Octopartition pt. II

This uncommon term is used to describe the act of dividing a thing into eight sections, called octants; colloquially, "pieces of eight."  I Ching lends itself well to illustrating the notion since it can be octo-partitioned twice in succession as the following graphic depicts.

The largest cube represents I Ching as a holism.  The mid-sized cube represents Ba Gua (one of the Eight Diagrams), a three-line figure or trigram, two of which, when arranged in superposition, produce an hexagram.  The smallest cube, its six faces standing for the six lines, represents an individual hexagram out of the 64 that comprise the I Ching.

Octopartition pt. I

The figure on the right is a representation of the Mayan One God Hunab-Ku.  According to Dr. C.J. Calleman, author of Purposeful Universe, other names given to this supreme entity of the Maya include Eight-Partition Place, the One Giver of Movement and Measure, and the One Giver of Energy and Boundary.  This notion of eight partitions or octopartition would present itself again.  It should be mentioned that Hunab-Ku is not regarded as an individual being, but as all BEING, the fundament of all existence.

Similarity between this hand-fashioned wireframe model at left and the 2x2x2 binary hypercube suggests itself.  Likewise, there is similarity between the process of fashioning the wireframe model and Taoist cosmogony:

• Measuring, closing a strand of wire (differentiation, singularity)
• Twisting (Great Axis) a loop yields two loops (Two First Powers)
• Two loops intermingle to produce quadrants (Four Symbols)
• Twisting a orthogonal third axis results in octopartition (Eight Diagrams or Ba Gua)

Binary hypercube

Three loops, three axes, three operations are needed to create space from a singularity.  It should be mentioned that the Taoist conception of nature is represented by Man, positioned or crucified "at the crossing" of Heaven and Earth.  These three are explicitly termed the Three Operations in The Great Treatise; we now have some idea of the reason for this terminology.

Octopartitioning is arguably special because it encompasses all spatial directions -- up, down, and all the cardinal points.  If one considers the Origin (the point at the center of the cube, within is also represented.

from "Purposeful Universe"

Astrophysicists have reportedly determined that the Milky Way galaxy is similarly octopartitioned by the orbit of the Earth as it travels about the galactic center.  




Thus, a galaxy, our Earth, or any physical object may be visualized or modeled by means of the octopartition.  Indeed, navigation makes extensive use of this feature.

Hand-wrought copper wire

In theory, the number of partitions could have continued to double indefinitely; this is one reason why they do not: with only Three Operations on a simple closed loop, we have the basis of matter and phenomena to be allotted discrete locations in space and enter Being from non-existence.  No additional dimensions are necessary to support the emergence of Humanity with its power of Consciousness coupled with its ability to undergo Experience.

Thus, an octopartition represents akasha, or space, but what about time?  Time implies Change, else it is pointless to measure time.  
In order to represent the fourth dimension, we must account for Change, but how?  
The answer: repetition.  That is, to arrange two similar objects to represent the first object both before and after a change as depicted in the graphic at right.