On the Dayan Yarrow Stalk Method

Modern practitioners usually approach the Zhouyi through the "Coin Oracle" (tossing three copper coins) due to its simplicity. However, if one speaks of the most orthodox method—rich in cosmogonic philosophy and revered by Confucius and the sages of the pre-Qin era—it is the Da Yan Divination Method (Great Expansion Method) using yarrow stalks.

The Da Yan method is not merely a predictive technique; it is a solemn ritual simulating the evolution of the universe from chaos (Taiji) to the generation of all things (the sixty-four hexagrams). This article will conduct a multi-dimensional investigation into this ancient technique across four domains: philosophical principles, operational rituals, mathematical probability, and historical evidence.

I. The Philosophical Foundation of the "Great Expansion Number"

"The number of the Great Expansion is fifty; of these, forty-nine are used. Divide them into two to represent the two primal forces; suspend one to represent the three powers; count them by fours to represent the four seasons; return the remainders to represent the intercalary month; in five years there are two intercalations, therefore return the remainders again and then suspend." — Zhouyi: Xici I (Appended Utterances)

This passage of fewer than a hundred characters constructs the core syllabus of ancient Chinese numerology (Shushu).

1. Why "Fifty"$1

Regarding the origin of the "Great Expansion Number of Fifty," scholars throughout history have offered various views:

• The Sum of Heaven and Earth Numbers: The Xici states, "The number of Heaven is 25, the number of Earth is 30; together they make 55." The Song dynasty scholar Zhu Xi believed that 50 is the "Great Expansion Number" derived by subtracting 5 (the generative numbers of the Five Elements) from 55.
• The Center of the Hetu and Luoshu: In the Hetu, the center is 5 and 10, which multiply to 50. In the Luoshu, the center is 5, and the 10 of the five directions (eight directions plus center/up/down) also equals 50.
• The Pythagorean Theorem (Gougu): The sum of the squares of the sides of a 3-4-5 triangle ($9+16+25$) is exactly 50.

Regardless of the interpretation, "Fifty" symbolizes the "total capacity" and "fixed constant" of the universe.

2. Why is "Forty-nine Used"$2

In actual practice, one stalk must be removed from the fifty and respectfully returned to the tube or placed in front, untouched for the remainder of the process. This single stalk holds supreme status.

• The Dialectic of Essence and Function (Ti-Yong): This stalk represents "Taiji" (The Great Ultimate). Taiji is the source of the world; it is silent and motionless, yet it resonates and connects with everything. It is precisely because of the "stillness" of the Taiji that the "motion" of the remaining forty-nine stalks is possible.
• The Interplay of Void and Reality: This is a profound philosophical metaphor—Truth (Dao) is often hidden and non-manifest. What we can operate and calculate is the "Function" (Yong) manifested by the Dao, not the "Essence" (Ti) itself.

II. The Four Operations and Eighteen Changes: A Ritual of Divine Communication

The operation of the Da Yan method is extremely complex, known as the "Four Operations and Eighteen Changes."

• The Four Operations: Dividing into two, Suspending one, Counting by fours, and Returning the remainders. These four actions constitute one "operation" (one change).
• The Eighteen Changes: It takes three operations (three changes) to produce a single Yao (line). A hexagram has six lines, thus $3 \times 6 = 18$ changes are required to complete a hexagram.

This process is not just about finding a number; it is designed to help the diviner collect their thoughts and enter a state of "Sincerity" (Cheng) through meticulous labor.

Preparation

• Tools: 50 yarrow stalks (ancient people used stalks of Achillea millefolium; today, bamboo sticks or Go stones are often used).
• Setting: A clean desk, sitting facing south (or north, depending on tradition), with a heart full of reverence.

【Calculating the First Line】 (Requires Three Changes)

The First Change

1. Extract the Taiji: Remove 1 stalk from the 50 and set it aside. 49 stalks remain.
2. Divide into Two (Symbolizing the Two Forces): Randomly divide the 49 stalks into two piles (left and right). This symbolizes the initial separation of Heaven and Earth, Yin and Yang.
3. Suspend One (Symbolizing the Three Powers): Take one stalk from the right pile and place it between the pinky and ring finger of the left hand. This symbolizes "Man" born between Heaven and Earth, forming the "Trinity" (Heaven, Earth, Man).
4. Count by Fours (Symbolizing the Four Seasons):
   • First, count the left pile in groups of four. The remainder will be 1, 2, 3, or 4 (Note: if it divides evenly, the remainder is 4, not 0). Place this remainder between the ring finger and middle finger.
   • Next, count the right pile in groups of four. Place that remainder (1, 2, 3, or 4) between the middle and index finger.
5. Return the Remainders (Combined Remainder): Combine all stalks currently held between the fingers of the left hand (the 1 suspended + left remainder + right remainder) and set them in the corner of the desk. These are "discarded" for this change.

Mathematical Validation: The total stalks removed in the first change can only be 5 or 9. (The stalks remaining in hand will be 44 or 40).

The Second Change

Combine the remaining stalks (44 or 40) and repeat the steps:

1. Divide into two.
2. Suspend one from the right.
3. Count by fours on both sides.
4. Return the remainders to a separate pile.

Mathematical Validation: The stalks removed in the second change can only be 4 or 8. (The stalks remaining in hand will be 32, 36, or 40).

The Third Change

Repeat the process one last time with the remaining stalks.

Mathematical Validation: The stalks removed in the third change can only be 4 or 8.

Determining the Line (Yao)

After three changes, count the remaining stalks held in hand. The total will only be one of four numbers. Divide this number by 4 to get the Line Number:

• 24 stalks left: $24 \div 4 = 6$ —— Old Yin (Changing line, marked as X).
• 28 stalks left: $28 \div 4 = 7$ —— Young Yang (Unchanging, marked as —).
• 32 stalks left: $32 \div 4 = 8$ —— Young Yin (Unchanging, marked as --).
• 36 stalks left: $36 \div 4 = 9$ —— Old Yang (Changing line, marked as O).

With this, the first line (the bottom line) is drawn. Repeat this "Three Changes" process six times total, moving from bottom to top, to complete the hexagram.

III. God Does Not Play Dice Fairly: The Probability Aesthetics of Da Yan

This is the most fundamental difference between the Da Yan method and the Coin Oracle. The Coin Oracle is based on a simple binomial distribution with relatively uniform probabilities. The Da Yan method, through its complex "suspending one and counting by fours," constructs a highly asymmetrical probability model.

1. The Logic of Variations

In the three changes, the stalks removed (Suspended + Left Remainder + Right Remainder) follow specific patterns:

• 1st Change removal: 5 or 9
• 2nd Change removal: 4 or 8
• 3rd Change removal: 4 or 8

To get the final result, we look at the combinations of remaining stalks:

• To get Old Yang (9): One must have 36 stalks left. This means $49 - (5 + 4 + 4) = 36$.
  • Condition: Each of the three changes must result in the minimum number of stalks being removed.
• To get Old Yin (6): One must have 24 stalks left. This means $49 - (9 + 8 + 8) = 24$.
  • Condition: Each of the three changes must result in the maximum number of stalks being removed.

2. Probability Calculation

Based on the derivations in Zhu Xi's Introduction to the Study of the I Ching and modern mathematics, the probabilities of the four line types are as follows:

3. The Philosophical Meaning Behind the Data

This yields a startling discovery: The probability of Old Yang (9) is three times that of Old Yin (6)! Simultaneously, the probability of Young Yin (8) is much higher than that of Young Yang (7).

This imbalance contains the profound worldview of the pre-Qin era:

1. Yang is Abundant, Yin is Scarce: Yang energy (creativity, movement) is generally dominant and active. However, when it reaches its peak and begins to decline (Old Yang), it occurs more easily than when Yin reaches its peak to turn into Yang (Old Yin). This symbolizes that "achieving success (Yang) is difficult, yet Yang energy itself is plentiful."
2. The World's Keynote is "Young Yin": The most probable result, Young Yin (8) at 43.75%, represents a state of stillness, latency, and material existence. This implies that for most of the time, the real world is in a state of quietude, preservation, and non-radical change.
3. Six is Rare, Nine is Frequent: In I Ching studies, "Six" represents the ultimate Yin—symbolizing total collapse or transformation, a condition extremely difficult to achieve in nature. "Nine" represents the ultimate Yang—reaching the limit of energy release is relatively easier.

This makes the Da Yan method closer to the complex rhythms of the real world than the coin toss—the world is not black and white, nor is it a perfectly fair randomizer; it is an evolutionary system with specific tendencies.

IV. Historical Evidence: The Logic of Duke Mu of Qin's Invasion of Jin

To truly understand how Da Yan was applied in antiquity, we must return to the Spring and Autumn period. The Zuo Zhuan records many divination cases, among which the "Invasion of Jin by Duke Mu of Qin" (15th year of Duke Xi) is a perfect template for pre-Qin interpretation logic.

1. Historical Background

In 645 BCE, the State of Jin suffered a famine and borrowed grain from Qin. Duke Mu of Qin was generous. The following year, Qin suffered a famine and asked Jin for grain. Duke Hui of Jin not only refused but also attempted to take advantage of Qin's weakness by attacking them. Enraged, Duke Mu decided to invade Jin. Before deploying, he ordered the diviner Tu Fu to perform a divination.

2. The Resulting Hexagram

"He divined it and obtained 'Gu becoming Dui' (蛊之兑). The judgment was: 'A thousand chariots are thrice repulsed; after the three repulses, a male fox is captured.'"

This involves a key ancient recording method: "Hexagram Gu becoming Dui."

• Original Hexagram: Gu (山风蛊, Mountain over Wind).
• Resultant Hexagram: This is debated. In the Zuo Zhuan tradition, "Gu of Dui" often refers to a specific line change or the inner trigram changing to Dui (Lake). Most commentators believe this indicated the internal trigram (the bottom three lines) changed from Xun (Wind) to Dui (Lake).

3. Tu Fu's Brilliant Deduction

Tu Fu did not simply read the text of the Zhouyi. Instead, he used the "Taking of Images" (Qu Xiang) method:

• Image I: Wind Falling Below the Mountain In Gu, the upper trigram is Gen (Mountain) and the lower is Xun (Wind/Wood). Wind falling below the mountain suggests not just "decay," but the idea of "returning to roots" and "rectification." Duke Mu used this to rectify the treacherous Duke Hui of Jin.
• Image II: Thrice Repulsed This is a structural deconstruction. Xun (Wind) in the lower trigram can represent order and chariots. More subtly, the nuclear hexagram contains Zhen (Thunder/Chariots). "Thrice repulsed" predicted the battle's progression: the Jin army would be pushed back three times.
• Image III: Capturing the Male Fox The word Gu carries the meaning of "delusion." Duke Hui of Jin was treacherous and muddled, like a suspicious fox. From the trigrams, Gen (Upper) is a dog or a hand; Xun (Lower) is a fox. In the hexagram Gu, the Upper Mountain (Gen/Stop) presses down on the Lower Wind (Xun/Fox). When a mountain pins a fox, the result is naturally "Capturing the male fox." This "male fox" referred directly to Duke Hui of Jin.

4. Verification

In the ninth month of that year, the armies of Qin and Jin fought at Hanyuan. The Qin army won a total victory and captured Duke Hui of Jin—the "male fox."

V. From Yarrow to Coins: The Decline and Evolution of Divination

The Da Yan method flourished from the Shang and Zhou dynasties through the Han. However, as history progressed, it was gradually marginalized.

1. Complexity is the Enemy

A standard Da Yan divination takes 15–20 minutes even for a fast practitioner, and up to half an hour for others. It is incredibly easy to miscount; a single error ruins the entire hexagram. For urgent battlefield decisions or marketplace divination, this was simply too slow. Consequently, after the Tang and Song dynasties, the "Huo Zhu Lin" method (Coin Oracle) rose to prominence.

2. The Price of "Sincerity"

The Da Yan method emphasizes ritual and achieving "Unity of Heaven and Man" during the long counting process. As divination became secularized and commercialized, people became more concerned with the accuracy of the result rather than the psychological cultivation of the process.

3. A Modern Perspective: Why Do We Still Need Da Yan$3

In an age where computer algorithms can generate billions of random numbers per second, does the Da Yan method still matter$4 The answer is yes.

• The Wisdom of Slowness: In an era of double-speed everything, Da Yan forces us to slow down. The repeated dividing and combining of those forty-nine stalks is a process of organizing one's own thoughts. By the time you finish eighteen changes, you may already have the answer in your heart before the hexagram even appears.
• Simulating Chaos Theory: As mentioned, the unique probability distribution of Da Yan is an ancient simulation of "non-linear systems" in nature. It reminds us that world development tends toward inertia (Young Yang/Ying), while sudden mutations (Old Yang/Yin), though critical, are rare.

VI. Conclusion

The Da Yan divination method was a grand attempt by the Chinese ancestors to capture the rhythm of the universe through mathematical logic.

The fifty stalks in the hand are not just plant stems; they are the physical manifestation of the "Great Expansion Number." Every division is a reenactment of Taiji generating the two poles; every suspension is a symbol of humanity finding its place between Heaven and Earth.

When we look back at Duke Mu of Qin's divination before the Battle of Hanyuan, we see more than just a magical prophecy of a "captured fox." We see an ancient civilization facing an unknown destiny, using a web woven of reason (Numbers) and intuition (Images) to capture the courage of the future.

Today, we restudy the Da Yan method not necessarily to predict good or bad fortune, but to feel, through the touch of our fingertips, that thousand-year-old reverence and contemplation of the Great Dao of Heaven and Earth.

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