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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.
(Score: 2) by PartTimeZombie on Thursday November 08 2018, @07:29PM (2 children)
It's interesting they mentioned the Assymetrics. This ancient empire was well known for its advanced mathematics, inventing skipping maths class as early as the late bronze age.
They were conquered by the Egyptians, who figured out pi = exactly 3.0 which enabled them to ditch the chariot in favour of infantry.
(Score: 2) by FatPhil on Friday November 09 2018, @12:06AM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 1, Funny) by Anonymous Coward on Friday November 09 2018, @02:02AM
Funny thing about those Assymetrics that you forgot to mention: they developed their advanced math because of their obsession with measuring their donkeys (or so it was said; others said they were interested in more risque measurements). But you never know about those ancient rumors.
That's a common miscontraception. No, the Assymetrics were conquered by the Bah-baloneyians, who developed a special base 60 system for measuring cheap processed sausages. They were so obsessed with their 360-degree sausage angles and minutes and seconds that other peoples of the ancient world took to shouting "Bah! Baloney!" when they encountered them, hence their name.
The EE-gyp-shuns got fed up (no pun intended) with all this meat tube nonsense and conquered the Bah-baloneyians, but other people hated the EE-gyp-shuns and shunned them because they tended to screw people over in financial dealings, causing their customers to shout a squeaky "EE!" all the time in response.
Finally, though, real math and science came to the ancient world with the Geeks, who somehow managed to overcome the other empires, even though they learned philosophy and crafts at Playdough's Academy. That wasn't to last long, as the Roamin' people were on the rise, wandering around Europe and plopping down roads everywhere. The Roamin's roamed right into the Geek homeland, and before you know it, there was a whole Roamin' Empire led by some guy named "Seize-Her" (who must've had some Trump-like behavior around women).
Fast forward a few centuries, and the Roamin' Empire came to ruin as Barberarians invaded with their sexy new hairstyles (either that, or a weird fascination with bad sci-fi movies starring Jane Fonda in skimpy outfits). But some guy named Charlie who had a really big Hammer brought some order, and his grandson Shar-the-Main was eventually crowned Holy Roamin' Emperor after he wandered around conquering people again in Europe.
The Holy Roamin' Empire lasted for like a thousand years with its remnants moving about until finally it was ended with the Great War -- the War to End All Wars -- whose centennial ending we celebrate this weekend with Armin' This Day on November 11th, ironically the day people put down their arms for good.
Well, that was the plan, but some stupid Germans misunderstood and started armin' again. Hitler brought the New Math to bear as he ordered Himmler to undertake the Final Solution to Goebbels' Incompleteness Theorem, which must've had something to do with advanced topology or knot theory, given that they called themselves Knot-zies.
The Knot-zies almost took over the world, but were only stopped when Richard Feynman and Davy Crockett teamed up at the Alamo Laboratories (Remember the Alamo?) to combat Santa, Anna, Rudolph the Red-Nosed Reindeer, Rudolph Hess, and the whole Knot-zie establishment with cool math that made nukular weapons possible.
Unfortunately the fallout from this math war followed Newton's Law of Cooling to make a Cold War, where humanity could be annihilated, or at least blown back to the Stone Age, where we'd have have to start over with those metrics of asses all again.
At least, that's my understanding of the situation.