## Thursday, September 20, 2012

### Sphere: Squared

In the diagram at right, each figure's cell is identified by two numbers: traditional sequence at upper-right, and scalar quantity at lower-left.
This 64-cell grid is arranged so that each cell is placed at 180 degrees of rotation from its logical complement.

Other ways of expressing this spatial relationship are that the complementary figures are maximally-separated, that they are antipodally-
positioned, or that they are diametrically-arranged .

Complementary hexagram pairs comprise a symbolic whole when their scalar values are summed, represented by the number 65.  Seen together, one figure will have YANG lines where the other figure has YIN lines.

In the diagram following, complementary relationships are also depicted by color pairs: RED with VIOLET, ORANGE with INDIGO, YELLOW with BLUE, or GREEN with GREEN.  Complementary pairs on the 8 x 8 grid are precisely analogous to antipodally-positioned hexagram pairs on any of the thirty-two spherical axes.

Key

RED + VIOLET = 2 polar cells (absolutely polarized)ORANGE + INDIGO = 12 cells (strongly polarized)
YELLOW + BLUE = 30 cells (weakly polarized)
GREEN = 20 equatorial cells (non-polarized)

Explication

RED and VIOLET figures establish a pole that vertically bisects the grid
YELLOW and BLUE figures are located close to GREEN and far from RED and VIOLET, thus they are weakly polarized: young, static, stable
ORANGE and INDIGO figures are located close to the RED and VIOLET polar figures, thus they are strongly polarized: old, dynamic, changing
GREEN figures horizontally bisect the grid, are located between BLUE and YELLOW, and are generally farthest from the poles; thus they are neutrally- or non-polarized

Classified per line-type count,

YELLOW and ORANGE have predominantly open lines and have YIN character
GREEN have YANG and YIN in equal measure
BLUE and INDIGO have predominantly closed lines and are YANG in character

NOTES:

Wen's traditional pairing schema is preserved within the xian tian arrangement.  Wen's pairs are defined as
1. a figure pairing with its figurate inversion where such inversion produces a figure different from the original; otherwise by
2. a figure mated to its logical negation, as in the case of (#01, #02).
Icosahedral characteristics
30 EDGES, 20 triangular FACES, 12 VERTICES

Dodecahedral characteristics
30 EDGES, 12 pentagonal FACES, 20 VERTICES

xiang::nucleotide bases: adenine + uracil  & cytosine + guanine
hexagram equivalent in RNA language: three nucleic acids :: codon :: hexagram

xiang::nucleotide pairing schema:

adenine: (INDIGO, old yang, 9) + uracil (ORANGE, old yin, 6)
cytosine (YELLOW, young yin, 8) + guanine (BLUE, young yang, 7)

ROYGBIV Color "octave"

Figures #01 and #02, located in the diagram at the high and low corners, are poles of the reference axis.  The remaining 62 paths, or 31 axes are "free"

Human peripheral nervous system comprises 31 nerve pairs

Tun calendar :: 18 * 20 = 360

Tzolkin calendar :: 13 * 20 = 260

20 * (13 + 18) = 20 * (31) = 620