This article provides an analysis of a fundamental issue in Yijing studies (易学), that is, how to obtain a gua (卦, or hexagram) from Yijing divination. It modifies existing interpretations of the Dayan Divination method (大衍筮法) and proposes a new algorithm, thereby discovers the probability distribution of all gua in Yijing (易卦).The sixty-four hexagrams (重卦, 或六爻卦) of Yijing have appeared during the Shang Dynasty (ca BCE 1600-1046) and became prevalent during the Zhou Dynasty (ca BCE 1045-256), forming the foundation of Yijing. The images of gua (卦象, 64 hexagrams with six lines (爻) each and 8 trigrams (单卦) with three lines) constitute a systematic whole. Any interpretation of Yijing needs to be based on the full set of gua images. Yijing is well known as the foremost origin of all the Chinese classics, and the “divine intent” revealed by the Yijing gua is the source from which various concepts as well as their interpretations of Chinese civilization are drawn. As Yijing being a divination book, the “divine revelation” embodied in the gua serves as the authentic source in Chinese tradition to seek guidance for all kinds of risk decision-making. Regardless of applications of wide variety, the wisdom of Fuxi (伏羲, ca BCE 4600-?), the archaic sage of Chinese civilization and the root source of Yijing, has been congealed and conveyed through Yijing gua.How to acquire a gua related to “my issue,” viz., how to get know the divine intent from Heaven guiding the matters of my concern is the key question to all Yijing users. The answer involves three stages: requesting in earnest; throwing divination to obtain the gua; interpreting the underlying meaning of gua. Of them, the legitimacy of the request depends on sincerity of the prayer; the interpretation of mystic revelation of the acquired gua benefits from collective experience and intelligence. The divination throw, the stage in the middle, however, relies on the Dayan Divination method, which is the only authentic way to obtain a gua in Yijing.The Dayan Divination method is essentially a random number generator. The four numbers entailed from the divination process represent the four primary symbols (四象): 6 (六) represents the Great Yin (⚏, 老阴), 7 (七) represents the Lesser Yang (⚎, 少阳), 8 (八) represents the Lesser Yin (⚍, 少阴), and 9 (九) represents the Great Yang (⚌, 老阳). The probabilities to obtain the random number 6, 7, 8, 9 are 1/16, 5/16, 7/16, and 3/16, respectively. (This probability distribution is way different from the simplified method used in the public commoners known as the “coin flipping method.”)With the Dayan Divination, the probability distribution of the entire system of gua in Yijing can be inferred, which is of significant importance for examining and calculating the connections and evolutions among gua. (See Appendix II)In Appendix I, the author provides a thorough analysis of Shao Yong’s “doubling method” and its close association with Leibniz’s binary algorithm. With the new perspective created by the binary coding, he is therefore convinced that the Shao Yong-Leibniz sequence is indeed a substantial advancement in the overall ordering of gua in Yijing, and subsequently proposes an innovative approach enabling, extending and deepening Yijing studies.
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