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.

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:

		externalized	or	not
		objectified	or	not
		internalized	or	not

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,

		active	versus	passive
		pasitive	versus	negative
		strong	versus	weak

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

Resilient	Li	Opposite	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.

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)