[HN Gopher] The Art and Mathematics of Genji-Ko
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       The Art and Mathematics of Genji-Ko
        
       Author : olooney
       Score  : 155 points
       Date   : 2024-11-27 14:33 UTC (1 days ago)
        
 (HTM) web link (www.oranlooney.com)
 (TXT) w3m dump (www.oranlooney.com)
        
       | doctorhandshake wrote:
       | Loved this. Great writing and a bit of cultural arcana I knew
       | nothing about but which resonates into the present day.
        
       | tromp wrote:
       | Obligatory entry in The On-Line Encyclopedia of Integer
       | Sequences: https://oeis.org/A000110 which has 3 links mentioning
       | Genji only one of which is not broken:
       | 
       | Xiaoling Dou, Hsien-Kuei Hwang and Chong-Yi Li, Bell numbers in
       | Matsunaga's and Arima's Genjiko combinatorics [1]: Modern
       | perspectives and local limit theorems, arXiv:2110.01156
       | [math.CO], 2021.
       | 
       | [1] https://arxiv.org/abs/2110.01156
        
       | rezmason wrote:
       | A couple years ago I made a codepen to generate arbitrarily long
       | Genji-mon from a ruleset, and managed to write a rule that
       | reduces the number of required special cases to one. However,
       | these rules are very fragile, and "break" with lengths > 5 (edit:
       | or maybe they don't! this deserves further exploration). Glad to
       | see someone else discovering the structure behind this
       | interesting system!
       | 
       | https://codepen.io/rezmason/pen/ejWogV
        
         | olooney wrote:
         | I tried setting `width` to 5 and found that your algorithm
         | handles Yugiri correctly out-of-the-box. I tried commenting out
         | various special case rules, such as lines 162-170, but it's the
         | recursive algorithm itself that causes this. As you note on
         | lines 204-214, your algorithm is not guaranteed to find the
         | shortest solution; but the fact that it correctly handles
         | Yugiri while mine does not suggests that it's closer to the
         | intuitive, aesthetic judgement originally used to decide on the
         | traditional layout.
         | 
         | That really surprised me (in a good way), because I had viewed
         | Yugiri as an _exception_ to an otherwise regular rule, while
         | you showed it actually a natural consequence of a different
         | rule! Of course, your algorithm _also_ has special cases that
         | need to be handled, so ultimately it may just be an aesthetic
         | choice after all, but it proves that Yugiri may not be as
         | irregular as I thought.
        
         | gowld wrote:
         | This codepen's presentation strongly presents the "phantom
         | squares crossroads" optical illusion.
        
       | spirographer wrote:
       | This is a great article! Funny about Yugiri (39), because your
       | version is a mirror image to Eawase (17), and the traditional
       | Japanese Yugiri breaks that symmetry.
       | 
       | Every Genji-mon that is not self-symmetrical should have a mirror
       | image, which I was able to quickly verify in the Genji-mon table
       | you displayed.
       | 
       | Minori (40) is the only non symmetrical Genji-mon that breaks the
       | rule, because it's the only one whose mirror image is also
       | isomorphic to itself.
       | 
       | I can only imagine that there was something deliberate about the
       | symmetry breaking for Yugiri, given the almost fanatical
       | attention to detail in Japanese arts in general, and the equally
       | strong penchant for deliberate imperfection in traditions like
       | Kintsugi.
        
       | steele wrote:
       | No irony detected despite the tyranny of low expectations for the
       | ability of bored Japanese nobles.
        
         | bccdee wrote:
         | "Low expectations"? This article is about the specific language
         | of literary allusion used to describe the solutions to
         | competitions based on discerning subtly different incenses.
         | Does that sound easy to you?
         | 
         | I don't think you understand what nobility was _for._ The point
         | of aristocratic culture is to mediate alliances between
         | powerful families. This:
         | 
         | > There has never been a group of people, in any time or place,
         | who were so driven to display their sophistication and
         | refinement. It wouldn't do to merely put out a few sticks of
         | incense; no, you would have to prove that your taste was more
         | exquisite, your judgment more refined, your etiquette more
         | oblique.
         | 
         | is the micro-politicking which undergirded macro-political
         | moves like marriages, trade deals, and wartime alliances. Like
         | a bird with colourful plumage, competence in this "frivolous"
         | game represented having the wealth and power to spend all your
         | time thinking about incense. Being good at this stuff was part
         | of the job, and it mattered.
         | 
         | If your point is that aristocracy is a ridiculous system, sure,
         | I don't disagree. But these people were not fooling around.
        
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