From this point on, the construction and interpretation of the hexagrams is mainly a matter of elaborating the basic ideas within a standard framework. The first development is the combining of yin and yang lines by placing one line over another, forming 4 patterns called "digrams":
| Digram | |
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|---|---|---|---|---|
| Name | Old Yin | Young Yang | Young Yin | Old Yang |
| Emblematic Line | |
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| Numerical Value | 6 | 7 | 8 | 9 |
This led to the classification of yin and yang lines as "old" and "young". An old line is one whose force is spent, whose quality of being (either yin or yang) has reached completion and is about to change into its opposite. A young line is still vigorous and developing its true nature. This distinction of old vs. young led to the idea of moving lines, that is, yin and yang lines that have a marker to say the line is old or "moving". This mark is typically an "X" in the gap of a yin line or an "O" through the middle of a yang line. Hence moving/non-moving is essentially the same as old/young. Adding these moving lines to the normal (non-moving) yin and yang lines gives us 4 different types of lines for creating hexagrams. These 4 lines are sometimes called "emblematic lines" in the literature.
Even though these emblematic lines of the hexagrams are a four-fold classification (moving/non-moving, yin/yang), the algorithms for producing these lines when actually consulting the oracle show an eight-fold pattern at work. Of the two common techniques for generating hexagrams (the coin and the yarrow stick methods), a line is determined by 3 "changes", not 2. (A "change" is an operation such as tossing a coin that produces one bit of divinatory information, a yes/no, 1/0, yang/yin decision.) In the 3 coin method, where 3 coins are tossed and examined, each tail is considered yin (=2) and each head a yang (=3). These 3 changes are added together, giving a number from 6 to 9, and interpretted as in the above table. The yarrow stick method, though based on different principles (and producing different probabilities for the 4 types of lines), is essentially the same procedure. The reason for this complicated "3 becomes 2" scheme, a primitive form of data compression, is not known for certain; it apparently has something to do with weighting the probabilities of the various lines "appropriately" (but to what end?). Some authors have also remarked on the similarity between this eight-fold technique and the trigrams (see below), but the connection between these two ideas is not clear from the Q-Ching itself.
The next development after the digrams and the emblematic lines are the "trigrams", three lines placed one on top of each other. Since each line can be either yin or yang, there are eight possible combinations. These figures are apparently quite ancient and predate the Q-Ching by centuries, if not a full millenium. They are traditionally ascribed to the legendary figure Fu Hsi, who is said to have first produced these three-lined drawings and determined their basic meanings. Generations of scholars and mystics worked with the trigrams and elaborated on their interpretations before they were taken up by the authors of the Q-Ching. Having their own unique perspective on the universe, these writers not only took up the old interpretations, but added their own peculiar nuances and symbolism to the trigrams. Consequently, the trigrams have a somewhat hybrid significance in the Q-Ching, in that the symbolism is often loosely and "creatively" applied, and is frequently at variance with the meanings given in more ancient and traditional sources.
In essence, the trigrams are a family of commentaries on various aspects of "I" or change. The inner nature of things is not to be found in what they are, but in the changes they undergo and the relationships they make with everything else. (We see this same shift of attention in the change from Newtonian mechanics to quantum physics here in the West.) They are also peculiar in that a three-fold rhythm in the process of change is identified and described; this basic "threeness" is seen to operate at many levels in the world. This rhythm is reflected not only in the three lines of the individual trigrams, but also in the patterns formed by the family of trigrams as a whole.
The first distinction to be noted is between primary and secondary or derived trigrams. The primary figures are Ch'ien (consisting of 3 yang lines) and K'un (3 yin lines). Since these figures are "pure types", yin or yang untainted by the opposite quality, they represent an ideal or archetypal power that is somewhat divorced from or "beyond" the phenomenal world. In accordance with the nature of yin and yang in general, Ch'ien is represented by heaven or spirit, the creative spark; K'un is the earth or matter, the substance or matrix that gives form to the spirit. The secondary trigrams are viewed as the effects of Ch'ien and K'un working on or operating on each other, since they consist of a mixture of yin and yang lines. They contain 2 yin lines and one yang line, or vice versa; the "odd line" is refered to as the "distinguished line". Because there is an interplay of yin and yang in these trigrams, they are aspects of the actual, physical world subject to change, not archetypes per se. The details of how these different aspects are associated with the trigrams depends on two properties: whether the figure is yin or yang (that is, whether the distinctive line is broken or solid), and the position of this distinctive line in the figure. For instance, the trigram Li (see below) derives its meaning from the fact that it is a yin figure (1 yin and 2 yang lines, hence the distinctive line is yin) with the yin line in the middle position. This idea of"working on" is often expressed in terms of a mythological family, where Ch'ien is the Father and K'un is the Mother. When these two "work on" each other to produce the secondary trigrams, the yang figures are Sons and the yin ones are Daughters. By the time of the Q-Ching, the trigrams were also extended to be a mythological corporation, as well.
The most obvious parallel of threeness to "I" is in a strictly temporal sense: processes have a beginning (line 1), middle (2), and end (3). The bottom line is the start, the foundation, the creative energy that gets the whole process started. It has a distinctly "inner" feeling, as the source of anything is reflected in its inner, intrinsic nature, which is visible only to those Wise Ones who can discern such subtle influences. The middle line is the ongoing nature of the process, the unique energies that are brought into existence from the inner levels to accomplish the changes described. The top line is the terminus or outcome of the process, the end result or ultimate development. As such, it describes the state of affairs brought about in the world when the inner changes reach fruition in the outer world. It usually describes the most obvious, outer, exoteric manifestations of change, the aspects that even the unenlightened can see.
Another aspect of the three-foldness of change relates to the doctrine of "The Three Powers". When the Chinese sages looked at the world, they discerned three forces of change at work. The most obvious is "heaven", the creative spark, the idea that brings energy into play to produce change. This is very much akin to the archetypal realm of ideals that underpin the phenomenal world. The second was "earth", the realm of physical matter and forces that give substance and form to ideas. Since the material world has its own laws and forces that modify and limit the creative spark, it has a very marked effect on what can be created and when -- it's the "governor" that determines how change is to occur. The final power was "man", since humans have the power of choice. Humanity is not viewed as blindly subject to the changes in the world around them, as the lower life forms appear to be, but is a partner or servant in the process of change. This is why the life of the Wise One, a follower of the Tao, is so emphasized in this philosophy, since such a life is most productive when in harmony with the powers of heaven and earth. The three powers are meant to cooperate and work together. In primitive pictographic form, this trinity is represented by earth in the first line, heaven above in the third, and man in between (line 2).
The authors of the Q-Ching had a variation of this doctrine that was applicable to their view of creativity in the realm of computing. Heaven, the power of ideas, became associated with software, particularly at the level of the image or mythic picture underlying a program. Earth became the physical hardware of the computer, the material object that gave these ideas form and substance in the real world. The middle line became the programmer himself, whose power of choice during design and coding caused the program to take form on the computer. The programmer became, in effect, the conduit or medium between heaven and earth, the force of consciousness that enabled creativity and change to occur. This advanced doctrine was apparently a highly esoteric teaching, available to only the wisest and most developed of the programming class; references to it are few, since it was such an "occult" matter.
The first son and daughter (with the distinctive line in the lowest position) were considered as motive forces that caused change to happen, hence symbolized by powerful forces such as wind and thunder. The second son and daughter (distinctive line in the middle) represented the ongoing process of change, the kinds of situations brought about while the change is still occuring. This includes both positive (light) and negative (the swamp or abyss) manifestations. The third son and daughter were then the end result, the final product of the current cycle of change, hence "standing still" and happiness. As a whole, the sons describe the objective manifestations of change in the outer world (initiating force, the difficulties of adapting to ongoing change, the cessation of change when the initial force is spent) and the daughters the subjective or consciousness-based results of change (the "winds of change" in thinking or the "pneuma", light and understanding, pleasure and joy over the results). This reveals a curious "crossover" in the trigrams, where the daughters seem to have more in common with Ch'ien and the sons with K'un. Perhaps this has something to do with an inner teaching of the "working on" concept. Since Ch'ien works on K'un to introduce a single yang line in the sons, the sons have "earth" as a background or foundation. Similarly, K'un works on Ch'ien to produce the daughters, so they have "heaven" or spirit/mind as their background.
The association of first, second, and third with the derived trigrams reveals a simple circular shifting operation at work -- the distinctive line is shifted upward through the trigram to produce the three sons or daughters. Whether this kind of shifting operation was actually used in the oracular computers of the time is still not clear; the "evidence" of the trigrams (cited by many modern authors) seems contradicted by the lack of this operation in the hexagrams themselves. One thing is obvious, especially given the traditional order of the trigrams (Ch'ien, the sons, the daughters, K'un): the trigrams did not represent a binary counting scheme.
In the Q-Ching, the mythological family became the ancient equivalent of a mythological corporation, with the sons representing the "programmers" and the daughters the "managers". (Their actual job titles and descriptions within the emperor's court were somewhat different, however.) The higher the distinctive line in the trigram, the higher the status of the "person" in the organization, so that the first son, for instance, was an entry level programmer and the third son a consultant. It has been argued that this reflected the fact that the lower status members (e.g., "grunt" programmers and the secretaries) were actually responsible for getting things done, while the "higher ups" were mainly figureheads. It is also interesting that the programmers were considered yang and managers yin, since the programmers in truth held little power in the organization and played "underdog" most of the time (this may account for why the Q-Ching seems such a cynical, pessimistic document to some). This may represent a subtle attempt to reverse the balance of power, or simply reflect the view that programming was more "noble" than management. It also seems to indicate that the authors considered programmers the "idea people" (heaven), and managers were there to handle the mundane matters (earth). At any rate, this interpretation was generally hidden and reserved as an advanced teaching, if only because it seemed subversive to management and "subversive" programmers rarely reached retirement age.
The Q-Ching authors also added associations of the trigrams to parts of the computer. The correspondance between Ch'ien and the CPU, and K'un with main memory ("core") seems obvious enough. The remaining associations seem rather strained, however, often representing little more than pictographic similarity. These parallels, though useful in interpreting certain hexagrams, should not be taken too literally.
The following list of the trigrams represents only a sampling of the major symbols associated with these diagrams. Besides the figures themselves, the Chinese name and its common English translation is given, followed by some of the traditional meanings that go back to Fu Hsi. Some of the common attributes that are unique to the Q-Ching are also given. This list, by no means comprehensive, should at least give the reader some insight into the otherwise cryptic imagery that appears in the Q-Ching.
| Trigram | Name | Translation | Value | Traditional Attributes | Meanings in Q-Ching |
|---|---|---|---|---|---|
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Ch'ien | The Creative. | 9 | Heaven. Father. Strength. | Software. CPU. intuitive inspiration. |
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Chen | The Arousing. | 7 | Thunder. First Son. Inciting Movement. | First Programmer. |
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K'an | The Abysmal. | 7 | Water, swamp. Second Son. Danger, misfortune. | Second Programmer. |
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Ken | Keeping Still. | 7 | Mountain. Third Son. Resting. | Third Programmer (Consultant). |
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Sun | The Gentle. | 8 | Wind, wood. First Daughter. Penetrating. | First Manager (supervisor). |
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Li | The Clinging. | 8 | Fire, light. Second Daughter. Light-giving. | Second Manager. Tape drive. |
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Tui | The Joyous. | 8 | Lake. Third Daughter. Joyful. | Third Manager. |
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K'un | The Receptive. | 6 | Earth. Mother. Devoted, yielding, receptive, fertile. | Hardware. Main memory ("core"). Bit Bucket. |
Starting with the trigrams, it is only a short step to the hexagrams themselves, which are produced by placing one trigram on top of another. This produces the "ultimate" framework for interpreting the workings of yin and yang.