# THE MOST ANTICIPATED GAME IN HISTORY

A visual novel about disabled girls with origins from 4chan based on some extra pages in some doujin sounds like the most horrible thing and shouldn’t exist, but it exists and is actually not horrible at all. But everyone knew that already when the demo came out, what, three or four years ago? Everyone was waiting for it, but kind of like Starcraft II, I don’t think anyone expected it to get released within our lifetime.

So, the story goes the main character, Hisao, gets a heart attack and discovers he has a heart condition which leads to him being enrolled in a high school for students with disabilities. And then life becomes an adventure with choices.

Katawa Shoujo is a galge and seeing as how I played it right after I finished Little Busters, it was really hard not to compare it to Key’s brand of visual novels. I’d talked about Little Busters before and mentioned that it seemed more ridiculous than the usual Key stuff. Instead, Katawa Shoujo was able to get me to care about the characters more, simply because what they were going through was a real thing that could happen.

And because these were real things, the characters felt more like real people. A big reason why moe template characters don’t feel like real people is because the only flaw that they have is whatever otherworldly problem manifests soon after they meet you. Real and serious problems make the characters more believable and it seems like the writers really had to think about the implications of what each disability meant for the development each character.

For instance, one of the more interesting characters in Little Busters was Kud, whose problem was basically being half-Japanese and half-foreign and not knowing where she belonged. Of course, her Engrish was played up for the uguu factor occasionally, but her being unable to find belonging made her much more interesting than other uguu~s.

Realistic problems affect the characters. Some of them are born with them. They act differently than those who weren’t. Some of them overcompensate for what they don’t have. Some of them don’t care. In some ways, it’s not so much the disability affecting the character, but how the character’s personality is magnified by how they deal with it.

The characters have very strong and distinct personalities. Normally, the main character is a blank stand-in so that you can feel like that guy, but Hisao has just enough written about him that he’s his own character. At the same time, he’s still undefined enough that his personality changes depending on which girl’s route you’re on. A result of this is that in every route, he has really good chemistry with the heroine.

So since the individual routes matter and hit upon different things, let’s go through them.

Shizune’s route was the least enjoyable. I’ll admit that a large part of why I didn’t like Shizune’s route is because I didn’t like Shizune or Misha. They’re interesting when they’re together, but I didn’t like either of them because I don’t think I’d get along with them. I’m not really into the short hair or megane either. But most importantly, I thought most of the route was kind of boring, probably because the problem in this route was relationship drama.

Lilly’s route was enjoyable. Like Shizune, Lilly’s had her disability since birth, so she’s used to it by now and none of her problems really come out of that. And in fact, she’s a well-adjusted person who’s doing well, so she’s not having any problems on that front either. Most of the route is actually about Hisao dealing with his new life and how that affects his relationship with Lilly.

Emi’s route was one that I didn’t expect to like as much as I did. I don’t usually like the archetype that Emi’s character is drawn from, but I think her trolling with the nurse made her more likeable than just the energetic girl. She’s one of the characters who wasn’t born with her disability and has it play a role in the story (the other being Hanako). While the theme in both of their stories is kind of the same, their stories are different in the way they handle their situation. Emi is pretty conscious about her situation and does stuff about it, whether or not it’s actually helpful. Also, the nurse seemed eerily similar to Souma from Working!! (and by transitivity, Izaya from DRRR!!).

Rin’s route was the most surprising. In the other routes, Rin’s disconnectedness and resulting lines are pretty amusing, so I went into it kind of expecting some eccentricity and laughs. It turned out to be rather serious and not hilarious at all. It definitely colours her responses, even outside of her route. Like Lilly, her disability isn’t the root of any problems she’s facing. I can’t recall off the top of my head of any other visual novels where the protagonist and one of the heroines have such unpleasant development and struggle to understand each other.

Hanako is my favourite character, if not necessarily my favourite route. Out of all the characters, I think Hanako’s backstory and story are the most Key-like. She’s basically the shy, quiet girl with tragic past (so the opposite of Emi) and most of the route involves protagonist-kun breaking her out of her shell. Well, at least until the end, where the resolution to her route is not very Key-like at all. While the ending was good, it seemed kinda short. Or I don’t know, maybe I just wanted to see Hanako be happy some more.

Obviously, Katawa Shoujo isn’t about disabilities or disabled people or how disabled people are people just like us. I’d like to think that we don’t need a visual novel to teach us that. And, I mean, the central problems to the stories have very little to do with the characters’ disabilities. It’s all about Hisao learning to understand people, especially the girls he’s building relationships with. The caveat is that they, and most people, make that very hard to do.

# Suugaku Girl supplementary handout for chapter 2: Prime numbers

She doesn't seem that excited

So last time, Tetra was being enlightened by MC-kun about definitions. This actually arises from MC-kun using prime numbers as a motivating example.

Primes are megas important in mathematics and even more important today. The entire branch of mathematics called number theory is all about studying the properties of prime numbers. They’re so useful that we’ve done stuff like extend the notion of prime elements to algebraic structures called rings or apply analytic techniques to learn more about them, but we’ll stick with elementary number theory for now.

Now, for hundreds of years, we’d been studying number theory only because it’s cool and mathematicians love prime numbers. Last time, I mentioned some examples of math preceding useful applications. Well, number theory is a really good example of that, because in the 70s, we found a use for it, which is its main use today, in cryptography. There have been some new techniques using some algebra as well, but for the most part, modern cryptography relies on the hardness of factoring primes. Neat!

Okay, so we’re back to the original question that MC-kun tries to get Tetra to answer, which is, what is a prime number?

Definition. An integer $p$ is prime if and only if $p\geq 2$ and the only positive divisors of $p$ are 1 and itself.

MC-kun explains that the motivation for excluding 1 from the definition of a prime number is because we want to be able to say that we can write every number as a unique product of prime numbers. This is very useful, because now we know we can break down every number like this and we can tell them apart because they’re guaranteed to have a unique representation. This is called unique prime factorization.

Theorem. Let $a > 0$ be an integer. Then we can write $a = p_1p_2\cdots p_k$ for some primes $p_1,\dots,p_k$. This representation is unique up to changing the order of terms.

We can show this by induction on $a$. We’ve got $a=2$ so that’s pretty obvious. So let’s say that every integer $k\lt a$ can be decomposed like this and suppose we can’t decompose $a$ into prime numbers, assuming $a$ itself isn’t already a prime since it would just be its own prime decomposition. Then we can factor $a=cd$ for some integers $c$ and $d$. But both $c$ and $d$ are less than $a$, which means they can be written as a product of primes, so we just split them up into their primes and multiply them all together to get $a$. Tada.

As a sort of side note, I mentioned before that primes are so useful that we wanted to be able to extend the idea of prime elements into rings. Well, it turns out for certain rings, it isn’t necessarily true that numbers will always have a unique representation when decomposed into primes. This is something that comes up in algebraic number theory, which is named so because it involves algebraic structures and techniques. This was invented while we were trying to figure out if Fermat’s Last Theorem was actually true (which needed this and other fun mathematical inventions from the last century that implies that Fermat was full of shit when he said he had a proof).

So at the end of the chapter, after Tetra gets her chair kicked over by the megane math girl, we’re treated to a note that acts as a sort of coda to the chapter that mentions that there are infinitely many primes. How do we know this?

Suppose that there are only finitely many primes. Then we can just list all of the prime numbers, like on Wikipedia or something. So we’ve got our list of primes $p_1,p_2,\dots,p_k$. So let’s make a number like $N=1+p_1\cdots p_k$. Well, that number is just a regular old number, so we can break it down into its prime factors. We already know all the primes, so it has to be divisible by one of them, let’s say $p_i$.

Now we want to consider the greatest common divisor of the two numbers, which is just the largest number that divides both of them. We’ll denote this by $\gcd(a,b)$. So since $p_i$ is a factor of $N$, we’ve got $\gcd(N,p_i)=p_i$. But then that gives us $p_i=\gcd(N,p_i)=\gcd(p_i,1)=1$ by a lemma that says that for $a=qb+r$, we have $\gcd(a,b)=\gcd(b,r)$. This means that we have $p_i=1$, which is a contradiction, since 1 isn’t a prime number, and so I guess there are actually infinitely many primes.

So the nice thing is that we won’t run out of prime numbers anytime soon, which is very useful because as we get more and more computing power, we’ll have to increase the size of the keys we use in our cryptosystems. Luckily, because factoring is so hard, we don’t need to increase that size very much before we’re safe for a while. Or at least until we develop practical quantum computers.