A Jow Forums poster may have solved part of a very tricky math problem that mathematicians have been working on for at least 25 years. The user was just trying to figure out the most efficient way to watch episodes of a nonlinear anime series, but the result has generated considerable interest from mathematicians around the world who have no way to identify the anonymous user.
Yesterday, Robin Houston, a computer scientist and mathematician tweeted about the bizarre intersection of Jow Forums and mathematics, inadvertently setting off a wave of public interest in the story. Within hours of his tweet, his phone was vibrating constantly. “It started to go mad,” he says. “My phone started going crazy.”
The Jow Forums part of this saga began on September 17th, 2011, when a poster posed a question: if you wanted to watch 14 episodes of the anime The Melancholy of Haruhi Suzumiya in every possible order, what’s the shortest string of episodes you’d need to watch?
There are 14 episodes in the first season of Haruhi, a 2006 anime based on a series of Japanese light novels. The episodes, which feature time travel and are otherwise chronologically challenging for the viewer, originally aired in a nonlinear order. When the series went to DVD, the episodes were rearranged, and it’s become something of an obsession for fans to rewatch the series over and over again, going through as many chronologies as possible.
An anonymous poster figured out one possible way to solve to the Jow Forums problem, satisfying the more mathematically inclined Haruhi fans. But in the process, they also helped puzzle out an issue that mathematicians have been working on since 1993. The anonymously authored proof (which was recently reposted on a Fandom wiki) is currently the most elegant solution to part of a mathematical problem involving something called superpermutations. It’s an enigma that goes well beyond anime.
In mathematics, a permutation is the order of a set of numbers.
An anonymous Jow Forums post could help solve a 25-year-old math mystery
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In anime terms, one permutation of Haruhi would be watching all 14 episodes in the order that they aired. But what if you’re a Haruhi superfan and watching the season once isn’t enough for you? In that case, you might be interested in a superpermutation, or all of the possible permutations of a set strung together. Think of it as the ultimate Haruhi marathon.
Think of it as the ultimate ‘Haruhi’ marathon
The branch of math that deals with permutations and superpermutations is called combinatorics. It doesn’t require years of study to be good at it, either. “It’s more accessible to amateur and casual mathematicians,” Houston says.
The poster’s anonymity doesn’t invalidate the solution for the mathematicians. “What’s beautiful about mathematics is that it’s a proof that starts with your hypothesis and leads to your conclusion,” Jay Pantone, a mathematician at Marquette University says. “You have to convince a skeptical reader that you’re correct. That doesn’t rely on your identity being known.”
Pantone was that skeptical reader for the Jow Forums proof. This week, he translated it from the more informal Jow Forums posting into a more formal layout that mathematicians like himself could more easily understand. He says the proof holds up.
With the Haruhi problem, people were looking for the shortest possible superpermutation for the 14-episode set. But no one has found a formula that would actually solve that problem. The 1993 paper suggested one part of that solution. But in 2014, Houston figured out that the math used in the 1993 problem didn’t work for sets containing more than six numbers. The result got mathematicians really excited about the problem again after it had languished in the literature for a quarter century. Eventually, one of them found the Jow Forums proof, and all those numbers and symbols started to fall into place.
The Jow Forums proof outlines how to find the smallest possible number of episodes for the solution.
But that doesn’t fully solve the problem. An even bigger breakthrough came earlier this month when sci-fi author and mathematician Greg Egan wrote up a proof that outlined how to find the largest possible number for any given superpermutation problem.
Pantone crunched the numbers of the Haruhi problem for The Verge and found that you’d need to watch at least 93,884,313,611 episodes to watch the season in any possible order. At most, you’d need to watch 93,924,230,411 episodes to accomplish the task. There’s still a ways to go to narrow down the exact answer, but they’re getting there.
Now, mathematicians have a way to figure out the range of answers, and a group of them — including Houston and Pantone — are actively working to figure out a formula that combines Egan’s work and the anonymous proof into a cohesive formula. “It might be possible to crack the thing completely open,” Houston says.
Beyond answering obscure anime questions, there are no known applications for the formula
Beyond answering obscure anime questions, there are no known applications for the formula, which isn’t unusual in the field. It often takes decades, Pantone says, for formulas that are discovered in pure mathematics to make their way into real-world applications. But the Jow Forums episode does show that math can be accessible to anyone.
“This proof shows that you don’t need to be a professional mathematician to understand mathematics and advance the frontier of knowledge,” Pantone says. “That’s the beautiful thing about math, is that anyone can understand the questions.”
Cool
free speech is an evolutionary environment for ideas
whats the formula then? it doesn't sound like a difficult thing to work out. how is it different than finding out all the possible combinations of a 4 digit pin number, except that it is a 14 digit number and all numbers must be used?
>it doesn't sound like a difficult thing to work out.
*for a mathematician obviously.
You're right, it doesnt seem overly complex, if I understand it correctly, which maybe I don't. And I thought there would be a few real world applications for it too...
You want to order it in a way that includes as many permutations within as possible. For instance, the series 1234213 contains the series 1234, 3421 and 4213, so by going over 7 digits you have covered 3 permutations, instead of going over 123434214213 which gets the same result, but you have to go over 12 digits. So you want to get a minimal string of digits that contains all possible permutations. This is not so simple.
Also, thanks OP for this cool factoid
I am almost falling asleep from boredom thinking about Anime and all the possible ways to watch some lame japanese series of CDs.
What are the name of the episodes? You get the name of the episodes and begin entwining. Until you’ve absorbed the series fully.
Until you’ve seen nothing. Oh gee that was quick.
That was me
Give /a/ the Fields Medal
>tfw no Haruhi gf
Stop taking credit for my work
So what's the answer?
Your approach would mean that if there were only two episodes, the answer would be 4. When in fact, it's 3.
This is old news
>The Melancholy of Haruhi Suzumiya
SAO tier trash, literally no reason to watch it, problem solved.
why not just watch them all at the same time 14 times?
This.
>hurr major important math equation!!!
>it's about anime
How gay and uninteresting. Dropped.
KYON-KUN DENWA
I've seen stuff like this talked about before. Makes me wonder what other 'Math mysteries' are out there just ripe for the taking if someone would actually just sit down and work it out
math is jewish trick
muh imaginary numbers existing solely to show goyim that they pay is also imaginary
What fucking car uses locks like these?
>How many episodes does it takes to watch every permutation of Haruhi
0 because haruhi is trash.
There I just saved them lot of work.
My gma has one of these on her old minivan, her keycode doesn't exist in that block of #'s. I don't understand how this would work.
woops
True. But what the heck was the proof? What was posted on Jow Forums. Well-trolled, poo OP, leave out the one interesting part.
this story is a few weeks old
mathsci.wikia.com
This "problem" is a typical algorithm in programming that consists of nested for loops.
Why don't the mathematicians just: for sum and iterate each element?
What's her keycode?
>I just realized what the problem has to be while writing this post
Haruhi is part of the reason anime became large in the west. It could be posted in full on YouTube back in the day and fan subs kick started millineals and late gen x into it. The series is one of the earliest example of memes that helped it to spread. I couldn't imagine current internet culture without Haruhi.
Minivans
>solved part of a very tricky math problem that mathematicians have been working on for at least 25 years
Shits in the street
> be shitty mathematician
> disguise a hard problem as anime
>???
> profit from concentrated autism
Fields medal when?
youtube.com
Here´s another one.
If i read it correctly it was the way the user went about it that by accident was part of a puzzle to solve a different mathematical problem that was quite a bit harder. So by encorporating part of that approach into solving that other problem, they might now have a chance of actually solving it.
This. You will never see someone on twitter create a proof this complex. Also talking about fanservice anime on Reddit or Resetera is grounds for a ban, so this couldn't have happened there, either.
I still find it hilarious that internet autists obsessing over some order of how to watch an anime series, partially by this obsessing end up participating by accident in solving a more complex mathematical problem because some mathematicians noticed this discussion, and noticed how this approach could help with that.
It's not as cut and dry as it may seem. The previous thought solution to the problem, n!, had edge cases where this simply did not work for this problem like when n = 6.
The anonymous poster looked at the gaps in ordering instead of looking at the ordering itself, basically adding together all the corners of the problem until he came to a solution. Pretty clever idea that will go completely uncredited because he did it entirely for the purpose of showing some anime fags how smart he was.
And I guess he sure showed them.
Literally millions, for every single possible ordered sequence of numbers.
It's just weaponized autism is a hell of a drug.
>And I guess he sure showed them.
That user will always know it was him anyways regardless. And i'm fairly certain that if he comes forward, a lot of these mathematicians would gladly invite him to have his or her take on other math problems. Which he can then take full credit for if he has similar fortune.
Overlapping is allowed. So for example in a 3 episode series you could watch episode 1 then 2 then 3 (1,2,3), or 1,3,2, or 2,1,3, or 2,3,1, or 3,2,1, or 3,1,2. There are 6 permutations and a total of 18 episodes. However, by overlapping these individual sets of numbers you can reduce the total number of shows you must watch to less than 18. So in this case you could watch 1,2,3,2,1,3,2,3,1,2 for a total of 10 episodes.
brainlet here. doesnt make sense to me. if you're trying to find all possible permutations of 14 numbers why isnt it always just 1 number? how can you have "smallest" number of permutations? because the smallest wouldnt be all permutations because it would leave out those included in the "largest" number of permutations?
nevermind. i read the thread. permutations within a permutation are included in this bullshit
7
This concept has been around since late 1800's. It's a de Brujin sequence, which is different than the postulate from OPs post.
oh ok now it makes sense
>Pantone crunched the numbers of the Haruhi problem for The Verge and found that you’d need to watch at least 93,884,313,611 episodes to watch the season in any possible order. At most, you’d need to watch 93,924,230,411 episodes to accomplish the task. There’s still a ways to go to narrow down the exact answer, but they’re getting there.
>Jow Forums is just a distributed computing system that uses autists instead of computers