Tuesday, October 12, 2010

Quantifying Change: Conjecture

Quantifying Change: Conjecture

One feature of the King Wen sequence particularly intrigues the author: Changes (expanded first-order differences) are defined over the ordered set of Wen pairs; this apparently causes the Changes to reproduce the King Wen sequence.  In the table of Changes following, as one reads across the vertical columns and down the rows in order, the Changes replay the King Wen sequence of the hexagrams with increased detail at the level of the individual hexagram lines.  The Change operation effectively recovers information about the internal statics and dynamics of the hexagram figures.  This recovered information allows us to derive the yao-numbers corresponding to the sixty-four hexagrams.  The yao-numbers, in turn, give us a means to quantify and categorize Change.
We term a pair 'unbalanced' when the yao-numbers of the pair-members are unequal.  Such unbalanced pairs appear four times in I Ching:  [1,2], [27,28], [29,30], and [61,62].  The hexagrams composing these pairs, incidentally, do not produce one another through fangua or hexagram inversion (reversing the order of the lines); they employ pantonggua (complementary opposition) to form a pair.  

King Wen pairs each seem to represent extremes of a continuum, since we can always determine the other half of a Wen pair provided we know the generative rules.  The Gates of Change, Chi’en and K’un, are the “father and mother” of the cosmos, but each King Wen pair can be similarly seen as constituting its own cosmos or continuum.  The self-similarity that permeates the actual world appears to be re-enacted via the relationships that obtain through the Change operation.

Now complete, how can we validate these findings?  What, if any, assurance have we that the Changes have a reflection in consensus reality?  Can we find corroboration of these findings there?

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