I read the page and went through the "verify the cycles for yourself" sequence and I still have no earthly idea when defining the cycles, what is the rule that says "if you're currently on hexagram X, you can calculate the next hexagram Y by doing..."
Each hexagram has two positions: one in the binary natural order (0-63), and one in the King Wen sequence. The rule is: a hexagram
moves from its natural order position to its King Wen position. For example, Qian is at position 63 in the natural order and position
0 in the King Wen sequence, so σ(63)=0. Then look at position 0 (Kun), which is at position 1 in the King Wen sequence, so σ(0)=1.
Follow this chain until you return to the start. There is no formula — σ is defined by the mapping table between the two orderings.
You are right, the expected largest cycle of a random permutation is around 40. 52 is larger but not extreme. I did not claim this
result is statistically significant.
I found this by accident while analyzing the I Ching with code. 81% of hexagrams are locked in one chain, none stays in its original
position. You can verify it yourself in the browser. Has anyone seen this before?
We truly live in an age where facts that are worth "maybe one sentence of space on Wikipedia" can be expanded into full-blown AI-coded interactive websites. I'm not sure how to feel about this. I think in this case it ascribes an inappropriate sense of grandeur: making a mathematical curiosity (and is the result even that surprising?) seem like some deep truth has been unveiled, or we finally found God's Number.
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If you find this interesting, I suggest you study group theory - this seems pretty much a direct consequence of the group structure.
McKenna got deep into this...
https://www.fractal-timewave.com/articles/math_twz_10.htm