In the analysis of the properties of the I Ching a useful approach is through the perspective offered by the
'binary' sequence, associated with the 'Early Heaven' compass of trigram opposites credited to the mythical emperor
Fu Hsi.
In this sequence we derive an ordering of hexagrams based on strong differentiation of yin/yang properties such
that the sequence reflects a scale, from 'pure' yang (hexagram 01 - 111111) to pure yin (hexagram 02 - 000000).
We can interpret this scale as a spectrum where the hexagram sequence shows a dynamic of diminishing degrees of
yangness (in that we start at the pure yang position) that, after 32 hexagrams, crosses over into a developing
degree of yinnness, ultimately reaching the level of pure yin.
In this sequence of hexagrams each hexagram is 'opposed' by its structural opposite such that at one end is the
sequence of hexagrams 111111, 111110, 111101, 111100 etc and at the other the 'reflection' of 000011, 000010, 000001,
000000.
When we analyse the sequence from the perspective of trigrams we find that the sequence is made-up of eight octets,
each octet containing eight hexagrams all with the same base trigram. The ordering is:
heaven, lake, fire, thunder, wind, water, mountain, earth
Due to the nature of the method in creating this sequence (use of recursion ), when we
zoom-in to each octet we find that the hexagrams are ordered according to their top trigrams being in the same
order as the bottom trigrams across the whole sequence, i.e.
heaven, lake, fire, thunder, wind, water, mountain, earth
Thus for the octet of heaven we find the hexagram order of:
hexagram 01 heaven over heaven
hexagram 43 lake over heaven
hexagram 14 fire over heaven
hexagram 34 thunder over heaven
hexagram 09 wind over heaven
hexagram 05 water over heaven
hexagram 26 mountain over heaven
hexagram 11 earth over heaven
To bring out the octets we can fold the 64-hexagram sequence into a matrix format thus:
01 43 14 34 09 05 26 11 - heaven base octet
10 58 38 54 61 60 41 19 - lake base octet
13 49 30 55 37 63 22 36 - fire base octet
25 17 21 51 42 03 27 24 - thunder base octet
44 28 50 32 57 48 18 46 - wind base octet
06 47 64 40 59 29 04 07 - water base octet
33 31 56 62 53 39 52 15 - mountain base octet
12 45 35 16 20 08 23 02 - earth base octet
The full 64-hexagram sequence is thus ordered from top left to bottom right, read left to right.
What we find in this matrix format is that the format of the whole sequence, the focus on a spectrum from the strongly
differentiating, exaggerating and so asymmetric, nature of yangness reflected in hexagram 01, to the strongly integrating,
balancing and so symmetric, nature of yinness reflected in hexagram 02, is reflected at all levels of analysis
such that the same pattern of exaggerate/balance, of differentiate/integrate, is repeated in the octets and even
down to PAIRS within the octets. In fact the whole sequence is interpretable as a sequence of 32 pairs of hexagrams,
where in each pair one element is overly differentiating in expression, the other overly integrating in expression.
Thus, for example, the general relationship of hexagram 01 to hexagram 02 is repeated in the octet of heaven-based
hexagrams (top row) through the particular relationship of hexagram 01 to hexagram 11. Zoom-in further and this
pattern is repeated at the level of a adjacent hexagrams, with the relationship of 01 to 43. (thus octet 1 is ultimately
made-up of four pairs: 01,43 14,34 09,05 26,11 )
Thus, the columns reflect octet relationships and the rows reflect full sequence relationships. As such, focusing
attention on the columns, so the relationships are column 1 to column 8, 2 to 7, 3 to 6, and 4 to 5 where columns
1,2,3, and 4 are focused on differentiations, exaggerations, (as are rows 1,2,3, and 4) and 5,6,7, and 8 are focused
on integrations, issues of balancing (as are rows 5,6,7, and 8)
With these distinctions in mind we can identify specific pairs in the octets that reflect these properties:
octet 1:
01 to 11 - hard core, sharp distinction of, differentiation nature of 01 is reflected in a more balanced format
by the integration nature of 11.
43 to 26 - hard core, sharp focus on 'spreading the word' is reflected in a more balanced format by the more 'subtle'
focus on holding firm to traditions, a generally integrating nature in 26. ( I say general in that, when we zoom-in
further to pairs so 11, 26 form a pair with 11 being integrating, 26 more differentiating).
14 to 05 - the strong assertion of direction of 14 is reflected in a more balanced format by the focus of waiting
and 'integrating' reflected in 05.
34 to 09 - the immediate inspiration of 34 is reflected in a more balanced format by the gradual accumulation (and
so integrating) small gains reflected in 09.
In all of these, the first entry makes sharp, exaggerated, distinctions when compared to the second entry.
octet 2:
10 to 19 - the sharp focus on hierarchy and so the association of 'correct' conduct, of knowing one's place in
the high/low relationships, reflected in 10 is reflected in a more balanced format by the focus on mixing high
and low (low approaches the high, high defers to the low) in 19 - the distinctions as such are not so 'severe'
as in 10.
58 to 41 - the sharp focus on cooperative exchange reflected in 58 is reflected in a more balanced format by the
focus in 41 upon concentration, of distillation of differences into one 'pure' form.
38 to 60 - the sharp issues of dealing with opposition, as covered in 38, is reflected in a more balanced format
by the use of standardisations, as reflected in 60.
54 to 61 - the sharp distinction of exaggeration through being immature is reflected in a more balanced format
by a focus on maturity 'inside' as reflected by 61.
octet 3:
13 to 36 - the exaggerated focus on 'likemindedness', of sharing the 'light' is reflected in a more balanced format
by a focus on covering-up the light (and so distinctly NOT likeminded).
49 to 22 - the exaggerated focus on revolution/revelation is reflected in a more balanced format by a focus on
facading, gloss-over.
30 to 63 - the exaggerated sense of 'fire', of an ideology etc is reflected in a more balanced format by a focus
on completion and 'correct ordering' (where fire comes up against water).
55 to 37 - the exaggerated sense of abundance and diversity (and so potential overflow) is reflected in a more
balanced format by a focus on rigid structuring.
octet 4:
25 to 24 - the exaggerated sense of asserting one's opinion without fear of, consideration of, consequence is reflected
in a more balanced format through a 'soft' return to a 'true' belief.
17 to 27 - the exaggerated sense of finding a particular belief system is reflected in a more balanced format through
a focus on using discernment in ingesting 'brain food'.
21 to 03 - the exaggerated sense of chewing over a problem is reflected in a more balanced format in the process
of sprouting, 'natural' getting over of difficulties.
51 to 42 - the exaggerated sense of 'enlightenment', of sudden awareness etc, is reflected in a more balanced format
through the process of augmentation.
octet 5:
44 to 46 - the exaggerated sense of persuation/seduction (44) is reflected in a more balanced format through a
focus in increased entanglement (46).
28 to 18 - the exaggerated sense of excess, of 'going beyond what is required', is reflected in a more balanced
format through the focus on correcting corruptions.
50 to 48 - the exaggerated sense of supplying nourishment through 'cooking' is reflected in a more balanced format
through the establishment of a 'well' of nourishment (requires less energy over the long run).
32 to 57 - the exaggerated sense of commitment is reflected in a more balanced format in the form of the 'gentle'
influence of the wind on cultivation and becoming influencial.
octet 6:
06 to 07 - the exaggerated sense of compromise, of not giving an inch but nore taking any, is reflected in a more
balanced format through a focus on establishing uniformity.
47 to 04 - the exaggerated sense of forcing integration with the context through enclosure is reflected in a more
balanced format through the masking of youth through education.
64 to 29 - the exaggerated sense of avoiding closure/making 'small' errors, is reflected in a more balanced format
through the use of containment/control. (this also gets into the issue of 'pure water' - 29 - versus water coming-up
against fire (64). As such one would assume that the ordering is 'wrong', surely the exaggeration is in water vs
the balanced of 64? no. as we move into the realm of integration so the exaggeration of a quality is in fact an
exaggeration of *integration* and so 29 is correctly mapped to the more 'balancing', if becoming a little over-balancing,
agent in this relationship)
40 to 59 - the exaggerated sense of loosening structure is reflected in a more balanced format through the dispelling
of illusions.
octet 7:
33 to 15 - the exaggerated sense of trickary/retreat in 33 is reflected in a more balanced format through the levelling-out
(and so make things more 'fair') reflected in 15.
31 to 52 - the exaggerated sense of wooing is reflected in a more balanced format through the development of discernment.
56 to 39 - the exaggerated sense of remaining loyal is reflected in a more balanced format in that of being an
obsticle to the 'mindless' flow of things; we do not advertise our loyalty, we just hold our 'ground'.
62 to 53 - the exaggerated sense of overplaying traditions to maintain the coherence of the collective is reflected
in a more balanced format through the focus on, as well as recognising the consequences of, maturing.
octet 8:
12 to 02 - the exaggerated sense of neutralising the attacks of other upon one's belief is reflected in a more
balanced format through one's simple but sturdy devotion.
45 to 23 - the exaggerated sense of celebrating one's faith is reflected in a more balanced format through the
continuous removal of 'weeds' that can gather around one's faith.
35 to 08 - the exaggerated sense of bringing something into the light is reflected in a more balanced format through
being a passive attraction.
16 to 20 - the exaggerated sense of open enthusiasm, foresight, and planning is reflected in a more balanced format
through being an example for others, a source of admiration and so motivation for others.
These general pairs reflect the same methodology used at the level of the full sequence where we pair the structural
opposites. BUT this method, as mentioned before, is also applicable to immediate pairs (hexagrams next to each
other) within octets such that, for example, using octet 1:
01 is strongly differentiating when compared to the integrating nature of 43 with its focus on 'seeding' on spreading
the word.
14 is strongly differentiating when compared to the more integrating nature of 34 that is inspiring.
09 is strongly differentiating when compared to the more integrating nature of 05 that focuses on 'networking'
whilst waiting for one's opportunity.
26 is strongly differentiating and conditional with its focus on holding firm to particular traditions when compared
to the more integrating nature of 11 with its focus on asserting harmony where that assertion is unconditional.
These properties of relationships that repeat at all levels of analysis are properties of the METHOD of deriving
the hexagram sequences, the use of recursion, and elsewhere I have demonstrated that finding sequences of hexagrams
in pairs reflects a derivation process focused on recursion and that applies to the traditional sequence of the
I Ching, such that we can identify octets in that sequence and so apply the same forms
of analysis BUT recognising that the perspective is slightly different where in the binary sequence the overall
focus is a spectrum from the characteristics of 01 to 02 whereas in the traditional sequence it appears more to
be a spectrum from the characteristics of 01 to 64 (pure to mixed).
As shown elsewhere (See my IC masking page) we can create all of the sequences
reflecting spectral analysis of pairs of hexagrams with the best initial source being that of 'opposite' hexagrams.
Thus stepping through hexagram 23 (bottom to top)I can generate a sequence of hexagrams reflecting the recursion
of the semantic seed of 23/43, pruning (cut back) vs seeding (spread out). Thus the pairings in this sequence bring-out
relationships across hexagram pairs that reflect in some way the semantic 'seed' of 23/43 (BUT there are issues
with this, covered below).
The obvious point here is that these 64-hexagram sequences come in PAIRS and so as there are two 64-hexagram sequences
based on 'opposites' of 01/02 so there are for all of the others - this gets us into hexagram rotations issues
etc (take the binary sequence with its poles of 01 and 02 and rotate all of the hexagrams in that sequence will
give you the changing-line sequence through hexagrams 01 or 02. Take the changing-line sequence for, say, 23/43
and rotate those hexagrams and you get a sequence for 24/44. Extract the changing-line sequence derived by stepping
through 24 or 44 and you get the other sequence of 23/43, and so on - there is a lot of work to be done in fleshing-out
what is being expressed in these sequence pairs etc - the matrices are all given in one
file - with the matrices I am focusing upon all under the table headings of "Horizontal Binary Sequence",
and the changing-line matrices ("Vertical Binary Sequence" tables) come out in the five-phase I Ching
work)
Since we previously used the 'naturally' derived matrix of the binary sequence ordering in identifying the exaggerate-balance
(and so differentate-integrate, yang-yin) hexagram relationships, rather than use the 64-hexagram sequence of 01/02
derived from changing-line patterns, lets assume that the best of the two possible sequences for the 23/43 seed
should be the one NOT directly derived from changing lines. In principle this sequence should show us relationships
across hexagram pairs that bring out the 23/43 relationships just as the 'natural' binary sequence appears to give
us a spectrum of the 01/02 relationships. The 23/43 matrix is:
23 02 20 08 35 16 12 45 - pruning (cut back)
52 15 53 39 56 62 33 31
04 07 59 29 64 40 06 47
18 46 57 48 50 32 44 28
27 24 42 03 21 51 25 17
22 36 37 63 30 55 13 49
41 19 61 60 38 54 10 58
26 11 09 05 14 34 01 43 - seeding (spread out)
Applying the same generic patterns used in the traditional binary sequence analysis to this matrix so the pattern
across the WHOLE sequence is of cutting-back (23, top left) to spreading-out (43, bottom right).
The pattern across the PARTS, the LOCAL, the pattern focused on the octets, is reflected in the COLUMNS from column
01 focused on pruning, to column 8 on seeding - and so the WHOLE is in all PARTS - Thus, focusing on the first
octet (top row) we have:
23 to 45 (cut back (prune) to spread out (seed)) - here we have the raw state of pruning, focusing on keeping one's
faith 'pure' through regular housekeeping compared to the 'spreading the word' nature of 45, where we congregate
to celebrate our faith. So I think we can 'see' the 23/43 relationship reflected in this pairing.
02 to 12 - here we have the contractive nature of 02 (and so reflecting devotion) compared to the explicit acts
of neutralising the attacks of other's on one's faith and with that comes the requirement in that act to promote
that faith. So I think we can 'see' the same 23/43 pattern at work in this pairing.
20 to 16 - here we have the passive nature of 20, of being an example, a source for admiration, a 'pure' form,
as compared to the enthusiastic planning, use of foresight etc, we see in 16 where 16 appears more focused on explicitly
'spreading the word' than does 20.
08 to 35 - here we have the passive nature of 08, its focus on eliciting a sense of belonging, of uniting and so
of 'purity' in belief vs the active nature of 35 with its focus on bringing something 'into the light' - a definite
act of 'seeding' rather than pruning ;-)
If we here jump to the last row, the row focused on seeding, on spreading-out, we have the relationships of:
26 to 43 (prune aspect of the row vs seeding aspect of the row) - here the pruning is in the focus on holding firm
to a particular set of traditions wheras the seeding is in the 'spreading the word' nature of 43.
11 to 01 - pruning in the form of harmonising vs the spreading out, the competitive nature of 01.
09 to 34 - pruning in the form of collecting 'quality' small gains to stand upon to be noticed, vs the explicit
inspirational focus of 34 (and so a focus on seeding)
05 to 14 - pruning through the use of 'housekeeping' [networking] whilst waiting for an opportunity vs the strongly-centered
focus on driving an ideology, asserting a direction (and so 'spreading the word')
I think here too we can easily 'see' the 23/43 relationships.
Lets do one more, say row 5: 27 24 42 03 21 51 25 17
27 to 17 - use of discernment in ingesting 'something' (and so to prune) vs a focus on developing a belief system
(that includes the need to 'spread the word')
24 to 25 - the focus on coming back to, on returning, to a belief/faith (and so more an aire of pruning) vs the
standing up to assert one's opinion regardless of consequences (or innocent of consequences) - a more 'spreading
the word' act.
42 to 51 - the focus on augmentation, a form of housekeeping, vs the sudden moment of 'enlightenment' that, IMHO,
comes with having heard 'the word'.
03 to 21 - the focus on initial difficulties in the process of sprouting (that can be interpreted as 'survival
of the fitest' and as such a 'pruning' focus) vs the creation of laws (the 'word') as an act of problem solving.
I think in these examples I have demonstrated a consistant pattern of meaning derivation based on a 'rigid' template
derived from recursion to which we 'seed' the template with a particular yin/yang meaning and derive relationships
across all parts to the whole.
Since the matrices reflect hexagram PAIRS (in particular with a focus on structural opposites) so there are 32
64-hexagram sequences that we can quickly create to flesh-out the 'spectrum' across structural opposites. (overall
there are 4096 64-hexagram sequences of 'interest' here but lets walk before we run! ;-))
Note that the above pairs remained constant in both the binary sequence (01/02) and the sequence derived from 23/43. What changed was the position of the pairs reflecting their ordering according to the 'bias' in perspective, thus the pairs reflect invarience within varience. What happens here is the octets remain constant but their content 'move around' depending on the context. This for the 01/02 context octet 1 is ordered 01, 43, 14, 34, 09, 05, 26, 11 whereas this octet in 23/43 is now expressed as row 8 and ordered : 26, 11, 09, 05, 14, 34, 01, 43
Thus we can then apply the SAME techniques to the traditional sequence etc etc etc
