Deciphering Wen - Exploring the Structure of The i-Ching - J.M. Berger

King Wen Pair Symmetry in Fu Xi King Wen's sequence is ordered into pairs. Each pair is clearly related to the other member of the set; the hexagram is either inverted or rendered as its yin-yang opposite. But the pairs are also presented in a specific order which has, thus far, proven mathematically impenetrable. The King Wen's circular arrangement of the eight trigrams is similarly difficult to explain structurally. ​ I propose that the Fu Xi (aka Earlier Heaven) and Lo Shu (later heaven) circular arrangements are key to understanding the King Wen pairing scheme. The Fu Xi arrangement is known as the "primal" sequence. The circular diagram can be used as the basis for grid (example). The resulting eight-by-eight chart orders the hexagrams according to their binary values. Within that 8x8 grid, I drew a simple line between each set of pairs, i.e., 1 to 2, 3 to 4, 5 to 6, etc. The result is shown below (rotated 45 degrees to highlight its symmetry). The colors in this figure were chosen to highlight the extraordinary vertical and horizontal symmetry of the diagram. The red lines are perpendicular, blue lines are at acute or obtuse angles, and the yellow indicates overlapping lines. UPDATE: I am not the first person to find this pattern. Bradford Hatcher published a black and white version of the diagram in "The Book of Changes: Word for Word" (1997). As Brad points out, given the age and amount of study devoted to the i-Ching over the centuries, we're probably not the first ones to find it either... The same illustration with the upper (hexes 1-30) and lower canons (31-64) in red and blue respectively. This illustration may go to the ordering of the hexagram pairs in King Wen. There is a broken symmetry between the upper and lower canons. The upper and lower canons are symmetrical to each other, except for following hexagram pairs, which break the quadrant symmetry: 23-24 (Mountain, Earth and Thunder); 47-48 (Lake, Water, Wind); 49-50 (trigrams Lake, Fire and Wind). The pairs 7-8 and 13-14 (Water and Earth, Heaven and Fire) break the upper-lower symmetry across the horizontal axis. They are symmetrical to each other. There are also pair sets that break overall symmetry, but not visibly, because they overlap perpendicular lines on the chart above. These include 21-22 (Fire, Thunder, Mountain); 51-52 (Thunder and Mountain), 57-58 (Wind and Lake), 31-32 and 41-42 (Lake, Mountain, Thunder, Wind). In total, four hexagram pairs from the upper canon break symmetry, and six from the lower canon. The lower canon contains four more hexagrams than the upper. If one places the symmetry-breaking pairs in their own category, one is left with two canons of 22 hexagram, and a "special" canon of 20. The hexagram pairs featuring doubled symmetrical trigrams (1-2, Heaven and Earth; 29-30, Water and Fire) are symmetrical on the diagram. The hexagram pairs featuring doubled asymmetrical trigrams (51-52, Thunder and Mountain; 57-58, Wind and Lake) are asymmetrical on the diagram. There are also four pairs which visually break the symmetrical logic of the arrangement in terms of upper and lower canons without accounting for directionality -- 3-4, 21-22, 35-36 and 51-52. These are highlighted in yellow below. The outer arrows are of particular interest in terms of directionality. Highlighted below (in indigo and yellow) are two sets of arrows where symmetry breaks occur in terms of the direction of the arrows. The arrows originating with strong yang hexagrams (1 and 11) have a direction that projects from the hexagram location, consistent with yang properties. The yin arrows, interestingly, do not simply reverse this polarity. In the yin arrows for hexagrams 2 and 12, the direction of the arrows shows that yin is a step along the path rather than being the destination of the path. Yin receives according to its traditional properties, but it also releases -- it is transient. This always-projecting vs. step-on-the-path structure may reflect (or account for) the prioritization of yang over yin on the basis of yang being eternal (celestial) and yin being transient, or "weak" in Taoist philosophy and other yin-yang based schemes. The dynamic can be seen more clearly as below, where all the non-relevant arrows have been removed. I believe the implication of this design reflects sequential time. From a yang posture, events (or energy, chi or whatever is being discussed) proceeds in every direction simultaneously. In contrast, events (or energy) pass through yin as one stage in a sequential -- and therefore temporal -- process. This suggests a princple of physics that logic also suggests -- to perceive the passage of time, there must be a stationary (or timeless) frame of reference that can be perceived for comparison purposes. (The stationary frame may only be timeless in relative terms, at least from a physics perspective.) The upper and lower canons are shown separately below. The upper skews to the left, and the lower skews to the right. There is no immediately discernable structual or systemic pattern to the ordering within each pair (i.e., why 1-2 instead of 2-1). There are narrative solutions, but the i-Ching inherently lends itself to narrative interpretation, so it's probably best not to read too much into this. However, it's worth noting that the diagram appears to reflect a mostly even, almost crystalline, balance of yin and yang. Pair symmetry in King Wen's circular diagram (Later Heaven)		I-Ching Links Hexagram Finder Hexagram Sequences Online I-Ching Readings Chaos Tarot (fractal tarot based on i-Ching) Egoplex Sites Egoplex Chaosdancer Quantum Chakras Intelwire JMBerger.com By J.M. Berger (As Contributor) (Click to Buy) (As Contributor) (Fall 2007)
About this site I'm J.M. Berger. I'm a freelance writer covering a wide variety of topics, including religion, spirituality and religion-science convergence. This site is devoted to a personal obsession of mine -- figuring out the logic that informs the King Wen sequence of the i-Ching. I hope you enjoy it. I have other Web sites relevant to this material, which are linked above. All text, images and Web design (C) 2006, J.M. Berger, all rights reserved.berger@egoplex.com for permissions. http://iching.egoplex.com/fuxi-pairsymmetry.html {tbody}{tr=top}{td=colspan:2|@x300} About this site I'm J.M. Berger. I'm a freelance writer covering a wide variety of topics, including religion, spirituality and religion-science convergence. This site is devoted to a personal obsession of mine -- figuring out the logic that informs the King Wen sequence of the i-Ching. I hope you enjoy it. I have other Web sites relevant to this material, which are linked above. All text, images and Web design (C) 2006, J.M. Berger, all rights reserved.berger@egoplex.com for permissions. http://iching.egoplex.com/pairsymmetry.html{/td} {/tr}{/tbody}{/td}{/tr}{/tbody} King Wen Pair Symmetry In an earlier discussion, we looked at pair symmetry in the Fu Xi square derived from the primal order circular diagram. You may find it useful to glance over that article, if you haven't already, since this one refers back to the Fu Xi diagrams. ​ The following images show the King Wen hexagram pairs as they lie on the 108 Cross grid (right), which is derived from the Later Heaven circular arrangement (sometimes called King Wen's circular arrangement). In these images, a single line joins each hexagram pair, according to the King Wen numbering of all 64 hexagrams. In all these images, the grid has been rotated 45 degrees to display the symmetry. I built the 108 cross grid from left to right while attempting to mimic the circular arrangement, but it's possible it should be mirrored or inverted to be read appropriately. (Chinese writing runs right to left, and hexagrams are built bottom to top. Either way, there are issues in turning a circular diagram into a straight line). Unlike in Fu Xi, the pair symmetry in King Wen is only vertical, not horizontal. (As long as the upper and lower trigram sequences in the 8x8 grid are identical, some form of symmetry will emerge.) The image below shows perpendicular lines in red, and angled lines in blue. The following animation shows the pairs being drawn in their numerical order. (Reload page to restart animation.) There is no immediately apparent reason for this sequencing. The graph below shows the numerical 108 Cross grid, illustrating the numerical associations with each line. The logic of pair-ordering is illuminated somewhat by this arrangement. Here's a look at the grid with arrows indicating the "direction" of the pair (i.e., 1-2 has an arrowhead pointing at 2). Suddenly, a sharp predisposition emerges. Although not perfect, there is a clear predisposition for the sequence to point to the right. Like flipping an hourglass, having yang on the bottom and yin on top allows yin to sink and yang to rise, mixing to create temporal order. Note that the careful arrangment of the hexagrams from Fu Xi (as highlighted in the previous section) has been completely disrupted, even more so that the shape of the diagram might suggest. Since the arrow-heads are "yin" (even numbers), this suggests an overlay with the yin-yang diagram that points out the dynamics of the King Wen system. Yin and yang wax and wane in this diagram. The arrows which reverse the overall trend of direction tend to deal thematically with reversals or the fruition of one cycle in preparation for a new one. (Forgive the flipping of the diagram unpredictably.) The image below is inverted. The top yellow dot is the version of the graph below shows location of the Heaven (1) hexagram -- pure yang. The lower yellow dot is the location of the Earth (2) hexagram -- pure yin. Red and blue indicate angles here and not the canons. The Tai Chi is shrunken here for reasons that will become apparent further down. Every single non-perpendicular line that crosses the vertical axis falls in the yang part of the diagram. None below the center line (the midpoint between heaven and earth) crosses the vertical axis. This suggests that the intersections have something to do with the nature or activity of yang. The white cross in the center of the illustration below shows the relationship between two critical hexgram pairs -- 1 and 2, pure yang and pure yin; and 63 and 64, already settled and not yet settled, which represent the pure blending of yang and yin. Above the 1 and below the 2, bounding the circle, are 29 (water, dark yin) and 30 (fire, bright yang). Let's turn it upside down again to its (presumably) correct orientation (yang down). As we plug in more hexagrams, the organizational logic begins to emerge. Yang and yin fall into place according to the diagram. Some hexagrams extend outside the circle of the Tai Chi symbol here. At the four compass points, yin and yang are deeply mixed -- Fire and Water at north and south, Not Yet Settled and Settled at east and west. While it would be premature to get into detailed speculation about the hexagrams outside the circle, I would suggest that the extension represents the interlocking mechanism by which one yin-yang cycle can evolve into or interact with a new one. For the i-Ching to represent the structure of reality, the system can't be self-contained. It must be able to propagate and expand into more elaborate structures. These are just some initial thoughts on this aspect. I will post more after I've had time to think about it for a while. Other Variations All variations (shown below for comparison purposes) also maintain some amount of symmetry as long as the upper and lower trigram sequences remain the same. That doesn't mean that all the possible variations of this mandala are equally meaningful, of course. The arrangement for Fu Xi was the only one out of several trials to display both horizontal and vertical symmetry, which is also highly suggestive of design. I expect there are a couple other possible variations which would be horizontal on both axes. In the white design, there are nodes of increased intersection but the significance is not as clearly related to the hexagrams as in the King Wen version of the chart.   I-Ching Links Hexagram Finder Hexagram Sequences Online I-Ching Readings Chaos Tarot (fractal tarot based on i-Ching) Egoplex Sites Egoplex Chaosdancer Quantum Chakras Intelwire JMBerger.com By J.M. Berger (As Contributor) (Click to Buy) (As Contributor) (Fall 2007)