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The Dialectic structure of the Taixuanjing 
The Tai Xuan Jing (T'ai Hsuan Ching) is constructed  using the dialectic of 
                      thesis + antithesis --> synthesis.  
This makes a tree structure with ternary branching,  resembling and acting like an 
organizational chart (see below). The lines (with three line types) are read from top down.  
     top level: 3 tetragrams (Heaven- Earth- Human) --> 3 total  
     next down : 3x3 tetragrams --> 9 total  
     next down : 3x3x3 tetragrams --> 27 total  
     bottom level: 3x3x3x3 tetragrams --> 81 total  
It does this using the nine phase sequence:  
1. + water (Heaven)  
2. - fire  
3. + wood  
4. - metal  
5. + earth (Earth)  
6. - water  
7. + fire  
8. - wood  
9. + metal (Human)  
The phase of any tetragram with is given by the digram of the bottom two lines.  
In five phase theory, alternate phases are opposites, the phase  
between is the synthesis. This can work backwards as well as forwards.  
thesis antithesis synthesis  
1. + water 2. - fire 3. + wood (forward)  
1. + water 5. + earth 9. + metal (backward)  
The second example suggests that number 5, + earth, might also be  
considered as - earth. (not sure).  
thesis antithesis synthesis  
1. + water 2. - fire 3. + wood  
tet.1 tet. 2 tet. 3  
(Center) (Full Circle) (Mired)  
where Mired would be an incomplete journey between  
the center of a circle and the full circle.  
1. + water 5. + earth 9. + metal  
tet. 1 tet. 5 tet. 9  
(Center) (Keeping Small) (Branching Out)  
1. + water 5. + earth 9. + metal  
tet.1 Tet. 41 tet.81  
(Center) (Response) (Fostering)  
(Heaven) (Earth) (Human)  
There is a parallel in numerology:  
thesis antithesis synthesis  
1 2 3  
father mother offspring  
1 4 7  
begin build essentially complete  
One could argue that 4 and 7 should be switched. Not sure.  
For anyone interested, we have a discussion group  
at taixuanching.yahoogroups.com (sic)  
Also I am currently reconstructing the website at  
The Time Structure of the I Ching and T'ai Hsuan Ching 
by Roger Clough 
The THC is structured in time like a calender, each tetragram corresponding to a hexagram of the I Ching (some hexagrams must be used twice).  The vertical heirarchy is social in nature, resembling a social organization, and was constructed from Ziproyn's essay above  on the time structure in the T'ai Hsuan Ching, together with the I Ching Correspondences. 
Structural Properties 
If we consider each tetragram or hexagram to represents person,  
the resulting structure somewhat resembles the organization chart of a modern business in that:  
  a) The vertical dimension is that of power. 
  b) Each level contains and controls all of the levels below it. 
However, it is unlike such an organization in that: 
  a) the horizontal dimension is time (a year). 
  b) the person in charge of an organizational unit is also a member of that unit as well as those below it. 
The organization chart given below is pyramidal, expanding by powers of 3 at each level (3 Directors, 9 Chiefs, 27 Heads, and 81 Staff Members). Note that there is necessarily some doubling of hexagrams (64 hexagrams but 81 tetragrams). In addition, the meanings of the tetragrams and hexagrams at any given position are equivalent.  
One of the uses of this for divination is that one can see triplets of 
events that tend to occur in time (What is the saying? Disasters come in threes?) For example, under the first grouping, hexagrams 61 (Good Faith at the Center), hex24 (Return) and hex3 (Difficulty at the Beginning) are clustered. My own interpretation of this is that if you cast hex61, you could almost as easily have obtained hex24 or hex3. 
In a sense 61, 24 and 3 are all the same hexagram, the first with a good luck twist, the second with a neutral twist, and the third with a bad luck twist. 
Executive Power 
While hexagrams 1(The Creative) and 2 (The Receptive) are the chief powers of the logical world, in the world of time, 1 and 2 are at lower levels. In the world of time, hexagrams 61 (Center), hex 28 (Change) and hex  55 (Diminishment) are the chief officers (below the CEO, Tai Chi). 
One can even more understanding by moving up the tree to see which hexagrams or tetragrams are controlling the event.  Each level contains and controls the level below. Taking the first highest level component, Center = hex 61 as an example, that is, 
For the I Ching (first third only), 
hex61 contains and controls hexagrams 24, 3, 15, 38, 46, 19, 62, 4, 42, 53,11,5,17, 35,40,34,16,6,18. 
hex62 contains and controls hexagrams 4, 42, 53,11,5,17, 35,40,34,16,6,18. 
hex17 contains and controls hexagrams 35,40,34,16,6,18. 
hex 3  contains and controls hexagrams 15 and 38 
hex 46 contains and controls hexagram 19  
hex 42 contains and controls hexagrams 53,11, and 5.  
hex 11 contains and controls hexagram 5 
hex 34 contains and controls hexagram 16 
hex 6 contains and controls hexagram 16 
From the above one can see the enormous power that hexagram 61(Good Faith at the Center) possesses. 
For the THC, first third only, 
THC1 contains and controls tetragrams 2-27 
THC10 contains and controls tetragrams 11-18 
THC19 contains and controls tetragrams 20-27 
THC4 contains and controls tetragrams 5 and 6 
THC7 contains and controls tetragrams 8 and 9 
THC13 contains and controls tetragrams 14 and 15 
THC16 contains and controls tetragrams 17 and 18 
THC22 contains and controls tetragrams 23 and 24 
THC25 contains and controls tetragrams 26 and 27 
One can see that THC1 (Center) is by far the most powerful. 
In this chart, context (nearby-ness) presumably  is context in time, rather than in logical space. Grouping tetragrams or hexagrams at the lowest, Staff Member, level, is one way of defining such context. These are events are statistically linked in time, so that at given moment in time, nearby events are more likely to happen.  But perhaps a more meaningful way of defining context is through administrative levels, the Staff members at the lowest levels having as context all of their superiors. 
The Tai Chi Corporation Organization Chart   
  (THC refers to T'ai Hsuan Ching tetragram number,   hex refers to I Ching hexagram number) 
Tai Chi Chief Executive Officer <tai chi> 
Center Director (THC1, Center) (hex61, Good Faith at the Center) 
  Center Chief (THC1, Center) (hex 61, Good Faith at the Center) 
      Center Head (THC1, Center) (hex 61, Good Faith at the Center) 
          THC1 Center (hex 61,Good Faith at the Center) 
          THC2 Full Circle (hex 24, Return) 
          THC3 Mired (hex 3, Difficulty at the Beginning) 
      Barrier Head (THC4, Barrier) (hex 3, Difficulty at the Beginning)   
          THC4 Barrier (hex 3, Difficulty at the Beginning)    
          THC5 Keeping Small (hex 15, Modesty)     
          THC6 Contrariety (hex 38, Opposition)   
      Ascent Head (THC7 Ascent) (hex 46, Pushing Upward) 
          THC7 Ascent (hex 46, Pushing Upward) 
          THC8 Opposition (hex 46 Pushing Upward) 
          THC9 Branching Out (hex 19, Approach)            
  Defectiveness Chief (THC10 Defectiveness) (hex 62, Minor Error) 
      Defectiveness Head (THC10 Defectiveness) (hex 62, Minor Error) 
          THC10 Defectiveness (hex 62, Minor Error) 
          THC11 Divergence (hex 62, Minor Error) 
          THC12 Youthfulness (hex 4, Youthful Folly) 
      Increase Head (THC13, Increase (hex 42 Increase) 
          THC13 Increase (hex 42 Increase) 
          THC14 Penetration (hex 53, Advance) 
          THC15 Reach (hex 11, Greatness) 
      Contact Head (THC16 Contact) (hex 11 Greatness) 
          THC16 Contact (hex 11 Greatness) 
          THC17 Holding Back (hex 5, Waiting)  
          THC18 Waiting (hex 5, Waiting) 
 Following Chief (THC19 Following) (hex 17, Pursuit) 
       Following Head (THC19, Following) (hex 17, Pursuit) 
          THC19 Following (hex 17, Pursuit) 
          THC20 Advance (hex 35, Progress) 
          THC21 Release (hex40, Deliverance) 
      Resistance Head (THC22 Resistance) (hex 34, Greatly Strong) 
          THC22 Resistance (hex 34, Greatly Strong) 
          THC23 Ease (hex 34, Greatly Strong) 
          THC24 Joy (hex 16, Amusement) 
      Contention Head (THC25, Contention) (hex 6 Conflict) 
          THC25 Contention (hex 6 Conflict) 
          THC26 Endeavor (hex 18 Undertakings) 
          THC27 Duties (hex 18 Undertakings)  
Change Director (THC28, Change) (hex 49, Moulting)   
  Change Chief (THC28, Change) (hex 49, Moulting)  
       Change Head (THC28, Change) (hex 49, Moulting)   
          THC28 Change (hex 49, Moulting)              
          THC29 Decisiveness (hex 43, Breaking Through) 
          THC30 Bold Resolution (hex 43, Breaking Through) 
       Packing Head (THC31, Packing) (hex 56, Travelling)   
          THC31, Packing) (hex 56, Travelling)    
          THC32 Legion (hex 7, The Army)     
          THC33 Closeness (hex 8, Holding Together)   
      Kinship Head (THC34 Kinship) (hex 8, Holding Together) 
          THC34 Kinship (hex 8, Holding Together) 
          THC35 Gathering (hex 9, Taming Powre of the Small) 
          THC36 Strength (hex 1, The Creative)            
  Purity Chief (THC37 Purity) (hex 1, The Creative) 
      Purity Head (THC37 Purity) (hex 1, The Creative) 
          THC37 Purity (hex 1, The Creative) 
          THC38 Fullness (hex 14, Great Possessions) 
          THC39 Residence (hex 37 Family Members) 
      Law or Model Head (THC40, Law or Model (hex 48 The Well) 
          THC40 Law or Model (hex 48 The Well) 
          THC41 Repose (hex 30 Adherence) 
          THC42 Going to Meet (hex 31, Influence) 
      Encounters Head (THC43 Encounters) (hex 44 Encountering) 
          THC43 Encounters (hex 44 Encountering) 
          THC44 Stove Back (hex 50, Tripod)  
          THC45 Greatness (hex 55, Abundance) 
 Following Chief (THC46 Enlargement) (hex 55, Abundance) 
       Following Head (THC46 Enlargement) (hex 55, Abundance) 
          THC46 Enlargement) (hex 55, Abundance) 
          THC47 Pattern (hex 59, Dispersal) 
          THC48 Ritual (hex10, Step) 
       Flight Head (THC49 Flight) (hex 33, Retreat) 
          THC49 Flight (hex 33, Retreat) 
          THC50 Vastness/Wasting (hex 33, Retreat) 
          THC51 Constancy (hex 32, Duration) 
      Contention Head (THC25, Contention) (hex 6 Conflict) 
          THC52 Measure (hex 62 Regulation) 
          THC53 Eternity (hex 32 Duration) 
          THC54 Unity (hex 13 Fellowship With Men)    
Diminishment Director  (THC55,  Deminishment) (hex 41, Decrease) 
  Diminishment Chief (THC55,  Deminishment) (hex 41, Decrease) 
      Diminishment Head (THC55,  Deminishment) (hex 41, Decrease) 
          THC55,  Deminishment) (hex 41, Decrease) 
          THC56 Closed Mouth (hex 12, Obstruction) 
          THC57 Guardedness (hex 12, Obstruction) 
      Gathering In Head (THC58 Gathering In) (hex 57, The Penetrating)     
          THC58 Gathering In (hex 57, The Penetrating)    
          THC59 Massing (hex 45 Gathering Together)     
          THC60 Accumulation (hex 26, Great Provisioning)   
      Embellishment Head (THC61 Embellishment) (hex 45, Ornamental) 
          THC61 Embellishment (hex 45, Ornamental) 
          THC62 Doubt (hex 57 Laying the Offering) 
          THC63 Watch (hex 20 Contemplation)            
  Sinking Chief (THC64 Sinking) (hex 20 Contemplation) 
      Sinking Head THC64 Sinking (hex 20 Contemplation) 
          THC64 Sinking (hex 20 Contemplation) 
          THC65 Inner (hex 55, Marrying Maiden) 
          THC66 Departure (hex 25 Innocence) 
      Darkening Head (THC67 Darkening) (hex 36 The Light Injured) 
          THC67 Darkening (hex 36 The Light Injured) 
          THC68 Dimming (hex 36 The Light Injured) 
          THC69 Exhaustion (hex 49, Hemmed In) 
      Severance Head (THC70 Severance) (hex 23 Splitting Apart) 
          THC70 Severance (hex 23 Splitting Apart) 
          THC71 Stoppage (hex 52 Resisting)  
          THC72 Hardness (hex 52 Keeping Still) 
 Contemplation Chief (THC73 Contemplation) (hex 63, After Completion) 
       Contemplation Head (THC73 Contemplation) (hex 63, After Completion) 
          THC73 Contemplation (hex 63, After Completion) 
          THC74 Closure (hex 21 Biting Through) 
          THC75 Failure (hex 28 Great Error) 
      Aggravation Head THC76 Aggravation (hex 28 Great Error) 
          THC76 Aggravation (hex 28 Great Error) 
          THC77 Compliance (hex 2, The Recepetive) 
          THC78 On the Verge (hex 64 Not Yet Complete) 
      Difficulties Head (THC79 Difficulties) (hex 39 Difficulty Walking) 
          THC79 Difficulties (hex 39 Difficulty Walking) 
          THC80 Laboring (hex 39 Difficulty Walking) 
          THC81 Fostering (hex 27 Providing Nourishment) 
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