I Ching divination
Encyclopedia
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.. 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.
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:
Once 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.
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.
. The following directions are from the ten wings of the I Ching. Other instructions can be found here, and a calculation of probabilities here.
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 three-coin method, because the required amount of accuracy occupies four binary bits of information, so three coins is one bit short. In terms of chances-out-of-16, the three-coin method yields 2,2,6,6 instead of 1,3,5,7 for old-yin, old-yang, young-yang, young-yin 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 re-used 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 re-used for the next change so that the total number of stalks in use remains high to keep all remainders equally probable.
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 three-coin method with adjusted probabilities can be found here.
Using this method, the probabilities of each type of line are as follows:
While there is one method for tossing three coins (once for each line in the hexagram), there are several ways of checking the results.
The numerical method:
An alternative is to count the "tails":
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:
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):
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.
border="1" borderwidth="1" cellspacing="0" cellpadding="4" style="text-align:center">
Sum
Coins
Line
4
T H T T
-------
5
T H T H
-------
6
T H H T
-------
7
T H H H
-------
border="1" borderwidth="1" cellspacing="0" cellpadding="4" style="text-align:center">
Sum
Coins
Line
8
H T T T
-------
9
H T T H
--- ---
10
H T H T
--- ---
11
H T H H
--- ---
border="1" borderwidth="1" cellspacing="0" cellpadding="4" style="text-align:center">
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
This method has been criticized on the grounds that it:
Step 2:
Step 3:
as a coin-equivalent: 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 three-coin method will use three dice.
Dice can also be used for the two-coin 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 two-coin method, and the other the "second toss." One roll of four dice will then determine a line, with probabilities matching the yarrow-stalk 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 six-sided 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 two-stage 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 three-coin method's probabilities can be duplicated with a single eight-sided 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 eight-sided (1d8), and 1 twenty-sided
(1d20). Roll both of them at once per line.
Another duplication of the yarrow stalks' probabilities can be done by taking the total of two eight-sided 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 six-sided 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...
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:
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.
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.
, 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, an 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 the each of the planets.
(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).
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
.
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, 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,
This arrangement produces Kennedy's calculated frequencies within 0.1%
Divination
Divination is the attempt to gain insight into a question or situation by way of an occultic standardized process or ritual...
is a bibliomancy
Bibliomancy
Bibliomancy is the use of books in divination. The method of employing sacred books for 'magical medicine', for removing negative entities, or for divination is widespread in many religions of the world:-Terminology:...
method using the I Ching
I Ching
The I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
(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
Bagua (concept)
The bagua are eight diagrams used in Taoist cosmology to represent the fundamental principles of reality, seen as a range of eight interrelated concepts. Each consists of three lines, each line either "broken" or "unbroken," representing yin or yang, respectively...
. Throughout China's region of cultural influence (including Korea
Korea
Korea ) is an East Asian geographic region that is currently divided into two separate sovereign states — North Korea and South Korea. Located on the Korean Peninsula, Korea is bordered by the People's Republic of China to the northwest, Russia to the northeast, and is separated from Japan to the...
, Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
and Vietnam
Vietnam
Vietnam – sometimes spelled Viet Nam , officially the Socialist Republic of Vietnam – is the easternmost country on the Indochina Peninsula in Southeast Asia. It is bordered by China to the north, Laos to the northwest, Cambodia to the southwest, and the South China Sea –...
), 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
I Ching
The I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
main article for historical and philosophical information).
The process of consulting the book as an oracle
Oracle
In Classical Antiquity, an oracle was a person or agency considered to be a source of wise counsel or prophetic predictions or precognition of the future, inspired by the gods. As such it is a form of divination....
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
Bibliomancy
Bibliomancy is the use of books in divination. The method of employing sacred books for 'magical medicine', for removing negative entities, or for divination is widespread in many religions of the world:-Terminology:...
. Confucius said that one should not consult the Oracle for divination until over the age of 40.. 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.
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
Yin and yang
In Asian philosophy, the concept of yin yang , which is often referred to in the West as "yin and yang", is used to describe how polar opposites or seemingly contrary forces are interconnected and interdependent in the natural world, and how they give rise to each other in turn. Opposites thus only...
to yang
Yin and yang
In Asian philosophy, the concept of yin yang , which is often referred to in the West as "yin and yang", is used to describe how polar opposites or seemingly contrary forces are interconnected and interdependent in the natural world, and how they give rise to each other in turn. Opposites thus only...
and back again:
| YinYang | Signification | Number | Symbol |
|---|---|---|---|
| old yin | yin changing into yang | 6 | |
| young yang | unchanging yang | 7 | |
| young yin | unchanging yin | 8 | |
| old yang | yang changing into yin | 9 | |
Once 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.
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 turtleTurtle
Turtles are reptiles of the order Testudines , characterised by a special bony or cartilaginous shell developed from their ribs that acts as a shield...
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
Ox
An ox , also known as a bullock in Australia, New Zealand and India, is a bovine trained as a draft animal. Oxen are commonly castrated adult male cattle; castration makes the animals more tractable...
shoulder bones, a practice called scapulimancy
Scapulimancy
Scapulimancy is the practice of divination by use of scapulae...
. 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 stalksYarrow
Achillea millefolium or yarrow is a flowering plant in the family Asteraceae, native to the Northern Hemisphere. In New Mexico and southern Colorado, it is called plumajillo, or "little feather", for the shape of the leaves. In antiquity, yarrow was known as herbal militaris, for its use in...
. 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 forty-nine are used. These forty-nine are first divided into two heaps (at random), then a stalk from the right-hand 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 three-coin method, because the required amount of accuracy occupies four binary bits of information, so three coins is one bit short. In terms of chances-out-of-16, the three-coin method yields 2,2,6,6 instead of 1,3,5,7 for old-yin, old-yang, young-yang, young-yin 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 re-used 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 re-used for the next change so that the total number of stalks in use remains high to keep all remainders equally probable.
Three-coin method
Coin
A coin is a piece of hard material that is standardized in weight, is produced in large quantities in order to facilitate trade, and primarily can be used as a legal tender token for commerce in the designated country, region, or territory....
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 three-coin 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
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.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 yarrow-stalk 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 left-most coin, then 4, 2 and 1 for a head in the right-most position. The full explanation relating it to the yarrow stalk method is at OrganicDesign:I Ching / Divination.| border="1" borderwidth="1" cellspacing="0" cellpadding="4" style="text-align:center"> | ||
| Sum | Coins | Line |
| 0 | T T T T | |
| 1 | T T T H | |
| 2 | T T H T | |
| 3 | T T 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 counter-clockwise 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 counter-clockwise 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 dieDice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
as a coin-equivalent: 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 three-coin method will use three dice.
Dice can also be used for the two-coin 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
Backgammon
Backgammon is one of the oldest board games for two players. The playing pieces are moved according to the roll of dice, and players win by removing all of their pieces from the board. There are many variants of backgammon, most of which share common traits...
sets. One pair can then be designated the "first toss" in the two-coin method, and the other the "second toss." One roll of four dice will then determine a line, with probabilities matching the yarrow-stalk 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 six-sided 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 two-stage 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 three-coin method's probabilities can be duplicated with a single eight-sided 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 eight-sided (1d8), and 1 twenty-sided
(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 eight-sided 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
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
. 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 six-sided 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 marblesMarblesA marble is a small spherical toy usually made from glass, clay, steel, or agate. These balls vary in size. Most commonly, they are about ½ inch in diameter, but they may range from less than ¼ inch to over 3 inches , while some art glass marbles fordisplay purposes are over 12 inches ...
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 riceRice
Rice is the seed of the monocot plants Oryza sativa or Oryza glaberrima . As a cereal grain, it is the most important staple food for a large part of the world's human population, especially in East Asia, Southeast Asia, South Asia, the Middle East, and the West Indies...
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 numerologyNumerology
Numerology is any study of the purported mystical relationship between a count or measurement and life. It has many systems and traditions and beliefs...
, esoteric cosmology
Esoteric cosmology
Esoteric cosmology is cosmology that is an intrinsic part of an esoteric or occult system of thought. It almost always deals with at least some of the following themes: emanation, involution, spiritual evolution, epigenesis, planes of existence or higher worlds , hierarchies of spiritual beings,...
, astrology
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...
and feng shui
Feng shui
Feng shui ' is a Chinese system of geomancy believed to use the laws of both Heaven and Earth to help one improve life by receiving positive qi. The original designation for the discipline is Kan Yu ....
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, an horary astrology
Horary astrology
Horary astrology is an ancient branch of horoscopic astrology by which an astrologer attempts to answer a question by constructing a horoscope for the exact time at which the question was received and understood by the astrologer...
that takes into account the number of calligraphic
East Asian calligraphy
East Asian calligraphy is a form of calligraphy widely practised and revered in the Sinosphere. This most often includes China, Japan, Korea, and Vietnam. The East Asian calligraphic tradition originated and developed from China. There is a general standardization of the various styles of...
brush strokes of one's query. Following the associations Carl Jung
Carl Jung
Carl Gustav Jung was a Swiss psychiatrist and the founder of Analytical Psychology. Jung is considered the first modern psychiatrist to view the human psyche as "by nature religious" and make it the focus of exploration. Jung is one of the best known researchers in the field of dream analysis and...
drew between astrology and I Ching with the introduction of his theory of synchronicity
Synchronicity
Synchronicity is the experience of two or more events that are apparently causally unrelated or unlikely to occur together by chance and that are observed to occur together in a meaningful manner...
, 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
Natal chart
In astrology, a natal chart is a stylized map of the universe with the "native" at the center. It is calculated for the exact time and location of the native's birth for the purposes of gaining insight into the native's personality and potential...
against the backdrop of Shao Yung's circular Fu Xi arrangement and the Western zodiac
Zodiac
In astronomy, the zodiac is a circle of twelve 30° divisions of celestial longitude which are centred upon the ecliptic: the apparent path of the Sun across the celestial sphere over the course of the year...
to provide multiple hexagrams corresponding to the each of the planets.
Wen Wang Gua Method
This method goes back to Jing FangJing Fang
Jing Fang , born Li Fang , courtesy name Junming , was a Chinese music theorist, mathematician and astrologer. Born in present-day Puyang, Henan during the Han Dynasty , he was the first to notice how closely a succession of 53 just fifths approximates 31 octaves...
(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
Earthly Branches
The Earthly Branches provide one Chinese system for reckoning time.This system was built from observations of the orbit of Jupiter. Chinese astronomers divided the celestial circle into 12 sections to follow the orbit of Suìxīng . Astronomers rounded the orbit of Suixing to 12 years...
and then the picture can be analyzed with the use of 5 Elements (Wu Xing).
By bringing in the Chinese calendar
Chinese calendar
The Chinese calendar is a lunisolar calendar, incorporating elements of a lunar calendar with those of a solar calendar. It is not exclusive to China, but followed by many other Asian cultures as well...
, 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
I Ching
The I Ching or "Yì Jīng" , also known as the Classic of Changes, Book of Changes and Zhouyi, is one of the oldest of the Chinese classic texts...
and the Four Pillars of Destiny
Four Pillars of Destiny
Four Pillars of Destiny is a Chinese and Japanese conceptual term that describes the four components creating a person's destiny or fate. The four components within the moment of birth are year, month, day, and hour...
.
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, 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%