Endless Thread - The Haruhi problem

Episode Date: September 25, 2026

Get out your graphing calculators, because today's episode of Endless Thread is about a math problem. Specifically: wt(π1, . . . , πm) = m−1 ∑ i=1 wt(πi , πi+1) Now, pencils down. Stumped? So were mathematicians for decades. That is, until the equation was solved in a thread on 4Chan about watching the anime The Melancholy of Haruhi Suzumiya.  Show notes: A lower bound on the length of the shortest superpattern (oeis.org) Sa-Shi-Su-Se-So: The Secret of Japanese Cooking Basics (Umami Insider) This content was originally created for audio. An auto-generated transcript is available on Apple Podcasts and Spotify. Heads up that some elements (i.e. music, sound effects, tone) are harder to translate to text.

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Sieberts and Git. And how did she do? That amory got A's in math, but it almost killed me. Yeah, I tried really hard, but I did well. All that try hard energy, Amory, is going to be put to use today. So get ready. All right. Our episode of Endless Thread from WBUR, Boston's NPR, today is about a math problem. Okay. Are you familiar with these words? Do they mean anything to you? A lower bound on the length of the shortest super pattern.

Not a bit. Okay. I'm going to read a math problem to you, and I want you to tell me if it makes any sense to you. I'm going to start to read it. WT, open parenz, pi 1, period, period, period, pi M, close Sperens equals E as in E equals MC squared. Is this making any sense to you so far?

Oh, yeah. Perfect sense. I got it. I'm following along. No, I have no idea. I know E equals MC squared. Okay. New topic.

What do you know about 4chan? It's not the darkest of dark webs, but it's not the light webs. I'll tell you that. It's like another internet forum, but has a more nefarine. Ferrious reputation than, say, Reddit. It might be a dark corner of the web, but it's not really, it's the, you know, it's the clear internet, as far as we know. It's accessible easily by a random user. It's not the kind of stuff behind the stuff that we see, which is what we think of as the dark web. So another question

for you. How much anime do you watch? I want to be the very best that no one ever was. them is my real test. To train them is my cause. Okay, okay. That's the excitement. I watched some Pokemon back in the day. Okay.

Not bad. I'll take it. So you're a Pokemon fan. It sounds like maybe you are not a big watcher of the anime series, the melancholy of Haruhi Suzamiya. Nope. Can't say that I am. Okay. So this show is a show that might be familiar to you if you've ever watched, I don't know, one of the seasons of Arrested Development would be an example.

Collidescope would be an example. Shows in which there's non-linear narrative at play. And what I mean by that, Amory, is in the case of the melancholy of Huruhe Susamia, there are 14 episodes, but you can watch them in any order that you want to. You can watch. watch episode one and then six and then two and then 14 and then et cetera, et cetera. Does that make sense? Yeah. And in that watching, you would kind of have a different experience of the show, right? And if you were a huge anime fan and a huge nerd of this particular anime series, you might want to experience every possible permutation or iteration of the narrative. as it's presented, right?

Hmm. Which is, you know, effectively a math problem. You combine all possibilities of these 14 different episodes, and that would be a huge number of different permutations of how you could take in the narrative of this show. Yeah. Does that make sense? Yeah. So you'd go like one, two, three, four, five, sit up to the 14, and then you'd go one, three, four, five, six, blah, blah, blah, blah.

And then, yeah, I can't even. Exactly. Yeah, yeah. But for instance, you know, every end, every last episode you watched, whether it was 14 or 6 or 1 or 2, et cetera, et cetera, that could actually be, that could serve as the beginning of the next permutation. Yeah. I mean, the last two could also serve as the beginning of the next permutation. Exactly. Or 3 or 4.

Oh, this is a mess. So it becomes this like very complex math problem, actually, if you wanted to say. say watch every permutation but in the most efficient way. And by efficient, I basically mean you wouldn't want to have to redo work of watching in a certain order. This is horrible. Why would you do this? It's a great question. Do you know how much green, green grass is outside?

Do you know how many species of flowers? Did you know there are 5,000 species of ladybugs? More than that. And we're going to, we're talking to, we're talking about fortune. users touch grass is not going to work. You're going to have to... You said it's 14 episodes. It's 14 episodes.

14 episodes. You're going to watch every permutation of 14 episodes in a different order. And you're trying to figure out how to do that as quickly as possible. Maybe so that you can touch all that green, green grass. But still, come on. By the way, since, you know, they did the math here on these 14 different episodes, the lower bound number of combinations is 93 billion. 884,381,313,611, while the upper bound is 93,924,213,4,11.

Which means that given the average episode length of a bit more than 20 minutes, watching the series in every possible order would require, drumroll, 4.3 million years. We don't have that kind of time. We must choose a new activity. So this is actually a decades-old math problem that exists outside of 4chan, outside of anime, and figuring out how to calculate this was so complicated that it was unsolved for decades. But in 2011, there was an anonymous 4-chan user who, maybe on purpose, maybe not, this thing tends to happen on the internet, got into an argument with another 4-chan user,

shocker, about the most optimal way to binge-watch anime specifically, the anime, the melancholy of Haruhi Suzamiya. I'm going to read you what was described on the message board, okay? Okay. The Haruhi Problem. If you wanted to watch the 14 episodes of the first season of the series in every possible order, what would be the shortest string of episodes you would need to watch? The proof for this lower bound came to the general public interest in October of

2018 after mathematician and computer scientist Robin Houston tweeted about it. So I'm going to send you this. I just want you to look at this very academic looking paper. And you can see under the title, can you read the title of the paper? A lower bound on the length of the shortest super pattern. Now, under the title of the paper are listed the authors of the paper. And as you know, with scientific papers, the authors are usually listed in order of... Importance.

Exactly. So, do you want to read the list of authors to this paper? First up, anonymous 4chan poster. Robin Houston, J. Pantone, and Vince Vatter. Can you say what the date of the paper is? October 25th, 2018. And just keep reading a little bit. if you would.

This proof is inspired by that posted anonymously at... Et cetera. Et cetera. Which itself was taken from a 4chan discussion archived at... Et cetera. Wow. So this is... I just think it's like one of those things that I find very funny,

which is essentially that like an internet argument resulted in a solution to this decades-old problem. An anonymous 4-10 user solved it in 2011, and it was discovered seven years later to have been solved. Hence, the publication date of this paper in 2018 on October 25th. And there you have it, folks. What do you think? Well, even though I would never use this solution personally to attempt to try to figure out the different, all the or, the super patterns of, say, episodes of a series, this does seem applicable to other things in life, right?

Like if you're trying to try all of the peanut butter and insert condiment of your choice sandwich that there is in the world. Every possible banana dog. Every possible banana dog. That's right. which for people who don't know, hot dog bun, banana, peanut butter in it, whatever else you want, it's genius. Yeah, I mean, there are other practical applications is what I'm saying of like trying to crack the super pattern dilemma, right? Yeah, I think so. And that all sounds great to have like real practical applications.

But can you go to the Reddit thread that I just sent you and read the top comment? Yeah. So what's the most optimal way to be? binge watch anime. People just, they just want to keep it grounded. Redditors focusing on the important questions, as always. That's right. That's right. Oh, man.

What could the Heru Kroohy problem solve for you? That's coming up right after we solve the math problem of sponsorship for podcasts. When you're a mid-sized business, you need every competitor. advantage you can get. Like an AI solution that works for you, not against you. SAP Grow is built with AI embedded at its core, working across every system. And it's ready to go from day one so you can hit the ground running. Bring it with SAP Grow, AI Cloud ERP for any size business.

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Visit Tim Hordons.ca.ca. For details. Is there any practical application that you would like this applied to, Amory? What, all my different banana dogs wasn't good enough for you? No, let me think about that. I mean, I feel like a saying that I've been using a lot, that I don't know if it came from somewhere or if it just feels true, is just like, man, there are a lot of different ways to live a life.

And so I don't know. I can't think of something where I would meaningfully want to check every box. Because it might take me four million years or something, you know? Yeah, I get that. What I would say is banana dog jokes aside, I'm sure there are scientific applications for this stuff that could get us, you know, to this like far-field goal more efficiently and effectively in a way that could be actually meaningful for a huge number of people, solving disease, for instance, or something else that is

scientifically really challenging because math. However, my head first goes not to solving disease necessarily, but to recipes and the combination of particular ingredients that results in the tastiness that I yearn for, you know? Like, sometimes things taste quite different depending on what you combine in what order. And so that's where my head goes. I'm not going to watch a bunch of anime based off of this, but I might think about the different orders in which I would put ingredients into a dish that I'm cooking. And can I say one more thing?

Yeah. Which is something I really appreciate about this is when I think about, education today, I have no idea how kids are learning today and forcing themselves to learn things today, especially when they have AI at their fingertips. But I do really believe in the journey, not the destination when it comes to learning things like math or trying to wrap your head around a mathematical problem and seeing where you end up. And so I appreciate that even though my first attitude about this was like, why do you need to know that? Just go outside, you know. The real takeaway is like, yeah, but what, it's about what we get when we put ourselves through the mental

gymnastics, how the mental gymnastics actually like forms connections in our brain that then might be put towards recipes or banana dogs or curing a disease, but we're, we're, better for having gone through the mental exercise of trying to solve things and are better for the hunger and the human desire that it takes to want to solve things like that, even if the proposed application of it is not, is not that rewarding on its face to most people. Let us know, folks, if you have an optimal way to consume a non-linear narrative, including every episode of Endless Thread. We are interested in finding out more. And yeah, thanks for listening, Amory. Of course. By the way, producer extraordinaire

Franie Monaghan has informed me that there is a Japanese version of this, the correct order in which you would put ingredients into a recipe in order for it to be as tasty as it could possibly be or as oishi as it could possibly be. And I believe it is Sashi Su-Saysa-Sol. So we'll put a link to that in the show notes. That's all, folks. See you next week. Endless Threat is a production of WBUR in Boston.

This episode was produced by Ben Brock Johnson and Franny Monaghan and co-hosted by me, Amory C. And me, Ben Brock Johnson. Mix and sound design by Emily Jankowski. The rest of our team is Grace Tatter, Dean Russell, production manager Paul Vikis, and our senior managing producer, Sumitajoshi. Endless Threat is a show about the blurred lines between the upper and lower bounds of the number of permutations of 4chan arguments that lead to the solution to a decades-old math problem.

If you have an untold history, an unsolved mystery, or some other wild story from the internet that you want us to tell, hit us up endless thread at wb ur.org.