Recently, I wanted to consult the I Ching. Traditionally 49 yarrow stalks are used to generate the hexagrams, but these days it is more common to use 3 coins. The problem with the 3 coin method though, is loss of accuracy in generating the hexagrams.
I vaguely remembered a method using 4 coins, that generated accurate hexagrams, but a quick Google revealed that this method necessitated using binary numbers to determine the result. Something I wanted to avoid.
The hexagrams of the I Ching are built up from six lines.
These lines can be one of the following:
old yin (yin changing into yang), which has the number 6
young yang (unchanging yang), which has the number 7
young yin (unchanging yin), which has the number 8
old yang (yang changing into yin), which has the number 9
The odds of producing each type of line with yarrow stalks is shown in Table 1.
Whilst comparing Table 1 with the corresponding graph for 4 coins (Table 2), I quickly realized that the results did not match. Indeed the most obvious problem being the five columns produced with the coins, as against only four columns with yarrow stalks.
It was whilst reflecting on this problem that inspiration took me. I recalled that with the Obi (divination method used with Egun and Orisha in Santería), when three whites and one black is thrown, a second throw is taken. Equating this with the coins, a throw of HHHT would be thrown again.
This would reduce the number of columns produced by the coins to four. The second throw could then be split amongst the remaining columns. After playing with the math, I found that the results of the second throw could be split amongst three columns, giving exactly the same results as per yarrow stalks.
Which prompted me to reflect. The Obi and the I Ching are both based upon divisions of 1/16th. Is this pure coincidence, or is there something deeper, connecting the two systems?