## Tuesday, March 1, 2011

### Xiang: The Yarrow Oracle Depicted Graphically

The yarrow oracle method as related through Ta Chuan (the Great Treatise) is attributed to Kung-fu Tze. The querent begins with 50 (fifty) yarrow stalks and manipulates them in a prescribed and probabilistic manner until few remain.  This remainder may take on one of exactly four possible symbolic values, though the actual number of stalks may vary according the the precise form of the ritual.  The symbolic values are sometimes referred to as 'xiang.'  Each manipulation of the stalks produces one line of a six-line figure commonly known as an hexagram.  Thus, six "randomly-generated" xiang produce an hexagram.  Once generated, the querent references the scripture according to that hexagram.

In recent years, capable persons have employed mathematics to reduce the yarrow-stalk oracle to the raw probabilities it produces for each of the four types of lines that may obtain from a divination operation.  The following table is a description of those lines and their relative probability of occurrence in divination:

dynamic yin,   represented by '6' and symbol ⚏ ( 4 in 64 = 0.0625)
dynamic yang, represented by '9' and symbol ⚌ (12 in 64 = 0.1875)
static yang,     represented by '7' and symbol ⚎ (20 in 64 = 0.3125)
static yin,       represented by '8' and symbol ⚍ (28 in 64 = 0.4375)

The graphic depicted here shows the xiantian arrangement overlaid on a tableau of concentric squares, each discretely colored. This presentation is remarkable in that it implicitly encodes the yarrow oracle probabilities; i.e.  each ring comprises a specific proportion of the hexagrams as shown in the table above.

1. Excerpted from related dialogue at onlineclarity.co.uk (posting under alias saharan):

Originally Posted by saharan
The utter simplicity of the concentric square rings on the 8x8 and the coincidence of their producing the same probabilities are the purported yarrow oracle ... it speaks to me. Truth often is betrayed that kind of straightforward simplicity -- at least in the stories.

Still, the historical record does not support the hypothesis, bummer. Truth is ever-elusive when treating with antiquity. I'm reminded of Tennyson's words "[Death] puts our lives so far apart we cannot hear each other speak."
==
Hey, no reason to despair, just as Brad pointed out, you did find a cool pattern that, as far as I know or recall, wasn't observed before (and boy, after three millennia of exegesis, that's hard as hell). Which makes me wonder more about those Song scholars, not only Zhuxi but also Shao Yong, from whom, it appears, the binary arrangement of the hexagrams comes from. OTOH, I'm not as disciplined or skeptical as Brad when it comes to attributing the Chinese more mathematical knowledge than he does. I am an optimist of the kind of Richard S. Cook, who wrote a phone-book sized monograph, attributing ancient Chinese a lot more mathematical sophistication than anyone I know. Mind you, nobody I know with scholarly credentials, including Ed Hacker, whom is in his 80's and spent at least half of his life musing about the King Wen Sequence (KWS), appears to have taken Cook seriously. Who knows, perhaps Cook suffers from the same kind of dismissal Chris Lofting did: "theoretical suicide by obfuscation"... Or perhaps, as it appears to be the ongoing attitude towards it, the man just created a humongous scaffolding wrapped around the KWS like a glove, as in "observe a pattern and apply an until then inexistent meaning to it".

My point is, I've no strong reason to dismiss the idea that those ancient Chinese sages did indeed observe what you have but also, perhaps, arrange things around, such as divination methods, to fit those patterns.
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