CHAPTER 00
Every hexagram is the same data structure.
Whether the input is coins, yarrow stalks, time, or a digest, Anygua reduces the result to six line positions. Each position can only be one of four states: 6, 7, 8, or 9.
line in { 6 old-yin, 7 young-yang, 8 young-yin, 9 old-yang }
7 / 8 are static lines
6 / 9 are moving lines that flip into their opposite
-> six lines bottom-to-top determine the primary hexagram
-> moving positions determine the changed hexagram
CHAPTER 01
Three coins: a simple binomial distribution.
Three coins, heads and tails counted as 3 or 2. The sum is exactly one of 6, 7, 8, or 9. Each line is independent; toss six times.
Classic
Procedure
heads = 3, tails = 2
sum of three coins in { 6, 7, 8, 9 }
-> P(6)=1/8, P(7)=3/8, P(8)=3/8, P(9)=1/8
Distribution
6 old-yin1/80.125
7 young-yang3/80.375
8 young-yin3/80.375
9 old-yang1/80.125
CHAPTER 02
Yarrow stalk: the asymmetric classical distribution.
Fifty stalks, one set aside, leaving forty-nine. Divide, hang one, count by fours, gather the remainder. Three variations make one line; eighteen make a hexagram. The distribution is not the same as the coin method.
Classic
Procedure
49 -> divide -> hang one -> count by fours -> gather
three variations make one line; eighteen make a hexagram
-> P(6)=1/16, P(7)=5/16, P(8)=7/16, P(9)=3/16
Distribution
6 old-yin1/160.0625
7 young-yang5/160.3125
8 young-yin7/160.4375
9 old-yang3/160.1875
CHAPTER 03
Plum blossom: number drawing as modular arithmetic.
Shao Yong's move was to rewrite casting as deterministic arithmetic. Any integer can enter the system. Time is just integers too.
From time
upper = (year_branch + month + day) mod 8
lower = (upper_sum + hour) mod 8
moving = (year_branch + month + day + hour) mod 6
From two numbers
upper = A mod 8
lower = B mod 8
moving = (A + B) mod 6
CHAPTER 04
From anything: inputs become stable bytes first.
Text, verse, audio, and images all work if they can be turned into stable bytes. Anygua then runs one SHA-256 digest pipeline.
01
Input
text / verse / audio / image
02
Bytes
UTF-8 text / raw file bytes
03
Digest
SHA-256 -> 32 bytes
04
Draw
digest bytes -> six bands
05
Lookup
binary -> 64 hexagrams
DESIGN PRINCIPLE
The same modern input always returns the same hexagram. Text and verse use the parity of the first 6 digest bytes plus the 7th byte for the moving line; audio and image files use six digest-band means against their median, with the largest deviation marking the moving line.
CHAPTER 06
What can it calculate, and what can it not calculate?
It can calculate that two identical modern inputs return the same hexagram. It can calculate that young-yin appears with probability 7/16 in the yarrow method.
It cannot calculate whether you will get a raise next year, because there is no causal chain between a probability distribution and your paycheck. Anygua makes the math reproducible; the cultural reading remains yours.