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.
III. God's Weighted Dice: The Probabilistic Aesthetics of the Great Expansion Milfoil Method
Here lies the most fundamental distinction between the Great Expansion Milfoil Method and the coin-toss method. The coin-toss method is based on a simple binomial distribution, yielding relatively uniform probabilities. The Great Expansion Milfoil Method, through its intricate "set one aside, count by fours" procedure, constructs a markedly asymmetric probability model.
1. Combinatorial Logic of the Variables
In the three transformations, the number of stalks removed each time (set-aside + left remainder + right remainder) follows specific patterns:
- First transformation removal: 5 or 9
- Second transformation removal: 4 or 8
- Third transformation removal: 4 or 8
To obtain the final result, we examine the combinations of remainders:
- Obtaining Old Yang (9): Requires 36 stalks remaining, i.e., $49 - (5 + 4 + 4) = 36$.
- Condition: All three transformations must remove the minimum number (5, 4, 4).
- Obtaining Old Yin (6): Requires 24 stalks remaining, i.e., $49 - (9 + 8 + 8) = 24$.
- Condition: All three transformations must remove the maximum number (9, 8, 8).
2. Specific Probability Calculations
Following the derivations of Zhu Xi in his Yixue Qimeng (Introduction to the Study of the Yijing) and those of modern mathematicians, the probabilities of the four line types are as follows:
| Line Type | Number | Formation Condition (Sum of Removals) | Probability Fraction | Probability Percentage |
|---|---|---|---|---|
| Old Yang | 9 | 13 (5+4+4) | 3/16 | 18.75% |
| Young Yang | 7 | 17, 21 (multiple combinations) | 5/16 | 31.25% |
| Young Yin | 8 | 17, 21 (multiple combinations) | 7/16 | 43.75% |
| Old Yin | 6 | 25 (9+8+8) | 1/16 | 6.25% |
3. The Philosophical Significance Behind the Data
This is a remarkable discovery: Old Yang (9) appears with a probability three times that of Old Yin (6)! Simultaneously, Young Yin (8) appears with a probability far exceeding that of Young Yang (7).
This asymmetry embodies a profound pre-Qin cosmological vision:
- Yang is abundant; Yin is scarce: Yang qi (creative force, dynamism) is typically dominant and active. Yet when at its peak and turning to decline (Old Yang), such a transformation occurs more readily than the turning of Yin at its extreme to Yang (Old Yin). This symbolizes that "although accomplishment (Yang) is arduous, Yang qi itself is plentiful."
- The world's dominant keynote is Young Yin: The most probable outcome, Young Yin (8) at 43.75%, represents a state of stillness, latency, and material existence. This suggests that the phenomenal world is, for the most part, quiescent — preserving rather than transforming, free of violent upheaval.
- Six is rarely obtained, while Nine comes readily: In Yijing studies, "six" represents Yin at its extreme, symbolizing total collapse or transformation — a condition exceedingly difficult to achieve in the natural world. "Nine" represents Yang at its extreme, where energy released to its fullest occurs comparatively easily.
This renders the Great Expansion Milfoil Method far closer to the complex rhythms of the real world than the coin-toss method — the world is neither black nor white, nor is it a perfectly fair randomness, but rather an evolutionary system possessed of specific tendencies.