The Haruhi problem

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 https://oeis.org/A180632/a180632.pdf (oeis.org) Sa-Shi-Su-Se-So: The Secret of Japanese Cooking Basics https://umami-insider.com/blogs/blog/sa-shi-su-se-so-the-secret-of-japanese-cooking-basics?srsltid=AU7gw4U19vvbOr8z4JA9-HpzFFQMakaYmykzE2lL-C0Ot5lqBhqpEasM (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.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Speaker 00

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• 1:20Ben Brock Johnson?

  WBUR Podcast, Boston.

• 1:30Ben Brock Johnson?

  In the subject of mathematics in high school, what kind of grades did future co-host of Endless Thread Amory Sivertson get? And how did she do?

• 1:45Amory Sivertson?

  That Amory got As in math, but it almost killed me. Yeah, I tried, I tried really hard, but I did well.

• 1:54Ben Brock Johnson?

  All that try-hard energy, Amory, is going to be put to use today. So get ready.

• 2:01Amory Sivertson?

  All right.

• 2:02Ben Brock Johnson?

  Our episode of Endless Thread from WBUR, Boston's NPR, today is about a math problem.

• 2:10Amory Sivertson?

  Okay.

• 2:21Ben Brock Johnson?

  Are you familiar with these words? Do they mean anything to you? A lower bound on the length of the shortest super pattern.

• 2:31Amory Sivertson?

  Not a bit.

• 2:33Ben Brock Johnson?

  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 parentheses, pi one, period, period, period, pi m, close parentheses, equals e, as in e equals mc squared. Is this making any sense to you so far?

• 2:52Amory Sivertson?

  Oh, yeah. Perfect sense. I got it. I'm following along. No, I have no idea. I know e equals mc squared.

• 2:59Ben Brock Johnson?

  Okay. New topic. What do you know about 4chan?

• 3:07Amory Sivertson?

  It's not the darkest of dark webs, but it's a, it's not the light webs. I'll tell you that. It's like another internet forum, but has a more nefarious reputation than, say, Reddit.

• 3:19Ben Brock Johnson?

  It might be a dark corner of the web, but it's not really, it's, it's the, you know, it's the clear internet as far as we know. It's, 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?

• 3:39Amory Sivertson?

  I want to be the very best that no one ever was. Dun, dun, dun.

• 3:52Ben Brock Johnson?

  Okay, okay.

• 3:53Amory Sivertson?

  That's the exclamation. I watched, I watched some Pokemon back in the day.

• 3:59Ben Brock Johnson?

  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 Suzumiya.

• 4:15Amory Sivertson?

  Nope. Can't say that I am.

• 4:17Ben Brock Johnson?

  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. Kaleidoscope would be an example. Shows in which there's nonlinear narrative at play. And what I mean by that, Amory, is in the case of The Melancholy of Haruhi Suzumiya, there are 14 episodes, but you can watch them in any order that you want to. You can watch episode one, and then six, and then two, and then 14, and then et cetera, et cetera.

• 4:51Amory Sivertson?

  Okay.

• 4:51Ben Brock Johnson?

  Does that make sense?

• 4:52Amory Sivertson?

  Yeah.

• 4:53Ben Brock Johnson?

  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? 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.

• 5:36Amory Sivertson?

  Yeah.

• 5:36Ben Brock Johnson?

  Does that make sense?

• 5:37Amory Sivertson?

  Yeah. So you'd go like 1, 2, 3, 4, 5, 6, up to 14, and then you'd go 1, 3, 4, 5, 6, blah, blah, blah. And then, yeah, I can't even imagine.

• 5:47Ben Brock Johnson?

  Exactly.

• 5:47Amory Sivertson?

  Yeah, yeah.

• 5:48Ben Brock Johnson?

  But for instance, you know, every end, every last episode you watched, whether it was 14, or six, or one, or two, et cetera, et cetera, that could actually be, that could serve as the beginning of the next permutation.

• 6:03Amory Sivertson?

  Yeah. I mean, the last two could also serve as the beginning of the next permutation.

• 6:08Ben Brock Johnson?

  Exactly.

• 6:08Amory Sivertson?

  Or three, or four. Oh, this is, this is a mess.

• 6:11Ben Brock Johnson?

  So it becomes this, like, very complex math problem, actually, if you wanted to, say, watch every, 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.

• 6:28Amory Sivertson?

  This is horrible. Why would you do this?

• 6:34Ben Brock Johnson?

  It's a great question.

• 6:35Amory Sivertson?

  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.

• 6:46Ben Brock Johnson?

  We're talking, we're talking about 4chan users. Touch grass is not going to work, Amory. You're going to have to.

• 6:51Amory Sivertson?

  You said it's 14 episodes?

• 6:54Ben Brock Johnson?

  It's 14 episodes.

• 6:55Amory Sivertson?

  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.

• 7:09Ben Brock Johnson?

  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 million, 313,611, while the upper bound is 93 billion, 924 million, 230,411. 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.

• 7:44Amory Sivertson?

  We don't have that kind of time. We must choose a new activity.

• 7:52Ben Brock Johnson?

  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 4chan user who, maybe on purpose, maybe not, this thing tends to happen on the internet, got into an argument with another 4chan user, shocker, about the most optimal way to binge-watch anime, specifically the anime The Melancholy of Haruhi Suzumiya.

• 8:27Ben Brock Johnson?

  I'm going to read you what was described on the message board, okay?

• 8:32Ben Brock Johnson?

  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?

• 9:09Amory Sivertson?

  A lower bound on the length of the shortest super pattern.

• 9:14Ben Brock Johnson?

  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

• 9:26Amory Sivertson?

  Importance.

• 9:28Ben Brock Johnson?

  Exactly. So do you want to read the list of authors to this paper?

• 9:35Amory Sivertson?

  First up, anonymous 4chan poster. Robin Houston, Jay Pantone, and Vince Vatter.

• 9:44Ben Brock Johnson?

  Can you say what the date of the paper is?

• 9:46Amory Sivertson?

  October 25th, 2018.

• 9:49Ben Brock Johnson?

  And just keep reading a little bit if, if you would.

• 9:53Amory Sivertson?

  This proof is inspired by that posted anonymously at

• 9:57Ben Brock Johnson?

  Et cetera.

• 9:58Amory Sivertson?

  Et cetera, which itself was taken from a 4chan discussion archived at

• 10:03Ben Brock Johnson?

  Et cetera.

• 10:05Amory Sivertson?

  Wow.

• 10:06Ben Brock Johnson?

  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 4chan 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, uh, and there you have it, folks. What do you think?

• 10:41Amory Sivertson?

  Well, even though I would never use this solution personally to attempt to try to figure out the different, um, all the orders, the super patterns of, of say, episodes of a series. This does seem applicable to other things in life, right? Like if you're trying to

• 11:04Ben Brock Johnson?

  Yeah.

• 11:04Amory Sivertson?

  Try all of the peanut butter and insert condiment of your choice sandwich that there is in the world.

• 11:13Ben Brock Johnson?

  Every possible banana dog.

• 11:15Amory Sivertson?

  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. Um, yeah, I mean, there are, there are other practical applications is what I'm saying of like trying to crack the super pattern.

• 11:34Ben Brock Johnson?

  Yeah.

• 11:34Amory Sivertson?

  Dilemma, right?

• 11:35Ben Brock Johnson?

  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?

• 11:44Amory Sivertson?

  Yeah. So what's the most optimal way to binge watch anime? People just, they just want to keep it grounded in.

• 11:56Ben Brock Johnson?

  Redditors focusing on the important questions, as always.

• 12:00Amory Sivertson?

  That's right. Oh, man.

• 12:09Ben Brock Johnson?

  What could the Haruhi problem solve for you? That's coming up right after we solve the math problem of sponsorship for podcasts.

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• 14:17Ben Brock Johnson?

  Is there any practical application that you would like this applied to, Amory?

• 14:21Amory Sivertson?

  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, 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, I can't think of like something where I would meaningfully want to check every box because it might take me four million years or something, you know?

• 14:55Ben Brock Johnson?

  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. Uh, solving disease, for instance, um, or something else that is scientifically really challenging because math. However, my head first goes not to solving, uh, disease necessarily, but to recipes.

• 15:30Amory Sivertson?

  Hmm.

• 15:31Ben Brock Johnson?

  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 gonna, I'm not gonna 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.

• 15:55Amory Sivertson?

  Hmm. And can I say one more thing?

• 15:58Ben Brock Johnson?

  Yeah.

• 15:59Amory Sivertson?

  Which is, um, 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, my first, uh, attitude about this was like, why do you need to know that? Just go outside, you know?

• 16:42Amory Sivertson?

  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, the mental exercise of trying to solve things and, and are better for the, the hunger and the human desire that it takes to, to want to solve things like that, even if the, um, the, the proposed application

• 17:23Amory Sivertson?

  of it is not, is not that rewarding on its face to most people.

• 17:29Ben Brock Johnson?

  Let us know, folks, if you have an optimal way to consume a nonlinear narrative, including every episode of Endless Thread. We are interested in finding out more and, uh, yeah, thanks for listening, Amory.

• 17:49Amory Sivertson?

  Of course.

• 17:50Ben Brock Johnson?

  By the way, producer extraordinaire Franny Monahan, uh, 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 se sol. So we'll put a link to that in the show notes. That's all, folks. See you next week.

• 18:28Amory Sivertson?

  Endless Thread is a production of WBUR in Boston. This episode was produced by Ben Brock Johnson and Franny Monahan and co-hosted by me, Amory Sivertson.

• 18:36Ben Brock Johnson?

  And me, Ben Brock Johnson. Mix and sound design by Emily Jankowski.

• 18:41Amory Sivertson?

  The rest of our team is Grace Tatter, Dean Russell, production manager Paul Vikes, and our senior managing producer, Suma Tijoshi.

• 18:47Ben Brock Johnson?

  Endless Thread 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.

• 18:58Amory Sivertson?

  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 WBUR.org.

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