Sunday, 10 July 2016

Book's page

Book pages can be very helpful to cast I Ching hexagrams. Russell Cottrell devised a simple method that uses even book's pages. Directly from his post on Clarity:
  1. Fan the pages of a book (such as the I Ching).
  2. Very casually divide the pages at a random position, as if cutting a deck of cards.
  3. Look at the last two digits of the number of the even-numbered page (generally on the left).
  4. If it is divisible by four, count it as “tails” or 2.
  5. If not, count it as “heads” or 3.
  6. To make the math easier, subtract a multiple of 4 from the page number, such as 40 or 80.
  7. Three divisions determine one line, just like using coins.
[...] The edges of the pages must be fairly clean and smooth, without irregularities that could throw off the results.


Probabilities

As Russel suggested, the probabilities are the same as the three coins method. In fact, picking at random an even number, the chance of it being divisible by 4 is 1/2 and hence:
Prob(6) = Prob(9) = 1/8 = 12.5%
Prob(8) = Prob(7) = 3/8 = 37.5%
Prob(yin) = Prob(yang) = 1/2

Sunday, 3 July 2016

Two dice (1d20+1d8)

This method was devised by Jason A. Wolcott and recorded in the I Ching methods page on the Lucky Mojo site.
It uses two dices: one with 20 faces (1d20) and one with eight faces (1d8) which are very easy to find being commonly used for bard games.
It proceeds as follows:
  1. Roll the dice;
  2. Draw the line:
    • If the 20 sided die shows an even number (2,4,...,20), draw  ;
      • If the 8 sided die shows 1, it's a moving line
    • If the 20 sided die shows an odd number (1,3,...,19), draw  ;
      •  If the 8 sided die shows 6, 7 or 8, it's a moving line
  3. Repeat steps 1-2 other five times drawing the hexagram from the bottom to the top

Probabilities

The 20 sided die gives the nature of the line (yin or yang) with probability 1/2. The process is designed to give the same probability of the Method of 16 one:
Prob(6) = 1/2 * 1/8 = 1/16
Prob(8) = 1/2 * 7/8 = 7/16
Prob(7) = 1/2 * 5/8 = 5/16
Prob(9) = 1/2 * 3/8 = 3/16
Prob(yin) = Prob(yang) = 1/2

Variations

Since the the 20 sided die is only used for even/odd probability it can be replaced by any die with an even number of faces.

Saturday, 2 July 2016

Eight Sticks

Improved Yarrow Stalk Divination

by Joel Benson
 
    The traditional forty-nine-stalk method of divination has long been known and has been supplanted by the quicker three-coin method and other relatively rapid modern methods, for example involving special dice or sixteen ritual objects such as colored marbles.
    I found it odd that in all the literature I examined, the assumption seems to be that yarrow divination is necessarily limited to the ancient method of sorting, counting and adding random bundles of thin sticks. I decided there has to be an easier way to perform a Yi Jing divination with yarrow, while enhancing the wonderful tactile feel and spiritual presence of yarrow stalks.
    After some thought I realized there is a simpler, quicker way to manipulate a limited number of sturdy, relatively thick yarrow stalks to randomly define primary hexagrams using the established Yi Jing yarrow probabilities.
    In my improved divination method only eight yarrow stalks are required. I prefer stalks about 10 inches long and about .25 inches in diameter. Each of the stalks has yin and yang ends that are marked in any way that may be preferred to designate old or young yin/yang in the accepted yarrow divination proportions.
    My preferred way of marking the eight yang ends of the stalks is to insert a magnetized pin in each yang end. So the yang ends generate magnetic energy in accordance with their yang nature. The yin ends have no such pins and are therefore identified by their receptive, non-energy nature. A black end color is used to designate a single old yin end and three old yang ends, as required for yarrow divination. The remaining ends that are not blackened define seven young yin and five young yang ends.
    In the divination ritual, the eight stalks are shuffled and then an end of one stalk is selected at random to designate the first level of the primary hexagram. The selected stalk is then returned to the group of eight, the stalks are shuffled again and a random end of a stalk is selected to define the second level of the primary hexagram. This is continued until the six-line hexagram is defined.
    This method is similar to Rule of 16 divinations, except colors need not be memorized and only eight sturdy yarrow stalks are used. Also, the magnetic yang ends may be detected by a compass to add a mystical touch to the divination.
    So a few substantial yarrow stalks may be used in an easy, quick and modern style of divination. Following is an image of eight yarrow stalks of the type described and an image of a magnetic pin inserted at the yang end of a stalk to illustrate how the yang ends of the stalks are marked.

Bagua tablet




In the picture you can see a simple device to cast hexagrams: an octagonal tablet (around 5cm wide) with one face displaying the eight trigram in the Fuxi Earlier Heaven arrangement and the other side with trigrams in the King Wen Later Heaven arrangement. Four lines, two on each side, are painted so that three yang (solid) lines and one yin (broken) lines are red.
To cast a hexagram the process is as follows:
  1. Turn and flip the tablet without looking;
  2. Stop and put a finger on one of the sides;
  3. Draw the topmost line on that side. If it's red, it's a moving line;
  4. Repeat steps 1-3 other five times drawing the hexgram from bottom to top
I built the one you see in the picture with laminated cardboard. You can see it is a little bit damaged in certain points due to the overuse (it has been my preferred method for more than a year). I believe it would be great if casted (or 3d printed) in metal.

Probabilities

Considering the two faces, the eight sides and the way the red lines are painted, the probabilities are the same as the Method of 16:

Prob(6) = 1/16
Prob(8) = 7/16
Prob(7) = 5/16
Prob(9) = 3/16
Prob(yin) = Prob(yang) = 1/2

I Ching Book

This method was devised and published on the internet by i@no-self in 2001. I took the liberty of changing the procedure a little to make it easier to memorize.

In this method, an hexagram is selected at random and the line is derived on the basis of the upper and lower trigrams:

  1. Open an I Ching book to a random page and look at the hexagram that page relates to;
  2. If the lower trigram has one or three yin (broken) lines, you got a yin line:
    • if the upper trigram has three broken line, draw  ;
    • otherwise  draw  ;
  3. If the lower trigram has one or three yang (solid) lines, you got a yang line:
    • if the upper trigram has exactly one solid line, draw  ;
    • otherwise draw  ;
  4. Repeat steps 1-2 other five times drawing the hexagram from bottom to top.
If you find difficult to memorize the rules, you can use the table below which is structured according the original formulation by i@no-self.

 


Probabilities

The actual probabilities of each line depends on how the book has been typeset (some hexagram may have more pages than others) and by how much one is inclined to pick up the pages that are towards the end or the beginning of the book.
Assuming, everything considered, that any combination of upper/lower trigrams has the same probability to be selected, the probabilities for each line are the same as the Method of 16:


Prob(6) = 1/16
Prob(8) = 7/16
Prob(7) = 5/16
Prob(9) = 3/16
Prob(yin) = Prob(yang) = 1/2



Friday, 1 July 2016

One die (1d6)

Anoher method using a single dice:
  1. Roll a die;
  2. Draw the line:
    • If it's an even number (2,4,6), draw  ;
    • If it's an odd number (1,3,5), draw  ;
  3. If it's 1 or 6, it's a moving line;
  4. Repeat steps 1-3 other five times drawing the hexagram from the bottom to the top. 

Probabilities

The probabilities are similar to the three coins one but there are more chances of producing moving lines:

Prob(6) = Prob(9) = 1/6 = 16.7%
Prob(8) = Prob(7) = 2/6 = 33.3%
Prob(yin) = Prob(yang) = 1/2

Variations

I've found that the company Antony Publishing sells dice that works with the same principle but can directly provide the resulting line (moving lines are marked with a dot). These two images have been taken directly from their site:


Single die

Set of six dice

Wednesday, 29 June 2016

Three cards

One of the drawbacks of using just one or two cards is that when shuffling them it may be possible to keep track of their orientation and position even without looking; it could take quite some time before losing track of which face is which.
Using three cards (considering only one face and two orientations) provides 48 combinations which make the result dependant on the orientation and the position of each card (and it is much more difficult to keep track of three cards at the same time).

I designed the following three cards (these are scanned images as I lost the original jpg!):







where each card can result in being yin or yang depending on both the other two cards.
They are to be used as follow:
  1. Shuffle the three cards at will; remember to rotate one of two of them from time to time while shuffling (it is important!);
  2. Turn the cards and look at the three ideograms on the upper left corner;
  3. If the same sequence appears on the left of one line, draw that line. Otherwise draw the other line. Note that any ideogram can be placed where a red circle appears.
  4. Repeat steps 1-4 other five times drawing the hexagram from bottom to top.
 The following  pictures show some examples.

Result: yin (broken line) as the sequence of the three upper ideograms doesn't appear at the left of any line

Result: moving yin (broken line) as the sequence of three upper ideograms appears at the left of any line (the red circle can be replaced by any ideogram)

Result: yang (solid line) as the sequence of the three upper ideograms appears at the left of any line

Result: moving yang (solid line) as the sequence of the three upper ideograms doesn't appear at the left of any line

Note that if you hold them in your rught hand is even easier to read them as your hand will cover the right side of card which is not relevat for the result.

Probabilities

The lines and the ideograms are set to provide exactly the same probabilities of the sixteen marbles method:

Prob(6) = 1/16
Prob(8) = 7/16
Prob(7) = 5/16
Prob(9) = 3/16
Prob(yin) = Prob(yang) = 1/2


Aleister Crowley's sticks

This method is attributed to the controversial occultist Aleister Crowley. It has been reported that he used six flat sticks prepared as shown in the image (a 3D reconstruction).
Each stick has one side completely flat (representing yang, solid lines) and one side with a circular groove painted in red (representig yin, broken lines).
One of the sticks has one side painted in black, that stick represents a moving line.

The images shows the hexagram 21.5>62.

The method proceeds as follows:
  1. Without looking mix and shuffle the six sticks;
  2. Throw them on the table;
  3. Align them, always without looking, to form the hexagram;
  4. Look at the formed hexagram.

Probabilities

This method, which is identical to the six coins one, always produces exactly one changing line meaning that there are only 276 possible responses (out of the 4096 that are theoretically possible).

The probabilities for each lines are:

Prob(6) = Prob(9) = 1/6 * 1/2 = 8.33%
Prob(8) = Prob(7) = 5/6 * 1/2 = 41.67%
Prob(yin) = Prob(yang) = 1/2


Sunday, 26 June 2016

Creating a casting method

At this point in time, or probably even earlier, you may be asking what this site is all about. Yes, I gave a brief explanation in the About  page but the fundamental problem still remains: is there any real need of so many methods for casting hexagrams? What is needed to create a new method? And, most importantly, why should anyone do it?

We all know (having tested it on the field) that the meaningfulness and the accuracy of I Ching responses do not depend on the method used but only on the ability to relate the question to the response. That's why formulating a good question is so important.

However, I believe, the hexagram casting process plays a key role in setting the right mindset which will lead to a successful interpreation. The problem is that what works for some, may not work for others. The long process of using yarrow stalks puts people in a right medadite state, they say, but for others the long time needed is distracting; their minds keep wandering making them unable to focus on the  question. The instantaneous response of a computer program can be a striking revelation for some, but may look cheap and impersonal to others. As always happens, no size fits all and the many existing methods are there to prove that many people tried to find their own way to connect to the I Ching.

What follows are just ideas that, I hope, could motivate anyone who feels uneasy with their current casting method to create their personal casting method to better fits their needs. Should this ever happen, I would declare full success for my efforts.

Why creating a new method?

I think there at least two key aspects:
  • Practicality: you may want to be able to cast I Ching hexagrams in a small space (e.g. a plane seat) or making no noise, or using as least objects as possible, or making it with as few passages as possible, etc.;
  • Connection: you may want to use a set of objects that have a special meaning to you. They may be something from a beloved person or something that reminds you of an important place or time. Or they just make you feel more inclined to hear what the I Ching has to say to you.
I would add a third one that is important to me: aesthetic. It can be something pleasant to the touch or to the eye; something mathematically elegant or uttely chaothic. Whatever appeals to your own sense of beauty.

As a motivation, making money from patenting and selling a casting method may seems appealing but, looking back, many already tried and failed to become rich this way.

How to create a new method? 

These are the three requirements I feel important for any new casting methods:
  1. Each one of the 64 hexagram should be possible in the response.
  2. The 64 hexagrams should all be equiprobable in the response.
  3. Each one of the 4096 possible outcomes (considering the moving linese) should be possible.
Only the requirement 1 is absolutely critical: a method that would rule out a group of hexagrams (say, all those whose second line is yin) would seem just plainly wrong to me.

Requirements 1 and 2 would be fullfilled by any method which assigns to each line the same probability of being yin or yang.

You may note that I refered to the method  probabilities to determine which requirements are more important. This reflects my view that randomness play a key role in the casting process as it determines the relevance of certain aspects (e.g. the number of moving lines) over other.
If you feel that randomness does not play such a key role you can determine which requirements are more important to you.

During the creation steps you will go through the following steps (not necessarily in this order)
  • Choose which objects to use and count the events you can generate with them;
  • Decide on a probability distribution;
  • Define a process to combine/manipulate the objects that will generate the hexagram lines with the desired probability.
As illustrated in the image below, you will probably move from one step to another refiing the method.

Let's go through a full example: the creatione of the one card method.

In this case the need was to have something very portable to tuck into my pocket copy of the I Ching and a single card seemed to be the right choice.
Let's examine our object: a card has two sides (front and back) and two possible orientations (up and down). This means that if we, during the process, rotate and turn the card multiple times we can generate four possible events as the card may end up showing:
  • front side/upward
  • front side/downward
  • back side/upward
  • front side/downward
We could also reduce the number of events, for example we could limit ourselves to only two possible events by having the back of the card to be neutral (like in the regular playing cards) and only considering the orientation. Or by not considering the orientation at all and only considering wether the front or the back face is showing.

Now, if we wanted to mimic the three coins method probabilities ( 1/8 ) we would need to combine at least two operation with the card so to have 16 possible events (4*4).

It is important that the association between the outcomes and the lines are as simple as possible, the users should not be forced to memorize too many things. For example the three coins method requires the user to remember just one things: which side is 2 (the other being 3), the sixteen marbles method requires the user to remember four things: the association between each color and the line types.

That said, for a one card (our object) method with the same probabilities as the three coins method, we need 8 events that we could by combining two operation in the process:
  • The first operation will give yin or yang (e.g by using front/back of the card): 1/2;
  • The second operation will tell if it's a moving line by considering which of the four possible outcomes happened: 1/4.
For the first point we could mark the front of the card with a yang line and the back; for the second point we can mark one of the corner of the front face (e.g. the upper left one) with a dot so we will be able to tell the orientation:
  • front/up → dot in the upper left corner
  • front/down → dot in the lower right corner
  • back/up → no dot visible
  • back/down → no dot visible
we can not tell the two last event apart but we don't really need it. Just being able to identify one of the events (front/up) is enough for our needs.
Here is a possible design for the card:

that you can use with this process:
  1. Without looking, flip, turn and rotate the card.
  2. When you feel it's the right time look at the card
  3. Draw the line you see on the card
  4. Again, without looking, flip, turn and rotate the card.
  5. When you feel it's the right time look at the card
  6. If you see a red circle on the upper left corner of the card, it's a moving line.
And that is done, you can start testing the new method.

Howewer you can start thinking about siimplifying the process considering that many other methods assing the same probabilities to each line. So you can think about modifying the card (your object) to make it possible to generate a line with a single operation:

Now you can define a new process for casting lines:
  1. Without looking, flip, turn and rotate the card.
  2. When you feel it's the right time look at the card
  3. Draw the line you see on the card
  4. If you see a red symbol on the upper left corner of the card, it's a moving line.
Pretty easy, right?

I won't go into the details needed to define a process that would give the yarrow stalks probabilities, you can see how it is done in the one card method that I published already.

There you will also see how I tried to add some image to make it look better. I used some free clipart, a design from a real artist would have made the card 100 times better.

This is just a simple example. Do not hesitate to contact me if you want any more detail.

What about rituals?

Being a very rational person, I feel rather uneasy discussing this topic. Personally, I do not follow any type of ritual. To me the I Ching is a possibility multiplier, an uncertainty machine, a mirror which reflects my self  I don't feel the need for any ritual in the casting process.
However, I know that rituals are important for many people. They help focusing, they provide additional (sometimes deeper) meaning to the whole process.
Unforunately I have no suggestion about them. I've read many suggestions like: using linen cloths to protect the I Ching book, consacrating (whatever it means) the objects used for casting, point toward East, keeping everything at eye level, etc.
My only advice about this is to experiment: find what it works best for you; everything that helps you focusing better, interpreting the response better, etc. it's, by definition, good.  And you may want to ask the I Ching himself for advice about how good rituals are for you.



Saturday, 25 June 2016

EZ Ching (4d4)

This method, using four 4-sided dice, was devised and made available commercially by Christopher and Avonne Thomson. These dice are no longer available on the internet but there is still a mention of them on Amazon. The original site (www.ezching.com) seems to have disappeard between 2008 and 2010 (according to the Way Back machine).
The four dice were, supposedly, hand made and were engraved so that for each group (yellow or blue) the eight trigrams appeared exactly onc.


They were used as follows:
  1. Throw the four dice;
  2. Pick the blue dice for the lower trigram;
  3. Pick the yellow dice for the upper trigram;
This method generates each hexagram with probability 1/64.

To add changing lines it was suggested to use a regular die (1d6) to identify the moving line.

You can also use these dice to generate an hexagram and then derive a single line as described in the I Ching Book method.




Two Cards

This is just another version of the "Two Aces" method and provides lines with the same probability distribution.
Instead of using two regular playing cards, I've devised a design for two special cards so that you can use them to cast hexagrams.
The pictures below shows the faces of the two cards. I've also made them available as 300dpi images in case you want to print them with your printer or through a custom playing cards service.

 


To cast a hexagram proceed as follows:
  1. Shuffle the two cards rotating one of them while shuffling (this is important);
  2. Turn them and put them one on the other so that two symbols in the upper left corner can be seen;
  3. Draw the same line you see on the top card;
  4. If the two symbols in the upper left corner are the same, it's a moving line.
  5. Repeat steps 1-4 other five times drawing the hexagram from bottom to top.
The image below provides some examples:



Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Sunday, 19 June 2016

Thirtytwo Tarot Cards

In an online article, Richard T Gault suggested a way to use 32 tarots to cast I Ching hexagrams. The idea is simple:
  • Represent yin lines with Cups and Pentacles (Coins) as they are round and receptive (feminine);
  • Represent yang lines with Swords and Wands as they are aggressive and strong (masculine);
  • Include cards in a proportion that mimics the yarrow stalks probabilities:
    •   2 cards of Cups;
    • 14 cards of Pentacles;
    • 10 cards of Swords;
    •   6 cards of Wands;
Once the association has been memorized, the method is very simple:
  1. Shuffle the 32 cards and pick a card;
  2. Draw a line based on the card suit:
    • If it's Cups,        draw  ;
    • If it's Pentacles, draw  ;
    • If it's Swords,     draw  ;
    • If it's Wands,      draw 
  3. Reinsert the card in the deck;
  4. Repeat steps 1-3 five more times drawing the hexagram from bottom to top

Probabilites

By construction, the method provides the same probabilities as the Method of 16 one.



Cards images: WikiMedia Commons
 

Paper Die (1d4)

In the first post about paper dice, I said I was not satisfied with the version that was marked to generate hexagrams with yarrow stalks probabilities: it could led me to getting too many (or too few) moving yin lines.
I found that the solution to this problem is to consider the paper die as having only four possible outcome (instead of eight) and use the same mechanic of the one card method.
I created another sheet to be printed for your convenience but you can simply fold the die from a blank sheet and draw the dots with a pen.
Each strip (remember: to be split in two squares) would appear like this:


After folding the die, two faces will have 4 dots, one face will have three dots and one will have five dots of which one red. If you are going to draw the dots with a pen, leave the central dot white and fill the other ones (or do the opposite).

To cast a line you need two operations. Proceed as follows:
  1. Without looking, turn and roll the die in your hand;
  2. When you feel the time is right, pick one of the faces and write down the number of black dots (either 3 or 4) you see;
  3. Repeat step 1;
  4. When you feel the time is right, pick one of the faces and write down the number of dots, regardless the color, (either 3, 4 or 5) you see;
  5. Sum up the numbers and draw the line according the following table:
    6 7 8 9
  6. Repeat steps 1-5 other five times and draw theline from th bottom to the top of the hexagram.
Probabilities
The faces are marked so that the first time we can get four possible outcomes: 3,4,4,4 while the second time we can get 3,4,4,5. Summing up as shown in the following table:

gives the same probabilities of the yarrow stalks method:
Prob(6) = 1/16 = 6.25%
Prob(8) = 7/16 = 43.75%
Prob(7) = 5/16 = 31.25%
Prob(9) = 3/16 = 18.75%
Prob(yin) = Prob(yang) = 1/2

Variants

Should you like the method but wanting the three coins pronbabilities you can use exactly the same method but marking the faces as follows:

Note that now there are two red dots in the group of five.
A file ready to be print is available (remember to print it at 100% of its size, with no automatic resize).