Sustainability through Magically Dancing Patterns

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Sustainability through Magically Dancing Patterns
Interweaving 8x8 and 9x9 within 19x19
Distinguishing the 8x8 patterns within the 19x19 pattern
Consideration of any process of extension to a 9x9 "arrangement"
Possibility of a dynamic pattern methodology
"Dancing patterns"
Formation dancing: a "body-centered" alternative?
Cross, swastika variants and lauburu
Some dynamic pattern questions
Triangular representation of 64 I Ching hexagrams
Double triangular representation of hexagrams: Star of David
Patterns of possible interactions between linear and triangular configurations
Dynamics, resonance hybrids and Pascal lines
Mirroring, enantiodromia and the engine of change
Patterning 60 within 19x19
Relevance of 19x19 to annual calendar and associated cycles
Towards the specification of a pattern dancing applet
Sustainability: sudoku, go, chess, yantras, sigils and bagua
Sustainable "cognitive engine" and emergent "wisdom engine"?
Conclusions
References

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This exploration has been stimulated by exchanges with Ye Zude, Maurice Yolles, Chris Lucas and Peter Collins, none of whom should be held responsible for its essentially speculative nature.

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Introduction

This is an exploration of the interrelationship between patterns fundamental in different ways to cultures of the East and the West. Specifically the focus is on the 8x8 pattern constituted by the 64 hexagrams of the I Ching (Yijing) and the 9x9 pattern constituted by the 81 tetragrams (or quadgrams) of the T'ai Hsüan Ching (Tai Xuan Jing). These two sets of patterns have as their root the 3x3 pattern of the BaGua and the 4x4 pattern. The 3-fold pattern is fundamental to thinking based on the enneagram. The 4-fold patterns has been extensively explored from a Western perspective by Carl Jung and thereafter in such patterns as the MBTI. The 3x4 pattern is of prime significance to thinking based on 12, notably that developed by Arthur Young on learning/action cycles.

Much attention has been given to such patterns by the mathematically inclined through the challenge of so-called "magic squares" and the interesting arrangements of numbers which emerge as significant.

Also of relevance is the manner in which such patterns have become fundamental to two distinct board games. The Eastern game of go (Wéiqí) is based on a board of 19x19. The Western game of chess is based on a board of 8x8. Such games have been the focus of a considerable amount of computer-enhanced thinking.

This exploration follows from a series of earlier papers on the I Ching and the Tao Te Ching (9-fold Higher Order Patterning of Tao Te Ching Insights: possibilities in the mathematics of magic squares, cubes and hypercubes. 2003; 9-fold Magic Square Pattern of Tao Te Ching Insights experimentally associated with the 81 insights of the T'ai Hsüan Ching, 2006). Early concern for the challenge was articulated in Representation, Comprehension and Communication of Sets: the role of number (1978).

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