Tuesday, November 8, 2011

Xiantian Cube

depiction of xiang

Abstract: Investigating ways to derive the 4th-order cube from the ashtapada informed by notions of  xiang and complementarity.

At the center of the diagram following is an 8X8 field with colored bands.  This field of action (Sanskrit: kurukshetra) is also known as ashtapada.  The bands represent the xiang; alternatively, the oracular probabilities representing them when expressed as fractions of 64.  

Surrounding that field are four 4 X 4 sections.  These are intended to represent xiang.  They are presented with the intention of providing a static internal view of the assembled cube.  

The xiang sit on a 2 X 2 grid with axis labels in white.  The labels serve to explain the depiction of the xiang relative to the 2 X 2 grid and 8 X 8 field.

CREATIVE indicates YANG, while STRUCTIVE indicates YIN.
STATIC & DYNAMIC are related to the notion of action or change, and the background against which it must be observed.

also: 'event vs. environment,' 'figure vs. ground,' or 'text vs. context,' even 'nature vs. nurture.'

Wednesday, November 2, 2011

Jörmungandr-Ouroborus, the Tesseract

According to legend, Odin threw the serpent Jörmungandr into the great ocean (primal void or akasha) surrounding the plane called Midgard. The serpent grew so large as to surround the Earth.
This tends to confirm the truism that Earth is encompassed by 4-D space-time -- exactly that which is represented by the tesseract.


Jörmungandr is known in the Greek mythic  tradition as Ouroborus.  Both are commonly represented by a serpent biting (swallowing) its own tail.  Indeed, the name itself means "tail-eating," or self-devouring.  This is an apt description of what we see in the animated graphic at top left.

hypercube pendant
The deeper significance, hinted in the opening paragraph, is that our three spatial dimensions, plus the temporal fourth, constitute an eternal self-devouring subject which acts as our existential domain.
The photograph at left presents a three-dimensional object commonly presented in two-dimensions as a cross within a circle, known as the Sun cross, or Odin's cross.  It is used in astrology to represent the planet Earth.

"Since each vertex of a tesseract is adjacent to four edges, the vertex figure of the tesseract is a regular tetrahedron."  (source)