论《周易》古经卦序构造的数学原理——先天六十四卦到今本卦序的幻方推演

Mathematical Principle Conceived in the Later Heaven Sequence of the 64 Hexagrams:A Deduction of Magic Squares from the Former Heaven to the Later Heaven Sequences

用先天六十四卦的序数构建一个八阶幻方,要求非覆即变的两卦必须在幻方中上下相邻,互补数亦尽可能上下相邻。然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右至左、自下而上的顺序依次编号1-32,偶数行的三十二卦按从左至右、自上而下的顺序依次编号33-64,从而使上下相邻的两卦既非覆即变又互为补数,即可得到一幅迭代图。取此迭代图中的六十四卦序号,遵循上下两卦非覆即变且互为补数的原则,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,总共可以得到九个幻方和九幅相应的迭代图,之后便进入循环。其中,居中的第五个幻方按特定方式展开,即是按今本卦序排列的上经三十卦和下经三十四卦。笔者认为,这是目前所知的今本卦序最简单的构造原则,也应当是《周易》古经卦序的真实来源。

Construct an eight-order magic square according to the ordinal number of the Former Heaven sequence of the 64 hexagrams,in which the two hexagrams based on the principle of inversion or conversion must be put in vertically adjacent positions and complementary numbers ought to be put in adjacent positions as far as possible.Then iteratively renumber the hexagrams in the magic square,the 32 hexagrams in odd-numbered rows being numbered consecutively from 1-32 from right to left and from the bottom up,the other 32 hexagrams in even-numbered rows being numbered consecutively from 33-64 from left to right and from top to bottom,thereby making the two adjacent hexagrams be in inversion or conversion and their numbers be complementary,by which we can get an iteration table of permutation of the 64 hexagrams.Taking the sequence number of the 64 hexagrams in this iteration table,abiding by the rule of inversion or conversion,and making the numbers of the two vertically arranged adjacent hexagrams complementary,we can obtain a new magic square,then we can derive another iteration table.Repeating the previous procedure,we can get overall nine magic squares and nine relevant iteration tables being in cycle,among which the fifth magic square will unfold in a particular way,i.e.,the sequence of the 64 hexagrams in this magic square is identical to the sequence of the 64 hexagrams in the received version of Zhou yi.The author holds that this is the simplest principle of construction of the sequence of the 64 hexagrams in the received version of Zhou yi as is known,which ought to be the true source for this received sequence of the 64 hexagrams.