今本卦序到《杂卦》卦序的幻方推演

A Deduction of Magic Squares from the Sequence of Hexagrams in the Received Version of Zhou yi to the Sequence of Hexagrams in the Zagua

将《周易》古经的三十二对非覆即变之卦按照从左至右、自上而下的顺序依次填入纵横各有八格的方阵中,要求非覆即变的两卦必须上下相邻。然后将奇数行中的三十二卦按从左至右、自上而下的顺序依次编号1-32,偶数行的三十二卦按从右至左、自下而上的顺序依次编号33-64。接下来,把按如上编号的六十四卦排入纵横皆八的方阵中,构建一个八阶幻方。之后采用迭代的方法给幻方中的各卦重新编号,奇数行的三十二卦按从左到右、自上而下的顺序依次编号1-32,偶数行的三十二卦按从右到左、自下而上的顺序依次编号33-64,即可得到一幅迭代图。取此迭代图中的六十四卦编号构造新的幻方,然后采用相同的迭代规则又可以导出一幅迭代图。重复上述步骤,总共可以得到十五个幻方和十五幅相应的迭代图,之后便进入循环。最后,令幻方八中的各卦上下体互换,再按从左至右、自上而下的顺序横向展开,即是《杂卦》卦序。笔者认为,这是迄今为止对《杂卦》卦序最为详尽的解说,也应当是《杂卦》卦序的真实来源。

Fill the 32 pairs of hexagrams based on the principle of inversion or conversion in a square which has eight grids horizontally from left to right and verticaly from the bottom up in which the two hexagrams in each pair must be put in vertically adjacent positions. Then number the 32 hexagrams in odd-numbered rows consecutively from 1-32 from left to right and from top to bottom, the other 32 hexagrams in even-numbered rows being numbered consecutively from 33-64 from right to left and from the bottom up. Construct an eight-order magic square by putting the numbered hexagrams in a square having eight vertical and horizontal grids. Then use interative method to renumber the hexagrams in the magic square, the 32 hexagrams in odd-numbered rows being numbered consecutively from 1-32 from left to right and from top to bottom, the other 32 hexagrams in even-numbered rows being numbered consecutively from 33-64 from right to left and from the bottom up, we can get an interation table. Take the sequence number of the 64 hexagrams in this interation table to obtain a new magic square, abiding by the same interative rule, we can get another interation table.Repeating the previous procedure, we can get overall fifteen magic squares and fifteen relevant interation tables being in cycle. Finally, exchanging the above and below trigrams’ position in each hexagram and then unfolding the square from left to right and from the bottom up, we can get the hexagram sequence in the Zagua(Hexagrams in Irregular Order). The author holds that this is the most detailed explication of the hexagram sequence in the Hexagrams in Irregular Order, which is ought to be the true source of this sequence of hexagrams.