Tag Archives: Anime

Time travel Anime inspires solution to puzzling math problem

Sometimes, the internet is extremely weird and beautiful at the same time — and this is a perfect example.

The problem

Formally, the math problem can be expressed thusly:

“What is the shortest string containing all permutations of a set of n elements?”

In a more “common language”, the problem sounds something like this:

“Say you want to watch a series with n episodes. You want to watch all the episodes in every combination possible. Overlapping is allowed, but the sequence must be continuous. For instance:

  • for a series with 2 episodes, 1-2-1 is a solution, because it contains both possible combinations (1-2 and 2-1);
  • for a series with 3 episodes, 1-2-1-3 is NOT a solution, because it does not contain the sequence 1-2-3. The solution is 1-2-3-1-2-1-3-2-1, as it contains all possible sequences (1-2-3, 1-3-2, 2-3-1, 2-1-3, 3-1-2, 3-2-1).

What is the least number of episodes you have to watch?

Anime maths

The problem is surprisingly complex and has remained as a rather obscure mathematical puzzle since 1993, when a demonstration was attempted and subsequently proven incomplete. Recently, Robin Houston, a mathematician and computer scientist, tweeted about finding what seems like a solution to this problem, in the unlikeliest of places: a board on an anime — Haruhi, a 2006 anime based on a series of Japanese light novels.

The reason why Haruhi became linked to this problem is also unusual. The series contains a lot of time travel and is overall very difficult to follow, as the chronology becomes very confusing. To make matters even funkier, when the series went to DVD, the episodes were rearranged, making viewers feel like they were watching a different chronology. Essentially, you can watch episodes in a number of different orders, which has become something of an obsession among fans.

Scientifically, the situation is extremely unusual. The solution seems to work, Houston points out, but mathematicians seem reluctant to address it formally since it’s not presented in a journal. But things get even more interesting.

Houston did a bit of digging and found that the proof was first submitted to 4chan — one of the darker corners of the internet, where threads are only kept for a limited time, though Houston was able to find a permanent mirror. Furthermore, 4chan is entirely anonymous, meaning we don’t know who submitted it, and it’s nigh impossible to verify the author’s identity.

So this anonymous proof posted on 4chan and reposted to an anime board is currently the most elegant solution to the problem. Another mathematician, Jay Pantone, transcribed the proposed solution into a formal layout — and he says it stands up.


So what is the solution? Well, for Haruhi’s 14 episodes, you’d need to watch at least 93,884,313,611 episodes to be sure you’ve watched all possible combinations. At most, you’d need to watch 93,924,230,411 episodes. Now, mathematicians are working on a more formal version of a formula. The explanation is quite long and difficult to follow, but you can read:

Fantastically Real: Amazing Anime-Inspired Technology

What is it about anime that makes an otaku out of a person?  An otaku – someone obsessed with a hobby or interest like anime – stays locked up in his room, shuts off from the rest of the world, and watches hundreds of episodes of his favorite Japanese cartoons.  Anime, unlike your usual cartoon, is actually not just for kids. Most of the anime today are inspired by Japanese comics (manga), which are read by both children and adults. While many of them are hilarious and suitable for a young audience, a lot of them also deal with introspective themes that you wouldn’t expect to find in the average Spongebob episode.  You can always expect Disney to fill you with rainbows, butterflies, romantic songs, and dance numbers.  Anime, on the other hand, you can expect to reside in a much wider landscape. Sure, there are lots of happy sunshine-y episodes to last you ‘til the golden years.  But there are also the growing pains of adolescence, the coming of the apocalypse, and the hilarious and often confusing postmodern world to think about. Love, sex, blood, gore, and the future are subjects anime creators aren’t afraid to tackle, and the fans consume them like a never ending absurd, comical, amazing, and/or mindblogging feast.

Given this, it’s understandable why anime is so addicting and why many otaku’s worlds are increasingly becoming a merge of fantasy and reality. But who is to say that what is fantastic cannot be real at some point?  In the world of an otaku, what exists in anime can also exist in the real world.  Here are some examples of technology that placed anime in the realm of the real:

Protein-based memory storage

Reserachers from Nara Institute of Science and Technology have developed ultrathin memory storage using ferritin, a protein that facilitates iron storage in almost all living organisms.  Ferritin has a hollow spherical structure that can be used for storing iron in a non-toxic form. By irradiation of ferritin-covered substrate with UV light, protein is removed, leaving behind metal deposits that could be used for making memory chips that are less than 1 micron in thickness.  These new protein-based microchips could be used on computers built on ultrathin films that can be integrated into clothing or eyeglasses.  If you’re a Detective Conan fan, then this awesome project should sound familiar to you.  In fact, the researchers were all inspired by the said anime and manga series when developing the memory storage., “Conan’s eyeglasses are no longer a dream,” says team leader Yukihiru Uraoka. Conan Edogawa’s computerized eyeglasses in the manga had a telescopic, night-vision feature on the right lens and criminal tracking feature on the left lens.  In one of the Detective Conan movies, modifications by Professor Agasa on the glasses gave it a bullet-proof feature and a miniature hidden microphone.

Akira Bike

Anime fans should at least be cognizant of the iconic 1988 cyberpunk action anime film Akira, which was directed by popular manga creator Katsuhiro Otomo.  Set in 2019 Neo-Tokyo, the film and manga portray a dystopian future with thuggish characters, bike gangs, and violent gun fights. The breath-taking motorcycle chases have spawned several customized Akira bikes; however, the only one that was officially recognized by Otomo is a replica of Shotaro Kaneda’s bike built by Masashi Teshima for charity. According to Kotaku Japan, which had the honor of having the first hands-on experience with the bike, the Akira bike felt heavy and sturdy and was surprisingly huge. It costs USD121, 000 and took seven years in the making. Masashi rode the bike to raise funds for children with autism. Afterwards, the bike was taken to its last stop in Tokyo where it is now on display to raise funds for victims of the 2011 tsunami and earthquake that hit Japan.


Anyone who’s ever watched Gundam, Voltes V, Mazinger Z, Transformers, and Voltron growing up would have dreams of becoming a robot pilot. Suidobashi Heavy Industry played heavily on this childhood dream when it created the massive Kuratas – a 13 foot wearable robot that puts its wearer inside its bombproof chest and transforms him into a real-life action figure robot.  Inspired by the anime series Armored Trooper VOTOMS, the 12,000 pound mecha robot took three years to code and forge. It can be controlled via 3G network or master controls inside the cockpit.  If you’re a business man by day and an anime fan by night, you wouldn’t need to worry, because you can take business phone calls via RingCentral even while inside this vehicle. It moves at a speed of 10 kilometers per hour, runs on a diesel engine, and sells for about USD 1.3 million. However, if you want it fully decked with eco-friendly weapons like the LOHAS launcher and twin BB gatling gun, the massive piece of metal costs a whopping USD 1.5 million plus. The downsides of this vehicle are you’d have to settle for wheels instead of feet, the LOHAS launcher is not exactly 100% accurate in the shooting range, and you’d have to release bullets from the gatling gun by smiling (yeah, you read that right). Still, the chance to traipse around town as a 4-ton VOTOMS trooper is just too cool to pass up if you have the moolah for it. What else can we say but “Move over Iron Man!”

The next time someone tells you to stop watching anime, just stare or give yourself a secret smile. They wouldn’t understand that in reality, you’re already creating the next big thing in computer technology or a fully-operable Iron Giant in your fantasies anyway.