#I just know that he has the lowest IQ of all the special characters

[sincerely-sofie]

Does anyone know what level Grovyle’s IQ is in PMD2? I need to know. For reasons.

[todonintendos]

The Genius Behind The Genius

It’s been already eight years since Pokémon Black and White were released for the Nintendo DS. Time sure flies. I think we can all agree that it seems like yesterday. This just comes to prove how big the mark these games have left is, not to mention the amazing sequels we got to play. One of the many reasons why it’s hard to forget these games is their story. In fact, it took over a year to write, and seeing the result, it was definitely worth the time spent.

But what makes up a good story? A decent amount of plot twists and an interesting theme to talk about are good answers, but this time we’ll be focusing in characters. There’s no good story without characters, and turns out Pokémon Black and White has plenty of them. Cheren, Ghetsis, Bianca, Iris, Juniper... the list feels endless. Each of them have their own unique origins, story and behavior... and then there’s N.

N is an anti-villain, since he’s the king of the villainous Team Plasma, but sees Pokémon as his friends and acts nicely towards the player.

When N was very young, he was abandoned in the woods, where he was raised by the Pokémon living there. One day, Ghetsis began taking care of him, claiming to be his father. Actually, it’s still a mystery who N parents are, to the point where Junichi Masuda, the current director of the Pokémon games, even suggested he could have been born from Pokémon. When the player meets N for the first time, N is already over eighteen years old. My guess is that he’s 19, but I’ll go deeper into that theory later.

Despite not having received proper education, his IQ is stated to be extremely high. His mind exceeds any other human mind from the Pokémon world. Junichi Masuda revealed that he can look into people’s past and future. But his most recognized talent is probably his skill with mathematics. He’s a mathematical genius. It’s said that he sees everything in a black and white fashion, and uses mathematical formulas as a way to make sense of it, since being raised by Pokémon prevented him from having our generic vision of the world. This is the exact same reason why he proves to have a closer relationship with Pokémon than humans.

Being a mastermind who was raised by Pokémon, N considers himself a personification of perfection.

Little more needs to be known about N to realize how distinct of a character he is. Nonetheless, N is still a fictional character, and as with any other work of fiction, there’s a real human mind behind it. The creator of the creation and, for N’s case, the genius behind the genius.

That person is, as you may have guessed already, Junichi Masuda himself. The director and lead composer of Pokémon Black and White and their respective sequels. It’s evident that a good character is never born out of nowhere. There’s always a source of inspiration behind it, and maths were definitely the strongest influence around his creation. At plain sight, the references may not seem obvious. But the same way N has a completely different point of view of what we see, we also need to change our perception of N to see them and figure them out.

Junichi Masuda next to Shigeru Ohmori, game designers and directors of many Pokémon games. Both worked on Black and White together.

By simply looking at N’s official artwork from Black and White, the only thing that’s worth talking about is the cube hanging from his belt. Since it doesn’t have any colors other than a dark shade of yellow, it can’t be a Void Cube, a variant of the well-known Rubik’s Cube with a hole in the middle of every face. Instead, we could be talking about the second iteration of a Menger Sponge, but try to remember what I just mentioned about Void Cubes.

Understanding what a Menger Sponge is can be relatively easy. It gets more complex when we try to approach it from a mathematical point of view. First, think of a big cube of infinite dimensions, which turns out to be the first step of the Menger Sequence. Now, split that big cube into 27 smaller cubes of the same dimensions, and remove the cube that’s in the middle of every face and in the very center of the cube. The shape that the 20 remaining cubes form should remind you of the Void Cube I mentioned earlier, and the cube hanging from N’s belt, of course. Now follow the same steps for those 20 cubes, and repeat the process infinitely. 

The result is a cube with infinite surface, but zero volume, as it will have an infinite amount of holes. Two different and equally valid points of view for the same concept.

One does not realize how the cube will eventually end up having infinite holes until it’s looked from a mathematical point of view.

The truth is, this cube doesn’t take any major, or even minor role in the story of the games, but early concept artworks and notes suggest that it was initially going to be relevant to the plot of the game. However, if N still wears it in the final games, there has to be a reason for that, and it’s probably because of the fact that no-one will find anything interesting in that cube unless it’s seen from a mathematical point of view, or N’s default point of view.

Moving away from his appearance, one of the things that gets the attention of most people is how he’s named after a single letter: the letter N, which happens to be the letter that’s used to represent the set of all natural numbers, which are all numbers without any decimals starting from zero (zero is not part of that set). In fact, this isn’t just a coincidence, as Junichi Masuda has revealed that N stands for Natural Number. However, if you’ve played through Black and White, you should know that N isn’t his actual name. His full name in every language is Natural Harmonia Gropius. And yes, there’s a mathematical context behind it. Actually, not all of the context has to do with math.

The natural set (N) is the most basic mathematical set, and is contained inside all of the bigger sets (real numbers, rational numbers...)

The first part of his full name, Natural, should be already figured out, and there isn’t much more to explain. However, the next part, his surname Harmonia, can be a little bit harder to understand, so let’s focus first on the last name, Gropius, since it’s not confirmed to have a specific origin. Gropius is a rather popular last name in Germany, and is often associated with Walter Gropius, pioneer of modernistic architecture during the XXth century. This could reference the fact that N wants to build a world where Pokémon and humans can live together in... well, harmony. Though it’s debatable whether this is true or not.

Regarding Harmonia, at first glance, it may seem like it refers to the musical term harmony: combinations of chords that create a pleasant melody. While that point of view is correct, the mathematical point of view we’re focusing on leads us to harmonic functions. I won’t go into detail on what they are because it requires a rather wide knowledge on maths to understand. In fact, we don’t really have to, as this only will help us realize there has to be a relation between music and maths somewhere in N’s development history, and by analyzing the well-known N Battle Theme, we’ll find out how math also influenced this tune.

Harmonic functions are those who have a first and a second derivative that always satisfy Laplace’s equation (df^2/dx(n)^2=0)

The genius we’ve been talking about all this time, Junichi Masuda, was in charge of composing this very specific theme, and states in a post from his personal blog that he was influenced by prime numbers to compose it. But why prime numbers? Masuda defends this idea by considering N as the “one” genius, and implying that prime numbers are the ones who get closer to being as unique as number one, due to the fact that they only have two divisors.

I’ve tried finding a music sheet of N’s Battle Theme so following the song becomes easier, however, I found nothing, which surprises me considering it’s a very popular theme. However, since all of this info comes from Junichi Masuda himself, we can definitely trust on it. As a replacement, here’s a video with the song so you can try to follow along, specially if you’ve got a good musical ear.

Right at the first part of the song, you can hear several combinations of eight ascending notes. Imagine the lowest note of the eight, which is always the first one of each set, is note #1, and that the number associated to every note increases by one whenever the key of the note also increases by one position. Do this in all of the sets, and you should get the following number combination: (1, 2, 3, 5, 7, 11, 13, 17, 19), which happens to be number one followed by the first seven prime numbers... with seven itself also being a prime number. Also, note that following the definition of prime number, 1 is NOT one of them.

After this intro, several sequences of three notes, with the last note playing for way longer than the other two, can be heard. The fact that it’s three notes isn’t a coincidence since three is a prime number. In music terms, a bar is the segment of time that corresponds to a specific amount of beats stated at the beginning of the music sheet, which is usually four, and the longest note of the three extends for five bars... with five also being a prime number. But this doesn’t end here. This whole theme extends for 83 bars before it begins to loop... and guess what? 83 is also a prime number!

All prime numbers from 1 to 100 appear green on this chart. 1 isn’t a prime number.

We can also find some relations between N and prime numbers on the character itself and not just on his battle theme. For example, in the game, he’s said to be 5′ 11′’ tall. At this point I don’t think I should remind that 5 and 11 are prime numbers, but I’ll do just in case. His trainer ID number in Pokémon Black and White is 00002 (two is the only even prime number). And he’s also the only trainer in Generation V that uses all 17 types of Pokémon at least once during the game. And yes, 17 is also a prime number. Though this info I just mentioned isn’t confirmed, and could be just a coincidence.

Also, there’s much more in N’s Battle Theme other than all of the influence from prime numbers. The clocks ticking in the middle of the song, the sudden bursts of energy... all of these elements aren’t random, and Junichi Masuda explains all of them on his personal blog, so definitely check it out if you’re interested in knowing more about it! https://www.gamefreak.co.jp/blog/dir_english/?m=201110

...and you reached the end of the article!

As you saw, the creativity put into the creation of N is simply insane. People often tend to ignore the development stories of their favourite characters no matter how much they love them, but if you attempt to do a small research to find out, you may end up finding something as surprising as this. Authors and developers care about their characters, to the point where they end up putting all of this effort to make it stand out. Thanks for reading!

~TodoNintendoS, as part of Daily Nintendo Fact #100