Cards, Yarrow Sticks, coins or Dice?

roman_slayer · Jan 16, 2008

How about a dice approach like this?

In a local Pagan group meeting, another member told me how he and several others will occasionally draw a hexagram by sitting in a circle, and each person will take a turn rolling a die, making one line at a time, even numbers Yin and odd numbers Yang. I didn't think to ask him what kind of die, as in, 6 sided or 8 sided. When I suggested using three dice to cover the possibility of a moving line, he shrugged his shoulders and said that they didn't worry about it. I would.

But, thinking about it made me want to experiment with rolling dice, with polyhedral 20 sided dice, the type you use when playing Dungeons and Dragons, and my way, with three of them. It seems like an even more random element, more than you would get from just three 2 sided coins.

roman_slayer · Jan 17, 2008

Update!

I just now ordered several 30 sided dice for this experiment, which will make for even more randomness

Sparhawk · Jan 17, 2008

Here is an interesting opinion from 1975:

It is evident that for any of the three countings required to produce a line of the hexagram, once the left-hand heap has been counted out and the remainder obtained, then the final score is already determined and it is not strictly necessary to count through the right-hand heap of stalks. It seems likely, however, that the whole process of counting through the stalks was seen as a representation of the interplay of various cosmic forces, and for this reason it was thought desirable to carry it through to completion. The Ta Chuan or Great Treatise, one of the ancient commentaries on the book, contains a section relating various numbers associated with the counting of the stalks to such cosmic entities. Thus the two heaps correspond to the two primal forces, the bundles of four to the four seasons, etc.

The Coin Oracle is a much simpler and more speedy affair. To obtain any line of the hexagram one tosses three coins in the air. Traditionally, old Chinese coins are used with a hole in the middle and an inscription on one side. Each coin scores 2 if it lands with the inscription face-up and 3 otherwise. The scores for the three coins are then summed, to give a total of 6, 7, 8 or 9 as before, and the corresponding line is obtained.

3. ANALYSIS
Looking now at the total score-which determines the nature of the line obtained we have :

(a) Yarrow-stalk Oracle

prob. {total score of 6) = 1/4x 1/2x 1/2 = 1/16,
prob. {total score of 7) =
(3/4 x 1/2x 1/2)+(1/4 x 1/2x 1/2)+(1/4 x 1/2x 1/2) = 5/16,
prob. {total score of 8) =
(1/4 x 1/2x 1/2)+(3/4 x 1/2x 1/2)+(3/4 x 1/2x 1/2) = 7/16,
prob. {total score of 9) = 3/4 x 1/2x 1/2 = 3/16.

(b) Coin Oracle

prob. {total score of 6) = 1/2x 1/2x 1/2 = 1/8,
prob. {total score of 7) = 3(1/2 x 1/2x 1/2) = 3/8,
prob. {total score of 8) = 3(1/2 x 1/2x 1/2) = 3/8,
prob. {total score of 9) = 1/2x 1/2x 1/2 = 1/8.

Thus, in each case we have
prob. {yin line) =prob. {yang line} = 1/2
and
prob. {moving line, i.e. total score of 6 or 9) = 1/4.

APPLIED STATISTICS
However, in the Yarrow-stalk Oracle, a moving yang line is three times more probable than a moving yin line. In the Coin Oracle the two are equally likely. It follows that, if the outcome depends solely on chance, the two methods of consulting the oracle will in general produce different results-not a very satisfactory situation!
It can be argued, however, that the outcome of any true divination is not dependent upon chance-that external factors are operating which ensure that the result is what it "ought to be". As Jung says, "whoever invented the I Ching was convinced that the hexagram worked out in a certain moment coincided with the latter in quality no less than in time", and he speaks of the old tradition that "spiritual agencies" are involved which act "in a mysterious way, that make the yarrow stalks give a meaningful answer". Thus at any given moment, the fall of the coins or the outcome of the division of the stalks is what it necessarily must be, in so far as it is an essential part of that moment and hence possesses the particular quality peculiar to it. The fall of coins or division of stalks observed is thus a token or "sign" of the situation prevailing at the time at which they are cast, and the problem becomes that of extracting the significance from the outcome-i.e. "reading the signs". This amounts to associating the different outcomes with particular types of line, and it is at this point that the two Oracles diverge. The Coin Oracle associates the possible outcomes with the four kinds of line in a symmetrical fashion, whereas the Yarrow-stalk Oracle does not.
As the Yarrow-stalk Oracle is the one which has been in use since antiquity, and as the ancient Chinese were no strangers to the mathematical arts, it seems likely that they were aware of the lack of symmetry inherent in the method, and indeed that it was even intentional, as it can be easily justified in terms of the underlying philosophy. Lines of a hexagram are considered to "move" as a result of internal tension; only lines possessing sufficient power are able to change. Since yang lines represent the light, positive, strong element and yin lines represent the dark, negative, weak element, is it not reasonable that a yang line should be more likely to move than a yin one?

4. CONCLUSIONS
The Book of Changes has a dual function. Quite apart from its use as a book of divination, it can be read as a Book of Wisdom-a sort of practical handbook of Taoist philosophy-and my own view is that it is in regarding the book as such that its true value lies. If it is read in the light of later Taoist teachings then it has, I believe, a great deal to offer-although, as Fung Yu-Lan (1947, Chapter V) has pointed out, the "tao" of the I Ching is not the "eternal Tao" of Lao Tzu and Chuang Tzu. However, the Oracle itself has acquired something of a cult status in recent years-without any reference being made anywhere to the discrepancy between the two methods of consulting it. In deference to the wisdom of the ancients who composed the book and devised the method of counting the changes, I would recommend that anyone wishing to consult the Oracle should do so by means of the yarrow stalks rather than using the Coin Oracle.

Divination in Ancient China
D. Robinson
Applied Statistics, Vol. 24, No. 3. (1975), pp. 329-332

hilary · Jan 17, 2008

...which would make perfect sense if the yarrow method we have today actually was older than the three coin method...

Sparhawk · Jan 17, 2008

hilary said:
...which would make perfect sense if the yarrow method we have today actually was older than the three coin method...

Not sure about the method itself, as described in the received text, but yarrow use for casting hexagrams is perhaps a tad younger than cracking tortoise shells... I cannot find much of a mention to coin casting in the Han, or Qin, or prior extant literature but yarrow divination is all over the place.

buzzurro · Jan 17, 2008

hilary said:
...which would make perfect sense if the yarrow method we have today actually was older than the three coin method...

That's great, I was just going to report a couple of links about this:

http://www.onlineclarity.co.uk/learn/consult/yarrow-or-coin.php

and also:
http://www.biroco.com/yijing/stick.htm

Now, one thing I've being wondering for a long time: there are several faster, easier methods that give the same probabilities as the yarrow stalks, but it seems as if nobody ever wanted to go the other way around, that is, modify the yarrow stalks method in order to obtain a slower, more elaborate method with the same symmetric probabilities as the three coin... is this true?
Yet it would be extremely simple...
:bows:

willow · Jan 18, 2008

As I've thought about this over the last couple of days (referring to my casting without a full set of marbles but nevertheless trusting the result), I'm wondering if it's useful to make a distinction between "divining" and "dialogue with the universe." Of course "divining," done with integrity, includes the dialogue, but also, divining is not the only form of dialogue, and perhaps it is lazy or even fundamentally unfair to call forms of dialogue that aren't specifically divination by its name.

When I located a proper 16th marble and restored my set, I asked
Q: What is the difference between casting with a full set and casting without all my marbles?
A: 6 (1,4) => 61
Haven't fully parsed that answer, but it seems to have a cautionary joviality to it, something like, "Sure, sometimes you can hear the inner truth station through all the static of a broken radio, but that is not the most elegant way - don't make a practice of it!"

petrosianii · Jan 18, 2008

Reply to the 1975 article

"Since yang lines represent the light, positive, strong element and yin lines represent the dark, negative, weak element, is it not reasonable that a yang line should be more likely to move than a yin one?"

To round out this comment (which is a great one, by the way). This is why the card method works so well, I think. The seven cards of a suit correspond to a stable yin line, reflecting yin's tendency toward inertia. Thus, it is most likely, that when you get a yin suit, it will be unchanging, which corresponds to the oldest traditions of Taoist thought as discussed in the excellent 1975 article.

Conversely, the one card of a suit corresponds to a changing yin line, since yin is full of inertia and least likely to change spontaneously. The 5 of a suit correspond to a chaging yang line, as it is relatively more likely that yang lines (the typcial "rulers" within a hexagram) will be the authors of change in a given situation. And the 3 of a suit represent a stable yang line, as it is relatively unlikely for yang to remain inert.

Thus, the card-method preservers the original asymmetrical understandings of ancient Taoist philosophy, gives the diviner enough time and touch to induce the quasi-hynotic sate of mind necessary for deeper insight, yet doesn't take quite as long as the stalk method (a vauable commodity in our time-economizing culture).

For a couple of interesting articles on I Ching mathematics, visit my site

Cheers,
Eric

petrosianii · Jan 24, 2008

Reply

I like your statement about removing the ego's over-influence...Jung stated the same thing. He said that the I Ching helps the seeker "get in touch with non-egoistic material."

Very enlightening!

Eric

charly · Jan 24, 2008

buzzurro said:
... it seems as if nobody ever wanted to go the other way around, that is, modify the yarrow stalks method in order to obtain a slower, more elaborate method with the same symmetric probabilities as the three coin... is this true?...

Hi:

Maybe such a method is described by Chang Chen-Lang in the chapter 3 «A Conjectural Schema of Yarrow Stalk Divination» of AN INTERPRETATION OF THE DIVINATORY INSCRIPTIONS ON EARLY CHOU BRONZES, generously posted by Sparhawk at another forum.

Download it from: http://www.yitoons.com/pdf/chang-cheng-lang.pdf

Years ago I used some simplified methods usings sticks or little stones or beads:

Using sticks (or little stones):

I used a set of 50 brochette sticks. With one stick in the right hand I divides randomly the remainder 49 into 3 subsets.

Then I counted each subset from stick 1 to 8, I continued counting form 1 to 8 until no more sticks in the subset.

I retained the last number counted.

If the number was 1 the value was 9,
if it was 2 the value was 6,
if 3, 5 or 7 the value was 7
and if 4, 6 or 8 the value was 8.

Then with 3 subsets I had the inner trigram.

I proceed another time for getting the outer trigram.

I believe that the probabilities are the same than from coins method, but I'm not sure.
I was inspired in Jou Tsung-Hwa simplifications (1).

Using a necklace of similar beads:

Taking randomly two points with right and left hands, I counted the beads between form 1 to 8 and another time if necessary.

I used the last number counted for getting the values 9,6,7,8, but with this method I counted one time for each line, 6 times.

I was inspired by a tibetan method for divination using neckages (not the Yi).

Yours,

Charly

____________________________
(1) inspired too in the game of «palitos chinos»

buzzurro · Jan 27, 2008

Hey, thank you very very much, Charly, for all this very interesting info!
:bows:

I still have to read through the entire article, but I notice that the method described by the author is almost the same as your brochette sticks method, except for this:

"sixty-four stalks are divided each time into four groups, with the first group being discarded and not used"

Well, this is the problem I foresee in the method you describe: when you divide the sticks into three subsets, each subset representing a line, you can only obtain half of the eight possible trigrams! That is, maybe you can get the remaining four in the relating hexagram, I don't know, but surely you won't get them in the primary one...

That's because of the way odd and even numbers work:
e + e = e
e + o = o
o + o = e
So, when summing three numbers:
e + e + e = e
e + e + o = o
e + o + o = e
o + o + o = o
So, since 49 is odd, you can only divide it in these two possible ways:
e + e + o = 49
o + o + o = 49

This must be the reason why you quitted using this method years ago, and rightly so

Unless I overlooked something in your explanation...

By the way, I don't even know what the Jou Tsung-Hwa simplifications are, I'll try to google for this... I'm still a newbie, and it shows, because I hadn't yet realized how the idea of modifying yarrow probabilities must sound like a swear-word to some ears! :rolling:

My humble opinion about which probabilities should be used is: both seem to work.
Maybe different probabilities (yarrow, coins or else) work better for different persons, this is what I tend to believe so far...
Anyway I'm intrigued by the great variety of methods that are used to cast hexagrams, that's it.

Thanx again! :bows:

charly · Jan 29, 2008

buzzurro said:
... I foresee in the method you describe: when you divide the sticks into three subsets, each subset representing a line...

So, since 49 is odd, you can only divide it in these two possible ways:

e + e + o = 49
o + o + o = 49

... I don't even know what the Jou Tsung-Hwa simplifications are...

Maybe different probabilities (yarrow, coins or else) work better for different persons, this is what I tend to believe so far...

Thank you:

1) that's surely the reason why Cheng divides by four. I never was sure if the probabilities were the same as with coins. It's clear the bias in favor of odd numbers.

2) I go to search some Jou Tsung-Hwa paragraphs for quoting here.

Yours,

Charly

roman_slayer · Feb 2, 2008

roman_slayer said:
I just now ordered several 30 sided dice for this experiment, which will make for even more randomness

Update!

I found that the 30 sided dice are too bulky, so I tried rolling three 20 sided dice. I considered the even numbers "Yin/yielding lines" and odd numbers "Yang/firm lines". It works great! You would not believe how great they roll. I highly recomend to everyone to try using three 20 sided dice to draw Hexagrams. That's certainly the way I'm doing it from now on :^)

dobro · Feb 3, 2008

Twenty-sided? How does it work?

buzzurro · Feb 3, 2008

dobro said:
Twenty-sided? How does it work?

If I understand well, it's the same as using the three coins: the dice have 20 sides, but you simply count even numbers as 2 and odd ones as 3.
The difference lies in the fact that dice roll (I don't remember having seen 20 sided dice, but they must be nearly as round as balls!), while coins can only fall on either side: not different probabilities, but a different procedure...

This leads me to this consideration: probabilities are not the only thing that matters when choosing a method for casting hexagrams. I believe there must be something in the material and/or in the way you use it that can provide you with a better connection, because it acts like a catalyst for your psyche... I mean, it's been said that the complex procedure used with yarrow stalks induces a particular state of mind... and also the material, I believe, contributes to this, because it's the same that was used nearly 3000 years ago... what I'm trying (and probably failing

) to explain is that I think every (good!) method can have a somewhat similar effect, even though for different reasons, on those who enjoy using it... coins, dice, cards, rocks, beads...

Last summer, when I had just begun being seriously interested in the Yi, I talked about it with a cousin of mine for whom I feel great admiration and affection.
I told her that I wanted to get a set of coins, not necessarily chinese, but other than the ones I could really use as money... Her boyfriend was there too, and he was biking through Europe, so she asked him to look into his wallet for three coins of the same kind from one of the countries he had been, and in a matter of seconds I got these three little coins from Estonia, with the number 10 on one side (which is the binary for 2, or 2 digits if you prefer) and 3 lions on the other... perfect!
They're currently my favourite means of casting hexagrams, because of their affective value, you know...

petrosianii · Feb 3, 2008

Summing up this very rich discussion

Thank you all for your insightful comments! You have really enriched my understanding of the different methods of divination.

It seems to me that the summary of this topic is this: equally as important as the method's probabilistic implications, are the psychological implications. When choosing a method of divination - whether coins, dice, stalks or something else - I need to consider not only whether the probability of the chosen method remains true to the tendencies and nature of yin and yan, but also whether the method enables me to enter into the quasi-hypnotic or meditative mental state needed to really plumb the depths of the hexagrams and my subconscious.

keep up the great insights!

Eric

dobro · Feb 3, 2008

petrosianii said:
It seems to me that the summary of this topic is this: equally as important as the method's probabilistic implications, are the psychological implications.

Sorry to harp on this (straight from the flogging a dead horse department?) but the probabilisitc implications are null if probability doesn't enter into it.

How do you explain the startling and uncanny resonance between the situation you're in and the hexagram you draw on so many occasions, and which so many people report, if it's only probability at work?

hilary · Feb 3, 2008

buzzurro said:
I believe there must be something in the material and/or in the way you use it that can provide you with a better connection, because it acts like a catalyst for your psyche...

Mm. Certainly the material I use affects me. Working with yarrow gives a huge sense of connection and continuity, much stronger than with other things. (I know the method isn't ancient, but the use of yarrow in one way or another is about as old as the oracle.)

I mostly use a set of beads that LiSe gave me

hug

. Over the years they've really started to affect the way I see the lines. I tend to visualise hexagrams as I cast them rather than writing them down, and the stones become part of how I 'see' the lines as I fix them in memory. Yang is smoky quartz, for instance, and moving yang is clear quartz. Now, for me, moving yang lines are the place the hexagram 'lights up' and becomes more translucent.

hilary · Feb 3, 2008

dobro said:
Sorry to harp on this (straight from the flogging a dead horse department?) but the probabilisitc implications are null if probability doesn't enter into it.

How do you explain the startling and uncanny resonance between the situation you're in and the hexagram you draw on so many occasions, and which so many people report, if it's only probability at work?

Probability can be at work, and other things can be at work along with it. Like we can have this conversation over the internet and with some forum software - easier than using carrier pigeons - but Vbulletin isn't the sum total of our conversation.

:deadhorse:

dobro · Feb 3, 2008

hilary said:
Probability can be at work, and other things can be at work along with it.

Yes, thanks for reminding me of that. Both the law of accident (probability) and the law of intention operate simultaneously. And depending on one's degree of awareness, one is stronger than the other. And if the law of accident predominates, the Yi is still useful insofar as it acts as a mirror or foil for one's intuition to kick in and provide useful insight.

Very nice.

(walks away from thoroughly dead, thoroughly beaten dead horse)

roman_slayer · Feb 5, 2008

buzzurro said:
If I understand well, it's the same as using the three coins: the dice have 20 sides, but you simply count even numbers as 2 and odd ones as 3.
The difference lies in the fact that dice roll (I don't remember having seen 20 sided dice, but they must be nearly as round as balls!), while coins can only fall on either side: not different probabilities, but a different procedure...

Very astute of you dobro, that is what I do, although as I said, my exact method is that I consider the even numbers yielding lines and the odd numbers firm lines. And, very good visualization on your part, having never seen 20 sided dice (also called d20's), and yet still being able to estimate their shape

As a matter of fact, I will share a picture of them here. Click this link to see them ---->

http://find-ccg.com/Products/20_Sided_Dice_in_Random_Colour_and_Style.html

I don't know if links are clickable on this forum, but if they aren't, copy and paste the link into your browser to see the picture.

And Hilary, please believe me when I say that I'm not trying to spam the message board. Yes, it is a website that sells these dice, but it's not my website, and unfortunately, it was the only real good picture I could find of them on the web.

Like I said before, I am very pleased with the way these dice work with drawing Hexagrams, and I recomend to everyone who uses the "3 Coin Method" to try the "d20 Method", as I call it, at least a few times. As a matter of fact, I highly recomend it! Also, d20's are cheap and easy to obtain, whether at online stores or at actual physical stores. If you want to buy some at a physical store, go to stores that sell games like "Dungeons and Dragons" and "Magic: The Gathering".

~roman_Slayer

hilary · Feb 6, 2008

roman_slayer said:
... And Hilary, please believe me when I say that I'm not trying to spam the message board. Yes, it is a website that sells these dice, but it's not my website, and unfortunately, it was the only real good picture I could find of them on the web.

Of course you're not. You're posting a helpful link - doubly so, since it provides people with a place they can get said dice. Thanks!

Sparhawk · Feb 15, 2008

Here is some information I just posted about some historical background on Milfoil Divination. Enjoy.

Cards, Yarrow Sticks, coins or Dice?

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