Tuesday, April 10, 2012

Dodecagonal Depiction of Change

The author revisited yao-numbers, recalculating them based strictly on the divination ritual values of Ch'ien (9) and K'un (6).

The outcome is a distribution that naturally accords with the combinatorics of a 6-bit system.  
There are seven groups with the following distribution: 
[1 6 15 20 15 6 1].
This is a departure from the prior distribution of yao-numbers, which incorporated 9 groups: 
[1 3 6 12 20 12 6 3 1]

the author had the recent fortune to discover a website that treats systems like Change (and the genetic code) in some depth. That author makes the unqualified claim that the genetic code is a dodecahedral system.  The Book of Changes, again, is based on the same underlying grammatical components (four basic elements, arranged in triplets).  One tremendously useful product of the website is the depiction of the genetic code on a dodecahedron (12-faceted Platonic solid).  Several tools and perspectives are additionally presented to facilitate pattern-recognition.

The current author observes that the array [1 6 15 20 15 6 1] can also be depicted as [2 12 30 20] when that array is "folded" on the central value (20).  What we find is that at least three of the values of the resultant array find direct correspondence to attributes of a dodecahedron, perhaps confirming the author's claim.

Dodecahedra have 20 vertices, 30 edges, and 12 pentagonal faces.  The array value of '2' is not nearly as unambiguous, but could correspond to symmetry axes or polarity.  An arrangement suggested by the author of the mentioned website involves four (tetrahedral) poles corresponding to the four genetic nucleotides.  

In the Book of Changes, four corresponding elements exist called symbols (or xiang). When we computed the Wen distribution based on the divination ritual values of xiang (6,7,8,9), no correspondence (to date) is found with any real-world objects.  
Conversely, when we computed (as described in the open paragraph) the Wen distribution based on 6 and 9 (the ritual values of Ch'ien and K'un), the characteristics of a dodecahedron emerge as just described.  This is the rationale for asserting that the value '2' in the array [2 12 30 20] may indicate the number of poles to incorporate in the dodecahedral depiction of the Book of Changes. 

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