Toroidal mappings of wisdom questions and answers

Enabling Wisdom Dynamically within Intertwined Tori (Part #2)

[Parts: First | Prev | Next | Last | All] [Visuals] [Links: To-K | From-K | From-Kx | Refs ]

It is intriguing that engagement with "wisdom" can be explored through the questions which are the primary characteristic of each of the 48 koan. In that culture they can, alternatively, be explored through the nature of the answers which are a primary characteristic of decision-making in relation to the conditions indicated by the 64 hexagrams of the I Ching. There is of course a degree of debatable ambiguity in this distinction raising the issue of the nature of question and answer in relation to wisdom. Potentially interesting is then the possibility of relating the mapping of 48 koans to a mapping of the 64 hexagrams of the I Ching.

Unique amongst simpler polyhedra is the drilled truncated cube, a toroidal polyhedron with 64 edges (one of the Stewart toroids) onto which the 64 hexagrams can be mapped. There are of course various translations of the hexagram names (cf List of hexagrams of the I Ching in Wikipedia). The names mapped into the image below derive from an extensive adaptation identifying the "causal loops" by which the conditions indicated by the hexagrams are traditionally related (as noted above).

Drilled truncated cube of 64 edges with hexagram names (some faces transparent, see other variants below)

By contrast, but also unique amongst simpler polyhedra, is the drilled square bicupola of 48 edges, a toroidal polyhedron with 64 edges (another one of the Stewart toroids) onto which the 48 koan can be mapped as shown below. As with the drilled truncated cube, "drilled" implies a central hole -- as with any ring-shaped torus.

Curiously both structures, although complex to describe, are relatively easily to comprehend when viewed -- especially by rotation in three dimensions.

Drilled square bicupola of 48 edges (different views with different faces transparent)

[Parts: First | Prev | Next | Last | All] [Visuals] [Links: To-K | From-K | From-Kx | Refs ]