When 4chan helped the mathematicians



Mathematics overwhelms us. Some people feel palpitations in the presence of a square root alone, and not precisely because of a crush. This is such a widespread phenomenon that there are even specialized psychologists in their study. Anxiety to mathematics, this is what they call it. The surprising thing is that it is not a true hatred of mathematics, but what seems mathematical.

Without going any further, think about those posts viral social networks where with drawings of different types of fruit they ask you to calculate how much each one is worth based on a series of operations. People love it and do not hesitate to face them, but under that infographic appearance what is found is a system of equations with three or four unknowns.

It seems contradictory, but all this tells us about how much mathematics has been stigmatized, when in reality we should see it as one of the most interesting, entertaining and exciting activities with which to challenge our brain. Because deep down, we can all do math, and that's what this story is about. The anonymous forero who solved a problem that had been open for more than 25 years.

Haruhi Suzumiya

Haruhi began as the typical light novel of Japanese teenagers who, suddenly, absolutely crazy things happen to them. In this case, the premise was time travel, and as every screenwriter knows, that was a double-edged sword. On the one hand, time travel likes the public and allows the creation of narrative threads away from what we are used to. On the other hand, it is very easy to get lost in confusing loops that turn the work into gibberish, or worse, an inconsistency from end to end.

However, Haruhi triumphed and adapted to new formats giving life to an anime. The chapters jumped from front to back, fleeing from the boring linearity. The fans were even more hooked than with the book, but what really ended up reinforcing the community was the challenge suggested by the first DVD compilation of the work. In it the chapters had been reordered, but nevertheless they maintained a meaning. The followers were so excited that they even began to meet in a "religion," Haruhism. The viral challenge was sung, because if they could reorder once and feel that one was watching the series for the first time, how many times did each of the 14 episodes have to watch to cover all possible orders?

In this attempt to make the series immortal, a user of the well-known 4chan forum published the blissful question and the thread was filled with answers. Some more sensible, others completely lysergic. Although, of course, there was a special one, the answer that brings us here, the answer that helped solve a complex mathematical problem. Let's talk about superpermutations.

Supermuting

A permutation consists in reordering a set of numbers or symbols. For example: 132 is a permutation of 123, just like 213 or 321. So how many permutations exist for a set of three digits? Or put another way: how many different ways can we order 213? We can express them by hand and we will find that they will be equivalent to the factorial of the number of elements of the set (in this case 3x2x1) The problem is when we take another twist and talk about superpermutations.

In this case, what we have to find is the sequence of numbers where we will consecutively find all the possible permutations of our set. Of course, this is easy to do, we just have to paste all possible permutations one after the other. But things get complicated if they ask us to find the shortest superpermutation of a set. In the case of 123, it is 123121321, much less than the 18 figures we need to concatenate the 6 possible permutations of 123. The negative part is that we don't know how to find them automatically. A few mathematicians had tried and there was even a publication that he thought had solved it, but it turned out not to be generalizable to sets of more than five elements.

And this is the place where both paths intersect, because if we want to see the 14 episodes in all possible ways we will find that there are 87,178,291,200 combinations. Eighty-seven billion sets of 14 episodes about 55 million years ago, if we had begun to see them with the great extinction of the Cretaceous, which ended most of the dinosaurs, we would barely have 10 million years left to visualize everything. It is clearly not practical, but what if we could order them in a minimal superpermutation?

Recovering the thread

That is what was being raised in the thread, a matter of time economy finding the shortest superpermutation to scratch a few minutes before going to sleep. And that's where the math came in, one of the answers stood out. In ordinary language and without mathematical devices, an anonymous user seemed to have found not only the answer, but the demonstration of why he was right. It was necessary that a mathematician came to the thread to appreciate what that anonymous had done and dressed it up, translating it into the precise language of mathematicians. His name was Greg Egan and he was not the last professional to notice that publication.

Some time had to pass, since our anonymous friend answered this in 2011, but by chance, the thread ended up in the hands of a group of mathematicians who found in him what they needed to generalize a formula that answered the great question of the least superpermutation for any number. Now, fans could breathe easy, because of 55 million years, superpermutation had managed to lower the figure to only 4.3 million years. A number thirteen times less, but unfortunately a task still quite impracticable, of those that break your afternoon. The contribution of the anonymous 4chan user was so crucial that he appears as the first author of the publication.

The power of the amateur

There are other stories like these. People without great mathematical knowledge who face camouflaged problems, great enigmas whose difficulty they do not know and who, precisely because of this and because of their lack of training, face a touch of fresh naivety that almost no one had tried until then. Because to solve many mathematical problems it is not necessary to know how to make your thinking sound “mathematical”, you do not need to know great tools or tricks, you just have to think and be creative. Some guesses are deceptively easy and no matter who tries to prove them, the chances of getting it are almost nil (like Goldbach or Collatz) However, some of the most difficult ones seem to only need a change of approach within the reach of an amateur.

Although of course, if that is what we want, the most important thing will be to reach as many people as possible and for that we must go unnoticed, that antimatematic radars do not detect the presence of an inequality or a percentage. Unfortunately we have to hide them to make them friendlier, as if we were hiding a dog's pill in a juicy sausage that talks about fruits. What other big problems will fans solve? Or more importantly, what excuse will convince them this time to take pencil and paper and math?

DON'T KEEP IT UP:

  • The anonymous user did not solve the problem by himself, but he sowed the seed that, with the formalization of Greg Egan and the generalization of Robin Houston, Jay Pantone and Vince Vatter would lead us to the solution.

BIBLIOGRAPHIC REFERENCES;

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