A Treatise on Hexagram 16, Self-Reflexive

by Martin Bulgerin, BioPsciences Institute

(Originally published in the Spring 2002 issue of JOAC.)

According to legend, Confucius waited until the age of 70 before taking up the study of the I-Ching, not considering he had the necessary knowledge, wisdom and philosophical maturity to delve into the oracle until that age. As I look over hexagram 16 of the Q-Ching, I feel very similar qualms about having the necessary depth to understand this most cryptic of figures.

Opinions about hexagram 16 among the scholars who have studied it vary all over the map. According to older Chinese writers, "Self-Reflexive" was one of the deepest and most vital teachings of the entire Q-Ching. It was considered a "core teaching" that a young programmer must master before being considered a Wise One in the emperor's court. In this regard, it was akin to a Zen koan of later centuries: a seemingly meaningless story that boggles the rational mind until enlightened understanding dawns on the seeker. Needless to say, many a hack in the court never made head nor tail (let alone yang nor yin) of this hexagram. You can practically see the amused smile on the Wise One's face as the young one's answers clearly mark him as a Fool. On the other hand, some modern scholars have speculated that Lao Tse Kaud was trying to make a Fool out of everybody that studied this hexagram, that it was only a perverse hoax he was attempting to pull on everyone. My own recent analysis tends to dispute the modern cynics. However, with a wily philosopher such as LTK, it's doubtful any one explanation fully captures the true story. The text is both profound and a prank at the same time, as the teachings of the Wise Ones tend to be. Behind the hexagram is the quiet, impish smile of Lao Tse Kaud himself, challenging us to a deeper participation in the Tao of Code.

Needless to say, the translation process for this hexagram was more challenging than most. Our first translations seemed comical and amateurish compared to other parts of the Q-Ching. We wondered how this one page could sound so meaningless when the rest of LTK's masterpiece seemed to fall in place so easily. However, "Self-Reflexive" has a unique way of growing on you, the longer you linger with it. Over the space of many months, it slowly started to dawn on me how deep and convoluted this figure is. As you will see, it provides an unprecedented window of insight into the way LTK approached the writing of his oracle and of his search for the Golden Code. The more time you spend with the old Master, the more he becomes an old friend.

Self-Reflexivity as a Philosophical Concept

Something that is self-reflexive or self-referential is simply something that refers to itself. In the realm of English sentences, most sentences talk about some subject matter. A self-reflexive sentence somehow manages to loop back and talk about itself. Quite frequently, this is done with the phrase "this sentence" or some variation; more informally, the pronoun "I" can say the same thing (assuming you grant sentences the power of speech). Some simple examples include:

The mechanism of self-reference can be much more convoluted than a simple pronoun, for instance:

Of course, the usage of self-reference is commonplace in the realm of homo sapiens who speak English. People talk about themselves all the time and most sentences seem to start with the pronoun I. But more to the point, self-reference gives people the ability to reflect on themselves, to experience and report on their inner, subjective lives. Self-reflexivity is a highly pertinent property of conscious beings. It's hard to call an entity a "person" if there is nobody inside. This is part of the mystery of consciousness itself.

The most conspicuous and sophisticated example of self-reference was in a paper by Kurt Gödel (1931) where he proved his famous "Incompleteness Theorems" that literally shook the world of mathematics to its foundations. He started with one of the simplest mathematical systems available, the numbers we count with (0, 1, 2, ...) and simple operations on them such as plus, times and equals. The facts of what we know about this number system can be expressed in the language of symbolic logic. The theory of numbers consists of logical statements assumed to be true (axioms) and rules of logic that let us prove new true statements (theorems) from old truths. Gödel then showed, using a numerical code now known as "Gödel numbering", how to translate all the logical statements into numbers and the rules of logic into standard numerical operations. This Gödel numbering is similar in spirit to representing all the statements as ASCII codes that in turn are long integers (although the details of his coding are much different). So the theory talks about the numbers and the numbers talk about the theory -- the loop is closed. When he gave numbers a voice like this and made them conscious, a strange thing happened -- they showed evidence of having an unconscious. We normally think of statements as being true or false. But Gödel produced statements (that are "obviously true" from our vantage point) that when you asked the numbers if they were true or false, all it could say is "I don't know." Incredibly, the statement "I am free from contradiction." is one of these don't-know statements. (Unless, of course, there already are contradictions in arithmetic/logic, in which case all bets are off. However, most mathematicians consider this option utterly unthinkable, if only for job security reasons.) In one brilliant stroke, Gödel dashed one of the grandest hopes of the intellect, a proof that mathematics is correct. The validity of something even as simple as arithmetic rests as an article of faith, not a result of logic. All systems of knowledge "suffer" from this problem.

I like to summarize Gödel's Theorems for human beings and math alike as:

  1. No conscious entity can possibly know everything.
  2. Any entity that says they know everything is full of s***.

In our case, we are dealing with a hexagram called "Self-Reflexive". We're off to a good start: any hexagram that pretends to "talk about itself" is doing a good job with a name like this. But if Hx. 16 is indeed self-reflexive (both in name and in fact), it should show evidence that it not only talks about hexagrams in general, but about itself in particular. As I will argue, this figure and its commentary seems to do nothing but talk about itself. Here's the koan! By studying a hexagram that claims to be conscious, the young programmer is forced to reflect on all conscious entities, including... um ... himself... gulp. Only the fool sees utter nonsense here.

The Search for Keywords in the Text

In order for a hexagram to talk about itself (and hexagrams in general), at a minimum it needs to "talk the talk" and use the right vocabulary. A quick reading of the poetic imagery in the commentary of this figure leaves the firm impression of "keywords" from the Q-Ching mythos scattered all over.

To begin with, terms related to the doctrine of The Eight Trigrams show up throughout the various commentaries. Terms like "light" and "fire" are attributes of the trigram Li, the second daughter. Li is also both the upper and lower trigram of Hx. 16, so it is natural to see her attributes mentioned. By itself, the mention of "fire" is not self-reflexive. But when the Judgment starts out "Fire reflects in fire," you might start to have some second thoughts. The persistant references to "sons" and "daughters" is also suspicious.

The doctrine of The Three Powers also appears frequently, especially in the descriptions of the moving lines. In particular, the word "earth" only appears in lines 1 and 2, the "earth" part of a hexagram. Similary, lines 5 and 6 up on top talk about "heaven", a very natural topic for the heaven lines to discuss. And in lines 3 and 4, the proper place of the third power man, stands the "Wise One" himself. Perhaps LTK even imagined himself in this place.

Terminology relating to yin and yang lines, in both their moving and non-moving forms, can be teased from the text. There are many references to yang attributes (light, strength, beauty) as well as yin (darkness, soft, yielding, receptive, nurturing). The mythic figures mentioned in the text are variously described as "moving" or even "dancing". Yet in opposition, there are two emphatic repetitions of the phrase "but [it] moves not". Could it be that Hx. 16 is talking about its own lines?

So Self-Reflexive is at least using the correct words. But what is it saying? And does its purported "message" correspond with what is actually going on within the hexagram itself?

Digrams and Trigrams in the Figure

Hexagrams are meant to be interpreted -- the Q-Ching is "nothing but" interpretations of hexagrams. Without the ability to see the inner meaning of these figures, they are little more than the yin/yang scribblings of a Wise One wannabe. (There's part of me that is still impressed that the old sages could make an entire career, let alone become a legend, for inventing 8 trigrams...) Self-Reflexive (pardon the anthropomorphizing, since this is where the hexagram "comes alive" for me) gives us two very important clues in the first and last moving lines. It tells us a meaning, but it also describes how to figure out this meaning in the first place.

In line 1, Self-Reflexive starts out with the sentence: "From Oneness comes the Two, and Two becomes Three." What a straightforward and succinct summary of the philosophical roots of this entire discipline! From the Tao (=1) comes Yin (=2) and Yang (=3). It's a minor point of translation, but a telling detail, that "Yin becomes Yang", not "Yang comes from Yin." Traditionally, especially in the old Tai Chi symbol, Yin and Yang change into each other; they are co-equal and neither comes before the other. Perhaps an alternate reading of "from one comes two" is that undifferentiated Tao produces the two lines (duality), kicking off the process of change or "I" between them. Yet another reading of this same sentence is: starting with your basic Yin and Yang lines by themselves, you can build digrams and trigrams. (It's not unusual that one sentence could encode multiple meanings like this; in fact, a Wise One would greatly admire such economy of expression.) In short, line 1 is indeed the foundation or root of the figure, a philosophical bootstrap sequence that creates the entire Q-Ching. As the line later notes, "From such simple beginnings comes the ten thousand things of heaven and earth." To some scholars, the "ten thousand things" can refer in certain contexts to the 4096 possible hexagrams when moving lines are considered. Line 1 definitely achieves "bootstrap complete".

However, line 6 (the completion of the process) contains a warning that is really a hint. "Though six lines appear, yet there is still but Two and Three." This moving line text is admonishing us to look past the surface structure of the hexagram and examine its deep structure instead. In particular, look for digrams and trigrams within Hx. 16, and play with them using all the conceptual machinary developed by the ancient sages. You can almost hear Self-Reflexive say to us, "Look past my skin-deep appearance and see my true inner beauty!"

If the figure insists that it contains wisdom, let's heed its advice for a time and see where it takes us.

Examining the Digrams

As a first step to considering the "Twos and Threes" in the hexagram, let's look at the pairs of lines corresponding to The Three Powers.

"Earth" corresponds to the lowest lines in the figure, lines 1 and 2. With a Yin line sitting on a Yang line, this is the same as the digram called Young Yin or non-moving Yin. Remember that in a digram, the upper line determines the Yin/Yang nature of the digram, while the lower line is solely responsible for the movement. If Self-Reflexive is to live up to its name, we would expect line 2 to express the Yin qualities of the digram and line 1 to describe its non-movement. In fact, this is exactly what we see. Line 2 contains the sentence "The earth below is receptive and nurturing", keywords that depict Yin. Meanwhile, line 1 says "The earth below is yielding and soft, but moves not." The text for these lines perfectly describe the lines themselves. Non-moving Yin is also a very appropriate picture of "earth", soft and yielding, but solid (not moving).

The situation for "Heaven", lines 5 and 6, is very similar. Here we have a Yang line sitting on a Yin, producing a Young Yang digram or non-moving Yang, an appropriate symbol of the eternal splendor of Heaven. Line 6 says "Heaven sits above [in the top lines of the hexagram] and shows great strength and beauty", attributes of Yang. Line 5 tells us that Heaven "moves not", since this is a non-moving digram.

However, the middle lines (3 and 4), the digram for the third Power "Man", are a different story. We have 2 Yang lines here, generating Old Yang or moving Yang. The Wise One, standing between Heaven and Earth, must act as an intermediary, shuttling back and forth. By moving between them, he unites the inspiration of Heaven with the receptive stability of Earth, bringing the Golden Code down to the hardware where it becomes real in a physical sense. It's fitting that these two Yang lines resemble in miniature the 6 Yang lines of the hexagram for Golden Code (hx. 3), since the Wise One is always striving towards this ideal. Further, these two lines straddle the boundary between the upper and lower trigrams, giving them a split or dual focus. The text for line 4 is definitely Yang in nature, while line 3 expresses the movement of this old line through the metaphor of dancing and several Yin references as moving Yang changes to Yin. All told, these two lines describe the role of the Wise One quite nicely.

It should be remembered that emblematic lines, digrams and trigrams are all related via the standard "6-7-8-9 mapping", which allows certain data compression techniques to be used on the hexagram at this point. Each of the digrams we just discussed is equivalent to an emblematic line, condensing 6 lines down to 3. This forms the trigram Sun, the Gentle, one of whose attributes is wind. However, the middle line of this trigram is moving Yang. When this line is allowed to change, Sun transforms into Ken, Keeping Still, which has the attribute of resting. This "dance" reflects the observation in Line 6 (after the "Twos and Threes" hint) that "When they dance together, even the wind stands still." This part of the moving line commentary, dismissed by most scholars as either poetic exaggeration or pure nonsense, makes perfect sense as a description of Sun changing into Ken.

Examining the Trigrams

The interpretations of a hexagram are generally determined more by the component trigrams in the figure than by any other feature, so we can safely assume that studying the trigrams will produce much insight into Self-Reflexive. In fact, some of the most obscure passages in the text suddenly make perfect sense when you realize they are talking about the hexagram's own trigrams and their movements.

Both the upper and lower trigrams (consisting of lines 4-5-6 and 1-2-3, respectively) are the trigram Li, the Clinging, commonly symbolized by fire or light. The concepts of fire above and fire below are woven into many sections of the text. Lower equals Earth, the material world, the lower part of the body, while upper relates to Heaven, the subjective world of the observer, and the upper part of the body. The image describing the hexagram starts out "The same light that shines on the seen shines on the seer." The seer is the observer himself, while the seen is the material world he sets eyes upon. They are both bathed in the same divine light, joining them together and banishing any dualistic separation between them. Similarly, "Fire reflects in fire" as the light of consciousness is revealed in the outer world as well. The upper fire shines on the face of the Great Empress (line 5), while the lower fire illuminates her feet (line 2). All told, some of the most important symbolism in the text is a faithful reflection (as it were) of Li on Li.

"While Daughters become Sons..."
Trigram:1-2-32-3-4 3-4-54-5-6
Third Line

Things start getting pretty complicated when the inner trigrams are brought in also, especially since line 3 insists on "dancing". Line 4 (the upper half of the Wise One lines) is part of 3 separate trigrams. Interestingly enough, they are the 3 daughters of the Trigram Family. This explains the sentence in the 4th moving line text that "The daughters dance with him [the Wise One, lines 3 and 4], making four [this is the 4th line]." Further, the trigram consisting of lines 3-4-5 is Tui, the Joyous. Perhaps this is why "There is great joy [3-4-5] as he [the Wise One, 3-4] gazes into heaven [5-6]." In fact, Tui is exactly what the middle lines see as they look towards the top of the hexagram. With line 3, we see a similar pattern, since the 3 trigrams here are still the 3 daughters. Remember, however, that the Wise One is represented by 2 Yang lines, moving Yang. This means that line 3 is changing from Yang to Yin. When the change is made, these 3 trigrams suddenly become the 3 sons instead! (The upper trigram, lines 4-5-6, is not affected by the movement of line 3.) This explains one of the most nonsensical sentences in the entire hexagram: "He dances with the Great Empress, while daughters become sons." Long considered evidence that LTK was drinking something stronger than green tea as he wrote, we can now see that this silly looking phrase is actually a very deep insight into the inner structure of Self-Reflexive.

No wonder the Judgment says, "Within her [the Great Empress, the hexagram?], all the sons and daughters dance between heaven and earth." Self-Reflexive seems to bring the entire Trigram Family together within her lines. Not bad for a hexagram that seeks to bootstrap the entire Q-Ching.

Who is the Great Empress?

There is one last trick to be used with the trigrams. Using data compression on the upper and lower trigrams, each copy of Li turns into a Yin line, forming Yin on Yin or moving Yin. This moving Yin, the counterpart in the hexagram of the moving Yang of the Wise One (lines 3-4), sheds light on one of the biggest mysteries of this hexagram: who is the Great Empress?

Scholars have speculated for years on the identity of the Great Empress. Most authors agree that she represents some kind of divine or otherworldly being of importance to the programmers, possibly some inspirational Muse that leads them to the Golden Code. More psychologically oriented writers insist she is some kind of "anima projection" for LTK, his "inner woman" of the deep psyche (not a bad metaphor for two Yin lines hidden deep within the outer trigrams, actually). Less mystically inclined critics, not impressed with "all that mumbo-jumbo" in the Q-Ching, tend to promote the view that the Empress is simply some woman LTK knew and idolized in his youth, and he tried to immortalize her in his later years. Theories about the identity of this "mystery woman" range from a sage/teacher that was a major influence on LTK, to a young lover, even to some geisha he met when out drinking. In my opinion, such an explanation (though remotely possible) is highly reductionist and hardly warrants comment. Since Self-Reflexive is the hexagram to introduce the Great Empress to us, I feel it necessary to let the hexagram provide its own explanation of who she is.

Recall that Yang is bright while Yin is dark and moving Yin is the "dark so dark" that it's about to flip over into light, again. Further, these Yin lines are a compression of the trigram Li, symbolized by fire or light. If the Great Empress is described by moving Yin, you'd expect the symbolism of dark vs. light to be present throughout the hexagram. And in fact, the juxtaposition of light and dark occurs regularly in this text, starting right with the description of the Image. The figure of Li over Li is imagined as: "The same light that shines on the seen shines on the seer. The same darkness moves around them both." (The choice of the verb "moves" may reflect that we are looking at moving lines.) Similarly, the Judgement starts out: "Fire reflects in fire, revealing the Great Empress moving in the dark." Evidentally, light/consciousness is needed to reveal the Empress. Line 5, the middle line of the upper trigram, tells us "The fire shines on the face of the Great Empress"; line 2 in the lower trigram says "The fire shines on the feet of the Great Empress as she dances." (The lower Yin line governs the movement of the digram.) Line 2 also has the image "Two sits upon Two, giving rise to moving and standing still.", a perfect description of Yin (=2) over Yin leading to moving Yin. In short, the Empress seems to be equated with this "inner" digram of moving Yin.

The Wise One (lines 3 and 4) is represented by moving Yang. So we see the Wise One transforming into the Great Empress (as Yang changes to Yin), just as she mutates into him (Yin becomes Yang). This is just like in the traditional Tai Chi symbol for the Tao, where Yin and Yang dance the dance of duality. The Judgement even says "The Wise One... moves to be her groom", hinting at a kind of mystical, alchemical marriage or "hieros gamos" between them. Apparently the relation between these two beings is so close they merge and literally become as one. The Empress is literally the "soul" of the Wise One.

(As a curious aside, recall that 3 of the 4 digrams are present in this hexagram. The missing digram, moving Yin, is represented by the Great Empress. The presence of this hidden digram within the hexagram completes this important quaternity.)

In meditational practices, the highest states of consciousness are often described as "becoming one with the object of your meditation". For the sages in the emperor's court, the objects of their contemplation were the programs they were writing. They sought the Golden Code relentlessly. Notice that the hexagram for Golden Code (Hx. 3) consists entirely of Yang lines, while the Wise One is represented by a digram of all Yang lines. In effect, the sage enters the Tao (the matrix underlying and resolving Yin and Yang) by becoming one with the Golden Code. The marriage of Empress and Wise One is also a symbol of the Tao. She is both the object of contemplation and the light/consciousness that contemplates. She is both the end of the journey and the path that leads there. She is the Muse that leads the sages to aspiring to the Golden Code. She may actually be the Golden Code incarnate.

On another level, the Great Empress and Self-Reflexive are also one and the same. If you fathom hexagram 16, you too will meet the Empress, who is the spirit hiding within these 6 lines and throughtout the Q-Ching as a whole.

This state of blissful union is obviously multi-faceted and difficult to pin down. Like many key notions in the philosophy of the Q-Ching, this is a state that can be experienced, but not defined. At some point, all attempts to pidgeonhole the Great Empress are doomed to failure, or at best, half-successes. Self-Reflexive, as a meditational tool, leads one inevitably to the Great Empress and ultimate union. To understand Self-Reflexive, you must experience your own self-reflexive consciousness in meditation, you must become the hexagram yourself. This is why the same light shines on the seer and the seen. This is why the Wise One "sees great mysteries, but seals his lips with a smile." Nobody can tread this path for you.

And the Fool?

As for the fool who cannot see great mysteries, this act of reflecting on himself is totally beyond him. He doesn't see that the light illuminating the object of his desire shines within himself as well. The inner light is invisible and all he sees is the phenomena of the outer world. Hence, "The fool sees only the fire."

The fool will always stare into the glowing coals of the campfire and never achieve a flight of imagination. Enlightenment will always elude him, at least until some sage hits him over the head with an abacus...