Monday, February 13, 2012

I Ching in 3-D

The presented diagram depicts the 8 x 8 field known as ashtapada. The colored bands represent the oracular probabilities corresponding to the four xiang (symbols). In this entry, the author extends the notions implied by this diagram into three-dimensions through the use of 64 colored cubes.

The idea is simple: a cube has six faces; while an hexagram has six places, commonly denoted as bottom2nd3rd4th5th, and top.  Each cube face, therefore, may represent one place of an hexagram and its associated text.

representation of xiang
Tradition asserts that bottom place is nascent, and top place is retiring.  It follows, therefore, that the bulk of a hexagram's meaning or action is found in the middle of the hexagram, sometimes called a 'tetragram'.  These four middle places of the hexagram, akin the four walls of a room, correspond to the four sides of a cube; corresponding furthermore, to the four seasons, four cardinal directions (xiang), four elements, four tarot suits, or any other quaternity.

Since the oracular probabilities are depicted by the colors, all that remains is to devise unambiguous means of associating a particular cube face with an hexagram place.  
We may appropriately mark the six faces, 1) to indicate the relative positions of the faces, and 2) to determine their yin or yang character, and perhaps, 3) with its index (for easy reference).  This permits us to determine easily the quality of the upturned face when a cube is selected.

Proceeding to appropriately label each of the 384 cube faces, we now have a device whereby the identity of an hexagram is determined by the unique configuration of its faces. Simultaneously, that same cube indicates by its color if the upturned face is a changing line or static.  Alternately, six cubes may be selected blindly with replacement to generate an hexagram line-by-line with color alone as an the line-type indicator . 

Addendum (26April12):
Yarrow Oracle
The author has fashioned for himself a compact set of divination cubes that are functionally equivalent to the yarrow oracle.   Since the yarrow probabilities reduce to multiples of 1/16, four colors in the proper proportions reproduce the oracle.  Six cubes are selected individually and randomly with replacement.  Further, the author employs a webcam to film a blind-selection procedure to reduce the possibility of inadvertently influencing the outcome while divining.

Human Body: the Field of Action

Vastu Purusha mandala over ashtāpada
In the graphic at right, Cosmic Man, Purusha; the "enjoyer of the field of activity" is overlaid on ashtapada, the 8x8 grid.  He is positioned face-down, his head pointing toward North-east.  It should be noted that in the Manduka mandala the Vastu Purusha is depicted with the head facing east and the feet facing west.  Here, grid-points along the NE-SW main diagonal enjoy congruence with the seven chakras.

Ashtāpada, the uncheckered 8 × 8 board, is presumed to be of Hindu derivation.  The literal meaning of ashtapadi is "eight steps." This word is the origin of the word ashtāpada, an Indian board game, the forerunner of chess. The word now primarily refers to the board itself.

The 8 x 8 grid, ashtapada, manduka, or chandita mandala, is regarded by several sources to represent a "field of action[1]."
Ashtapada is depicted here as four concentric square bands with areas of 28. 20, 12, and 8 units relative to the whole. The areas of the four banded regions are precisely mirrored by the divination probabilities given by the yarrow-stalk oracle commonly used to consult the Book of Changes.  

Vastu Purusha mandala presents Purusha over the 8 x 8 grid, implying that the grid symbolizes Purusha's dwelling-place, or Prakriti, the material body or world, material contrast to Purusha.  Furthermore, when Purusha (Cosmic Man, Universal Soul, or Atman) is positioned on the ashtapada, the grid can be said to represent the human body -- which is itself considered a "field of action," or "kurukshetra[2]."  

When the divination ritual numbers (6, 7, 8, and 9) and their respective divinatory probabilities (4, 12, 20, and 28 taken as fractions of the 8 x 8 field) are treated as vectors and the inner-product taken between them, the result is the "perfect" number 496.  We can regard this number as a defining characteristic of ashtapada within the context of I Ching divination.

We may again relate 496 to the human body because the body possesses 31 pairs (or 62) of spinal nerves.  The prime factorization of 496 is 31 times 16 which is also 62 times 8; thus 62 is the octopartition of 496, which number defines the divination field; the field, in turn, representing the human body.

  • Related to the game Chaturanga: (Skt: "four-limbed"), ancestor of modern chess
  • Related to Manduka/Chandita mandalas
  • Populated by the 64 hexagrams, it represents 2080
  • Overlaid by xiang probability bands, it represents 496, the third "perfect number"
  • Kurukshetra (site of the war in Mahabharata)
    • kuru, from the Sanskrit root kri="work, material action" and ksetra="field".  This "field of action" is the human body with its physical, mental and soul faculties, the field (kurukshetra) on which all activities of one's life take place. 
    • Characterized as a "field of activity," indicating the body, or even the World, suggesting metaphoric identity relation between these
    • References
      • Bhavagad Gita: ch. 13, v1-2
        • Arjuna said: O my dear Kṛṣṇa, I wish to know about prakṛti [nature], puruṣa [the enjoyer], and the field and the knower of the field, and of knowledge and the object of knowledge.The Supreme Personality of Godhead said: This body, O son of Kuntī, is called the field, and one who knows this body is called the knower of the field.
      • Ta Chuan pt.1; ch.11; v.5-6
        • Therefore there is in the Changes the Great Primal Beginning. This generates the two primary forces. The two primary forces generate the four images. The four images generate the eight trigrams.  The eight trigrams determine good fortune and misfortune. Good fortune and misfortune create the great field of action.
      • Foundations of Oriental Art and Symbolism, ch. 9, "Symbolism of Chess" 
        • The form of the chess-board corresponds to the "classical" type of Vāstu-mandala, the diagram which also constitutes the basic layout of a temple or a city. It has been pointed out[3] that this diagram symbolizes existence conceived as a "field of action" of the divine powers.