gezhengwen

3 ms·

1.
by gezhengwen 7mo ago
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
2.
by gezhengwen 7mo ago
The I Ching has a historical connection to magic squares — the Lo Shu is a 3x3 magic square traditionally linked to the I Ching. But cycle decomposition analyzes the permutation between two orderings, which is a different mathematical s
3.
by gezhengwen 7mo ago
The Shang dynasty people knew the pairing structure of hexagrams (inverted/complementary pairs), but cycle decomposition is a modern group theory tool that did not exist until the 19th century. These are two different levels of analy
4.
by gezhengwen 7mo ago
The observation itself is the value — it tells you the King Wen sequence is not a bunch of small local adjustments, but a holistic rearrangement. But it cannot tell you why King Wen arranged it this way.
5.
by gezhengwen 7mo ago
Yes, it is essentially the same mathematical concept — both are cycle decompositions of permutations. Carmack used a permutation to ensure every pixel is visited exactly once.
6.
by gezhengwen 7mo ago
You are right, the presentation may be overdone. The result itself is a small mathematical fact. I made the interactive page so people can verify it themselves, not to make it look grand. Thank you for the criticism, I will adjust.
7.
by gezhengwen 7mo ago
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.
8.
by gezhengwen 7mo ago
You are right, zero fixed points does not mean total structural difference. Your counterexample is good. My wording was wrong, I will fix it. What interests me is not the statistical rarity, but that 81% of elements are in one orbit — thi
9.
by gezhengwen 7mo ago
The I Ching has influenced China for over 3000 years. I believe there must be a reason for that. In China, the I Ching is often treated as mysticism. But I believe in science. The end of mysticism must still be science. So I did a lot of
10.
by gezhengwen 7mo ago
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?
11.
Show HN: The King Wen Permutation: [52, 10, 2](gzw1987-bit.github.io)
65 points by gezhengwen 7mo ago|27 comments