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I Ching

Examples of Integrated, Multi-set Concept Schemes (Annex 2)

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See other Examples of Integrated, Multi-set Concept Schemes. The concept scheme described here is discussed in the paper on: Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation (1984). This was prepared for a sub-project meeting of the Forms of Presentation group of the Goals, Processes and Indicators of Development (GPID) project of the United Nations University (UNU). The annexes were published in Patterns of Conceptual Integration. Brussels, UIA, 1984, pp. 161-204


The Chinese Book of Changes (I Ching) embodies a special system which represents the results of three thousand years of reflection on the nature of change. The binary notation system used has attracted the attention of western philosophers and mathematicians. As a model of change processes in human beings it has been studied by psychoanalysts. The poetry of its imagery has helped to make it widely consulted by the younger generation. The points below are extracted from the

- The I Ching or Book of Changes. Princeton University Press, 1967 (English version of the original 1924 Richard Wilhelm translation; with foreword by C G Jung)

0.1 The Book of Changes: "Its principles contain the categories of all that is -- literally, the molds and the scope of all transformations. These categories are in the mind of man; everything, all that happens and everything that undergoes transformation, must obey the laws prescribed by the mind of man. Not until these categories become operative do things become things." [p. 296)

0.2 The Master said: Writing cannot express words completely. Words cannot express thoughts completely.

Are we then unable to see the thoughts of the holy sages ?

The Master said: The holy sages set up the images in order to express their thoughts completely; they devised the hexagrams in order to express the true and the false completely. Then they appended judgments and so could express their words completely." (p.322)

0.3 "The established language for communication with supra-human intelligences was based on numbers and their symbolism." (p. 263)

1.1 "The number one could not be used, as it is too abstract and rigid and does not include the idea of the manifold." (p. 263)

1.2 "In the Book of Changes a distinction is made between three kinds of change: nonchange, cyclic change (recurrence), and sequent change (non-recurrence). Nonchange is the background, as it were, against which change is possible. For in regard to any change there must be some fixed point to which the change can be referred; otherwise there can be no definite order and everything is dissolved in chaotic movement. The point of reference must be established, and this always requires a choice and decision. It makes possible a system of coordinates into which everything else is fitted. Consequently at the beginning of the world, as at the beinning of thought, there is the decision, the fixing of the point of reference....The ultimate frame of reference for all that changes is the unchanging." (p. 280-1)

2.1 "The Creative produces the invisible seeds of all development. At first these

seeds are purely abstract, therefore with respect to them there can be no action nor acting upon; here it is knowledge that acts creatively. While the Creative acts in the world of the invisible, with spirit and time for its field, the Receptive acts upon matter in space and brings material things to completion.... The nature of the Creative is movement. Through movement it unites with ease what is divided....The nature of the Receptive is repose. Through repose the absolutely simple becomes possible in the spatial world. This simplicity, which arises out of pure receptivity, becomes the germ of all spatial diversity." (p. 285-6)

2.2 "There is heaven, the upper world of light, which though incorporeal, firmly regulates and determines everything that happens, and over against heaven there is the earth, the lower, dark world, corporeal and dependent in its movements upon the phenomena of heaven...The two principles are united by a relation based on homogeneity; they do not combat but complement each other. The difference in level creates a potential, as it were,, by virtue of which movement and living expression of energy become possible. This association of high and low with value differentiations leads to the differentiation of superior and inferior. This is expressed symbolically in the hexagrams of the Book of Changes which are considered to have high and low, superior and inferior places. Each hexagram consists of six places, of which the odd-numbered ones are superior and the even-numbered ones inferior. There is another difference bound up with this one....The firm, the stong, is designated as the principle of movement, the yielding as the principle of rest. The firm is represented by an undivided line, corresponding with the light principle, the yielding by a divided line that corresponds with the dark, principle.

yang ---- yin -- --

(p. 261-2)

2.3 "When the trigrams intermingle, that is, when they are in motion, a double movement is observable: first, the usual clockwise movement, cumulative and expanding as time goes on, and determining the events that are passing; second, an opposite backward movement, folding up and contracting as time goes on, through which the seeds of the future take form." (p. 266-7)

3.1 Three world principles:

3.2 Three positions in trigram

3.3 Three position-pairs in hexagram: heaven, man, earth

4.1 "These are the two primary forces later designated as yang, the bright principle, and yin, the dark. Then, through doubling, there arise the four images:

4.2 "There is nothing that has more movement or greater cohesion than the four seasons." (p. 319)

4.3 "What manifests itself visibly they called an image; what has bodily form they called a tool. What is established in usage they called a pattern. That which furthers on going out and coming in, that which all men live by, they called the divine." (p. 318)

4.3 "Therefore four operations are required to produce a change" (p. 312)

5.1 "Since the Han period especially, when the magic of the "five stages of change" became associated with the Book of Changes, more and more mystery and finally more and more hocus-pocus have become attached to the book." (p. 356)

5.2 "The "five stages of change" are usually incorrectly translated as elements." (p. 309)

5.3 "There are five heavenly numbers (1,3,5,7,9). There are also five earthly numbers (2,4,6,8,10). When they are distributed among the five places, each finds its complement." (p. 310)

5.4 "Five operations are undertaken in order to obtain a change." (p. 315)

6.1 Six derived trigrams representing forces acting in pairs to engender cyclic movement:

6.2 "The six places in the hexagram are distinguished as follows: The lowest and topmost are, so to speak, outside the situation. Of these, the lowest is inferior, because it has not yet entered the situation. The uppermost is superior; it is the place of the sage who is no longer involved in worldly affairs, or, under certain circumstances, of an eminent man who is without power. Of the inner places, the second and thefourth are those of officials, or of sons or women. The fourth is the higher, the second inferior to it. The third and fifth are authoritative places..." (p. 292)

6.3 "The trigrams contain only the images (ideas) of the things they represent. It is only in the hexagrams that the individual lines come into consideration, because it is only in the hexagrams that the relationships of above and below, within and without,appear", (p. 325)

6.4 A changing divided line (old yin) is associated with the number 6 (p. 311)

7.1 It is not in the scheme of hexagrams that a sevenfold division appears but rather as a factor underlying the emergence of a particular hexagram in a given set of circumstances through a ritual procedure with a set of 50 yarrow stalks. "The number of the total is fifty. Of these, forty-nine are used. They are divided into two portions, to represent the two primal forces." (p. 310)

7.2 Yarrow stalks "are symbols of heaven and the spirit. Their basic number is seven, their total number is forty-nine (7x7)." (p. 317)

7.3 An unchanging, undivided line (young yang) is associated with the number 7. (p. 311)

8.1 "The four images generate the eight trigrams." (p. 318)

8.2 "Heaven and earth determine the direction.
The forces of mountain and lake are united.
Thunder and wind arouse each other.
Water and fire do not combat each other.
Thus are the eight trigrams intermingled." (p. 265)

8.3 An unchanging, divided line (young yin) is associated with the number 8 (p. 311)

8.4 Thunder (Arousing) brings about movement Wind (Gentle) brings about dispersion Rain (Abysmal) brings about moisture Sun (Clinging) brings about warmth Keeping still (Mountain) brings about standstill Joyous (Lake) brings about pleasure Creative (Heaven) brings about rulership Receptive (Earth) brings about shelter. (p. 267)

8.5 Arousing: all things come forth! awakening; stirring, germination and sprouting; thunder and electrical energy

8.6 The 64 hexagrams are considered to be divided into B "houses" of 6 each (p. 725)

9.1 A changing, undivided line (old yang) is associated with the number 9 (p. 311)

10.1 "There are five heavenly numbers. There are also five earthly numbers" (p. 310)

12.1 Although not explicitly mentioned, a given 6-position hexagram, together with the hexagram into which it is changing (or which is its inverse), total 12 positions.

18.1 "Eighteen mutations yield a hexagram." (p. 312)

25.1 "The sum of the heavenly numbers (1,3,5,7,9) is twenty-five, that of the earthly numbers is thirty" (p. 310)

30.1 "The sum of the heavenly numbers is twenty-five, that of the earthly numbers (2,4,6,8,10) is thirty", (p. 310)

49.1 "The number of the total is fifty. Of these forty-nine are used. They are divided into two portions to represent the primal powers." (p. 310)

50.1 "The number of the total is fifty." (p. 310)

55.1 "The sum total of heavenly numbers and earthly numbers if fifty-five."(p. 310)

64.1 There are 6x8, namely 64 hexagrams in the scheme. These are divided into eight houses of eight each. (p. 725)

144.1 "The numbers that yield the Creative total 216; those which yield the Receptive total 144,making in all 360." (p. 311)

216.1 "The numbers that yield the Creative total 216; those which yield the Receptive total 144,making in all 360." (p. 311)

360.1 "The numbers that yield the Creative total 216; those which yield the Receptive total 144, making in all 360. They correspond to the days of the year." (p. 311)

384.1 Each of the 64 hexagrams with 6 lines has commentaries on the consequences of the change or movement of the individual lines, making a total of 6x64, namely 384 commentaries

4096.1 "Each of the sixty-four hexagrams can change into another through the

appropriate movement of one or more lines. Thus we arrive at a total of 4096 C64 x 643 transitional stages, and these represent every possible situation." (p. 313)

11,520.1 "The numbers of the stalks in the two parts amount to 11,520, which correspond with the number of the ten thousand things." [p. 312)

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