I Ching divination

Among the many forms of divination is a bibliomancy method using the I Ching (易經) or Book of Changes. The book is structured as 32 pairs of hexagrams, divided in half after the first 30. The text was a subject for civil service exams in Imperial China. To aid in learning these 64 hexagrams, an 8x8 matrix of the 64 hexagrams in terms of all the hexagrams having the same top three lines, called a trigram. Throughout China's region of cultural influence (including Korea, Japan and Vietnam), scholars have added comments and interpretation to this work, one of the most important in ancient Chinese culture; it has also attracted the interest of many thinkers in the West. (See the I Ching main article for historical and philosophical information).
The process of consulting the book as an oracle involves determining the hexagram by a method of random generation and then reading the text associated with that hexagram, and is a form of bibliomancy. Confucius said that one should not consult the Oracle for divination until over the age of 40.^{[citation needed]}. This work discourages compulsion (i.e., asking the same question over and over in hopes of either a different/better answer or some kind of enlightenment as to the meaning of the answers one gets). The Hexagram 4 description talks about the problems with "the youthful and inexperienced" asking the same question three or more times.^{[1]}
The text is extremely dense reading. A list of English translation can be found in the main article  I Ching#Translations. It is not unknown for experienced soothsayers to ignore the text, building the oracle from the pictures created by the lines, bigrams, trigrams, and final hexagram.
Each line of a hexagram determined with these methods is either stable ("young") or changing ("old"); thus, there are four possibilities for each line, corresponding to the cycle of change from yin to yang and back again:
YinYang Signification Number Symbol old yin yin changing into yang 6 xyoung yang unchanging yang 7 young yin unchanging yin 8 old yang yang changing into yin 9 oOnce a hexagram is determined, each line has been determined as either changing (old) or unchanging (young). Old yin is seen as more powerful than young yin, and old yang is more powerful than young yang. Any line in a hexagram that is old ("changing") adds additional meaning to that hexagram.
Taoist philosophy holds that powerful yin will eventually turn to yang (and vice versa), so a new hexagram is formed by transposing each changing yin line with a yang line, and vice versa. Thus, further insight into the process of change is gained by reading the text of this new hexagram and studying it as the result of the current change.
Contents
Methods
Several of the methods use a randomising agent to determine each line of the hexagram. These methods produce a number which corresponds to the numbers of changing or unchanging lines discussed above, and thus determines each line of the hexagram.
Plastromancy  turtle shell cracks
Plastromancy or the turtle shell oracle is probably the earliest record of fortune telling. The diviner would apply heat to a piece of a turtle shell (sometimes with a hot poker), 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 (dated from about 1100 BC) 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. The following directions are from the ten wings of the I Ching. Other instructions can be found here, and a calculation of probabilities here.
 One takes fifty yarrow stalks, of which only fortynine are used. These fortynine are first divided into two heaps (at random), then a stalk from the righthand heap is inserted between the ring finger and the little finger of the left hand. The left heap is counted through by fours, and the remainder (four or less) is inserted between the ring finger and the middle finger. The same thing is done with the right heap, and the remainder inserted between the forefinger and the middle finger. This constitutes one change.
 Now one is holding in one's hand either five or nine stalks in all. The two remaining heaps are put together, and the same process is repeated twice. These second and third times, one obtains either four or eight stalks. The five stalks of the first counting and the four of each of the succeeding countings are regarded as a unit having the numerical value three; the nine stalks of the first counting and the eight of the succeeding countings have the numerical value two.
 When three successive changes produce the sum 3+3+3=9, this makes the old yang, i.e., a firm line that moves. The sum 2+2+2=6 makes old yin, a yielding line that moves. Seven is the young yang, and eight the young yin; they are not taken into account as individual lines.
The correct probability has been used also in the marble, bean, dice and two or four coin methods below. This probability is significantly different from that of the threecoin method, because the required amount of accuracy occupies four binary bits of information, so three coins is one bit short. In terms of chancesoutof16, the threecoin method yields 2,2,6,6 instead of 1,3,5,7 for oldyin, oldyang, youngyang, youngyin respectively.
Note that only the remainders after counting through fours are kept and laid upon the single stalk removed at the start. The piles of four are reused for each change, the number of piles of four is not used in calculation; it's the remainders that are used. The removing of all the fours is a way of calculating the remainder, those fours are then reused for the next change so that the total number of stalks in use remains high to keep all remainders equally probable.
Coins
Threecoin method
The three coin method came into currency over a thousand years later. The quickest, easiest, and most popular method by far, it has largely supplanted the yarrow stalks, and produces outcomes with different likelihoods. A threecoin method with adjusted probabilities can be found here.
Using this method, the probabilities of each type of line are as follows:
 old yang: 1 in 8 (0.125)
 old yin: 1 in 8 (0.125)
 young yang: 3 in 8 (0.375)
 young yin: 3 in 8 (0.375)
While there is one method for tossing three coins (once for each line in the hexagram), there are several ways of checking the results.
How the coins are tossed
 use three coins with distinct "head" and "tail" sides
 for each of the six lines of the hexagram, beginning with the first (bottom) line and ending with the sixth (top) line:
 toss all three coins
 write down the resulting line
 once six lines have been determined, the hexagram is formed
How the line is determined from the coin toss
The numerical method:
 assign the value 3 to each "head" result, and 2 to each "tail" result
 total all the coin values
 the total will be six, seven, eight or nine
 determine the current line of the hexagram from this number: 6 = old yin, 7 = young yang, 8 = young yin, 9 = old yang.
An alternative is to count the "tails":
 3 tails = old yin
 2 tails = young yang
 1 tail = young yin
 0 tails = old yang
Another alternative is this simple mnemonic based on the dynamics of a group of three people. If they are all boys, for example, the masculine prevails. But, if there is one girl with two boys, the feminine prevails. So:
 all tails = old yin
 one tail = young yin
 one head = young yang
 all heads = old yang
Twocoin method
Some purists contend that there is a problem with the threecoin method because its probabilities differ from the more ancient yarrowstalk method. In fact, over the centuries there have even been other methods used for consulting the oracle.
If you want an easier and faster way of consulting the oracle with a method that has nearly the same probabilities as the yarrow stalk method, here's a method using two coins (with two tosses per line):
 first toss of the two coins: if both are "heads," use a value of 2; otherwise, value is 3
 second toss: a "head" has a value of 2, a "tail" a value of 3. Add the two values from this toss and the value from the first toss.
 the sum of the three values will be 6 (old yin), 7 (young yang), 8 (young yin), or 9 (old yang). This provides the first (bottom) line of the hexagram.
Repeat the process for each remaining line.
The probabilities for this method are: old yin 0.0625, young yang 0.3125, young yin 0.4375, and old yang 0.1875.
Four coins
If you're comfortable with binary, four coins can be very quick and easy, and like 2 coins matches the probabilities of the yarrowstalk method. Here's a table showing the different combinations of four coin throws and their binary sum and corresponding line (six lines making a full changing hexagram starting at the bottom). To calculate the binary sum of a four coin throw, place the coins in a line, then add up all the heads using 8 for the leftmost coin, then 4, 2 and 1 for a head in the rightmost position. The full explanation relating it to the yarrow stalk method is at OrganicDesign:I Ching / Divination.
Sum Coins Line 0 T T T T x1 T T T H o2 T T H T o3 T T H H oSum Coins Line 4 T H T T 5 T H T H 6 T H H T 7 T H H H Sum Coins Line 8 H T T T 9 H T T H 10 H T H T 11 H T H H Sum Coins Line 12 H H T T 13 H H T H 14 H H H T 15 H H H H Another 4 coin method uses two different pairs of coins. Each coin in the higher pair counts as one coin, but the lower pair acts as a single coin. If the coins are valued as follows, the mathematics are identical to the use of yarrow sticks. In the following example, heads will count as three, and tails as two. The lower pair are tails if and only if both are tails.
HH (hh)= 9 HH (ht)= 9 HH (tt)= 8 HT (hh)= 8 HT (ht)= 8 HT (tt)= 7 TT (hh)= 7 TT (ht)= 7 TT (tt)= 6
Therefore the odds of 6 = 1/16 Therefore the odds of 7 = 5/16 Therefore the odds of 8 = 7/16 Therefore the odds of 9 = 3/16
Six coins
Take five identical coins, and a sixth that is similar to the five.
 Shake them in your hand for a couple of seconds.
 Toss them up into the air.
 The coin that lines the farthest from one is the sixth line.
 The coin that lands the closest to one is the first line.
 The coin that is different from the others is the moving line.
 Generally, "heads" is considered to be yang, and "tails" to be yin.
This method has been criticized on the grounds that it:
 Forces every hexagram to be a "Moving Hexagram";
 Ignores the statistical probabilities of both the standard three coin method, and the traditional yarrow stalk method.
Ba Qian
Step 1:
 Take eight identical coins.
 Mark one in a small way.
 Shake them up in your hand while focusing on your wish or problem.
 Place the coins counterclockwise on a diagram of the Fu Xi Order of the triagrams.
 The marked coin indicates the lower triagram of the hexagram.
Step 2:
 Shake the coins again.
 Place the coins counterclockwise on a diagram of the Fu Xi Order of the triagrams.
 The marked coin indicates the upper triagram of the hexagram.
 Remove two unmarked coins from the set.
Step 3:
 Shake the coins.
 Starting at the bottom, place on the lines of the hexagram.
 The line with the marked coin is the moving line.
Dice
Using coins will quickly reveal some problems: while shaking the coins in cupped hands, it's hard to know whether they are truly being tumbled; when flipping the coins, they tend to bounce and scatter. It's much easier to use a die as a coinequivalent: if an odd number of pips shows, it counts as "heads"; if an even number of pips shows, as "tails." Obviously, the 50/50 probability is preserved — and rolling dice turns out to be easier and quicker than flipping coins. Thus the threecoin method will use three dice.
Dice can also be used for the twocoin method. It is best to use two pairs of dice, each pair having its own color — e.g., a pair of blue dice and a pair of white dice, such as are commonly found in backgammon sets. One pair can then be designated the "first toss" in the twocoin method, and the other the "second toss." One roll of four dice will then determine a line, with probabilities matching the yarrowstalk method.
The number values on a single die can also be used to determine the hexagram's lines. Designate odd numbers as yang, even numbers as yin, and roll a sixsided die once for each of the six lines. Roll the die a seventh time to determine the moving line. This method mimics Zhou court divinations in which yarrow stalks were used in a twostage divinatory process, first casting the hexagram, then designating one line as moving (see Shaughnessey, 1996, pp. 7–8).
Since a single toss of three distinct coins allows for eight possible combinations of heads & tails, the threecoin method's probabilities can be duplicated with a single eightsided die, rolling it once to generate each line. Use an odd and an even number on the die, 1 and 8 for instance, to designate a moving line when either number is obtained. This preserves the equal 1/4 chance that a given yin or yang line will be moving.
A similar distribution to yarrow stalks is possible using two dice, 1 eightsided (1d8), and 1 twentysided (1d20). Roll both of them at once per line.
 If the 1d20 is an even number
 then
 if the 1d8 = 1 X moving yin (1/16 probability)
 if the 1d8 = 2  8   yin (7/16 probability)
 then
 If the 1d20 is an odd number:
 then
 if the 1d8 = 1  5 ––– yang (5/16 probability)
 if the 1d8 = 6  8 0 moving yang (3/16 probability)
 then
Another duplication of the yarrow stalks' probabilities can be done by taking the total of two eightsided die rolls (2d8; odd totals indicating yang lines and even totals indicating yin), to produce each hexagram line. The 1:1 distribution of yin and yang is preserved, and the chances of obtaining certain totals will be used to match the yarrow stalks' weighted distributions of moving yin and yang lines.
The 2d8 roll provide four possible instances where the total is either two or four, which equates to the yarrow stalks' chances of a yin line being moving. This can be demonstrated by mapping all totals on an 8x8 grid, each axis representing the numbers on one die. The chance of an even (yin) total being two or four (moving) is then 4/32, equaling 1/8. Weight the distribution of moving yang lines similarly, by using totals that equate to a 3/8 (or 12/32) chance of obtaining that result among the 32 odd possibilities, such as seven and 11 (which can likewise be diagrammed on the 8x8 grid). So a total of two, four, seven or 11, when yielded by one 2d8 roll, can indicate that the resulting yin or yang line is moving.
A very simple method on casting the I Ching whereas one has only one changing line for the hexagram would be using a single sixsided die. Even numbers are yin, odd numbers are yang. Roll six times to create the hexagram, a seventh time to determine the changing line. 1 is the bottom line, 2 is the second line from the bottom, 3 is the third line from the bottom, etc...
Marbles or beads (method of 16)
This method is a recent innovation, designed to be quick like the coin method, while giving nearly the same probabilities as the yarrow stalk method (see Probability Analysis below).
 use 16 marbles of four different colours but the same size, distributed as follows
 1 marble of a colour representing old yin (such as blue)
 5 marbles of a colour representing young yang (such as white)
 7 marbles of a colour representing young yin (such as black)
 3 marbles of a colour representing old yang (such as red)
 place all the marbles in a bag or other opaque container
 for each of the six lines of the hexagram
 shake all 16 marbles together in the container to "shuffle" them
 draw out one marble
 the marble drawn determines the current line of the hexagram
 replace the marble in the container
 once six lines have been determined, the hexagram is formed
A good source of marbles is a (secondhand) Chinese checkers set: 6 colors, 10 marbles each.
Using this method, the probabilities of each type of line are the same as the distribution of the colours, as follows:
 old yin: 1 in 16 (0.0625)
 old yang: 3 in 16 (0.1875)
 young yang: 5 in 16 (0.3125)
 young yin: 7 in 16 (0.4375)
An improvement on this method uses 16 beads of four different colors but with the same size and shape (i.e., indistinguishable by touch), strung beads being much more portable than marbles. You take the string and, without looking, grab a bead at random. The comments above apply to this method as well.
Rice grains
For this method, either rice grains, or small seeds are used.
One picks up a few seeds between the middle finger and thumb. Carefully and respectfully place them on a clean sheet of paper. Repeat this process six times, keeping each cluster of seeds in a separate pile – each pile represents one line. One then counts the number of seeds in each cluster, starting with the first pile, which is the base line. If there is an even number of seeds, then the line is yin – –, otherwise the line is yang –––, except if there is one seed, in which case one redoes that line.
One then asks the question again, and picks up one more cluster of seeds. Count the number of seeds you have, then keep subtracting six, until you have six seeds or less. This gives you the number of the line that specifically represent your situation. It is not a moving line. If you do not understand your answer, you may rephrase the question, and ask it a second time.
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 Han period (206 BCE220 CE)… saw the combination and correlation of the I Ching, particularly in its structural aspects of line, trigrams, and hexagrams, with the yinyang and wu hsing (Five Element) theories of the cosmologists, with numerical patterns and speculations, with military theory, and, rather more nebulously, with the interests of the fangshih or “Masters of Techniques,” who ranged over many areas, from practical medicine, through alchemy and astrology, to the occult and beyond.
— Hacker, Moore and Patsco, I Ching: an annotated bibliography, “The I Ching in Time and Space”, p. xiii
The eleventh century NeoConfucian philosopher Shao Yung contributed advanced methods of divination including the Plum Blossom Yi Numerology, an horary astrology^{[2]} that takes into account the number of calligraphic brush strokes of one's query.^{[citation needed]} 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.^{[3]} Chu and Sherrill provide five astrological systems in An Anthology of I Ching^{[4]} and in The Astrology of I Ching^{[5]} 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.^{[2]} 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 the each of the planets.^{[2]}
Wen Wang Gua Method
This method goes back to Jing Fang (78–37 BC). 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 12 Earthly Branches and then the picture can be analyzed with the use of 5 Elements (Wu Xing).^{[6]}
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.
Probability analysis of I Ching divination
Most analyses on the probabilities of either the coin method or yarrow stalk method agree on the probabilities for each method. Examples are
 http://www.dentato.it/iching/, an alternative calculation of the yarrow stalk probabilities;
 OrganicDesign:I Ching / Divination, explains the traditional probabilities of 1,3,5,7 out of 16.
The coin method varies significantly from the yarrow stalk method in that it gives the same probability to both the moving lines and to both the static lines, which is not the case in the yarrow stalk method. The calculation of frequencies (generally believed to be the same as described in the simplified method using 16 objects in this article) using the yarrow stalk method, however, embodies a further error, in the opinion of Andrew Kennedy,^{[7]} which is that of including the selection of zero as a quantity for either hand. The traditional method was designed expressly to produce four numbers without using zero. Kennedy shows, that by not allowing the user to select zero for either hand or a single stick for the right hand (this stick is moved to the left hand before counting by fours and so also leaves a zero in the right hand), the hexagram frequencies change significantly for a daily user of the oracle. He has produced an amendment to the simplified method of using 16 colored objects described in this article as follows,
take 38 objects of which
 8 of one color = moving yang
 2 of another color = moving yin
 11 of another color = static yang
 17 of another color = static yin
This arrangement produces Kennedy's calculated frequencies within 0.1%
References
 ^ Legge, James (1899). The I Ching. 16. Sacred Books of the East.
 ^ ^{a} ^{b} ^{c} Hacker, E.A.; Moore, S.; Patsco, L. (2002). I Ching: an annotated bibliography. Routledge. p. 6,21,68,8788,125,250. ISBN 9780415939690. http://books.google.com/books?id=S5hLpfFiMCQC&lpg=PA125&pg=PA125.
 ^ Grasse, R.; Houck, R.; Watson, B.; Erlewin, M.; Defouw, H.; Braha, J. (1997). Eastern Systems for Western Astrologers: An Anthology. S. Weiser. ISBN 9781578630066. LCCN 97001457. http://books.google.com/books?id=1JYOAAAACAAJ.
 ^ Sherrill, W.A.; Chu, W. (1978). An Anthology of I Ching. Routledge & Kegan Paul. ISBN 9780710085900. LCCN 78303708. http://books.google.com/books?id=f6M9AAAAIAAJ.
 ^ Chu, W.; Sherrill, W.A. (1993). The Astrology of I Ching. Penguin Group USA. ISBN 9780140194395. LCCN 93234616. http://books.google.com/books?id=thojAQAAMAAJ&q=Ho+Map+Lo+Map+Rational+Number#search_anchor.
 ^ Wen Wang Gua, Joseph Yu
 ^ Andrew Kennedy, Briefing Leaders, Gravity Publishing, UK, 2006, ISBN 954483138
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