More Hexagram Pairs
As I have identified elsewhere (see pages on IC+ website - ) the I Ching manifests
itself as a language where the whole is broken down into parts and the ordering of the parts brings out aspects
of the whole.
The derivation of the parts is done through the use of recursion [see diagram] and so the use of self-referencing.
As an example, here we derive representions of the I Ching trigrams through the application of recursion to the
initial 'cut' of the whole into yin and yang, where yin is represented as 0 and yang as 1:
[0] <T'ai Chi> [the undifferentiated whole]
[1] 0 / 1 [first differentiation]
[2] 00, 01 / 10, 11 [second... digrams]
[3] 000, 001, 010, 011 / 100, 101, 110, 111 [trigrams]
This 'template' allows for ANY dichotomy to be mapped to [1] above followed by the fleshing-out of specific parts
of that pair such that at [3] we have eight parts that reflect the whole.
At [3] note that the elements of the original dichotomy of 0 / 1 have been pushed outwards to the 'poles' of the
sequence (manifest as 000 / 111) such that given any recursively-derived sequence of hexagrams we can identify
quickly the overall theme of the sequence by looking at the pole trigrams/hexagrams.
The process of recursion encodes the whole (limited here to the PAIR of 0/1 at level [1] above) into all parts
and as such forms all parts into PAIRS. Thus at level [3] above we have four pairs:
(000,001), (010,011) / (100,101), (110,111)
Each pair reflects underlying qualities of the original pair such that in each pair the elements reflect the differences
in the original pairing of 0/1.
We can use brackets to bring out the pairs at each level of analysis packed into one level:
((((000), (001)), ((010), (011))), (((100), (101)), ((110), (111))))
Thus the process of recursion of yin/yang to the level of hexagrams, level [6], (dodecagrams take us to level [12])
will give us pairs of hexagrams that reflect different manifestations of the main pair, that of pure yin vs pure
yang at level [1] and so 'colour' interpretations of trigrams/hexagrams.
The sequence of 64 hexagrams derived from recursion of pure yin/pure yang is bounded by hexagram 02 and hexagram
01 and the 32 pairs of hexagrams reflect the different *qualities* in expression of this pair, thus, for example,
the ordering of hexagrams at the yin end is: 02, 23, 08, 20, 16, 35, 45, 12....
WITHIN the context of yin (base trigram of yin lines) we have nuances of expression mapped to PAIRS such that we
have:
integrating hexagram (02 qualities)/ differentiating hexagram (01 qualities)
02 / 23
08 / 20
16 / 35
45 / 12
If we fold this particular sequence of 64 hexagrams 'backwards', moving back 'up' the levels, to the level of the
original pair we come up with the pair manifesting the qualities of hexagrams 02/01 - the hexagrams at the 'poles'
of the sequence of 64 hexagrams. It is the QUALITY in these base hexagrams that influences the interpretations
of the PAIRS of hexagrams at level [6] - the level of 64 hexagrams, 32 pairs. Thus in 02/23, 02 reflects qualities
of 02, 23 reflects qualities of 01, 08 reflects qualities of 02, 20 reflects qualities of 01 and so on. Each level
adds an element of the base pair such that the eight hexagrams with the earth trigram as base will, IN GENERAL,
reflect qualities of 02, a focus on integration. WITHIN that general finer distinctions are made still using the
qualities of the base pair.
In the traditional sequence we find hexagram pairing, demonstrating that the order was derived from analysis of
the qualities of the two 'pole' hexagrams in the sequence - 01/64 (see the page on pairs in traditional sequence
) Here the quality seems to be related to purity/mixing, individual/group perspectives.
The derivation of the sequences is rooted in recursion and we can derive sequences specific to each hexagram through
applying recursion to each hexagram where each hexagram is considered to be a whole - T'ai Chi.
This process of recursion is achieved through stepping through the hexagram bottom-to-top in the order of binary
numbering and 'flipping' yin into yang, yang into yin to derive a sequence of 64 hexagrams. (see a sample of the order of flipping lines
)Thus, for example, if I apply this process to hexagram 23 I get a sequence of 64 hexagrams from 23 to 43. The
focus is thus on the 23/43 pair and the manifestation of different qualities of this pair in the other pairs of
the sequence. So, working from the 23 end of this sequence I have:
23, 27, 04, 41, 52, 22, 18, 26 as the first eight hexagrams. These will form into pairs where the interpretation
of the elements of each pair is *biased* by the qualities of the root pair, 23/43. Thus we have:
23 / 27
04 / 41
52 / 22
18 / 26
The left column hexagrams reflect in their interpretations basic qualities of 23 WHEN COMPARED to the right column
of hexagrams that reflect basic qualities of 43. As such the left column reflects issues of 'pruning', the right
column issues of 'seeding'. IOW general reflections upon the pair of hexagrams 04/41 will elicit qualities rooted
in the pair of 23/43 - thus the common ground between 04 and 41 is rooted in the concepts encoded in the 23/43
pair of opposites. Thus identifying the sequence of hexagrams where two hexagrams are paired other than as opposites
will identify the common ground between that pair as being derived from the pole hexagrams of the sequence.
Using the 23/43 example, the generic sense of pruning in 23, the focus on cutting back to the core faith, the removal
of chaff from wheat is reflected in the other hexagrams:
23 - reduce to core faith
04 - core 'true' education
52 - core sense of quality
18 - removing corruption leaving 'core' belief
For the other column, focused on the generic sense of seeding, of 'spreading the word', in 43, we have:
27 - hungering for a 'seed'
41 - concentration/distillation of the seed
22 - glossing-up the seed
26 - holding firm to the seed
Thus, for example, the relationship of 18 to 26 is in 18s focus on correcting corruption and 26s focus on sticking
to the 'tried and true' and this relationship reflects overall qualities of the 23/43 pair of binary 'opposites'.
In my Five-Phase
I Ching pages as well as the I Ching matrix page I have mapped-out 64-hexagram
sequences that can be used for analysis where each pair in the sequences reflects the overall relationship of the
two pole hexagrams.
What we are dealing with here is a high degree of complex information encoding that is a property of recursion
and so not something unique to the I Ching but discoverable within the I Ching.