I Ching divination


Among the many forms of divination is a cleromancy that is applied to the I Ching or Book of Changes. The text of the I Ching consists of sixty-four hexagrams—six-line figures—and commentaries upon them. By using one or another of several methods, one randomly generates the six lines; one then studies the commentaries in the I Ching associated with the generated hexagram. The meanings derived from such study can be interpreted as an oracle.
Oracular uses of the I Ching—changing lines and resulting changed hexagrams—are documented before and around the Warring State period. The practice is earlier than many schools of Chinese philosophy, including that of Confucius. The I Ching was also used by later schools, such as the School of Yin-Yang. As the I Ching was one of only a few books that were not burnt, and it enjoyed for more than two millennia the status of one of the five key books that had to be studied as preparation for the examinations of government officials, the traditions of its rules and interpretation have continued to the present.
Throughout China's region of cultural influence, scholars have added comments and interpretations to the I Ching. It has also attracted the interest of many thinkers in the West; historical and philosophical information, as well as a list of English translations, can be found here. The text is extremely dense reading—in fact, the original interpretation of the oracle is based not only on the groupings of six lines, but also on groups of three lines and even pairs of lines.

Methods

Each hexagram is six lines, written sequentially one above the other; each of the lines represents a state that is either yin or yang, and either old or young. The usual methods for consulting the I Ching as an oracle produce a "sacred" or "ritual" number for each type of line: 6, 7, 8, or 9. The six lines are produced in order using the chosen method, beginning at the first one and proceeding upward to the sixth line, each with its corresponding number. Then, the commentaries applying to the generated hexagram are studied; if the hexagram contains no old lines at all, that concludes the consultation, but if there are one or more old lines, the separate commentary for each such line is also studied. Then, the lines are appropriately changed, which—with the young lines in the original hexagram remaining the same—results in a second, different, hexagram, the commentarial material on which is then also studied.
The method used by the diviner to generate the hexagram depends on their circumstances and beliefs; the yarrow-stalk method is usually employed by traditionalists who find significance in its complexity, and in the resulting time needed to manipulate the stalks to produce a hexagram. Coin methods, and others, are used either by those short of time, or by fortune-tellers who need a quick reading. There are also methods to generate a hexagram by interpreting the time, direction, person, etc., instead of throwing coins or dividing and counting yarrow stalks.
Several of the methods described below force exactly one, or no, moving lines; the traditional yarrow-stalk method allows from zero to six moving lines. The yarrow-stalk method favours static lines over moving lines in the ratio 3:1.

Precursor to ''I Ching'': Cracks in turtle shell

Plastromancy or the turtle-shell oracle is probably the earliest recorded form of fortune telling. The diviner would apply heat to a piece of a turtle shell, and interpret the resulting cracks. The cracks were sometimes annotated with inscriptions, the oldest Chinese writings that have been discovered. This oracle predated the earliest versions of the Zhou Yi by hundreds of years.
A variant on this method was to use ox shoulder bones, a practice called scapulimancy. When thick material was to be cracked, the underside was thinned by carving with a knife.

Yarrow stalks

Hexagrams may be generated by the manipulation of yarrow stalks. These are usually genuine Achillea millefolium stalks that have been cut and prepared for such purposes, or any form of wooden rod or sticks which are plain, lacquered, or varnished. When genuine Achillea is used, varieties local to the diviner are considered the best, as they would contain qi closer to, and more in tune with, the diviner, or they may come from a particularly spiritual or relevant place, such as on the grounds of a Confucian temple. When not in use, they are kept in a cloth or silk bag/pouch or a wooden case/box.
Fifty yarrow stalks are used, though one stalk is set aside at the beginning and takes no further part in the process of consultation. The remaining forty-nine stalks are roughly sorted into two piles, and then for each pile one stalk is initially "remaindered"; then the pile is "cast off" in lots of four. The remainders from each half are combined and set aside, with the process then repeated twice. The total number of stalks in the remainder pile will necessarily be 9 or 5, in the first count, and 8 or 4, in the second. 9 or 8 is assigned a value of 2; 5 or 4, a value of 3. The total of the three passes will be one of just four values: 6, 7, 8, or 9 —that value is the number of the first line.
The forty-nine stalks are then gathered and the entire procedure repeated to generate each of the remaining five lines of the hexagram.
The yarrow-stalk method produces unequal probabilities for obtaining each of the four totals, as shown in the table. Compared to the three-coin method discussed next, the probabilities of the lines produced by the yarrow-stalk method are significantly different.
Note that the Yarrow algorithm is a particular algorithm for generating random numbers; while it is named after the yarrow-stalk method of consulting the I Ching, its details are unrelated to it.

Coins

Three-coin method

The three-coin method came into use over a thousand years after the yarrow-stalk method. The quickest, easiest, and most popular method by far, it has largely supplanted yarrow stalks, but produces outcomes with different likelihoods. Three coins are tossed at once; each coin is given a value of 2 or 3, depending upon whether it is tails or heads, respectively. Six such tosses make the hexagram. Some fortune-tellers use an empty tortoise shell to shake the coins in before throwing them on a dish or plate.

Modified Three-coin method

The three-coin method can be modified to have the same probabilities as the yarrow-stalk method by having one of the coins be of a second coin type, or in some way be marked as special. All three coins are tossed at once. The results are counted just as in the original three-coin method, with two exceptions: one to make yin less likely to move, and one to make yang more likely to move.
In the case where the special coin is tails and the other two are both tails—which would normally produce a 6—re-flip the marked coin: if it remains tails, then treat it as a 6 ; otherwise, it remains an 8. As a 6 can become a 6 or an 8, it reduces the probability of the moving 6. In other words, it makes the old yin less likely to change.
In the case where the special coin is heads and the other two are both tails—which would normally produce an 7—re-flip the marked coin: if it remains heads, then treat it as a 7 ; otherwise, it remains an 9. As a 7 can become a 7 or an 9, it reduces the probability of the static 7. In other words, it makes the young yang less likely and hence more yangs change as a result.
This method retains the 50% chance of yin:yang, but changes the ratio of moving yang to static yang from 1:3 to 1:7; likewise, it changes the ratio of moving yin to static yin from 1:3 to 3:5, which is the same probabilities as the yarrow-stalk method.

Two-coin method

Some purists contend that there is a problem with the three-coin method because its probabilities differ from the more ancient, yarrow-stalk, method. In fact, over the centuries there have even been other methods used for consulting the oracle.
The two-coin method involves tossing one pair of coins twice: on the first toss, two heads give a value of 2, and anything else is 3; on the second toss, each coin is valued separately, to give a sum from 6 to 9, as above. This results in the same distribution of probabilities as for the yarrow-stalk method.

Four coins

With tails assigned the value 0 and heads the value 1, four coins tossed at once can be used to generate a four-bit binary number, the right-most coin indicating the first bit, the next coin indicating the next bit, etc. The number 0000 is called old yin; the next three numbers—0001, 0010, and 0011 —are called old yang, with a similar principle applied to the remaining twelve outcomes. This gives identical results to the yarrow-stalk method.
The two-coin method described above can be performed with four coins, simply by having one pair of coins be alike—of the same size or denomination—while the other two are of a different size or denomination; the larger coins can then be counted as the first toss, while the two smaller coins constitute the second toss.

Six coins

Six coins—five identical coins and one different—can be thrown at once. The coin that lands closest to a line drawn on the table will make the first line of the hexagram, and so on: heads for yang, tails for yin. The distinct coin is a moving line. This method has the dual failings that it forces every hexagram to be a changing hexagram, and it only ever allows exactly one line to be changing.

Eight coins on Ba Qian

Eight coins, one marked, are tossed at once. They are picked up in order and placed onto a Bagua diagram; the marked coin rests on the lower trigram. The eight process is repeated for the upper trigram. After a third toss, the first six coins are placed on the hexagram to mark a moving line. This has the deficiency or allowing at most one moving line, whereas all six lines could be moving in traditional methods.

Dice

Any dice with an even number of faces can also be used in the same fashion as the coin tosses, with even die rolls for heads and odd for tails. An eight-sided die can be used to simulate the chances of a line being an old moving line equivalent to the yarrow-stalk method. For example, because the chances of any yin line or any yang line are equal in the yarrow-stalk method, there is a one-in-eight chance of getting any basic trigram, the same chance held under the ba qian method, so the ba qian method can be used to determine the basic hexagram. The d8 can then be used by rolling it once for each line to determine moving lines. A result of 1 on a yin line, or 3 or less on a yang line, will make that line a moving line, preserving the yarrow-stalk method's outcomes.
Another dice method that produces the 1:7:3:5 ratio of the yarrow-stalk method is to add 1d4 + 1d8. All odd results are considered yin, with the result of 11 denoting an old yin. Any even results would be considered yang, with both 4 and 10 treated as old yang.
Two dice methods that not only produce the yarrow-stalk probabilities but maintain the traditional even–odd associations of yin and yang are the 3d4 and 2d8 methods. In the 3d4 method, one rolls three four-sided dice and adds their outcomes, treating all odd totals as yang and all even totals as yin, with totals of 4, 7, and 12 indicating a moving line. The 2d8 method works analogously for two eight-sided dice, but here, any total over 10 is considered moving.

Marbles or beads (Method of Sixteen)

Sixteen marbles can be used in four different colours. For example:
The marbles are drawn with replacement six times to determine the six lines. The distribution of results is the same as for the yarrow-stalk method.

Rice grains

For this method, either rice grains or small seeds are used. Six small piles of rice grains are made by picking up rice between finger and thumb. The number of grains in a pile determines if it is yin or yang. The rice grain method doesn't mark any lines as moving, while the traditional yarrow method can mark any of the six lines as moving.

Calendric cycles and astrology

There is a tradition of Taoist thought which explores numerology, esoteric cosmology, astrology and feng shui in connection with the I Ching.
The eleventh-century Neo-Confucian philosopher Shao Yung contributed advanced methods of divination including the Plum Blossom Yi Numerology, a horary astrology that takes into account the number of calligraphic brush strokes of one's query. Following the associations Carl Jung drew between astrology and I Ching with the introduction of his theory of synchronicity, the authors of modern Yi studies are much informed by the astrological paradigm. Chu and Sherrill provide five astrological systems in An Anthology of I Ching and in The Astrology of I Ching develop a form of symbolic astrology that uses the eight trigrams in connection with the time of one's birth to generate an oracle from which further hexagrams and a daily line judgement are derived. Another modern development incorporates the planetary positions of one's natal horoscope against the backdrop of Shao Yung's circular Fu Xi arrangement and the Western zodiac to provide multiple hexagrams corresponding to each of the planets.

[Wen Wang Gua] method

This method goes back to Jing Fang. While a hexagram is derived with one of the common methods like coin or yarrow stalks, here the divination is not interpreted on the basis of the classic I Ching text. Instead, this system connects each of the six hexagram lines to one of the Twelve Earthly Branches, and then the picture can be analyzed with the use of 5 Elements.
By bringing in the Chinese calendar, this method not only tries to determine what will happen, but also when it will happen. As such, Wen Wang Gua makes a bridge between I Ching and the Four Pillars of Destiny.

Software methods

The preceding methods can be simulated in software. This has the theoretical advantage of improving randomness aspects of consulting the I Ching. For all methods, one must pre-focus/prepare the mind.
Here is a typical example for the "modified three-coin" method:

  1. !/usr/bin/env python3
  2. iChing_Modified_3_coins.py
  3. see https://github.com/kwccoin/I-Ching-Modified-3-Coin-Method
  4. Create I Ching hexagrams: present > future.
  5. With both "3-coin method" and "modified 3-coin method".
  6. 3-coins Probabilities:
  7. old/changing/moving yin "6 : x " = 1/8
  8. yang "7 :

    " = 3/8

  9. yin "8 : " = 3/8
  10. old/changing/moving yang "9 : o " = 1/8
  11. 3-coins Probabilities:
  12. old/changing/moving yin "6 : x " = 1/8
  13. yang "7 :

    " = 3/8
  14. yin "8 : " = 3/8
  15. old/changing/moving yang "9 : =o=" = 1/8
  16. Modified 3-coins Probabilities:
  17. old/changing/moving yin "6 : x " = 1/8 * 1/2 = 1/16
  18. yang "7 :

    " = 3/8 - 1/8*1/2 = 5/16
  19. yin "8 : " = 3/8 - P = 7/16
  20. old/changing/moving yang "9 : =o=" = 1/8 - p = 3/16
  21. see
  22. https://aleadeum.com/2013/07/12/the-i-ching-random-numbers-and-why-you-are-doing-it-wrong/
  23. especially see the remark why 1st round are 1/4-3/4 whilst 2nd and 3rd round are 1/2-1/2
import random
def toss -> int:
"""Toss."""
rng = random.SystemRandom # Auto-seeded, with os.urandom
special_coin = 0
val = 0
for flip in range: # Three simulated coin flips i.e. coin 0, 1, 2
val += rng.randint # tail=2, head=3 for each coin
if flip 0:
special_coin = val # Coin 0 as the special coin
if method "coin": # Coin method note tth or 223 is 7 or young yang
return val # Probability of 6/7/8/9 is 1/8 3/8 3/8 1/8
elif method "modified 3 coins":
# method similar to "yarrow-stick" need to have prob.
# for 6/7/8/9 as 1/16 5/16 7/16 3/16
# now coin method is
# for 6/7/8/9 as 2/16 6/16 6/16 2/16
# modified to change
# -1/16 -1/16 +1/16 + 1/16
# 6 7 8 9
if and :
special_coin = rng.randint
if special_coin 2:
val = 6
else:
val = 8
elif and :
special_coin = rng.randint
if :
val = 7
else:
val = 9
return val # probability of 6/7/8/9 is 1/16 5/16 7/16 3/16

else: # yarrow-stick method as effectively default
# start_sticks, sky-left, sky-reminder, human, earth-right, earth-reminder, bin
# value-> 49 0 0 0 0 0 0
# index-> 0 1 2 3 4 5 6
# on table:
# heaven
# heaven-left human earth-right
# earth
#
# sometimes use finger to hold above
def printys:
# String format example: f"Result: "
width = 3
print
return
def ys_round:
if debug "yes": print
if debug "yes": print
if debug "yes": print
# Generate a number somewhere in between 1/3 to 2/3 as human do not trick
if debug "yes": printys
ys = rng.randint
ys = ys - ys
ys = ys - ys - ys
if debug "yes": printys
ys = 1
ys = ys - ys
if debug "yes": printys
ys = ys % 4
if ys 0:
ys = 4
ys = ys - ys
if debug "yes": printys
ys = ys % 4
if ys 0:
ys = 4
ys = ys - ys
if debug "yes": printys
ys += ys + ys + ys
ys = 0
ys = 0
ys = 0
ys = ys + ys
ys = 0
ys = 0
if debug "yes": printys
return ys
ys = # May be better use dictionary
ys = 55
# printys
ys = 49
# printys
# Round 1 need to ensure mod 4 cannot return 0 and cannot have 0
# wiki said cannot have 1 as well not sure about that
ys = ys_round
ys = ys_round
ys = ys_round
return ys // 4
  1. We build in bottom to top
print
toss_array =
for line in range:
toss_array = toss
print
  1. Hence we print in reverse
def print_lines_in_reverse:
for line in range:
val = toss_array # The changing line/hexagram need another program
if val 6: print
elif val 7: print
elif val 8: print
elif val 9: print
print_lines_in_reverse
print

With a modified three-coin method as default, this may avoid the Sung dynasty issue, i.e., when you have an easily available and simple method, you use it—but with a wrong probability!
A , which generates slightly different probabilities, is available in open source form at GitHub.

Probability analysis of ''I Ching'' divination

Most analyses of the probabilities of either the coin method or yarrow-stalk method agree on the probabilities for each method. The coin method varies significantly from the yarrow-stalk method, in that the former gives the same probability to both of the moving lines and to both of the static lines, which is not the case in the yarrow-stalk method.
However, the calculation of the frequencies for the yarrow-stalk method—generally believed to be the same as those described in this article in the simplified method using sixteen objects—contains a further error, in the opinion of Andrew Kennedy, which is that of including the selection of zero as a quantity for either hand. The yarrow-stalk procedure expressly requires that the four numbers be produced without using zero; Kennedy shows that by not allowing the user to select zero for either hand, or a single stalk for the right hand, the hexagram frequencies change significantly for a daily user of the oracle. Kennedy has modified the simplified method of using sixteen coloured objects described in this article as follows:
take 38 objects, of which
  • 8 are of one colour = moving yang
  • 2 are of a different colour = moving yin
  • 11 are of a different colour = static yang
  • 17 are of a different colour = static yin
This arrangement produces Kennedy's calculated frequencies within 0.1%.

In popular culture