The binary divination method for the I Ching

易經

0110 6

Designed by Luciano Ramalho, programmer, game inventor and Yi Jing student

Classic divination methods

● Yarrow stalk● material:

50 yarrow stalks● probabilities:

● Coins● material:

3 identical coins● probabilities:

6 1/16 6.25%

7 5/16 31.25%

8 7/16 43.75%

9 3/16 18.75%

6 1/8 12.50%

7 3/8 37.50%

8 3/8 37.50%

9 1/8 12.50%

Binary divination method

6 1/16 6.25%

7 5/16 31.25%

8 7/16 43.75%

9 3/16 18.75%

● Material: 1 coin● Probabilities: same as the yarrow stalk method

● Procedure: for each line, flip the coin 4 times; record result according to table on next slide...

0110two zeroes,interrupted by two ones

6

1001

1011

1101

two ones,interrupted by one or two zeroes

9

00000010

...1110

any othersequence endingin zero

8

00010011

…1111

any othersequence endingin one

7

How to remember● Tails is Yin:

● Heads is Yang:

● A changing Yin is Yin interrupted by Yang:

● Also, 0110 is 6 in binary

6

8

7

How to remember

● A changing Yang is Yang interrupted by Yin:

● Also, 1001 is 9 in binary, while 1011 is 11 and 1101 is 13 (the next odd numbers)

9

How to remember

● Any other sequence ending in Yin is unchanging Yin:

● Any other sequence ending in Yang is unchanging Yang:

8

7

Designer's notes● The smallest probability in the yarrow method is 1/16● For 16 combinations we need 4 bits = 4 coin tosses● It's better to use 1 coin than 4, and write down each bit from

left to right, because the ordering is important● Even combinations, ending in 0, are Yin● Odd combinations, ending in 1, are Yang● 6 in binary is 0110, which reminds me of● for the 9, we need three combinations to get

the same probabilities of the yarrow method, in whichYin lines are less likely to change than Yang lines:● 9 in binary is 1001, which reminds me of● the next odd values 11 (1011) and 13 (1101) we read as 9