Glossary

What follows is a meditation on the history and development of the trigrams, from the earliest records, taken from the Ten Wings (十翼 Shi Yi) commentary to the Yi Jing, believed to have been composed during the Warring States period and compiled during the 3^rd century BCE and was responsible for transforming the Yi Jing from a simple divination tool to a moral and philosophical system. Prior evidence is largely archaeological and points to the Yi Jing as a divination system that used six lines during the Western Zhou (c. 1000–750 BCE) but about which little is written, and the and the "judgements" (卦辭 Guaci) and "Line Statements" (爻辭 Yaoci) which make up the oldest layers of the Yi Jing text, potentially coming from this early period, or earlier. Historian Li Shuo even suggests that these lines may be references to the Shang Dynasty practice of human sacrifice and conditions in which prisoners were kept, recorded by King Wen of Zhou while in captivity and leading to their eventual overthrow and abolition of the practice (Wu, 2023, Book of China, 2024). Therefore it is mainly the Ten Wings that concerns us, since the Judgements and Line statements are more about the interpretation of the resulting hexagrams than their cosmological significance and sequence.

It should be noted that historically, these things developed in the opposite order, with the hexagrams actually predating the trigrams and the Later Heaven arrangement of the trigrams appearing before the Early Heaven sequence, that was determined by Shao Yong in the Song Dynasty (11^th century). The Later Heaven Sequence is described in the section of the Ten Wings called Explanation of the Hexagrams (說卦傳 Shuo Gua Zhuan), which provides some references to the pairing of the trigrams in the third chapter:

天地定位，山澤通氣，雷風相薄，水火不相射，八卦相錯
Heaven and earth determine the directions.
The qi of the mountain and lake are united.
Thunder and wind are close to each other.
Water and fire are not in conflict with each other.
Thus are the eight trigrams intermingled.

While the fifth chapter describes the Later Heaven Sequence with the words:

帝出乎震，齐乎巽，相见乎离，致役乎坤，说言乎兑，战乎乾，劳乎坎，成言乎艮。
The Divine Emperor comes forth from Zhen (Thunder, East, Spring);
Brings things to completion in Xun (Wind, Southeast);
Causes them to appear in full brightness in Li (Fire, South, Summer);
Gives them service in Kun (Earth, Southwest);
Rejoices in Dui (Lake, West, Autumn);
Struggles in Qian (Heaven, Northwest);
Toils in Kan (Water, North, Winter);
Brings them to fruition and conclusion in Gen (Mountain, Northeast).

However, the presence of an Early Heaven sequence is implied by the existence of the Luo Shu Magic Square, which is a 3x3 grid of numbers, where all sides add up to 15, which has been found on items in a Western Han dynasty tomb in Fuyang dated to 2^nd century CE (So et al., 2015). Other ancient references include the Ten Wings and the even earlier Book of Documents (尚書 Shang Shu) which has a chapter on the Perfect Plan (洪範 Hong Fan) which references a perfect nine part system of governance which later became associated with Luoshu. However, it is first referenced explicitly in the 6^th century by Lu Bian in his commentary of the Book of Rites (大戴禮記 Dai De Li Ji), in which the layout of the Mingtang (Ritual Hall) is given as:

The second and fourth are the shoulders;
The sixth and eighth are the feet;
The three on the left and the seven on the right;
The nine is on the head and the one is on the tail;
The five is in the center.

As time has progressed, philosophers have added analyses and commentary on the original system of hexagrams to try and understand the fragmented records we have from the past. What follows is a similar analysis, that attempts to make sense of these early systems and unite them into a progression that begins with the famous He Tu, Yellow River Map, said to been on display during the Zhou dynasty and which also has textual evidence dating to the Four Books and Five Classics of ancient Chinese literature (Sun, 2020) and progresses to the channel and Zangfu attributions found in the Neijing which have become canonical in medical practice to this day.

The Evolution of the Trigrams

The fundamental assumption of the following analysis is that the trigram system of the Yi Jing is essentially mathematical, based on the observation that the trigrams represent a binary numerical system, consisting of contrasting Yin and Yang lines. However, a straightforward interpolation of binary numerals onto the trigrams quickly proves problematic, so in order for this to work a few modifications of a standard binary system need to be considered:

• 0 and 5 are at the centre so these numbers do not exist in the outside
• This makes ☷ = 1, so the generative numbers (below 5) are +1 of their standard binary values
• Extinction numbers (above 5) are therefore +2 of their true binary values as they do not include 0 and 5

He Tu

This diagram represents the Taiji ☯ as odd and even numbers flow out in two clockwise spirals from the centre (1 → 3 → 7 → 9 and 2 → 4 → 6 → 8). This pattern also sets up the first complementary pairs which go on to become the opposing sides of the Luo Shu Magic Square, by combining one of the generative numbers (below 5, in the inner part of the spiral) with an extinction number (above 5, in the outer part of the circle).

• 1 ☷ is complemented by 9 ☰
• 2 ☳ is complemented by 8 ☴
• 3 ☵ is complemented by 7 ☲
• 4 ☱ is complemented by 6 ☶

The sequence of generative and extinction numbers also describes the intermingling of Yin and Yang from the top and bottom numbers as they draw inwards towards a harmonious balance in a figure 8 cycle:

1. ☷ Pure Yin emerges from the Dao
2. ☳ Yang emerges from within Yin
3. ☵ Yang rises within Yin and takes the centre
4. ☱ Yang dominates Yin, and Yin departs
5. Yin returns to the Dao as do all things, and becomes its opposite.

0, 5 and 10 are identical in this system, so after returning to the Dao, the number sequence begins from 10 and counts down.

9. ☰ Pure Yang emerges from the Dao
10. ☴ Yin emerges from within Yang
11. ☲ Yin rises within Yang and takes the centre
12. ☶ Yin dominates Yang, and Yang Departs
13. Yang returns to the Dao, where it becomes its opposite.

The simple reason one is called the Generative numbers and the other are the Extinction numbers is simply because the numbers 1 - 4 start with Yin, the principle of generation, and move towards Yang, the active principle, while the number 9 - 6 move from light of Yang towards the darkness and stillness of Yin.

Another observation that can be made of this sequence is that it mirrors the spectrum of light, moving from:

• Black-blue (Water, Old Yin)
• Blue-Green (Wood, Young Yin)
• Yellow (Earth, Centre)
• Red (Fire, Young Yang)
• White (Metal, Mature Yang)

The invisible parts of the spectrum (infrared and ultraviolet) have been represented as black and white in this schema, but this choice in itself is interesting because, if they had wanted to represent colours as a continual cycle, metal could have been represented with purple which would then have allowed a transition back to blue, but instead a spectrum has been chosen to represent a continuum.

Luo Shu

The Luo Shu "Magic Square" arrangement looks like:

In this diagram, the odd and even numbers follow a zigzag pattern crossing the centre.

Some notable trends:

• The odd / Yang numbers occupy all the cardinal directions, while the Yin numbers occupy the ordinal direction.
• The middle line is unbroken / Yang across the entire eastern side, from the northeast to the south
• Conversely, the middle line is broken / Yin across the entire western side, from southwest to north

This has some important implications for the magic square. Although all the numbers add up to 15 across all directions, in terms of adding yin and yang lines together, all the directions that cross the centre complement each other perfectly and effectively cancel each other out. However, the sides are not the same. The northern side leaves us with ☷, the southern side leaves us with ☰, the western side leaves us with ☲, and the eastern side leaves us with ☵, the four cardinal signs.

To obtain the Luo Shu from He Tu the Yang numbers move to the cardinal directions, with their associated Yin numbers moving to the ordinal directions. In order to acquire this arrangement, the He Tu must transform in the following way:

In this arrangement, something interesting happens. To follow any numerical sequence, it is necessary to zigzag across the centre continuously. This is true regardless of whether you count sequentially, or follow the odd and even numbers. Another way of looking at this, is that it follows the spectrum of light in a straight line along the horizontal, with the two extremes (black and white) moving counterclockwise to occupy the north and south.

To create a magic square in the Eight Directions, the odd numbers remain in the cardinal directions while the Yin numbers move counterclockwise to the ordinal directions, forming a rotating hooked sun cross with Metal / Qian / Mature Yang and White above, Water / Kun / Mature Yin and Black below, while the sides are occupied by Fire and Li / Growing Yang / Red to the right and Wood Kan / Growing Yin / Green to the left forming Waxing and Waning Rising and Falling Bigrams to each of the four directions:

It can be observed that, in this arrangement:

• The two Generative Yang numbers (below 5) remain in place and have the Yin Extinction numbers, with +5 to their value, to their clockwise direction
• The two Extinction Yang numbers (above 5) move and have the Yin Generative numbers, with -5 of their value, to their clockwise direction
• Moving counterclockwise, we see a pattern of Mature Yin → Growing Yang → Mature Yang → Growing Yin, with the Yin trigrams having the Yin of Taiyin and Shaoyin to the cardinal direction and the Yang trigrams of Taiyang and Shaoyang having their Yang trigrams to the cardinal directions
• If we follow the spectrum of light, from black → blue-green → yellow → red → white, we also have to zigzag across the centre is a large S shape

Standard Arrangements

Early Heaven

The standard Early Heaven sequence goes like this:

In this arrangement, the hexagrams do balance one another, but there is no numerical harmony and the sides do not add up to 15, nor do they really follow a sequential pattern revolving around the edge. However, this sequence is a formulation given by Shao Yong in the Song Dynasty (11^th century) and so may not the original sequence, especially as the maths does not add up when the trigrams are taken as binary entities. It also alters the attributions of the five phases to the trigrams, which do become divorced from their directions, but it seems appropriate that this should happen during the transformation to Later Heaven than before.

One may to make a logical sequence, would be to switch Kan and Li in this scheme, which starts to make this cycle make numerical sense:

Here, starting from Kun in the north, Yang emerges at the bottom line, moves up to the second securing the centre, whereupon another Yang line appears at the bottom, establishing a majority of Yang and the departure of Yin, followed by pure Yang and then the sequence returns. This also means that the generative numbers count up from north to southeast (1 - 4), and then count down from south to northwest (9 - 6), as was observed in the earlier He Tu diagram. Then, by a simple switch of the Fire and Wood trigrams of 2 and 8 in the northeast and southwest, we recreate the Luo Shu square:

Its mathematical balance make this seem like the most appropriate layout for the Early Heaven sequence, in my opinion. Therefore, the only switch from the original He Tu diagram actually maintains harmony by keeping the Wood and Fire trigrams together, and could be seen as a representation of the Taiji diagram, by the fact that an Extinction number is inserted into the middle of the Generation sequence that progresses along the Eastern side, while a Generative number is inserted into the Extinction cycle that runs along the western side.

Another observation is that the Generation sequence, with the addition of 8 instead of 2, now adds up to 16, while the Extinction sequence now adds up to 24, both multiples of 8. The Generative numbers being 2 x 8 is significant since they begin from 1, Pure Yin, and even numbers (2) are considered Yin. The Extinction numbers, which start from Pure Yang and count down, with 8 changed to 2, now adds up 24 which is 3 x 8, and odd numbers (3) are considered Yang.

Later Heaven

With the Later Heaven Sequence, this argument cannot be applied since this order is given explicitly in the Ten Wings, the oldest commentary known on the I Ching, as are the complementary trigrams, meaning that this order cannot be disputed but must be arrived at by some mathematical means. The sequence has no harmony in terms of pairs or numbers, or apparent relationship to the He Tu or Luo Shu diagrams:

Since the numbers do not harmonise, we can assume that numerical harmony is not important in this sequence. The same can be said for opposing trigrams which clearly are not designed to complement one another. Instead, the main task is to determine how and why the Luo Shu sequence is transformed into this Later Heaven sequence and what this can teach us. In order for this to happen, the following transformations must occur:

Some notable trends:

Moving in a clockwise direction:

• 2 trigrams move 2 places
• 2 trigrams move 3 places
• 2 trigrams move 5 places
• 2 trigrams move 6 places

Looking in further detail, some interesting numerology emerges:

• East (☵ 3) and west (☲ 7) both move 6 places to occupy the north and south respectively
• Northeast (☴ 8) and northwest (☶ 6) both move 2 places to occupy the southeast northeast respectively
• North (☷ 1) and southwest (☳ 2) moves 5 places to occupy southwest and east respectively
• South (☰ 9) and southeast (☱ 4) moves 3 places to occupy northwest and west respectively

• All the southern directions and the cardinal north-south axis move an odd/yang number of places
• All the northern directions and the cardinal east-west move an even/yin number of places

Looking at the opposing poles of balancing trigrams:

• The east ☵ and west ☲ both move 6 places (= 12)
• The northeast ☴ and southwest ☳ move 2 & 5 places (= 7)
• The north ☷ and south ☰ axis move 5 & 3 places respectively (= 8)
• The southeast ☱ and northwest ☶ move 2 & 6 places (= 8)

These are some important astrological numbers in Chinese cosmology:

• 12 Earthly Branches (east and west are when the sun rises and sets)
• 7 Stars in the Big Dipper (the Big Dipper moves around to determine the seasons)
• 8 Trigrams (repeated twice as the number 8 can be arrived at by adding two yang/odd numbers, or two yin/even numbers)

To speculate one step further:

• East ☵ and west ☲ move the north and south, moving 6 places each (12), with each movement generating the 12 Earthly Branches, and along with them, the template for the 12 Zangfu and their associated channels.
• Southwest ☳ and southeast ☱ move 5 & 2 places (7) to occupy the east and west, symbolising the Big Dipper's role in indicating the transition of the seasons (it is also notable that the east and west are Wood and Metal, and the 12 Earthly Branches usually run in a cycle starting with Metal and ending in Wood).
• North ☷ and south ☰ move 5 & 3 places (8), to the ordinal directions of southwest and northwest
• Southeast ☱ and northwest ☶ move 2 & 6 places (8), also ending up in the ordinal directions of northeast and southeast
• The Bagua is a hidden pattern behind creation, which is why the trigrams whose movements add up to 8 are sent to the ordinal directions, instead of the cardinal ones. There are two because the I Ching relies not just one but two trigrams, each with 8 possibilities, to make the 64 hexagrams.

In both cases, it is worth noting that only the trigrams move, but the numbers attributed to the directions based on the Luo Shu Diagram remain fixed, as directionality is a property of Early Heaven, while the trigrams have degenerated into a Late Heaven system.

This makes the movements of the Bagua make sense, unfolding from the unknowable Wuji to a spiral of emanating Yin and Yang in the He Tu diagram, from which the Taiji symbol and the essential Five Phases are derived, to a mathematically balanced sequence in the Luo Shu Square, which then transforms into the unbalanced and imperfect reality of our existence in the King Wen Sequence, and in doing so generates the 12 Earthly Branches through the rotation of Kan and Li to assume their positions at the north and south. It also explains why it is possible to use the knowledge of the King Wen sequence to read the Dao of Heaven in the cycles of time through an understanding of the movements of the Big Dipper through the 12 Earthly Branches and knowledge of the hidden cycles of the 64 hexagrams.

On the Generation of the Six Divisions and Meridian Sequence

The names for the Six Divisions are based on the six trigrams that follow a "rising and falling" or "waxing and waning" sequence. In Early Heaven, the these are arranged sequentially, giving rise to the following pattern:

When transformed into the Later Heaven King Wen sequence, these attributions are as follows:

The cycle of the 12 channels can be observed amongst this arrangement:

• The Taiyin and Yangming (Lungs, Large Intestine, Stomach, Spleen) are on the top row
• The Shaoyin and Taiyang (Heart, Small Intestine, Bladder, Kidneys) are on the bottom row
• The Jueyin and Shaoyang (Pericardium, San jiao, Gall Bladder, Liver) are on the middle row

This is probably not a coincidence, and the fact that the two unrepresented trigrams are the ones that travel through 12 places to arrive at their north-south poles just reinforces the idea.

Another very important observation is that Five Phase attributions have changed, with transformations that almost certainly have cosmological significance:

• The cardinal directions are now occupied by the same Phases as the He Tu diagram
• Metal retains the same trigrams of ☰ and ☱, the Yin and Yang forms of Mature Yang ⚌ reflecting the unchanging nature of Heaven
• Earth comes from the centre to occupy two spaces, whose trigrams it takes from Water, ☶ and ☷, setting up the fundamental poles of Heaven and Earth
• Water comes to be represented by the trigram of ☵, which it acquires from Wood, setting up the Fire and Water axis
• Wood, the element of growth, acquires ☳ that was previously the Yin trigram in the Fire pair, making the two Wood trigrams represent the return of a Yin line within Yang and and Yang line from within Yin, the sprouting of new transformations.

However, this is not the end of the transformation and a further step needs to be taken to end up with the following:

Three things can be clearly seen:

1. The Yin and Yang relative properties have become divorced from their trigrams
2. The pairings that were made from the last transformation now balance each other
3. Qian and Kun become the retired trigrams instead of Li and Kan

This latter observation may be because the human body is an environment where everything is mixed, where Yin and Yang can no longer exist in their purest forms within the regular Zangfu and Channel system. Here is one suggestion of how the Six Divisions come to inhabit the directions they do based on two fundamental premises:

1. As Qian and Kun have retired, their associated Divisions must vacate
2. Yang Divisions move easily, travel greater distances, and proactively initiate a move to restore balance. Yin Divisions move little and only to complement their partner

Based on these premises, a series of moves enables the pairings made by the previous transformation to harmonise one another, while vacating Qian and Kun.

1. Taiyang, as the most Yang, moves first, where it occupies the most Yang available trigram, Li ☲ in the south
2. Since it is paired with Shaoyin, this moves one place to Kan ☵ in the north to complement its Taiyang partner
   The remaining trigrams also seek to form complementary pairs and attempt to resolve this. The following solution results in the fewest steps and the least moves for the Yin divisions.
3. Yangming occupies the available space in the northeast becoming Gen ☶. Yangming, as the Yang trigram with a Yin nature within, moves the least, only two spaces, to the other side of Jueyin
4. This allows Jueyin to occupy Xun ☴ the southeast. Jueyin possesses a Yang nature within its Yin, and so may have some proactive qualities and initiate this movement
5. Shaoyang can now to occupy Zhen ☳ the east, where it can complement Jueyin in Xun ☴
   
6. Taiyin can now move one place to vacate the retired trigram Kun and now occupies Dui ☱ the west, where it complements Yangming in Gen ☶ to the northeast

Amazingly, this adds up to exactly 12 spaces moved, the number of movements that was allocated for the generation of the 12 Earthly Branches above. 6 moves are clockwise and 6 and are anticlockwise, making a perfect balance.

Any alternative, such as Shaoyang moving to the northeast, would result in its Yin pair, Jueyin to move four places, and then Taiyin would have to move another three places to complement Yangming instead of Yangming moving, so for Yangming to move is the only logical and efficient step, given the reluctance of Yin to move.

Another possibility would have been that Jueyin moves to the northeast instead of Yangming, thereby complementing Shaoyang. This is plausible, especially considering the possibility that Jueyin is the one Yin Division that might initiate a move, but this would then require Taiyin to move more places to occupy the east, or southeast if Yangming were to move to the east, both of which would break the dynamic with Yin Divisions being more active than the Yang Divisions, which barely move, if at all.

Both of these alternatives would also not move a perfect 6 places clockwise and anticlockwise, leaving an imbalance in the number of changes made.

This then brings us to chapter 9 of the Explanation of the Hexagrams in the Ten Wings, where it states:

幹為首，坤為腹，震為足，巽為股，坎為耳，離為目，根為手，兌為口。
Qian [☰] represents the head [Du Mai],
Kun [☷] represents the abdomen [Ren Mai],
Zhen [☳] represents the feet [Shaoyang],
Xun [☴] represents the thighs [Jueyin],
Kan [☵] represents the ears [Shaoyin],
Li [☲] represents the eyes [Taiyang],
Gen [☶] represents the hands [Yangming],
and Dui [☱] represents the mouth [Taiyin].

These associations seem quite self evident since:

• The Du Mai governs the head, brain and neck
• The Ren Mai governs the abdomen
• The Gallbladder channel contains the Hui of tendons (Yanglingquan GB-34), the largest of which is found in the feet (the Achilles) and its Luo runs across the feet
• The Liver channel runs along the inner thigh to the hip (the word 股 also includes the haunches)
• The Kidneys govern the ears
• The Bladder channel originates from the inner canthus of the eyes
• The Large Intestine channel has the main point for the hands (Hegu LI-4) and the Ling Shu ch. 10 describes how the thenar eminance is a prognosticator of the health of the Stomach.
• The Spleen and Lung channels both affect the mouth (and nose and throat)

It is not quite complete here though and some inconsistencies remain. For example, the Heart is now assigned to the north as a Shaoyin organ, while the Neijing clearly attributes it to Fire and the south. This is because, in order for the pairings to truly intermingle, one of each pair is made to stretch across the grid, forming a bridge between the pairs. Hence the Heart becomes both a Shaoyin organ of the north in its pairing with the Kidneys, but also a Fire organ of the South in its pairing with Small Intestine. One of each pair does this stretching to make the network complete:

• The Heart extends to the south, to become Shaoyin Fire, uniting with the Small Intestine
• The Bladder extends to the north, to become Taiyang Water, uniting with the Kidneys
• The Liver extends to the east, to become Jueyin Wood, uniting with the Gallbladder
• The Large Intestine extends to the east, to become Yangming Metal, uniting with the Lung
• The Spleen extends to the northeast, to become Taiyin Earth, uniting with the Stomach
• The Pericardium extends to the southeast, to become Jueyin Fire, uniting with the San Jiao

From here it is possible to now see the standard channel order emerging, based upon the 12 Earthly Branches, which forms a pattern that:

• First covers the horizontal axis of east to west before returning to the centre:
  • Wood (Liver ䷗ / Gallbladder ䷒)
  • Metal (Lung ䷊ / Large Intestine ䷡)
  • Earth (Stomach ䷪ / Spleen ䷀)
• Followed by the vertical axis, also returning to the centre:
  • Fire (Heart ䷫ / Small Intestine ䷠)
  • Water (Bladder ䷋ / Kidneys ䷓)
  • Ministerial Fire (Pericardium ䷖ / San Jiao ䷁)

One very interesting observation to make about this pattern, is that the route it takes is very similar to the that of the He Tu map at the beginning, which, if you count the numbers upwards, goes from north to south and east to west and back again. This sequence does travel east to west and then south to north, but the similarity of movement is undeniable. It can also be observed that the yin and yang of the directions become followed again, with a 90° twist, with Taiyang and Shaoyin forming opposing pairs in the north and south (in the He Tu map they are east and west), and Taiyin and Shaoyang forming opposing pairs in the east and west (in the He Tu map they are north and south). These appear to reconnect the cycle of the meridians with a corrupted version of the original emanation of yin and yang from the Dao in the He Tu, providing the means for a return.

So at the end of this long journey, the Six Divisions finally arrive at their absolute state of manifestation, no longer bearing their original undifferentiated unity, or the mathematical harmony of their earlier forms, yet they still retain balance through their elemental and channel pairings, even in an imperfect and chaotic world, and maintain the potential to reconnect with the original Dao.