Coins, Marbles, Yarrow and Probabilities

[justjoolz]

I was thinking (again ;-)

The mathematical odds for the coins are thus:

1/6 yin changing
1/3 yin stable
1/3 yang stabale
1/6 yang changing

chance of changing line = 1/3
1 in 3 lines on average will change

for the marbles (which Karcher claims has the same mathematical odds as the yarrow stalk method)

1/16 yin changing
3/16 yang stable
5/16 yin stable
7/16 yang changing

so the odds are the same for yin and yang balance (1+7) and (3+5)

However it's more probable that the changing line is from yang to yin.

Therefore the change is on average in the direction of the yin-receptive opening up.

Not balanced equally.

Any comments and criticism / light to shed on my thoughts would be warmly welcomed.

I apologize in advance if my write up here is inaccurate as I do not have my workings on me.

thanks in advance

JustJoolz@hotmail.com

[bradford_h]

RE:
1/16 yin changing
3/16 yang stable
5/16 yin stable
7/16 yang changing

These numbers are incorrect for yarrow
I don't know (or care) about marbles.
They should be 1,5,7,3 /16 for 6,7,8&9 respectively. What you said about yin and yang
being even in odds is correct though.

A lot of folks think that the skewed yarrow probabilities are something to be preserved because of their great antiquity, but the fact is, we cannot be sure that the method we have now is any older than Zhuxi of the Song. The original method may have had evener odds.

[justjoolz]

Evener Odds? now there is a concept!

So this may or may not be of interest....

It makes me think of the fact that certain changing lines are more common.

That is the Changing Hexagram is more likely to contain yang->yin changes

[freemanc]

Brad, and all, hi,

I've been waiting for this sort of topic to come up for some time. I went through a phase of perseverating about the yarrow-stalk odds, and my inability to remember, and cogently describe, the yarrow rule.

I do believe that I've come up with a nifty piece of "intellectual propery" that can't make a nickel, but is pretty fun, so I'm herewith giving it to the community, more or less. (Is this worth asserting a GPL?)...

So here goes:

The Official Chameleon Book Yarrow-Odds Preserving I Ching Dice (c) (TM) etc (ha.)

Make 2 Bar-shaped, 4 sided dice.

Mark the sides as follows:
<pre>
A 6 - -
B 9 ---
C 7 -X-
D 8 -0-
</pre>
Roll'em both. Use the higher letter of the two to pick the yao line. So, getting a hexagram takes six rolls, and only one rule that's easy to remember.

Proof it works and gives the Yarrow stalk odds: Voila!
<pre>
* ABCD
A 6978
B 9978
C 7778
D 8888
</pre>
Basically this table is the operator table for the "greater or equals" operator. Um, did I make any typos? Also, has anyone invented this before?

best,
FC

[justjoolz]

To correct my earlier posting:

1/16 yin changing ---- XX ---- 6
5/16 yang stable ============== 7
7/16 yin stable -------------- 8
3/16 yang changing ==== xx ==== 9

These odds relate to the ?original? yarrow stalk method and to the 16marble method of Karcher, or even to the 2x4 dice method mentioned above.

All of these above methods contrary to the 3coin method, produce a changing hexagram with an uneven probability of yang/yin.

Changing Hex Yang Prob: 5+1 / 16 = 3/8
Changing Hex Yin Prob: 7+3 / 16 = 5/8

This is what I was originally questioning in this thread. Can anyone shed any light of understanding on this phenomena.

The Greater Than or Equal too has really got me thinking....

We've got this 16 choice probability field. With a mathematical >= function in there somewhere. This gives the changing hexagram a Earth or Yin 'bias'.

Thanks Freemanc for the >= maths explanation of the 1,3,5,7 odds.

And thanks too to Bradford... your site has some very interesting information. I've only just started exploring the world of the older Yi Jing. Until recently I've only read the Wilhelm translation.

More Later.....

[freemanc]

Jools,

Thanks for the kind word about the 2x4d method. I was just delighted with this little pattern. I kinda hope someone steals the idea and tries marketing 'em.

Now, I don't think there's really a >= function buried in the yarrow-stalk algorithm. But there are 16 possible outcomes that group into 6's, 7's 8's and 9's in that same proportion. These are developed out of modulo 4 arithmetic. I don't feel energetic enough to geek out and parse out how.

Now my next question is, why the hell that proportion? I don't recall ever reading a rationale for this, but it makes sense, just in terms of Yin-Yang theory.

Look at it this way. The Yangs are 3 times as dynamic (likely to be moving) as the yins, yet on the other hand, the probability of the line actually being yin or yang is still equally balanced. To decide the random number generator should act this way wasn't a mathematical discovery, but rather a a philosophical or aesthetic decision. Note also that this makes the sort of mix of asymmetry and symmetry that's thematic all over the place in any generation of the Y you care to study. Nice.

Gee, maybe these probabilities are worth preserving... http://www.onlineclarity.co.uk/I_Ching_community/clipart/happy.gif

Bradford, who are the earliest to geek out with the yarrow method in writing? The Zhouyi mentions both turtles and yarrow readings. The big Yijing doesn't actually talk much about the yarrow method, does it? Or am I out to lunch again?

best,
Freeman Crouch

[bradford_h]

Hi Freeman-
The earliest description of the Yarrow method that we have is Zhuxi (1130-1200 ce), Yixue Qimeng, now in print, tr. Joseph Adler, titled: Introduction to the Study of the Classic of Change (I-hs&uuml;eh ch'i-meng). Binghamton, NY: Global Publications.
Bu divination IS mentioned in the Zhouyi and vague hints at the method in the Wings, but it's nothing anybody can follow.
Coins I think date from the Tang (618-907 ce), but I don't know who wrote them down. Maybe Kong Yingda or Li Dingzuo. Anybody know?

[justjoolz]

Hi FreeManc,

As for your question. "Why the hell that proportion?"

That's what I was getting at....

You mention the balance being the same of yin and yang lines.... but for the changing hexagram this is not the case. So I suppose that is where the proportions come into play.

It's this balance that really intrigues me, this addition or bias of yang being 3 times as 'dynamic' as ying.

It's the one the two and the three.

It seems to me this is another element often overlooked which may shed some light on the symmetrys and asymetrys you mention.

Your intiguingly....

[freemanc]

Brad, thank you for calling Zhuxi to my attention, he's really interesting, quite apart from my puzzlement about the Yarrow method. And thank you so much for giving a complete citation.

Wikipedia article on Zhu Xi (http://en.wikipedia.org/wiki/Chu_Hsi)

I'm fascinated that Life Magazine listed him as the 45th most influential person of the last millenium.

This is way, way speculating, but note the social context. This may indeed literally be the first time anyone felt compelled to write the Yarrow method down. This was during the rise of Buddhism in China, and Zhuxi wanted to defend the institution of divination, and with it the moral life of China, by writing an introductory treatise on the procedures.

Sounds like our kinda guy.