A hexagram is not a static form. It symbolizes a moment of frozen time. As time moves on so the hexagram changes. The full cycle of change is from a hexagram to it's structural opposite. But there are steps inbetween; There are points of balance.
For each hexagram, one can locate it's movement by:-
01 --> 11 --> 12 --> 02 --> 01 ...
Each pair of complements are the balance points of the other pair. e.g. [01,02] complement and therefore balance [11,12]. [11,12] are the structural balance points of the trigrams within [01,02]. The relationship of each set to the other can be treated both structurally and procedurally; the latter manifest in a movement around the circle and the former as one pair opposite and therefore balancing the other:
01
|
|
11--------+--------12
|
|
02
There is a common theme here in that these two modes of interpretation (balance/circumvent) are reflected in the traditional diagrams of early(opposite/balance/still) and late(circumvent/move) heaven, and continue the manifestation of the structural and the procedural wrapped into one.
By adding the concept of time, we can map these circles in the form of sine waves. In this we find that, for any set of pairs, the direction of movement changes. For example, in the pair 1,2 the direction of movement is left to right (Clockwise on the circle), whereas in the pair 11,12 the movement is right to left(Anti-Clockwise on the circle), although the order of the hexagrams is fixed for both. The sine wave is a template onto which we can place hexagram sequences. We can form a 12 point template thus:
*04
/ \
/ \
*03 *05
/ \
/ \
*02 *06
/ \
/ \ /
--*01---------------*07---------------*01--
/ \ /
\ /
*08 *12
\ /
\ /
*09 *11
\ /
\ /
*10
A sine wave template
Having derived the quartet patterns, one can insert other hexagrams within the sequence. For example, in the group (1,2,11,12) which is ordered 12 <-> 01 <-> 11 <-> 02, we can introduce hexagrams that are structurally inbetween the primary hexagrams of the group. This gives us the sequence (left to right) 12,33,44,01,43,34,11,19,24,02,23,20,12,... We find that this specific sequence infact consists of the twelve hexagrams traditionally associated with the seasons, the standard order of which is 19,11,34,43,01,44,33,12,20,23,02,24. In this sequence January is associated with hexagram 19 and December associated with hexagram 24 (Northern Hemisphere). This sequence 'maps' onto the sine wave starting at position 8 for hexagram 19, and then moves right to left, backwards in our language.
It is possible to create a sequence for each group of four hexagrams, which, as we will see, gives us a unique ordering of the hexagrams onto which can be overlaid the sine wave. Using the sine wave, the maxima (peak) and minima (trough) are associated with the current pair under review, with the 'balanced' pair being on the x-axis. The sine wave acts as a template of time in order of :
balance-increase-peak-decrease-balance-decrease-trough-increase-balance
The increase/decrease markers are reversible on direction.
Having come up with the sets of four hexagrams, I recalled a diagram and some comments regarding 'mutating hexagrams'. This is in chapter 9 of Diana ffarington Hook's book "The I Ching and Mankind". She gives as her reference the work of W.A.Sherrill titled "Heritage of Change" (I have some of his work with W.K.Chu but not this text). The diagram used gives the order for hexagram 01 as:
As we can see, this is the same order as I have used but with a different start point, it moves backwards, and there is no sinosodial emphasis. By mapping to a sine wave the cycle of behaviour becomes more apparent. Note that this sequence moves backwards whereas in my sequence, for 01, we move forwards. Closer examination shows that Sherrill's sequence results from the changing of line position values, one at a time, from the bottom up through a full cycle (originating hexagram to originating hexagram). For example in Hook/Sherrill's sequence for hexagram 11 the same process as for 01 is performed, starting with a root hexagram, each line is changed from the bottom up giving a sequence of hexagrams.i.e.
11 ,46,15,02,16,45,12,25,10,01,09,26,11
root change line: 1 2 3 4 5 6 1 2 3 4 5 6
Change line 1 of 11 gives 46. Change line 2 of 46 gives 15 etc. Hook/Sherrill's diagram gives this pattern for all hexagrams as roots.
The sine wave sequences are subtly different in that some work top down (e.g. the 01 set) and others bottom up. Furthermore, there is a variation of this in that the group analysis work shows sets of 4 hexagrams that can join other sets. For example, in the 1,2,10,12 set, group analysis shows (see chapter 1 page 20) an association with the 10,15,19,33 set. This suggests an eight point sine wave:
*01
/ \
/ \
/ \
*15 *19
/ \
/ \
start / \ /
--*12-------------*11-------------*---
/ \ /
\ /
\ /
*10 *33
\ /
\ /
\ /
*02
An eight point sine wave template
This reflect the 'flow' of highs and lows. As the wave moves to the left (or right) the next point becomes the maxima and it's complement the minima. (e.g. In the above, if the wave moves left one point then 15 becomes the maxima and it's complement 10 the minima. This causes the other balancing pair, 19 and 33, to take on the 'balance' points on the 'x' axis replacing 11 and 12).
From this analysis we can create a full sequence:
12, 15, 01, 19, 11, 10, 02, 33, 12,...
From the group analysis, the above numbers associate with the BALANCE line of the groups. This is complemented by the LIKENESS line. Therefore we can create a sixteen hexagram sequence:
12,15,01,19,11,10,02,33,12
44,07,25,36,24,13,46,06,44
44,12,07,15,25,01,36,19,24,11,13,10,46,02,06,33,44,...
For now I will continue with the sine wave as I have mapped it. I place the balance hexagrams along the x-axis. With Sherrill's concepts, I have added the relevant sequence to the details on each hexagram, and it is of interest to note that Sherrill's sequences can be mapped to the sine wave with the same behaviour in that each point on the y-axis (vertical) when extended through the wave has two intersect points that are numerically in sequence ((11,12), (44,43) etc). To get Sherrill's sequences (which are relative to each hexagram rather than groups of balanced fours) to map to a sine wave and maintain the balance concepts, we allocate the 12 sine wave positions in the following order for all of Sherrill's sets:
This methodology categorizes the current hexagram and it's complement as the maxima/minima regardless of their 'fixed' nature. Furthermore, if we take the sequence associated with hexagram pair 1,2 as a template, then each hexagram in each sequence is that sequence's 'mirror' of the template. For example, in the first sequence, hexagram 19 (Approach) symbolizes January if we interpret the sequence as the set of calendar hexagrams. In this context, in any sequence, the hexagram at sine position 08 relates to the whole sequence as does the january hexagram to the other calendar hexagrams (the near end of winter prior to the crossing (11 - stillness with potential) into the coming summer. This path moves backwards. At the height of summer (01) the return of winter is the return of the contractive (yin) through 44 and then 33 and then the crossing into the winter phase through 12 (Stillness only) heading down to 02.
To use the southern hemisphere we just need to swap the calendar associations (19 becomes associated with July.). In this context, the sequence for hexagram 03 has hexagram 30 in the sine's 08 position. Prior to crossing into the 'easier' ground (through 14 - management) we have a guide. For each sequence, therefore, mapping it onto the sine wave, the sine positions 01 and 07 are interpreted as the crossover points for the sequence.)
A possible wave nature for events can be the unification of different wave phases.
There is a circular trigram arrangement credited to King Wen. This is cyclic in form in that one starts in the sign of the Arousing and moves clockwise. This format seems to be derived from an ancient I Ching commentary (The Shuo Kua - Discussion of the Trigrams) in which paragraph 5 reads:
"5. God comes forth in the sign of the Arousing; he brings things to completion in the sign of the Gentle; he causes creatures to perceive one another in the sign of the Clinging(light); he causes them to serve one another in the sign of the Receptive. He gives them joy in the sign of the Joyous; he battles in the sign of the Creative; he toils in the sign of the Abysmal; he brings them to perfection in the sign of Keeping Still."
This quote is from R.Wilhelm's translation (p268). Other translations interpret 'God' to read 'Lord' or 'Sage' and there is an extended version of the first statement which reads " [God] comes forth, with his creation, in the sign of the Arousing". As we shall see the commentary comes into it's own when we use the binary sequence together with the MBTI and the extended version of the first phrase will seem the more appropriate.
Continue with Timeline sequences of the hexagrams