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  ADDENDUM
correlations with the I Ching

The sixty-four numbered 'hexagrams' in the Chinese classic I Ching Book of Changes are stacks of six horizontal yin/yang (broken/unbroken) lines. Commentaries describing the significance of each hexagram, I find, correspond remarkably with the sixty-four isomorphic corners of my Model (shown in the eight Figures of Part 4). Here I show how this is possible and why the depiction of the hexagrams on a hypercube gives advantages not found in their traditional arrays around a circle or in the spaces of a chessboard.

Fu-Hsi's Clock Such an arrangement was possible because the hexagrams have lower and upper sets of three lines, called trigrams. As has often been observed, the properties of each trigram can be seen as the eight corners of a cube. I have found it necessary to arrange the trigrams' oppositions according to the clock-like contrasts attributed to the Emperor Fu Hsi, circa 1,000 B.C..

You will see from the diagram that Fu-Hsi's opposing trigrams are symmetrical opposites, with broken and unbroken lines reversed. This is the arrangement I will follow throughout this presentation. The more common asymmetrical one in the bulk of I Ching literature reverses the trigrams shown here at 1:30 and 4:30 I reject. It does not permit the reproduction of my paradigm's distribution of problem-contexts and response-modes. (It has been suggested that the more popular arrangement of the trigrams results from an ancient flawed reconstruction of destroyed Texts.)

Fu-Hsi's oppositions are shown below. Each trigram is given its usual Chinese name and its usual English label. To each is assigned a color, and its opposite has the opposite color. These same sets of opposites will hold for both the Lower and Upper trigrams. This is shown tri-dimensionally in Figure 28. Colors of the Lower problem-context trigrams will be capitalized, and those of the Upper response-mode trigrams will be without a capitalized first letter.

 Li
'Fire / Sun'
Opposite Kan
'Water / the Deep'
 Kun
'Earth'
Opposite  Chien
'Heaven'
 Chen
'Thunder'
Opposite  Sun
'Wind / Wood'
 Ken
'Mountain'
Opposite  Tui
'Marsh / Mist'

Following the digital contrasts described in Part 1, the lower trigrams may be seen to depict 'problem-contexts' and the upper ones 'response-modes', I produced a hypercube with the Commentaries on its sixty-four corners (see Figure 31). It is strikingly similar to my Model's isomorphic combinations of hypercubes for individuals and collectivities as depicted in the cubic depictions of Part 4.

The correspondence becomes understandable when one sees the lower trigram's problem-context defined by the presence or absence of the three types of learning:

 - -externalizedornot---
---objectifiedornot- -
- -internalizedornot---

This resulted in the lower trigram offering eight distinct three-dimensionally opposite, problem contexts, at its cubic corners:


Judgmental
 Li
Opposite
Hedonistic
 Kan

Domestic
 Kun
Opposite
Worldly
 Chien

Productive
 Chen
Opposite
Protective
 Sun

Moralistic
 Ken
Opposite
Pragmatic
 Tui

For the upper trigram of response styles,

 ---activeversuspassive- -
- -pasitiveversusnegative---
---strongversusweak- -

This resulted in the 'upper' trigram offering eight distinct three-dimensionally opposite, styles of response, at its cubic corners:


Resilient
 LiOpposite
Collapsed
 Kan

Yielding
 Kun Opposite
Tough
 Chien

Flexible
 Chen Opposite
Rigid
 Sun

Stable
 Ken Opposite
Brittle
 Tui

[I stumbled upon this formulation while vacationing from France in California after completing my first paper on the paradigm: Stylistic Statics: The Isomorphic Mapping of Semantic Space (1991). The correspondence was so remarkable and seemingly significant that I immediately took out a copyright under the title Systems Design for the I Ching : A Proposed Distribution of Hexagrams within Human Systems.]

This unanticipated complication of my retirement publication project began when I noticed several I Ching volumes in a Dana Point, California book store. Having once read Cary F. Baynes' Bollington Series translation from German (Princeton Univ. Press, 1973) of Hellmut Wilhelm's (1960) Eight Lectures on the I Ching , and recalling that he mentioned sixty-four hexagrams, I bought what seemed to be a user-friendly book to see how they were described. It was when I saw cubic potentials in the trigrams that I began hours of trials on opened grocery bags that finally yielded, to my amazement, a striking correspondence with the isomorphic versions of my paradigm's prototypes as illustrated in the figures in part 3.

On rereading Wilhelm after returning to Paris, I found his view that the trigrams' three dimensions formed "a remarkably compact cube". I disagreed, however, with his conclusion that a graphic representation of the hexagrams "cannot but be inadequate, because three dimensions do not suffice." My arrangement of 'cubes within a cube' would seem to overcome that difficulty in a way infinitely preferable to the usual presentations of the sixty-four hexagrams around the rim of a circle or in the chessboard-like spaces of an eight-by-eight square.

[No "oracular" significance is claimed or implied.]

Figure 31 below shows, with their conventional numbering, the sixty-four hexagrams in the hypercubic context of my Model. The four pages that follow present the "evidence" for my contention that the correspondence exists. The reader will judge its validity and significance.

Figure 31

The Distribution of Hexagrams on the Systems Model
Governance
(Identity) [Policy]
30
55 13 22
46 36 37
63
Operative
(Personality) [Organization]
21
51 25 27
17 24 42
3
Maintenance
(Character) [Community]
14
34 1 26
43 11 9
5
Regulative
(Probity) [Piety]
56
62 33 52
31 15 53
39
Instrumental
(Habits) [Reciprocity]
38
54 10 41
58 19 61
60
Projective
(Agendas) [Ideology]
35
16 12 23
45 2 20
8
Expressive
(Emotions) [Belonging]
50
32 44 18
28 46 57
48
Situational
(Dispositions) [Interaction]
64
40 6 4
47 7 59
29

An advantage from picturing this hypercubic context for the hexagrams is the way it helps to underline oppositions - especially the four major ones at the extremes of:

  • black versus white (30 versus 29)
  • violet versus yellow (1 versus 2)
  • orange versus blue (51 versus 57)
  • green versus red (52 versus 58)

Erich Fromm might have termed them, respectively, the four existential oppositions existing between:

  • generation and degeneration
  • aggressivity and nurture
  • freedom and constraint
  • order and disorder

These contrasts will appear below, at the beginning of each archetype's set of three-dimensional oppositions.

GOVERNANCE
BLACK
Ethical Judgments

30 Resilient Clarifying Awareness (Li)
Transforming and protecting as fortunes shift.
Stalinian scrutiny.
versus
63 Collapsed After Completion (Chi Chi)
The calm before things fall apart
Don't rock the boat.

36 Yielding Damaged Illumination (Ming I)
Though wounded, accept overwhelming constraints,
bad luck and hardships. Play it smart.
versus
13 Tough Community (T'ung Jen)
Seeking a just, unselfish, social structure

55 Flexible Abounding Exuberance (Feng)
Honest and open movement across the board.
Judges objectively and acts purposefully.
versus
37 Rigid Family Values (Chia Jen)
Lack of submission to paternalism and duties
can lead to difficulties and even to destruction.

22 Stable Ornamental (Pi)
Waning of a beautiful period.
Beware of trickery. Administer diplomatically without judging.
versus
49 Brittle Change (Ko)
Incipient renewal.
Strip away the old. Revolt and renew.

 

HEDONISTIC
WHITE
Situational Choices

64 Resilient Before Completion (Wei Chi)
Refreshing challenge.
Good fortune near. Beware of overconfidence.
versus
29 Collapsed Double Bind (K'an)
Confronting the depths
One damn thing after another.

7 Yielding Discipline (Shih)
Organize confusion.
Nourish and persuade others. Be competent.
versus
6 Tough Conflict (Sung)
Dangerous contestation.
Argue, don't act. Retreat and maintain position.

40 Flexible Release (Hsieh)
Forgiving movement
New vitality. Untie knots. Deliverance, but plan.
versus
59 Rigid Dissolving Resistance (Haun)
Successful selfishness
Haste makes waste. Clear the way. Do things.

4 Stable Immaturity (Meng)
Dull and clouded.
Excusably in a fog. Concealing troublesome habits.
versus
47 Brittle Restrictions (K'un)
Repression. Trapped in an acquisitive struggle. Break out.

 

PROJECTIVE
YELLOW
Reflective Orientations

2 Yielding Peace (K'un)
Responsive. Be correct and firm, without initiative.
Nourish and give form. Yield. Ideal of docility. Devotion.
versus
12 Tough Discord (Pi)
Reality obstructs projects. Erect barriers.
Want of understanding. Stand off.

35 Resilient Advancement (Chin)
Welcome new day.
Step into the light. Peaceful and strong prospects. Prosper.
versus
8 Collapsed Seeking Accord (Pi)
Resistance to joining.
Find what you belong to. Change your strategy.

16 Flexible Delight (Yu)
Responsiveness will break you from lethargy.
Enthusiasm gives inspirational harmony.
versus
20 Rigid Contemplation (Kuan)
Project an example. Let all come into view. Strive toward an ideal.

23 Stable Separation (Po)
Strip away old habits and ideas.
Wait it out. Precarious, top-heavy, needs.
versus
45 Brittle Mobilization (Ts'ui)
Striving for advantage
Great effort and courage rewarding, despite fragility.

 

MAINTENANCE
VIOLET
Adaptation

11 Yielding Harmony (T'ai)
Luck. Passive success from absorption of the immediate.
Tranquillity. Use potentials.
versus
1 Tough Persisting (Chien)
Primal power. Energy, motion and duration.
Organize, develop, perfect and consummate.

14 Resilient Wealth (Ta Yu)
Creative abundance. Easy success.
while avoiding compromise. Produce and share results.
versus
5 Collapsed Delaying (Hsu)
Escapism in the face of impending threat.
Patience; easy does it. Waiting and hoping.

34 Flexible Great Power (Ta Chuang)
Perseverance needed along with flexibility
for flourishing fortune. Focus strength and go for it.
versus
9 Rigid Minor Adjustment (Hsiao Chu)
Maintain endangered integrity.
Stabilize and assemble. Gradually develop concerns.

26 Stable Storing Abundance (Ta Ch'u)
Hidden potential to overcome constraints on accumulation. Control.
versus
43 Brittle Breakthrough (Kuai)
Challenge City Hall with precaution.
Clean it out and bring to light. Manipulate countermeasures

 

OPERATIVE
ORANGE
Productivity

51 Flexible Arousing (Chen)
Challenging shake-up. Exciting power through danger.
Inner security allows triumph with style.
versus
42 Rigid Harvest (Yi)
Must please outsiders and superiors
to reap gains from all endeavors. Be resolute in a fertile time.

21 Resilient Union By Confrontation (Shih Ho)
Legitimate assertiveness. Chew on it. If innocent, you are safe.
versus
3 Collapsed Growing Pains (Chun)
Wait and seek help. Adjust.
Focus needs for protection. Has potential if nourished.

24 Yielding Restoration (Fu)
Realistic acceptance of slow development.
All is on your side, if timing is right.
versus
25 Tough Disentanglement (Wu Wang)
Must labor for gains and to protect property by 'natural law'
"Wait it out" for 2nd chance.

27 Stable Ingesting (I)
Substitute healthy desire for envy.
Provide nourishment. Selfishness and protectionism.
versus
17 Brittle Following (Sui)
Fragile, egocentric, dependency.
It is hard to find the right path. Don't fight it, go with the flow.

 

EXPRESSIVE
BLUE
Defensive

32 Flexible Perseverance (Heng)
Steadfastness and adaptability with freedom from error
on ritual occasions. Fixes power for Tao
versus
57 Rigid Willing Submission (Sun)
Modest success by submission to circumstances.
Realistic goals accomplished easily.

50 Resilient Restructuring (Ting)
Transform image. Double good fortune.
Family prosperity and spiritual well-being
versus
48 Collapsed Blocked Sharing (Ching)
Problems if resources abused. Wrong principles may cloud intuition.

46 Yielding Gradual Improvement (Sheng)
Gentleness and willing acceptance.
Freedom from anxiety. Make an effort.
versus
44 Tough Withstand (Kou)
Dangerously strong and willful.
Inequality fosters illicit behavior. Welcome, then let go.

18 Stable Fixing The Spoiled (Ku)
Do what is worth doing.
Seek out the sources of corruption. Let it rot, for renewal
versus
28 Brittle Predicament (Ta Kuo)
Avoid the imminent collapse in a distressful crisis.
Overreaching limits can bring disaster.

 

REGULATIVE
GREEN
Morality

52 Stable Keeping Still (Ken)
Maintain position. This brings benefits in the end. Isolate oneself.
versus
31 Brittle Tension (Hsien)
A tenuous accord despite mutual attraction.
Activity may be precarious. Bring things together.

56 Resilient Questing (Lu)
Searching alone and outside for fulfillment
brings glory to the traveler. Humility in wandering.
versus
39 Collapsed Difficulty (Chien)
Self-imposed obstruction.
Don't act, procrastinate. Incompetence in movement.

15 Yielding Modesty (Ch'ien)
Holding back. Observing social rules brings rewards.
The humble are eventual winners.
versus
33 Tough Curtail (Tun)
Reclusive hostility. Declining fortune.
Retreat in force. Be small; be happy.

62 Flexible Circumscribed Expansiveness (Hsiao Kuo)
Careful adaptations yield modest success.
Be flexible in nonessentials.
versus
53 Rigid Influence (Chien)
Enduring. Commitment to one's place in society.
Mild stubbornness. Can penetrate by steps.

 

INSTRUMENTAL
RED
Pragmatism

41 Stable Temporary Sacrifice (Sun)
Moderate desires and control anger.
Confidence in goal despite voluntary loss.
versus
58 Brittle Superficiality (Tui)
Expectancy. Pleasure without enlightenment.
Excessive talk brings misfortune.

38 Resilient Antagonistic Cooperation (Kuie)
Good fortune if goals realistic.
Opposites desire union. Dialectical resolution.
versus
60 Collapsed Discontinuity (Chien)
Restrain indiscriminate acts.
Accept imposed limitations. Inaction helps as road ends.

19 Yielding Approach (Lin)
Persuades with honesty and sincerity
Mutuality of trusting expectations. Good fortune on middle path.
versus
10 Tough Treading Carefully (Lu)
Tentative assertiveness.
Extreme caution needed for success. Risky step pays off.

54 Flexible Marriage Proposal (Kuei Mei)
Emphasize solid worth.
Impetuosity is chancy. Ceremonial actions may be futile.
versus
61 Rigid Balanced (Chung Fu)
Enemies permit no error.
Confidence can lead to misfortune, but right action is rewarded.

 

What should we make of this correspondence between my model of semantic space and the ancient oracle of the I Ching? Let it not be too quickly dismissed because of the oracular aspect seen by Carl Jung [1964] (1968) as evidence of "synchronicity", an acausal connecting principle. Fritjof Capra says in The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism (1985), "The use of the I Ching as a book of wisdom is, in fact, of far greater importance than its use as an oracle. It has inspired the leading minds of China throughout the ages.." (p.110) and in his Preface to this second edition, "I have found that a natural extention of the concepts of modern physics to other fields is provided by the framework of systems theory...the systems approach strongly enforces the parallels between modern physics and Eastern mysticism". Recently, Johnson F. Yan, in DNA and the I Ching: The Tao of Life (1991). arguing for a correspondence between hexagrams and both amino acids and the genetic code, notes that "..von Leibnitz, the inventor of binary arithmetic and an early investigator of probablility, was aware of the I Ching... Neils Bohr was so impressed with the connection between the I Ching and the various dualities in quantum theory that, when he was knighted, he made the Tai Chi symbol a part of his coat of arms."(p.x)

 
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