On the Great Expansion Milfoil Method: The Mathematical Ritual of Cosmic Genesis and Analysis of Authentic Divinations in the Zuo Zhuan
An in-depth analysis of the philosophical core, the detailed procedure of the Four Operations and Eighteen Transformations, and the mathematical mysteries of non-uniform probability in the Yijing's Great Expansion milfoil divination method, combined with the classic case of Duke Mu of Qin's campaign against Jin from the Zuo Zhuan (Duke Xi, Year 15) to reconstruct the hexagram-interpretation logic of the pre-Qin perspective.

IV. Historical Verification from the Zuo Zhuan: The Divinatory Logic of Duke Mu of Qin's Campaign Against Jin
To truly understand how the Great Expansion Milfoil Method was applied in antiquity, we must return to the Spring and Autumn period. The Zuo Zhuan records a wealth of divination cases, and among them, the case of Duke Mu of Qin's campaign against Jin (Zuo Zhuan, Duke Xi, Year 15) is a superb exemplar of pre-Qin hexagram-interpretation logic.
1. Historical Background
In 645 BCE (the seventh year of King Xiang of Zhou), the state of Jin suffered a famine and sought grain from Qin. Duke Mu of Qin generously obliged (the "Flotilla Campaign" to ship grain). The following year, Qin itself suffered a famine and requested grain from Jin. Duke Hui of Jin not only refused but attempted to exploit Qin's weakness by launching an attack. Duke Mu of Qin was enraged and resolved to campaign against Jin.
Before dispatching his troops, Duke Mu ordered his diviner, Tu Fu, to perform the yarrow stalk divination.
2. The Hexagram Obtained
"They performed the divination and obtained Gu (Decay) changing to Dui (Joy). The pronouncement was: 'A thousand chariots shall be thrice repelled; and from the remnant of the thrice repelled, the male fox shall be captured.'"
This involves a key aspect of the ancient method of recording: "obtained Gu changing to Dui."
- The primary hexagram: Shan Feng Gu (Mountain over Wind — Gen above, Xun below), the hexagram of Decay.
- The changed hexagram (zhi gua): Dui (Joy). This formulation is debated. Following the original Zuo Zhuan phrasing "Gu zhi Dui," it usually indicates that the lower trigram transforms to Dui, or that specific lines change.
- If the initial six (the bottom line) of Gu changes (Yin becomes Yang), the lower trigram Xun would become Qian, yielding Da Xu (Great Accumulation) — which does not match.
- Under the ancient conventions of the Zuo Zhuan, there are often special usages. Most commentators hold that this indicates Gu underwent a transformation ultimately pointing toward imagery associated with Dui. The mainstream interpretation is that the inner trigram (lower trigram) of Gu changed from Xun to Dui (which would in fact require the first, second, and third lines all to change — an extremely low probability event).
- An alternative authoritative interpretation (Du Yu's commentary): "Gu zhi Dui" does not mean the entire hexagram transforms into the Dui hexagram, but rather refers to the zhen-hui (inner-outer) relationship of Gu or the imagery of specific line statements.
Let us focus on Tu Fu's pronouncement, for therein lies the essence of pre-Qin Yijing studies.
3. Tu Fu's Brilliant Interpretation
Tu Fu did not simply recite the hexagram judgment from the Yijing (Gu: "Supreme success; it is advantageous to cross the great river"). Instead, he employed the method of "extracting images" (qu xiang):
- Image One: Decay beneath the mountain wind The Gu hexagram has Gen (Mountain) above and Xun (Wind/Wood) below. Wind falling beneath the mountain carries not merely the meaning of "decay" but also the sense of "leaves returning to their roots" and "rectification." Duke Mu of Qin would use this to rectify the perfidious Duke Hui of Jin.
- Image Two: A thousand chariots, thrice repelled
This is a deconstruction of the hexagram's structural imagery. In Gu, the lower trigram Xun represents wind, while the upper trigram Gen represents mountain.
- Tu Fu explained: "A thousand chariots, thrice repelled." This likely derives from an understanding of the Xun trigram, which signifies orderliness, as well as chariots and horses.
- A more refined explanation lies in the nuclear trigrams (hu gua). The nuclear trigrams of Gu contain shadows of Gui Mei (the Marrying Maiden) or Jian (Gradual Progress) — the third through fifth lines form Zhen (Thunder), and the second through fourth lines form Dui (Joy). Zhen symbolizes the chariot.
- "Thrice repelled" prophesied the course of the battle: the Jin army would be driven back three times, or the Qin army would cross the river three times.
- Image Three: Capturing the male fox
This is the most celebrated pronouncement.
- The Gu hexagram itself carries the meaning of "bewilderment." Duke Hui of Jin, having broken faith, was confused in judgment — hesitant and irresolute like a fox.
- From the trigram imagery: Gen (the upper trigram) signifies the young man, and can also symbolize the dog or the hand; Xun (the lower trigram) signifies the elder daughter, and can also symbolize hidden murmuring or the fox.
- The third line statement of Gu reads: "Rectifying the father's decay" (gan fu zhi gu). But Tu Fu employed the greater image (da xiang): Gen above (Mountain/Stopping) pressing down upon Xun below (Wind/Fox). A mountain pinning down a fox — naturally, this is "capturing the male fox."
- The "male fox" here directly refers to Duke Hui of Jin.
4. Verification of the Outcome
In the ninth month of that year, the armies of Qin and Jin clashed at the Battle of Hanyuan. The Qin army won a decisive victory and captured Duke Hui of Jin — the very "male fox." The prophecy of "capturing the male fox" was thus fulfilled.
5. Lessons from the Case: How Pre-Qin Yijing Studies Differed from Later Practices
From the case of Duke Mu of Qin's campaign against Jin, we can observe the distinctive characteristics of how the Great Expansion Milfoil Method was applied in the pre-Qin era:
- Emphasis on "images" over "numbers": When interpreting the hexagram, Tu Fu did not dwell on the mutual generation and conquest of the Five Phases (that was a development of the Han dynasty and later). Instead, he made extensive use of the material imagery of the Eight Trigrams (wind, mountain, fox, chariot) to construct a narrative.
- A flexible view of line changes: The phrasing "Gu zhi Dui" suggests that the logic of hexagram transformation at that time may have been more intuitive than later "changed hexagram" rules, placing greater emphasis on the flow of hexagrammatic qi toward a particular direction (such as Dui in the west, associated with metal and martial force).
- Narrative prophecy: The divinatory result was not a simple verdict of auspicious or inauspicious, but a passage of verse rich with narrative ("a thousand chariots, thrice repelled... capturing the male fox"). This was not only prediction but also a form of political rhetoric and psychological warfare.