解析大衍筮法及易卦的蓍占概率

The Structure of 64 Hexagrams in I Ching,Their Sequential Order from the Binary Arithmetic and Their Probability Distributions from the Yarrow Divination

邵雍的"加一倍法"及莱布尼茨所开创的二进制算法,当是对易卦整体排序的一大推进。然而邵雍和莱氏排序自上而下的计算有悖于规范的二进制算法。依据规范的二进制算法,易卦的"身份认定"应当从初爻到上爻来加倍计算,结果为数值排序。比较两种排序有助于洞察易卦的爻像结构,并为易卦的整体排序奠定基础。邵雍"加一倍法"的另一个贡献是指明每个六爻卦有64个变型,共4096种变化;其根源在于八个三爻卦,又各有八个变型。大衍筮法实质上是一个随机数发生器,筮仪过程得到的可变阴爻6、不可变阳爻7、不可变阴爻8、和不可变阳爻9的随机概率为十六分之(1∶5∶7∶3)。由此推算出整个易卦体系的概率分布,对于考察和计算易卦之间的联系及演变意义重大。

The author credits Shao Yong’s"Doubling Method"and the Binary Arithmetic initiated by Leibniz as instrumental in advancing the order sequence of hexagram system.Shao Yong-Leibniz Sequence however is calculated yaos in a hexagram top-down,which violates the normal binary arithmetic.The regular way should instead calculate them bottom-up,which entails the digital sequence.Comparing these two sequences sheds light to the structure of hexagrams,and lays a foundation for organizing all the 64hexagrams.Another contribution of Shao’s doubling method is the revelation of variations of hexagram indicating that there are 64variations of each hexagram.As the root of hexagram,each of trigrams has 8variations.The Yarrow Divination has an immemorially ancient root and was loyally followed in the long history of I Chingstudies over 3000years.The Yarrow Divination in essence is a random number generator.6,7,8,9,the four random numbers resulted from its procedure have the probability distribution of(1∶5∶7∶3)/16.This distribution is different from simplified methods in common applications of I Chingdivination.The probability distribution table is then accomplished,which will render substantial impacts in observing and interpreting hexagrams,and gauging changes among them.