find meaningful and helpful advice for themselves no matter what Gwae-Hyo-Sa they choose in Juyeok. This is because it was originally hidden in their inner space and just revealed concretely through Gwae-Hyo-Sang or Gwae-Hyo-Sa in Juyeok. In this sense, we connect the meaning Gwae-Hyo-Sang or Sa contains from Juyeok to their circumstances, read counsel or advice needed ourselves and make it our own to be able to have power to change and help ourselves. And at this very point may be evaluated as an important role of Juyeok.