Chapter Three: The Method of the Six Combinations -- Tracing the Astronomical Origins of the Pairings

Section 1: General Overview of the Six Combination Pairings

The pairings of the Six Combinations are:

Zi and Chou combine
Yin and Hai combine
Mao and Xu combine
Chen and You combine
Si and Shen combine
Wu and Wei combine

At first glance, these six pairings seem to follow no obvious pattern. Yet upon careful analysis, they contain profound astronomical underpinnings and yin-yang/Five-Phase reasoning.

First question: what is the pattern of these six pairings$24

Numerically:

Zi (1) + Chou (2) = 3
Yin (3) + Hai (12) = 15
Mao (4) + Xu (11) = 15
Chen (5) + You (10) = 15
Si (6) + Shen (9) = 15
Wu (7) + Wei (8) = 15

Except for Zi-Chou (whose sum is 3), the remaining five pairs all sum to 15. But if Zi is treated as 13 (12 + 1), then Zi-Chou also sums to 15. The number 15 is precisely the constant sum of the Luo River Document (Luoshu) magic square in any row, column, or diagonal. Is this coincidence$25 This will be discussed later.

Spatially, if the twelve Earthly Branches are arranged in a circle (like a clock face), the Six Combination pairings are symmetrically paired about the axis between Zi and Chou. More precisely:

Zi is at due north (0 degrees), Chou at north-northeast (30 degrees) -- adjacent; Yin at east-northeast (60 degrees), Hai at north-northwest (330 degrees) -- symmetric about the Zi position; Mao at due east (90 degrees), Xu at west-northwest (300 degrees) -- symmetric about the Zi-Chou axis; Chen at east-southeast (120 degrees), You at due west (270 degrees) -- symmetric about the Zi-Chou axis; Si at south-southeast (150 degrees), Shen at west-southwest (240 degrees) -- symmetric about the Zi-Chou axis; Wu at due south (180 degrees), Wei at south-southwest (210 degrees) -- adjacent.

From the perspective of yin-yang attributes:

Zi (yang) and Chou (yin) -- yin and yang combine
Yin (yang) and Hai (yin) -- yin and yang combine
Mao (yin) and Xu (yang) -- yin and yang combine
Chen (yang) and You (yin) -- yin and yang combine
Si (yin) and Shen (yang) -- yin and yang combine
Wu (yang) and Wei (yin) -- yin and yang combine

All six pairs consist of one yang and one yin, without exception. This accords perfectly with the principle of yin-yang union -- opposites attract, like repels like. Yang does not combine with yang, yin does not combine with yin; only yang with yin, yin with yang.

Section 2: The Astronomical Principle of Monthly Correspondence

What is the most fundamental astronomical basis of the Six Combinations$26 This has been an important topic of inquiry among scholars throughout history.

The Huainanzi, "Treatise on Celestial Patterns," contains a key passage:

"At the winter solstice, the Well (Jing) and Ghost (Gui) constellations are opposite; at the summer solstice, the Horn (Jiao) and Neck (Kang) constellations are opposite."

This states that the sun's apparent position (ri chan) at the winter solstice lies between the Well and Ghost lunar mansions (roughly in the region of modern Cancer), and at the summer solstice between the Horn and Neck mansions (roughly in modern Libra).

Even more critically, the ancients observed an important astronomical phenomenon: certain months' new-moon conjunctions (when sun and moon meet) occur in the same celestial zone.

Specifically, in the sun's apparent annual motion, the sun traverses one particular mansion zone each month. The moon's synodic period is approximately 29.53 days, and on the first day of each month (new moon), the moon and sun are in the same direction (conjunction).

Ancient calendrical specialists discovered that, measuring from the winter solstice point:

The Zi-month (eleventh month) and the Chou-month (twelfth month) have their solar positions symmetric about the winter solstice point.

This is the astronomical basis of the "Zi-Chou combination."

At the winter solstice, the sun is in a particular mansion. The Zi-month and Chou-month conjunctions have their solar positions respectively about half a "palace" (gong) before and after the winter solstice point, and the two conjunction zones are symmetric about the winter solstice point. This symmetric relationship is the original astronomical meaning of "combination."

Extending this principle to the entire year:

The solar positions of the Yin-month and Hai-month are symmetric about the winter solstice point
The solar positions of the Mao-month and Xu-month are symmetric about the winter solstice point
The solar positions of the Chen-month and You-month are symmetric about the winter solstice point
The solar positions of the Si-month and Shen-month are symmetric about the winter solstice point
The solar positions of the Wu-month and Wei-month are symmetric about the summer solstice point (complementary symmetry about the winter solstice point)

This is the astronomical root of the Six Combinations: the symmetry of the sun's ecliptic position about the winter solstice point (or the summer solstice point).

Why symmetry about the winter solstice, and not the vernal equinox or some other point$27

The winter solstice is the fundamental reference point of astronomical calendrics. The Shangshu, "Canon of Yao":

"The shortest day, with the star Mao the Pleiades, marks mid-winter" (ri duan xing Mao, yi zheng zhongdong).

On the winter solstice, the gnomon shadow is longest and easiest to measure. The ancients measured sun-shadows with an upright gnomon (tugui): the shadow is longest at the winter solstice and shortest at the summer solstice -- the basic observation for calendrics.

The Zhoubi Suanjing (The Gnomon of Zhou) records:

"On the day of the winter solstice, the gnomon shadow is one zhang, three chi, and five cun about 3.15 meters. On the day of the summer solstice, the shadow is one chi and six cun about 0.37 meters."

The winter solstice point is an extremum of the sun's annual motion (when the sun's declination is at its southernmost) and the turning point of yin-yang waxing and waning. From this point, yang qi begins to be born and all things begin to stir. Therefore, taking the winter solstice as the reference for establishing the Six Combination pairings is astronomically the most natural and reasonable choice.

Section 3: Detailed Derivation of the Monthly Solar-Position Pairings

For a clearer understanding of the astronomical principle of the Six Combinations, a detailed derivation follows.

Let the sun's position on the ecliptic at the winter solstice be 0 degrees. The sun moves approximately 30 degrees per month (360 degrees / 12 months). Then:

Zi-month (11th month): solar position approximately -15 to +15 degrees (around the winter solstice)
Chou-month (12th month): approximately +15 to +45 degrees
Yin-month (1st month): approximately +45 to +75 degrees
Mao-month (2nd month): approximately +75 to +105 degrees
Chen-month (3rd month): approximately +105 to +135 degrees
Si-month (4th month): approximately +135 to +165 degrees
Wu-month (5th month): approximately +165 to +195 degrees (around the summer solstice)
Wei-month (6th month): approximately +195 to +225 degrees
Shen-month (7th month): approximately +225 to +255 degrees
You-month (8th month): approximately +255 to +285 degrees
Xu-month (9th month): approximately +285 to +315 degrees
Hai-month (10th month): approximately +315 to +345 degrees

The more precise formulation of the Six Combinations' astronomical principle is: two months in which the sun's declination is the same.

Solar declination (the angle of the sun's position north or south of the celestial equator) varies with the seasons: southernmost at the winter solstice (about -23.5 degrees), zero at the vernal equinox, northernmost at the summer solstice (about +23.5 degrees), zero at the autumnal equinox.

Months sharing the same solar declination occupy symmetric positions in the sun's annual return -- equidistant from the winter solstice (or summer solstice). The azimuth of sunrise and sunset, the length of day and night, and similar astronomical phenomena are therefore identical for such months.

Measuring from the winter solstice:

1 month after the winter solstice (early Chou-month) and 1 month before the winter solstice (late Zi-month) have the same solar declination
2 months after (early Yin-month) and 2 months before (early Hai-month) -- same
3 months after (early Mao-month) and 3 months before (early Xu-month) -- same
4 months after (early Chen-month) and 4 months before (early You-month) -- same
5 months after (early Si-month) and 5 months before (early Shen-month) -- same
6 months after (early Wu-month) and 6 months before (early Wei-month) -- same

Thus, the Six Combination pairings are exactly the months equidistant before and after the winter solstice. This is the astronomical essence of the Six Combinations.

Section 4: Shared Sunrise Azimuths and the Formation of the Six Combinations

An even more intuitive astronomical phenomenon is that in the two months of a Six Combination, the sunrise azimuth is the same.

The ancients observed that over the course of a year, the sunrise point shifts north and south along the eastern horizon: farthest south at the winter solstice, farthest north at the summer solstice, and due east at the equinoxes.

Two months symmetric about the winter solstice necessarily share the same sunrise azimuth. For example:

The latter half of the Zi-month (about half a month after the winter solstice) and the first half of the Chou-month (about half a month to a month after the solstice) have extremely close sunrise azimuths -- both near the winter solstice's southernmost sunrise point.
The Yin-month (about 2-3 months after the winter solstice) and the Hai-month (about 1-2 months before the winter solstice) share similar sunrise azimuths.
And so forth.

This observation the ancient peoples could confirm with the naked eye. When they discovered that two months shared the same sunrise azimuth and similar lengths of day and night, they naturally concluded that a special connection existed between them -- and this connection was "combination" (he).

The Huainanzi, "Treatise on Celestial Patterns," records a relevant passage:

"The sun rises from the Valley of Light (Yanggu), bathes in the Pool of Totality (Xianchi), brushes against the Leaning Mulberry (Fusang) -- this is called the dawn's brightness..."

This passage describes the sun's daily journey in mythological terms, yet it also reveals the ancients' intense attention to the sun's rising and setting positions.

Further question: how did the ancient peoples precisely observe sunrise azimuths$28

This requires mention of ancient astronomical observatories. Archaeological discoveries at the Taosi site (c. 2300-1900 BCE) include remains of an observatory for observing sunrise azimuths. This observatory used gaps between multiple pillars to observe sunrise, enabling precise determination of the winter and summer solstices and other important solar terms.

The Shangshu, "Canon of Yao," records Emperor Yao's appointment of the Xi and He brothers to preside over the four cardinal astronomical stations:

"He then commanded Xi and He to attend with reverence to the great heavens, to compute and record the movements of the sun, moon, and stars, and to bestow the seasons upon the people with care. He separately commanded Xi Zhong to reside in Yuyi, called the Valley of Light -- to greet the rising sun with reverence, and to regulate the labors of spring... He commanded Xi Shu to reside in the Southern Crossroads -- to regulate the progress of summer... He commanded He Zhong to reside in the west, called the Valley of Twilight -- to bid farewell to the setting sun with reverence, and to regulate the accomplishments of autumn... He commanded He Shu to reside in the northern regions, called the Dark Capital -- to regulate the changes of winter."

Xi Zhong governed the east, observing sunrise to fix the vernal equinox; Xi Shu governed the south, observing the longest day to fix the summer solstice; He Zhong governed the west, observing sunset to fix the autumnal equinox; He Shu governed the north, observing the shortest day to fix the winter solstice. These four-directional observations constituted the basic framework of the calendar.

Within this framework, further division yields the eight nodes (the four "establishments" plus the two solstices and two equinoxes), and finer division gives the twenty-four solar terms. The twelve monthly "establishments" of the Earthly Branches divide the year into twelve equal segments. Within each segment, the sun's declination changes by approximately the same amount, and the two segments symmetric about the winter solstice (or summer solstice) have mirror-image declination trajectories. This is the astronomical basis of the Six Combinations.

Section 5: From Astronomy to Humanity -- The Symbolic Meaning of the Six Combinations

Astronomical observation provides the objective foundation of the Six Combinations, but the ancient sages did not stop there. They elevated astronomical phenomena into philosophical principles, endowing the Six Combinations with profound symbolic significance.

The "combination" of the Six Combinations is not merely the symmetry of astronomical positions, but the mutual resonance of yin and yang, the concordance of cyclic fortunes.

The Yijing, "Appended Statements, Part I":

"Heaven is exalted and Earth is humble; thus Qian and Kun are fixed. The humble and the lofty are arrayed; thus noble and base find their positions. Movement and stillness have their constancy; thus firm and yielding are distinguished. Things group by kind and beings divide by species; thus fortune and misfortune arise. In heaven, images are formed; on earth, shapes take form; thus changes and transformations become manifest."

"In heaven, images are formed; on earth, shapes take form" -- the images of the sun and moon's celestial movements, projected onto the earth, become the forms of mountains, rivers, and all things. The heavenly image of six-fold symmetric correspondence, projected onto the earth, becomes the six pairings of the Earthly Branches. This is the principle of Heaven-human correspondence.

The Huainanzi, "Treatise on Celestial Patterns," contains a passage directly addressing the six clashes:

"Zi-Wu, Chou-Wei, Yin-Shen, Mao-You, Chen-Xu, Si-Hai -- these are called the Six Clashes."

This speaks of the six clashes (liu chong): pairs of Branches separated by six positions (diametrically opposite). The Six Combinations, by contrast, are the other face of the Six Clashes: clashes represent opposition; combinations represent mutual resonance. The same set of astronomical symmetry relationships, viewed from the angle of opposition, yields clashes; viewed from the angle of mutual resonance, yields combinations.

Why are the Six Clashes and Six Combinations completely different pairings despite both being symmetry relationships$29

This question is critically important. The Six Clash pairings are: Zi-Wu, Chou-Wei, Yin-Shen, Mao-You, Chen-Xu, Si-Hai. Their axis of symmetry passes through the center -- diametric symmetry.

The Six Combination pairings are: Zi-Chou, Yin-Hai, Mao-Xu, Chen-You, Si-Shen, Wu-Wei. Their axis of symmetry lies between Zi and Chou (the direction of the winter solstice point) -- not diametric symmetry, but a folding symmetry about the winter solstice point.

The difference is:

Six Clashes are spatial symmetry: in the circular arrangement of the twelve Branches, the two Branches directly opposite each other clash. This is a static, spatial opposition.
Six Combinations are temporal symmetry: with the winter solstice as axis, the two months equidistant before and after it combine. This is a dynamic, temporal correspondence.

Spatial symmetry produces opposition and clash -- because the directions are exactly opposite, forces act in reverse. Temporal symmetry produces concordance and combination -- because the solar declinations are the same, climate and phenology are similar, so the qi of the two months is mutually attracted and harmonized.

This is the fundamental distinction between the Six Clashes and the Six Combinations. The Six Clashes are based on spatial opposition; the Six Combinations on temporal symmetry. And the ancient sages, through precise observation of the sun's annual motion, discovered this temporal symmetry and thereby established the method of the Six Combinations.