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posted by mrpg on Thursday November 08 2018, @03:15PM   Printer-friendly
from the p! dept.

Mystery Math Whiz and Novelist Advance Permutation Problem

A new proof from the Australian science fiction writer Greg Egan and a 2011 proof anonymously posted online are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

On September 16, 2011, an anime fan posted a math question to the online bulletin board 4chan about the cult classic television series The Melancholy of Haruhi Suzumiya. Season one of the show, which involves time travel, had originally aired in nonchronological order, and a re-broadcast and a DVD version had each further rearranged the episodes. Fans were arguing online about the best order to watch the episodes, and the 4chan poster wondered: If viewers wanted to see the series in every possible order, what is the shortest list of episodes they'd have to watch?

In less than an hour, an anonymous person offered an answer — not a complete solution, but a lower bound on the number of episodes required. The argument, which covered series with any number of episodes, showed that for the 14-episode first season of Haruhi, viewers would have to watch at least 93,884,313,611 episodes to see all possible orderings. "Please look over [the proof] for any loopholes I might have missed," the anonymous poster wrote.

The proof slipped under the radar of the mathematics community for seven years — apparently only one professional mathematician spotted it at the time, and he didn't check it carefully. But in a plot twist last month, the Australian science fiction novelist Greg Egan proved a new upper bound on the number of episodes required. Egan's discovery renewed interest in the problem and drew attention to the lower bound posted anonymously in 2011. Both proofs are now being hailed as significant advances on a puzzle mathematicians have been studying for at least 25 years.

Mathematicians quickly verified Egan's upper bound, which, like the lower bound, applies to series of any length. Then Robin Houston, a mathematician at the data visualization firm Kiln, and Jay Pantone of Marquette University in Milwaukee independently verified the work of the anonymous 4chan poster. "It took a lot of work to try to figure out whether or not it was correct," Pantone said, since the key ideas hadn't been expressed particularly clearly.

Now, Houston and Pantone, joined by Vince Vatter of the University of Florida in Gainesville, have written up the formal argument. In their paper, they list the first author as "Anonymous 4chan Poster."

"It's a weird situation that this very elegant proof of something that wasn't previously known was posted in such an unlikely place," Houston said.

[...] If a television series has just three episodes, there are six possible orders in which to view them: 123, 132, 213, 231, 312 and 321. You could string these six sequences together to give a list of 18 episodes that includes every ordering, but there's a much more efficient way to do it: 123121321. A sequence like this one that contains every possible rearrangement (or permutation) of a collection of n symbols is called a "superpermutation."

The story then describes parallels with the "Asymmetric" (aka weighted) traveling salesman problem as well as the fortuitous connections which led researchers to work together in finding calculations of upper and lower bounds for an arbitrary number of episodes. You'll have to RTFA to learn how many episodes you'd need to watch to view them in all possible orders.


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  • (Score: 0, Informative) by Anonymous Coward on Thursday November 08 2018, @03:31PM (8 children)

    by Anonymous Coward on Thursday November 08 2018, @03:31PM (#759386)

    Because "a very intelligent, and/or a well educated person" is likely to be at a university and post such an answer in those channels to be recognized for it.

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  • (Score: 4, Informative) by Runaway1956 on Thursday November 08 2018, @03:39PM (1 child)

    by Runaway1956 (2926) Subscriber Badge on Thursday November 08 2018, @03:39PM (#759390) Journal

    You kinda sorta missed the point. Not all intelligent and/or educated people go to university. And, even if this particular Anon were at university, he apparently didn't think the puzzle worthy of attention. It was just too damned SIMPLE to bother real mathematicians with.

    • (Score: 3, Insightful) by bzipitidoo on Thursday November 08 2018, @04:56PM

      by bzipitidoo (4388) on Thursday November 08 2018, @04:56PM (#759420) Journal

      You aren't seeing it either. You evidently like a particular narrative, that not all smart people go to college, so much that you are going way out on a limb to speculate that's the case here.

      Perhaps you don't appreciate how many barriers there are even after you manage to earn a bachelors. It never ends. Get a masters degree, and people will still wonder if you're worth listening to, because you don't have a doctorate. Get the doctorate, and you still have to deal with rampant skepticism, got to keep publishing. Are you a lightweight? Did you fail to see that some problem you worked hard on is in fact trivially easy?

      Often, you have to sell others on the difficulty of a problem. There are many problems with solutions that are easy to follow, but which were very hard to figure out the first time. That sort of problem is all too likely to be seen as not particularly important or hard, because it just looks too easy. It's almost a reflex to think that if the solution is easy to follow, then the problem can't have been hard.

  • (Score: 2) by tibman on Thursday November 08 2018, @04:41PM (3 children)

    by tibman (134) Subscriber Badge on Thursday November 08 2018, @04:41PM (#759413)

    What are those "very intelligent, and/or a well educated" people doing after they have moved on from university/college?

    --
    SN won't survive on lurkers alone. Write comments.
    • (Score: 1, Informative) by Anonymous Coward on Thursday November 08 2018, @06:27PM (2 children)

      by Anonymous Coward on Thursday November 08 2018, @06:27PM (#759463)

      What are those "very intelligent, and/or a well educated" people doing after they have moved on from university/college?

      In Trump's America? Getting as far away from the United States as possible.

      Next question?

      • (Score: 0) by Anonymous Coward on Friday November 09 2018, @12:26AM

        by Anonymous Coward on Friday November 09 2018, @12:26AM (#759620)

        In Trump's America? Getting as far away from the United States as possible.

        Oooooo how edgy! Please tell me more!

        How about I quote what someone told me in December 2008 "get over your butthurt self and get over it"

      • (Score: 2) by tibman on Friday November 09 2018, @12:48AM

        by tibman (134) Subscriber Badge on Friday November 09 2018, @12:48AM (#759627)

        Doubt it. Don't educated people know that the US President's term has limits? as in, you don't have to abandon your country because the current leader is literally temporary.

        --
        SN won't survive on lurkers alone. Write comments.
  • (Score: 4, Interesting) by Sulla on Thursday November 08 2018, @05:26PM

    by Sulla (5173) on Thursday November 08 2018, @05:26PM (#759434) Journal

    Not everyone wants to be recognized. A theme that runs through the various boards of 4chan is that the most insightful and important work is kept anonymous because it adds value to the work. People often come on and post "I'm a woman and this is what I think" or "I'm a parent and this is what I think" and the response is "why would who you are make your idea more valid". This post was particularly valid because it was posted on the merit of the idea alone, without any group or personal affiliation to try and elevate (or denigrate) it.

    --
    Ceterum censeo Sinae esse delendam
  • (Score: 2) by fyngyrz on Thursday November 08 2018, @08:23PM

    by fyngyrz (6567) on Thursday November 08 2018, @08:23PM (#759524) Journal

    Because "a very intelligent, and/or a well educated person" is likely to be at a university

    That's extremely short-sighted. Or IOW, no.

    First of all, most of those very smart students of institutes of higher education go on from those places into, you know, jobs. Jobs other than "professor at institute of higher education", a job category that cannot possibly absorb more then a very small fraction the people it educates because, you know, math.

    Secondly, not every intelligent person goes on to formal higher education. Libraries and bookstores have been a thing for a while now (cough /ROLLEYES.) Now there's the web... and that has pretty much changed everything WRT access to knowledge, training, equipment, parts, communication and ultimate education level anyway.

    So yes, there are some very smart people in those institutions. No, a random encounter with a very smart person who is well educated is not most likely to be found there.