II. The Four Operations and Eighteen Transformations: A Ritual of Communion with the Luminous Spirits

The procedural steps of the Great Expansion Milfoil Method are extraordinarily intricate, earning the name "Four Operations and Eighteen Transformations."

• The Four Operations: Dividing in two, setting one aside, counting off by fours, and gathering the remainders — these four actions constitute one operation (one transformation).
• The Eighteen Transformations: Three operations (three transformations) are required to determine a single line (yao). A hexagram contains six lines, hence $3 \times 6 = 18$ transformations are needed to complete a hexagram.

This process is not merely an exercise in deriving numbers; it is designed to allow the diviner, through the painstaking labor of the procedure, to gather and focus the mind, entering a state of utmost sincerity (cheng).

Preparations

• Instruments: Fifty yarrow stalks (the ancients used serrated grass stems; bamboo sticks or Go stones are commonly used as substitutes today).
• Setting: A clean table or desk. The diviner sits facing south (or north, depending on the lineage), with a heart full of reverence.

Determining the First Line (Requires Three Transformations)

The First Transformation

1. Extracting the Taiji: Remove one stalk from the fifty and set it aside. Forty-nine remain in hand.
2. Dividing in Two (Symbolizing the Two): Divide the forty-nine stalks at random into a left pile and a right pile, symbolizing the initial separation of Heaven and Earth, Yin and Yang.
3. Setting One Aside (Symbolizing the Three): Take one stalk from the right pile and place it between the little finger and ring finger of the left hand. This symbolizes "Man" arising between Heaven and Earth, forming the Three Powers (sancai): Heaven, Earth, and Man.
4. Counting by Fours (Symbolizing the Four Seasons):
   • First, count the left pile: group the stalks in sets of four (symbolizing spring, summer, autumn, and winter). At the end, 1, 2, 3, or 4 stalks will remain (note: if exactly divisible, take 4, not 0). Remove the remainder and place it between the ring finger and middle finger of the left hand (symbolizing the intercalary month).
   • Then count the right pile: likewise group by fours, and place the remainder (1, 2, 3, or 4) between the middle finger and index finger of the left hand (symbolizing the second intercalation in five years).
5. Gathering the Remainders (Combining the Remainders): Gather all the stalks held between the fingers (the 1 set aside + the left remainder + the right remainder) and place them in the upper-left corner of the table. They are set aside and not used again. This is the number of stalks removed in the "First Transformation."

Mathematical Verification: The total number of stalks removed in the First Transformation can only be one of two values: 5 or 9. (At this point, the number of stalks remaining in hand is either 44 or 40.)

The Second Transformation

Take the stalks remaining from the First Transformation (44 or 40) and combine them, then repeat the steps above:

1. Divide in Two: Divide the stalks in hand into left and right piles once more.
2. Set One Aside: Take one from the right pile and hold it.
3. Count by Fours: Count off both left and right piles by fours and take the remainders.
4. Gather the Remainders: Combine the set-aside stalk and the remainders, and place them to one side.

Mathematical Verification: The total number of stalks removed in the Second Transformation can only be one of two values: 4 or 8. (At this point, the number of stalks remaining in hand is 32, 36, or 40.)

The Third Transformation

Take the stalks remaining from the Second Transformation, combine them, and repeat once more:

1. Divide in Two.
2. Set One Aside.
3. Count by Fours.
4. Gather the Remainders.

Mathematical Verification: The total number of stalks removed in the Third Transformation can only be one of two values: 4 or 8.

Deriving the Number for One Line

After the three transformations, take the total number of stalks remaining in hand (those not removed through the gathering process) and calculate as follows. The remaining total can only be one of four numbers. Divide it by four to obtain the strategy number (ce shu) for that line:

• 24 stalks remaining: $24 \div 4 = 6$ — Old Yin (a changing line, notated as X or --x--).
• 28 stalks remaining: $28 \div 4 = 7$ — Young Yang (unchanging, notated as —).
• 32 stalks remaining: $32 \div 4 = 8$ — Young Yin (unchanging, notated as --).
• 36 stalks remaining: $36 \div 4 = 9$ — Old Yang (a changing line, notated as O or —o—).

With this, the first line (the bottom line) is drawn. Repeat the above "three transformations" a total of six times, drawing the lines from bottom to top — first, second, third, fourth, fifth, and sixth — to complete the hexagram.