Probability and the Yi Jing

Introduction

The Chinese Book of Changes, the Yi Jing, was compiled, as we know it today, by King Wen at the end of the Shang dynasty in the 12th century b.c. His sources were the oracular traditions employed by the sages of the Shang dynasty, which, according to legend, were originally devised at the dawn of civilization by the mythical culture hero Fu Xi, who had also invented writing, fishing, and trapping.

The Book of Changes serves as both a repository of timeless wisdom and as an oracle which may be consulted using a number of divinatory methods. All such methods involve the construction of a figure (termed a “hexagram” by Legge and subsequent Western scholars) composed of six elements, each element being either a simple line segment (——), considered to be Yang or “light, ” or a divided line segment (– –), considered to be Yin or “dark.”

Each of the 64 possible hexagrams has its own meaning and oracular value, each of which is described in the text of the Yi Jing and in its commentaries known as the “Ten Wings,” written by philosophers of the Confucian school. In addition, the Yi Jing provides for the construction of a secondary hexagram from the primary hexagram based on special cases of Yin and Yang called “moving lines.” Each moving line in the primary hexagram has a special comment written by the Duke of Zhou (son of King Wen, and younger brother of King Wu, who founded the Zhou dynasty). The secondary hexagram is formed as the moving Yang lines “change” into Yin lines, and the moving Yin lines “transform” into Yang lines. The secondary hexagram so formed has its own oracular value which is to be considered in the context of that of the primary hexagram and its moving lines.

The two traditional methods of constructing a hexagram are the “yarrow stalk method” and the “coin method.”

The Yarrow Stalk Method

• To employ the yarrow stalk method, one begins with a bundle of 50 straight, dried stalks of the yarrow herb.

• One stalk is set aside and not used again.

• The bundle of the remaining 49 stalks is then divided into two bundles.

• One stalk is taken from the bundle on the right and placed between the ring finger and little finger of the left hand.

• The bundle on the left is then taken up in the left hand, and stalks are removed therefrom and set aside in groups of 4 using the right hand, until 4 or fewer remain.

• The remaining stalks are placed between the middle finger and ring finger of the left hand.

• The bundle on the right is then taken up in the left hand, and stalks are removed therefrom and set aside in groups of 4 using the right hand, until 4 or fewer remain.

• The remaining stalks are placed between the index finger and middle finger of the left hand.

• The total number of stalks between the fingers of the left hand are then counted and noted. The possibilities are 9 and 5. Nine stalks results in the value of 2, and five stalks results in the value of 3. Here are the possible outcomes of the first operation:

• These 9 or 5 stalks are then set aside and the remaining bundle of 40 or 44 stalks is divided and counted out similarly. This time, eight stalks results in the value of 2, and four stalks results in the value of 3. Here are the possible outcomes of the second operation:

• These 8 or 4 stalks are then set aside and the remaining bundle of 32, 36, or 40 stalks is divided and counted out in the same manner for a third operation, the possible outcomes of which are identical to those of the second operation.

• Each operation has now produced a value of either 2 or 3, and these three values are now added together to produce a total of 6, 7, 8, or 9. The totals of 6 and 8 yield a Yin line (– –), the totals 7 and 9 yield a Yang line (——). A total of 6 is considered a moving Yin line (– x –), and a total of 9 is considered a moving Yang line (—o—).

• This first line is placed at the bottom of the hexagram and the entire operation is repeated five times to produce the remaining five lines. The sixth line is placed at the top of the hexagram.

The Coin Method

The other traditional method of constructing a hexagram employs three coins instead of 50 yarrow stalks, and is considerably quicker than the yarrow stalk method.

To employ the coin method, one begins with three similar coins. One side of each coin is assigned the value of 2, the other side is assigned the value of 3. If old Chinese coins are used, the side with the Chinese characters is assigned the value of 2. 

All three coins are tossed at once, and the values of the visible sides are added to produce a total of either 6, 7, 8, or 9. Thus, a single toss of three coins produces the equivalent of the three operations of the yarrow stalk method. 

The coins are then tossed five more times to construct the remainder of the hexagram. Again, the hexagram is constructed from the bottom upward. 

Probabilistic Comparison of the Yarrow Stalk and Coin Methods

Using either method, the probability of obtaining a Yin line or a Yang line is equal. The probability of obtaining either is once in two tries, or ½, or 50%. Using either method, the probability of obtaining any particular hexagram is once out of 64 tries, or 1/64. However, the probability of obtaining a moving line versus a stable line differs according to which method is used, as follows:

• Note that with the yarrow stalk method, it is easier to get a moving Yang line and more difficult to get a moving Yin line. This discrepancy in probability is all due to the first operation of the yarrow stalk method, which is biased towards an outcome value of 3 against that of 2 by a factor of 3 to 1.

A Modified Coin Method

The coin method can be modified to give approximately the same probabilities as the yarrow stalk method, as follows. Identify one of the three coins by some distinction in size, color, age, etc.; or paint a small dot on one of one of the coins, on the side which is valued 2. When the three coins are thrown and the “special” coin reads 3, the values of the three coins are added as usual. However, if the special coin reads 2, the special coin is thrown again, and then the values of the three coins are added.

The Flat Stick Method

Aleister Crowley was an avid student of the Yi Jing, and frequently consulted the oracle throughout his adult life. He usually obtained his hexagrams using a non-traditional method of his own devising. He used six flat, wooden sticks, each of which had a notch cut in the center of one side. He painted the inside of the notches red for contrast. With his eyes closed, he would shuffle the six and lay them out in front of him to form a hexagram, from bottom to top. Yin lines would be indicated by the sticks with the notched sides up, and Yang lines would be indicated by the sticks with the unbroken sides up. This flat stick method yields the same probability of obtaining any particular hexagram as either the yarrow stalk method or the coin method, and it has the added benefit of providing a graphical representation of the hexagrams. 

Crowley evidently used at least two methods to obtain “moving lines” for consulting the text on the lines by the Duke of Zhou. One method was to push one or more sticks slightly to the side, based on “feel,” to indicate the moving lines. Another method is indicated by the fact that one of Crowley’s sticks was marked with paint on one end. The marked stick would indicate a single moving line in each hexagram obtained. Obviously, the probability of obtaining a moving line would be very different with the latter method than with either of the two traditional methods. One moving line will always occur in every hexagram obtained, and there will never be more than one moving line in any hexagram obtained. This would obviously provide a simpler oracle to interpret, but it would also be somewhat deficient in subtlety with respect to an oracle obtained using either of the two traditional methods. In addition, the text for Hexagrams I and II, Qian and Kun, both include material which is applicable only when all the lines are moving lines; which material would be unusable with this method.

It is possible, however, to adapt the flat stick method, with its graphical image of the hexagram, to provide the same probabilities for moving lines as either the coin method or the yarrow stalk method.

To produce roughly the same probabilities as the coin method, twelve sticks must be constructed. Six of these are painted on one end only. When constructing a hexagram, all twelve sticks are shuffled, and six of the twelve are dealt out to build the hexagram. Those lines with the painted end on the left side only (or on the right side only – consistency is the key) are interpreted as moving lines.

To produce roughly the same probabilities as the yarrow stalk method, sixteen sticks must be constructed, six of which are painted on one end only. The 16 sticks are shuffled, and six are dealt out to construct a hexagram. Yang lines which are painted on either end are interpreted as moving lines; but Yin lines which are painted only on the left end (or only on the right end, as before) are interpreted as moving lines.

A Final Note

Probability theory is based on one fundamental assumption: that the events in question are random. If one holds oracular phenomena to be non-random, then considerations of probability are entirely irrelevant, and it is only necessary to ensure that all desired outcomes are possible. The oracle can be viewed as being guided by intelligence or a cosmic pattern; in which case the same hexagram would be produced for a given set of circumstances regardless of the method used, provided the guiding intelligence had been properly invoked through satisfaction of the moral and ritual requisites.

On the other hand, randomness, or Chaos, can be seen as an aspect of the Dao, or as the mirror of the Subconscious; and the selection of different oracular methods can be viewed as influencing the circumstances of the questioner and thus the outcome of the oracle. In the end, the consultation of any oracle requires the use of a well-developed intuitive capacity; and it is intuition which should be used to select the oracular method to be employed.

References

• Legge, James, The Yi King, in Sacred Books of the East, Part II, F. Max Mueller, ed., Oxford at the Clarendon Press, 1899

• Wilhelm, Richard & Cary F. Baynes (Trans.), The I Ching, or Book of Changes, [1950] Bollingen series XIX (Third Edition), Princeton University Press, New York 1967

• Ko Yuen (Aleister Crowley) (Trans.), Shih Yi, A Critical and Mnemonic Paraphrase of the Yi King, H. Parsons Smith, Oceanside, California 1971

• Hymenaeus Alpha 777 (Grady L. McMurtry), “On Knowing Aleister Crowley Personally,” in The O.T.O. Newsletter, Vol. III, No. 9, August 1979 e.v.

• Cornelius, J. Edward, “Crowley’s I Ching Sticks,” unpublished article

• Gardner, Martin, “Mathematics of the I Ching,” in Scientific American, January 1974