Anime fans stumbled upon a mathematical proof

Clicking around the previous discussions, it appears that the original question was posted on &#x2F;sci&#x2F;, a science and math board on 4chan, and not an anime board, as everybody who writes about this states.<p>This is apparently an archive of the original post:<p><a href="http:&#x2F;&#x2F;4watch.org&#x2F;superstring&#x2F;" rel="nofollow">http:&#x2F;&#x2F;4watch.org&#x2F;superstring&#x2F;</a><p>It&#x27;s a question to a math community, using an anime meme template and referencing another anime. The discussion is very much not some anime fans having fun with a silly question, not knowing they are dealing with frontiers of math. Instead it is math enthusiast having a go at what they know is a difficult problem. One even links to a stackexchange question, stating that this is an open problem, and the poster of the link says that if they solve it, they should post it to arxiv.

Previous discussions:<p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=18292061">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=18292061</a><p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=23968618">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=23968618</a><p><a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39325146">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=39325146</a><p>See also:<p><a href="https:&#x2F;&#x2F;mathsci.fandom.com&#x2F;wiki&#x2F;The_Haruhi_Problem" rel="nofollow">https:&#x2F;&#x2F;mathsci.fandom.com&#x2F;wiki&#x2F;The_Haruhi_Problem</a><p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Superpermutation#Lower_bounds,_or_the_Haruhi_problem" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Superpermutation#Lower_bounds,...</a>

I am not surprised that the author of this great article is Manon Bischoff. I have been reading her articles on Spektrum.de for years now, and they are always excellent. Here is a list of all her articles: <a href="https:&#x2F;&#x2F;www.spektrum.de&#x2F;profil&#x2F;bischoff&#x2F;manon&#x2F;1486871" rel="nofollow">https:&#x2F;&#x2F;www.spektrum.de&#x2F;profil&#x2F;bischoff&#x2F;manon&#x2F;1486871</a><p>Selected articles get translated and published by SciAm: <a href="https:&#x2F;&#x2F;www.scientificamerican.com&#x2F;author&#x2F;manon-bischoff&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.scientificamerican.com&#x2F;author&#x2F;manon-bischoff&#x2F;</a>

Oddly, the image that Scientific American chose to illustrate their article isn&#x27;t from any of the Melancholy of Haruhi Suzumiya projects, but from Aokana - Four Rhythms Across the Blue, a much more obscure title.

There&#x27;s something unbelievably funny to me that actual mathematical papers have to cite a 4chan post.<p>It does make me wonder how much hidden knowledge is hidden in parts of the internet; maybe this is the only genius mathematical thing we&#x27;ve <i>found</i> on 4chan...

At one of my old jobs, the bathroom was locked with a 4 digit code followed by the key symbol. We jokingly made up &quot;Bathroom Code&quot; as an interview question&#x2F;to nerd snipe each other instead of working, which was &quot;assuming you don&#x27;t have to press key, and that the bathroom door will unlock if the correct 4 digits are entered in order at any time, write the code to print the shortest possible test sequence to guarantee you entry&quot;. Obviously we didn&#x27;t give this to any candidates but it&#x27;s amusing to think that the problem is a lot more interesting than we gave it credit for.

2011 in the title would have been nice. Of course it&#x27;s the Haruhi problem.

I was impressed with how tight the known bounds are. For length 30, the upper bound is 1.0000397 times the lower bound. For 40 the ratio is 1.0000164 and it quickly approaches 1.

It could have been a mathematician , you never know with that Anon guy.

I played around with a related problem - find the shortest string containing every binary number of length n. There are 2^n substrings, and I seem to recall being able to to do it in 2^n + n - 1 bits. In other words, perfect overlap was possible at least up to n=10.<p>I was interested in this because it&#x27;s an optimal way to plot Julia sets by running the iteration backward and choosing one or the other square root. To visit all parts of the outline you&#x27;d want to apply every sequence of root selection (positive or negative) up to some length. Doing it at random is cool, but for a fixed number of points you want one of these sequences.

Should not the de Bruijn sequence work somehow for this problem?<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;De_Bruijn_sequence" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;De_Bruijn_sequence</a>

&gt; The researchers posted their mathematical work to the Online Encyclopedia of Integer Sequences that same month, and the first author is listed as “Anonymous 4chan Poster.”<p>I love the internet.

Woah, Haruhi is now considered classic.

It is funny that the article linked is from this month, but the actual anonymous post seems to be from 2011, and it looks like the research paper itself is from 2018.

I haven&#x27;t seen any Haruhi references in about as much time yeah, it was insanely popular back in the day.<p>Haruhi, 4chan, been a while.

Missed an opportunity to mention she was a god and the episodes were already out of order.

This is always how it works. Large fan bases are filled with extremely capable people with vastly different specialties so I have no doubt this 4chan user had a very strong math background and just couldn&#x27;t resist solving it for real.

Slightly offtopic: Has anyone tried watching Melancholy of Haruhi Suzumiya in a random order?<p>Does it tell a story with a beginning and an end? Or is it more like season 1 of the Simpsons, which you could also watch in any order you want.

Any recommendations on how to write stories where the chapters could be read in any other? I am curious how such thing could work.

isn&#x27;t this solved even on ancient east asian texts? and several other times on recent history?<p>i even found this much more interesting use searching for the name of the proofs <a href="https:&#x2F;&#x2F;hackaday.com&#x2F;tag&#x2F;ford-securicode&#x2F;" rel="nofollow">https:&#x2F;&#x2F;hackaday.com&#x2F;tag&#x2F;ford-securicode&#x2F;</a>

Non-paywall link: <a href="https:&#x2F;&#x2F;archive.is&#x2F;i140b" rel="nofollow">https:&#x2F;&#x2F;archive.is&#x2F;i140b</a>

Yea, that absolutely checks out.<p>Being able to apply your work to something you enjoy is a discipline and motivation multiplier.

Misleading rehash of (2011-2018) story.

This is honestly one of the coolest &quot;internet accidentally advances math&quot; stories I&#x27;ve seen

Now with our new understandings of super permutations, perhaps David Lynch’s rabbits can finally make sense.

This was done by 4chan.

Loath as I am to give 4chan credit for anything positive, I feel like the article subject is slightly dismissive with its use of the phrase &quot;stumbled upon.&quot; The anonymous 4chan user clearly <i>did the work</i>, it&#x27;s not as though they came upon a proof written in the sand. For all we know it was a grad student with an ABD in Statistics who just happened to like anime.<p>But the phrasing almost implies it&#x27;s not a true accomplishment because &quot;scientists&quot; didn&#x27;t discover it.

&quot;Permutate&quot;?

I have, for a long time, dismissed Scientific American as a pointless work of marketing. This article, on the other hand, makes me think I may be missing some things. The problem is stated in an interesting way that might be broadly understood and enjoyed. It gives some results that are explained well and easily understood. It also leaves some open questions that can be explored, letting the explorer dream about settling some famous open problem. The perfect sort of thing for high school math (and an old guy killing some time).<p>Thank you Manon Bischoff (author), Daisy Yuhas (editor), and Scientific American for giving me this to think about.

@gwern was it you?