those are there for the placeholder purposes, I am currently removing and substuting them with real user feedbacks, thank you for the feedback, thank you for taking time to share it.
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.
>> Zero fixed points — not a single hexagram occupies the same position in both orderings. The structural difference is total.
As a mathematical matter, the expected number of fixed points for any permutation is 1. Some have more. For some to have more, others must have less, and all of those will have 0.
But as a logical matter, "the structural difference is total" is pure gibberish. Consider these two permutations on 5 elements:
1. [2, 3, 4, 5, 1]
2. [5, 1, 2, 3, 4]
"Not a single element occupies the same position in both orderings."
But of course these two permutations have a nearly identical structure (they are rotations in opposite directions, and are each other's inverses); they are far more closely related to each other than either is to
3. [4, 3, 2, 1, 5]
even though permutation 3 shares the assigned position of "3" with permutation 1, and the assigned position of "2" with permutation 2.
Then:
>> We reframe the question:
>> Transform the question "what is the structural distance between two orderings"
>> into the mathematical problem "what is the cycle structure of a specific permutation in S₆₄?"
This is nonsense. The 'question' cannot be transformed into the 'problem', because they are completely unrelated ideas. It's like transforming the question 'what is the Levenshtein distance between two strings?' into the problem 'if a specific string were in alphabetical order, how would it be pronounced?'.
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 — this means the reordering is
highly coupled, not a bunch of small local swaps.
> What interests me is not the statistical rarity, but that 81% of elements are in one orbit — this means the reordering is highly coupled, not a bunch of small local swaps.
But what is the significance of the reordering being highly coupled?
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.
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.
Hi! The "real" PC-98 font (FONT.ROM) is different from the font bitmap that often ships with emulators. Kumdor comes with its own font data, though. My patch changes its single-quote character to look more like an actual apostrophe.
The PC-98 actually comes with a "kanji ROM" chip, that you poll 16x16 characters from one at a time. FONT.ROM is the data used to emulate this chip. Loading an entire font into RAM was not practical on old Japanese PCs. The earliest models, like the MSX, had 64kB of RAM, which was no match for the 3000×16×16 bits = 96kB of font data! (On the PC-98, it's something like 282kB of font data that would eat up half the available 640kB of RAM.)
I've seen games that have their own font data for drawing stylish hiragana/katakana/Latin characters but fall back to the "kanji ROM" for kanji. Kumdor's custom font only covers Latin characters. The typing tests in the game progress from QWERTY nonsense (sdfjkl jklsdf) to little texts in English and rōmaji. My translation patch leaves them perfectly untouched :)
