## Tuesday, July 5, 2011

### Taoist Cosmogony pt. II

To recap, the two First Powers interact to produce the Four Symbols.  The Four Symbols intermingle with the two First Powers again to produce the eight diagrams, or Ba Gua.

 arbitrary Ba Gua
Observe that the Ba Gua effectively combine to produce an octo-partitioned space in three dimensions.  The binary metric space allows for two values per dimension.  One of the Ba Gua is depicted here, with each of its corner given as a triplet of binary digits.

Three binary axes combine to yield 2 x 2 x 2 = 8 partitions in the metric space we've defined.  Each of the eight partitions may then be visualized as a cube.  The eight partitions also can represent the Ba Gua as eight cubes.

 Eight Ba Gua comprise an hypercube,

These 8 cubes come together at a common vertex (ORIGIN) to form a composite cube of a higher order, or hypercube.    Each of the eight Ba Gua cubes contributes one distinct corner to the higher-order composite cube.  A vector (path) drawn from the ORIGIN to each of the 8 corners of the hypercube defines direction in space and the bounds of the space.  If all eight paths measure equally, a spherical space results.

 Hexagram, Trigram, I Ching
Movement between corners indicates motion, or CHANGE.  Note that all observable phenomena are intrinsically based on motion.  Consider that we can't really observe something that does not change, and if we were to try, what would be the point?  Most interesting matters involve CHANGE, and understanding CHANGE is the whole point of I Ching.