Clarity,
Office 17622,
PO Box 6945,
London.
W1A 6US
United Kingdom
Phone/ Voicemail:
+44 (0)20 3287 3053 (UK)
+1 (561) 459-4758 (US).
chrislofting
(deceased)
- Joined
- Nov 19, 1971
- Messages
- 394
- Reaction score
- 3
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 - see http://pages.prodigy.net/lofting/btree.html), 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 (see http://pages.prodigy.net/lofting/cracked.html) 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).
Chris.
http://pages.prodigy.net/lofting
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 - see http://pages.prodigy.net/lofting/btree.html), 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 (see http://pages.prodigy.net/lofting/cracked.html) 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).
Chris.
http://pages.prodigy.net/lofting