Elsewhere on this website we have demonstrated how the use of recursion to create hexagrams results in the grouping of hexagrams into PAIRS. On this page we will map-out three sets of 32 pairs, those derived from the the binary sequence of hexagrams (often associated with Fu Hsi), those derived from folding the binary sequence into pairs of structurally opposite hexagrams (also associated with Fu Hsi), and the traditional sequence of hexagrams (often associated with King Wen). (also see the older pages on quartets)
In the process of applying recursion to the dichotomy of yang/yin we end-up with a sequence of 32 pairs of hexagrams. In this particular ordering there is an essential difference in the pairs through the application of the TOP line in the hexagrams where a YANG top line reflects a particular differentiating expression in the meaning of the hexagram, compared to a YIN top line that reflects a particular integrating expression in the meaning of the hexagram. In these pairs the hexagrams have been derived from one space, namely the pentagram (5 lines) where these pentagrams reflect a shared theme, expressed clearly when we add the top line to move from pentagrams to hexagrams, thus the difference in the elements of each pair is the nature of the TOP line:
01, 43
The overall sense of yangness, devotion to self, is reflected in the differentiating nature of hexagram 01, compared with the more integrating nature of hexagram 43.
14, 34
The overall sense of centered control is reflected in the differentiating nature of hexagram 14, compared to the integrating nature of hexagram 34.
09, 05
the overall sense of opportunist gratification is reflected in the differentiating nature of hexagram 09, compared to the integrating nature of hexagram 05.
26, 11
the overall sense of maintaining balance is reflected in the differentiating nature of hexagram 26, compared to the integrating nature of hexagram 11.
10, 58
The overall sense of intense focus is reflected in the differentiating nature of hexagram 10, compared with the integrating nature of hexagram 58.
38, 54
The overall sense of [opposing] is reflected in the differentiating nature of hexagram 38, compared to the integrating nature of hexagram 54.
61, 60
The overall sense of shared properties is reflected in the differentiating nature of hexagram 61, compared to the integrating nature of hexagram 60.
41, 19
The overall sense of reducing to sameness is reflected in the differentiating nature of hexagram 41, compared to the integrating nature of hexagram 19.
13, 49
The overall sense of purposeful grouping is reflected in the differentiating nature of hexagram 13, compared to the integrating nature of hexagram 49.
30, 55
The overall sense of ...... is reflected in the differentiating nature of hexagram 30, compared to the integrating nature of hexagram 55.
37, 63
The overall sense of rigidity is reflected in the differentiating nature of hexagram 37, compared to the integrating nature of hexagram 63.
22, 36
The overall sense of hiding is reflected in the differentiating nature of hexagram 22, compared to the integrating nature of hexagram 36.
25, 17
The overall sense of asserting/finding belief is reflected in the differentiating nature of hexagram 25, compared to the integrating nature of hexagram 17.
21, 51
The overall sense of solution seeking is reflected in the differentiating nature of hexagram 21, compared to the integrating nature of hexagram 51.
42, 03
The overall sense of development is reflected in the differentiating nature of hexagram 42, compared to the integrating nature of hexagram 03.
27, 24
The overall sense of seeking is reflected in the differentiating nature of hexagram 27, compared to the integrating nature of hexagram 24.
44, 28
The overall sense of 'going the extra distance' is reflected in the differentiating nature of hexagram 44, compared to the integrating nature of hexagram 28.
50, 32
The overall sense of refining is reflected in the differentiating nature of hexagram 50, compared to the integrating nature of hexagram 32.
57, 48
The overall sense of cultivating is reflected in the differentiating nature of hexagram 57, compared to the integrating nature of hexagram 48.
18, 46
The overall sense of involvement is reflected in the differentiating nature of hexagram 18, compared to the intergrating nature of hexagram 46.
06, 47
The overall sense of restricting is reflected in the differentiating nature of hexagram 06, compared to the integrating nature of hexagram 47.
64, 40
The overall sense of relaxed structure is reflected in the differentiating nature of hexagram 64, compared to the integrating nature of hexagram 40.
59, 29
The overall sense of ...... is reflected in the differentiating nature of hexagram 59, compared to the integrating nature of hexagram 29.
04, 07
The overall sense of establishing uniformity is reflected in the differentiating nature of hexagram 04, compared to the integrating nature of hexagram 07.
33, 31
The overall sense of drawing somone 'in' is reflected in the differentiating nature of hexagram 33, compared to the integrating nature of hexagram 31.
56, 62
The overall sense of loyalty is reflected in the differentiating nature of hexagram 56, compared to the integrating nature of hexagram 62.
53, 39
The overall sense of managing the flow is reflected in the differentiating nature of hexagram 53, compared to the integrating nature of hexagram 39.
52, 15
The overall sense of discernment is reflected in the differentiating nature of hexagram 52, compared to the integrating nature of hexagram 15.
12, 45
The overall sense of faith/worship is reflected in the differentiating nature of hexagram 12, compared to the integrating nature of hexagram 45.
35, 16
The overall sense of enthusiasm/foresight is reflected in the differentiating nature of hexagram 35, compared to the integrating nature of hexagram 16.
20, 08
The overall sense of admiration is reflected in the differentiating nature of hexagram 20, compared to the integrating nature of hexagram 08.
23, 02
The overall sense of devotion-to-another/others is reflected in the differentiating nature of hexagram 23, compared to the integrating nature of hexagram 02.
The above set of 32 pairs reflect high definition ordering of meanings derived from recursion. To refine the meanings it is useful to consider the opposite pair of each pair. By this I mean that the process of recursion ensures that each hexagram has a structural opposite (as in all lines reversed in yin/yang category) and that opposite is itself part of a pair. THAT pair then reflects some form of opposite/complementary meaning to the pair under consideration. Thus the pair of 01,43 reflects aspects of a pentagram that relates in meaning to the pentagram from which is derived 02, 23.
We will get into the details of pairs of opposite hexagrams in the next section (as in 01, 02 and 43, 23) but here the focus is on the pairs naturally-derived from the use of recursion (as in next to each other in the sequence of hexagrams) and their opposites/complements. Note that the top line of the pentagram as such reflects the expression of that pentagram as differentiating (yang top) or integrating (yin top). As such each PAIR of hexagrams fall within the bounds of the top line of the pentagram. For example, 01 is differentiating, 43 is integrating, but the pentagram from which they emerge is differentiating and that categorisation applies to the pair.
01, 43 - 23, 02 Devotion to Self vs Devotion to Another. (differentiate vs intgrate)
14, 34 - 20, 08 Centered Control (admiration of self) vs Admiration of Another. (integrate vs differentiate)
09, 05 - 35, 16 Opportunist Gratification vs Planned Gratification. (differentiate vs integrate)
26, 11 - 12, 45 Maintaining Balance/Harmony vs Maintaining Belief (integrate vs differentiate)
10, 58 - 52, 15 Intense Focus vs De-focus (differentiate vs integrate)
38, 54 - 53, 39 Reflecting the Flow vs Managing the Flow (integrate vs differentiate)
61, 60 - 56, 62 Shared Properties vs Shared Loyalties (differentiate vs integrate)
41, 19 - 33, 31 Reduction to Sameness vs Drawing Someone 'in' (integrate vs differentiate)
13, 49 - 04, 07 Purposeful Grouping vs Socialising (differentiate vs integrate)
30, 55 - 59, 29 (integrate vs differentiate)
37, 63 - 40, 64 Rigidity (Closure) vs Relaxed Structure (Openness) ( differentiate vs integrate)
22, 36 - 06, 47 Hiding vs Restricting (integrate vs differentiate)
25, 17 - 18, 46 Finding Faith (in self) vs Finding Faith (in/through others) (differentate vs integrate)
21, 51 - 57, 48 Solution Seeking vs Cultivating (integrate vs differentiate)
42, 03 - 32, 50 Development (move up) vs Development (cook) (differentiate vs integrate)
27, 24 - 44, 28 Devotion to ONE path [universal] vs Attraction to many paths [context sensitive] (integrate vs differentiate)
The relationship here is on the lines in the hexagrams being opposites in each pair. As such the elements of each pair reflect the opposite sides of the same coin - name the coin.
01, 02
This pair reflects a perspective on imbalance in the extremes of hexagram 01, differentiation, and hexagram 02, integration.
43, 23
This pair reflects a perspective on promotion through hexagram 43's focus on 'spreading the word' [seeding] versus hexagram 23's focus on 'housekeeping' [pruning].
14, 08
This pair reflects a perspective on
34, 20
This pair reflects a perspective on
09, 16
This pair reflects a perspective on foundation setting, through the accumulation of material as in hexagram 09, or through the focus on planning and so the use of foresight, as in hexagram 16.
05, 35
This pair reflects a perspective on the 'right moment', as in waiting for it (hexagram 05) or bringing something into the 'light' (hexagram 35).
26, 45
This pair reflects a perspective on
11, 12
This pair reflects a perspective on balance, in hexagram 11 the focus is on harmonising, in hexagram 12 the focus is on neutralising.
10, 15
This pair reflects a perspective on
58, 52
This pair reflects a perspective on
38, 39
This pair reflects a perspective on
54, 53
This pair reflects a perspective on
61, 62
This pair reflects a perspective on
60, 56
This pair reflects a perspective on
41, 31
This pair reflects a perspective on
19, 33
This pair reflects a perspective on
13, 07
This pair reflects a perspective on
49, 04
This pair reflects a perspective on
30, 29
This pair reflects a perspective on
55, 59
This pair reflects a perspective on
37, 40
This pair reflects a perspective on tension release, in hexagram 37 the release is thorough rigidity, in hexagram 40 the release is through relaxation.
63, 64
This pair reflects a perspective on ......, hexagram 63 with a focus on closure/completeness, hexagram 64 with a focus on remaining open/incomplete.
22, 47
This pair reflects a perspective on
36, 06
This pair reflects a perspective on
25, 46
This pair reflects a perspective on
17, 18
This pair reflects a perspective on
21, 48
This pair reflects a perspective on
51, 57
This pair reflects a perspective on
42, 32
This pair reflects a perspective on
03, 50
This pair reflects a perspective on
27, 28
This pair reflects a perspective on
24, 44
This pair reflects a perspective on
The following pairs reflect 'variations on a theme' where the differences in the elements of the pair are in the BOTTOM line rather than the top line.
01, 44
This pair reflects a perspective on
43, 28
This pair reflects a perspective on
14, 50
This pair reflects a perspective on
34, 32
This pair reflects a perspective on
09, 57
This pair reflects a perspective on
05, 48
This pair reflects a perspective on
26, 18
This pair reflects a perspective on
11, 46
This pair reflects a perspective on
10, 06
This pair reflects a perspective on
58, 47
This pair reflects a perspective on
38, 64
This pair reflects a perspective on
54, 40
This pair reflects a perspective on
61, 59
This pair reflects a perspective on
60, 29
This pair reflects a perspective on
41, 04
This pair reflects a perspective on
19, 07
This pair reflects a perspective on
13, 33
This pair reflects a perspective on
49, 31
This pair reflects a perspective on
30, 56
This pair reflects a perspective on
55, 62
This pair reflects a perspective on
37, 53
This pair reflects a perspective on
63, 39
This pair reflects a perspective on
22, 52
This pair reflects a perspective on
36, 15
This pair reflects a perspective on
25, 12
This pair reflects a perspective on
17, 45
This pair reflects a perspective on
21, 35
This pair reflects a perspective on
51, 16
This pair reflects a perspective on
42, 20
This pair reflects a perspective on
03, 08
This pair reflects a perspective on
27, 23
This pair reflects a perspective on
24, 02
This pair reflects a perspective on
The patterns here focus overall on rotation of hexagrams and as such raises the issue of invarient hexagrams (i.e. those that do not change in rotation) where rather than associate them with their opposites they should be associated with themselves, and so rather than 32 pairs we would end up with 36 pairs. Analysis of the derivation of the King Wen sequences shows us a focus on individual (pure) vs group (mixed) concepts. The eight octets cover:
01,02 03,04 05,06 07,08 - purity issues (01-08 oppose)
09,10 11,12 13,14 15,16 - gain issues (09-16 oppose)
17,18 19,20 21,22 23,24 - belief issues (17-24 oppose)
25,26 27,28 29,30 31,32 - involvement issues (25-32 oppose)
33,34 35,36 37,38 39,40 - tension release issues (33-40 oppose)
41,42 43,44 45,46 47,48 - foundation issues (41-48 oppose)
49,50 51,52 53,54 55,56 - loyalty issues (49-56 oppose)
57,58 59,60 61,62 63,64 - mixing issues (57-64 oppose)
Due to the recursion so the whole is encoded in all parts thus for each octet we have the same set of associations
as for all octets. Thus for each octet we have the same patterns in meaning:
Octet 1 - Purity Issues:
01 - purity, 02 - personal gain, 03 - belief, 04 - involvement, 05 - tension release, 06 - foundation issues, 07 - loyalty issues, 08 - mixing issues.
This is interpretable as 01 being the best example of purity. 02 as the best example of personal gain in a context of purity, 03 as the best example of establishing belief in a context of purity, 04 as the best example of involvement in a context of purity, 05 as an example of tension release in a context of purity, 06 as an example of foundation-setting in a context of purity, 07 as an example of loyalty in a context of purity, 08 as an example of 'groupness' in a context of purity.
Octet 2 - Personal Gain Issues:
09 - purity, 10 - personal gain, 11 - belief, 12 - involvement, 13 - tension release, 14 - foundation issues, 15 - loyalty issues, 16 - mixing issues
This is interpretable as 09 being the best example of purity in a context of personal gain. 20 as the best example of personal gain in a context of personal gain, 11 as the best example of establishing belief in a context of personal gain, 12 as the best example of involvement in a context of personal gain, 13 as an example of tension release in a context of personal gain, 14 as an example of foundation-setting in a context of personal gain, 15 as an example of loyalty in a context of personal gain, 16 as an example of 'groupness' in a context of personal gain.
Octet 3 - Belief Issues:
17 - purity, 18 - personal gain, 19 - belief, 20 - involvement, 21 - tension release, 22 - foundation issues, 23 - loyalty issues, 24 - mixing issues
This is interpretable as 17 being the best example of purity in a context of Belief issues. 18 as the best example of personal gain in a context of Belief issues, 19 as the best example of establishing belief in a context of Belief issues, 20 as the best example of involvement in a context of Belief issues, 21 as an example of tension release in a context of Belief issues, 22 as an example of foundation-setting in a context of Belief issues, 23 as an example of loyalty in a context of Belief issues, 24 as an example of 'groupness' in a context of Belief issues.
Octet 4 - Involvement Issues:
25 - purity, 26 - personal gain, 37 - belief, 28 - involvement, 29 - tension release, 30 - foundation issues, 31 - loyalty issues, 32 - mixing issues
This is interpretable as 25 being the best example of purity in a context of Involvement issues. 26 as the best example of personal gain in a context of Involvement issues, 27 as the best example of establishing belief in a context of Involvement issues, 28 as the best example of involvement in a context of Involvement issues, 29 as an example of tension release in a context of Involvement issues, 30 as an example of foundation-setting in a context of Involvement issues, 31 as an example of loyalty in a context of Involvement issues, 32 as an example of 'groupness' in a context of Involvement issues.
Octet 5 - Tension Release Issues:
33 - purity, 34 - personal gain, 35 - belief, 36 - involvement, 37 - tension release, 38 - foundation issues, 39 - loyalty issues, 40 - mixing issues
This is interpretable as 33 being the best example of purity in a context of Tension Release. 34 as the best example of personal gain in a context of Tension Release, 35 as the best example of establishing belief in a context of Tension Release, 36 as the best example of involvement in a context of Tension Release, 37 as an example of tension release in a context of Tension Release, 38 as an example of foundation-setting in a context of Tension Release, 39 as an example of loyalty in a context of Tension Release, 40 as an example of 'groupness' in a context of Tension Release.
Octet 6 - Foundation Issues:
41 - purity, 42 - personal gain, 43 - belief, 44 - involvement, 45 - tension release, 46 - foundation issues, 47 - loyalty issues, 48 - mixing issues
This is interpretable as 41 being the best example of purity in a context of Foundation setting. 42 as the best example of personal gain in a context of Foundation setting., 43 as the best example of establishing belief in a context of Foundation setting, 44 as the best example of involvement in a context of Foundation setting, 45 as an example of tension release in a context of Foundation setting, 46 as an example of foundation-setting in a context of Foundation setting, 47 as an example of loyalty in a context of Foundation setting, 48 as an example of 'groupness' in a context of Foundation setting.
Octet 7 - Loyalty Issues:
49 - purity, 50 - personal gain, 51 - belief, 52 - involvement, 53 - tension release, 54 - foundation issues, 55 - loyalty issues, 56 - mixing issues
This is interpretable as 49 being the best example of purity in a context of Loyalty issues. 50 as the best example of personal gain in a context of Loyalty issues., 51 as the best example of establishing belief in a context of Loyalty issues, 52 as the best example of involvement in a context of Loyalty issues, 53 as an example of tension release in a context of Loyalty issues, 54 as an example of foundation-setting in a context of Loyalty issues, 55 as an example of loyalty in a context of Loyalty issues, 56 as an example of 'groupness' in a context of Loyalty issues.
Octet 8 - Mixing Issues:
57 - purity, 58 - personal gain, 59 - belief, 60 - involvement, 61 - tension release, 62 - foundation issues, 63 - loyalty issues, 64 - mixing issues
01, 02
This pair reflects a perspective on purity, hexagram 01 as pure yang, pure differentiation, and hexagram 02 as pure yin, pure integration.
03, 04
This pair reflects a perspective on
05, 06
This pair reflects a perspective on
07, 08
This pair reflects a perspective on purity in the context of a collective, hexagram 07 through uniformity, hexagram 08 through unification.
09, 10
This pair reflects a perspective on [personal gain]
11, 12
This pair reflects a perspective on
13, 14
This pair reflects a perspective on
15, 16
This pair reflects a perspective on [establishing, maintaining personal beliefs]
17, 18
This pair reflects a perspective on
19, 20
This pair reflects a perspective on
21, 22
This pair reflects a perspective on
23, 24
This pair reflects a perspective on
25, 26
This pair reflects a perspective on
27, 28
This pair reflects a perspective on
29, 30
This pair reflects a perspective on
31, 32
This pair reflects a perspective on
33, 34
This pair reflects a perspective on
35, 36
This pair reflects a perspective on
37, 38
This pair reflects a perspective on
39, 40
This pair reflects a perspective on
41, 42
This pair reflects a perspective on
43, 44
This pair reflects a perspective on
45, 46
This pair reflects a perspective on
47, 48
This pair reflects a perspective on
49, 50
This pair reflects a perspective on
51, 52
This pair reflects a perspective on
53, 54
This pair reflects a perspective on
55, 56
This pair reflects a perspective on
57, 58
This pair reflects a perspective on
59, 60
This pair reflects a perspective on
61, 62
This pair reflects a perspective on
63, 64
This pair reflects a perspective on purity in MIXING.
Since this sequence also appears to be derived from recursion, so the same methods of analysis used above for the Fu Hsi sequence can also be used in analysis of King Wen. Here we focus on opposite pairs:
01, 64
This pair reflects a perspective on purity in purity, reflected in hexagram 01, as compared to purity in mixing reflected in hexagram 64.
02, 63
This pair reflects a perspective on
03, 62
This pair reflects a perspective on ......, 03 through being 'reborn', 62 through exaggerations of the old traditions etc to maintain social structure
04, 61
This pair reflects a perspective on ......, 04 through education, socialisation through masking, 61 through putting on a hard exterior to cover the soft core.
05, 60
This pair reflects a perspective on ......, 05 through biding one's time, 60 through adaption of standards
06, 59
This pair reflects a perspective on ......, 06 through a focus on compromise, 59 through dispelling illusions
07, 58
This pair reflects a perspective on ......, 07 as uniformity, 58 as intense reflection of self and being a mirror to others
08, 57
This pair reflects a perspective on
09, 56
This pair reflects a perspective on ..... 09 as using small gains to be noticed, 56 as using loyalty to be noticed.
10, 55
This pair reflects a perspective on ...... 10 as a focus on operating within rigid guidelines, 55 as diversity in operation
11, 54
This pair reflects a perspective on ..... 11 as a focus on harmony/balance, 54 as a focus on high expression of energy
12, 53
This pair reflects a perspective on grounding, 12 in the form of neutralising attacks and so strengthening belief, 53 through gradual development and so maturing
13, 52
This pair reflects a perspective on quality, 13 in the form of 'likemindedness', 52 as being discerning
14, 51
This pair reflects a perspective on center from which all flows - 14 as a director of events, 51 as an originator of things.
15, 50
This pair reflects a perspective on perculating - 15 through levelling-out, 50 through transformation (cooked food, kept warm)
16, 49
This pair reflects a perspective on .... - 16 focuses on foresight, planning, 49 on the need for revolution due to lack of foresight
17, 48
This pair reflects a perspective on foundations - 17 through acquiring a belief, 48 through setting down a well as a source for nourishment.
18, 47
This pair reflects a perspective on maintaining purity, 18 through correcting errors, 47 through enclosure to avoid 'wandering' from the 'true way'
19, 46
This pair reflects a perspective on going higher - 19 as approaching the high with out fear, 46 with getting more entangled with the hierarachy.
20, 45
This pair reflects a perspective on praise of another - 20 reflects admiration of someone, as does 45 with its focus on celebration of that someone.
21, 44
This pair reflects a perspective on conversion in that 21 seeks to solve a problem, 44 seeks to convert somone to a point of view (to seduce).
22, 43
This pair reflects a perspective on glossing over - 22 through a facade, 43 through pushing a particular perspective - both act to cover-up something else.
23, 42
This pair reflects a perspective on refinement - 23 strips away 'crap' to reveal a truth, 42 adds-on elements to bring out a truth.
24, 41
This pair reflects a perspective on focus to one thing - 24 reflects returning to a true faith, 41 reflects distillation to a pure form and so true faith.
25, 40
This pair reflects a perspective on release - 25 in the form of disentangling oneself from social 'rules' to say one's piece, 40 from the release of tension through relaxation of structure.
26, 39
This pair reflects a perspective on going against the 'mindless' flow - 26 through holding firm to traditions, 39 from obstructing the flow and so utilising it to drive things.
27, 38
This pair reflects a perspective on
28, 37
This pair reflects a perspective on exaggerations of structure/deed, 28 in the excess of going beyond what is required to do something or represent someone, 37 in the exaggerated structure of things (family/clan hierarchy) to ensure 'harmony'.
29, 36
This pair reflects a perspective on control through 29 - use of containment to control, and 36 use of being uncompromising.
30, 35
This pair reflects a perspective on introduction to light - 30 in the form of an ideology, 35 in the form of bring something into the light.
31, 34
This pair reflects a perspective on invigorating, 31 as intense stimulation (physical, wooing etc), 34 as a source of proactive support of others and so motivation.
32, 33
This pair reflects a perspective on focus, 32 in the form of commitment, 33 in the form of trickary, drawing-in the enemy.
The focus here is on variations on a theme.
01, 33
This pair reflects a perspective on
02, 34
This pair reflects a perspective on
03, 35
This pair reflects a perspective on
04, 36
This pair reflects a perspective on
05, 37
This pair reflects a perspective on
06, 38
This pair reflects a perspective on
07, 39
This pair reflects a perspective on
08, 40
This pair reflects a perspective on
09, 41
This pair reflects a perspective on
10, 42
This pair reflects a perspective on
11, 43
This pair reflects a perspective on
12, 44
This pair reflects a perspective on
13, 45
This pair reflects a perspective on
14, 46
This pair reflects a perspective on
15, 47
This pair reflects a perspective on
16, 48
This pair reflects a perspective on
17, 49
This pair reflects a perspective on
18, 50
This pair reflects a perspective on
19, 51
This pair reflects a perspective on
20, 52
This pair reflects a perspective on
21, 53
This pair reflects a perspective on
22, 54
This pair reflects a perspective on
23, 55
This pair reflects a perspective on
24, 56
This pair reflects a perspective on
25, 57
This pair reflects a perspective on
26, 58
This pair reflects a perspective on
27, 59
This pair reflects a perspective on
28, 60
This pair reflects a perspective on
29, 61
This pair reflects a perspective on
30, 62
This pair reflects a perspective on
31, 63
This pair reflects a perspective on
32, 64
This pair reflects a perspective on