Lupin III: The Woman Called Fujiko Mine 04 — Va, Tosca!

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「峰不二子という女」/「巖本英利」

So this week’s Lupin III/Fujiko show turned out to be Phantom of the Opera. Sure, operas are classy and this iteration of Lupin III is fairly classy, so why not? Well, it turns out the opera they used is one of the few that I had actually studied (to some degree) back in high school music. The opera is Tosca, by Giacomo Puccini, and is apparently near the top of the list of famous operas. That said, I think it’s safe to say that anime is near the bottom of the list of places I expected to hear an aria or something and make me go “Wait, this sounds awfully familiar”.

Tosca is about a famous singer, Floria Tosca, her lover, a painter by the name of Mario Cavaradossi, and Baron Scarpia, the chief of police and a guy who really, really wants Tosca. Basically, Tosca and Cavaradossi are in love. Cavaradossi also happens to be helping one of his Republican friends escape from the police. Conveniently, these two things make Scarpia hate Cavaradossi a lot. This causes a lot of trouble for the lovers. Spoilers: Tosca ends in tragedy.

There are two pieces that were used in this episode.

Tosca Divina

Part of this piece was performed on stage when the spotlight fell on Ayan. Just like in the episode, Scarpia arrives and is looking for Angelotti, the guy that Cavaradossi helped escape. Obviously, with the spotlight dropping on them, they had to improvise, but the first two lines that they sing kinda don’t make sense. After that, though, is pretty much what happens at the end of that scene.

The scene in context is basically Scarpia tricking Tosca into thinking that Cavaradossi is cheating on her with the lady he’s drawing in the painting. Tosca’s line about being a prisoner of royal celebrations (è prigioniera dei regali tripudi) is the end of a bit about her coming to the church to tell Cavaradossi that they wouldn’t be able to meet that night. Scarpia’s line after that, about his poison working (Già il veleno l’ha rosa!), doesn’t make sense without the context, because it’s about him thinking about how she’s buying into his bullshit about Cavaradossi cheating.

Basically, Tosca is pissed. She talks about how their beautiful nest is soiled with slime (Oh mio bel nido insozzato di fango!) and then basically says she’s going to kill that cheating bitch (so to speak) who isn’t going to have Cavaradossi tonight (Vi piomberò inattesa! Tu non l’avrai stasera, Giuro!). Scarpia goes “In church!” (In chiesa!) because they’re talking in a church and Tosca saying how she’s going to totally murder that lady is probably something she shouldn’t do in a church. That’s okay, replies Tosca, “Dio mi perdona”, or God will forgive her, presumably because the cheaters deserve it.

So Scarpia successfully gets Tosca pissed at Cavaradossi. After the singing from just above, Tosca goes off to find Cavaradossi and Scarpia gets a guy to trail her. This, of course, leads to all sorts of unfortunate things later on. For now, though, Scarpia gets to sing about how much he wants Tosca with the undertone being that he’s super evil and all this happens juxtaposed against a church procession and the act ends.

It’s not obvious in this part of the episode, but there are a few interesting parallels that we can extract from this if we maybe read too much into this. Obviously, Fujiko is Tosca and Zenigata is Scarpia. I’ve never seen much Lupin before, but here, Zenigata seems like a terrible person, what with molesting Fujiko and all. He really seems to despise Lupin, much like Scarpia hates Cavaradossi, and he uses Fujiko to try and get to him. And after this the analogy breaks down, but, oh well.

Vissi d’arte

This is probably the aria that Tosca’s known for. It plays on the record player in the hideout when Ayan is explaining the reveal to Fujiko. At this point, Scarpia has Cavaradossi taken away to prison after having revealed his Republican loyalties. He takes advantage of this situation and offers to free Cavaradossi if Tosca gives herself to him. As he waits for her answer, she starts singing this aria, which is basically her crying out to God asking why she has to go through this.

The opening line is “Vissi d’arte, vissi d’amore”, which is “I lived for art, I lived for love”. It could be fansubber cleverness, but Fujiko outright says that she gets Ayan “lived for love, but…” I think there’s more to the use of this piece in this part of the episode than there was with the first part. Here, Ayan talks about how all she wanted was to be with Darenzo but no one would accept it. Of course, the trial she has to go through isn’t as bad as Tosca’s and definitely ended up much better than Tosca did.

Actual spoilers for Tosca follow if you care about that kind of stuff. Shortly after Tosca finishes Vissi d’arte, Scarpia ups the ante by ordering Cavaradossi to be executed. Buuuuuuut, if Tosca gave herself to him, he’ll make it a mock execution. Tosca ends up agreeing, Scarpia gives the order, then Tosca knifes him. Everything works out, except that Scarpia is a pile of dicks and actually ordered the execution for realsies. Tosca throws herself over an edge in grief and to avoid the guys who just found Scarpia’s body.

The 2nd annual π day anime and mathematics post

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「涼宮ハルヒの消失」/「茨乃」

Happy $\pi$ day. Once again, Nadeko will bring us in:

Snowy Mountain Syndrome is the third story in The Rampage of Haruhi Suzumiya, the fifth volume of the light novel. It’s the first story that has yet to be animated. It’s also a story that contains the dread spectre of mathematics.

So our SOS-dan is stuck in a mysterious cabin in the middle of a snowstorm on a mountain. They find a mysterious contraption that has an equation displayed:

$$x-y=(D-1)-z$$

and they are to provide $x$, $y$, and $z$. Koizumi and Kyon are confused, but Haruhi rightly identifies this equation as Euler’s polyhedron formula, which is also very often referred to as just Euler’s formula. If you’re referring to it in context, it doesn’t matter that much, but it’s useful to distinguish between all the other things that Euler discovered, which is a hell of a lot.

First, we should probably go over some basic definitions. When we talk about graphs, we’re not talking about bar graphs or pie charts or the like. We’re also not talking about graphs of polynomials on a cartesian plane or other such functions. Graphs are a mathematical structure which, when drawn, looks like a bunch of circles and lines.

Formally, a graph is a pair $G = (V,E)$ where $V$ is a set of vertices and $E$ is a set of edges. Vertices can be any old thing, but each edge is defined as a pair $(u,v)$ where $u$ and $v$ are vertices in $V$. When we draw graphs, we just draw a vertex as a circle and draw an edge as a line that connects the two vertices it’s defined as.

And that’s it! That’s the most general definition of a graph, which means we can end up with a graph that’s completely empty or a graph that’s just a bunch of vertices with no edges in between them. We can even have multiple edges going in between two vertices. Of course, often times, we’d like to add some more constraints, depending on what we want to do with our graphs. Very often, we’d like to restrict the number of edges between two vertices to one and that’s what we’ll do.

Back to the formula, usually it’s given as $\chi=v-e+f$, where $v$ is the number of vertices, $e$ is the number of edges, $f$ is the number of faces, and $\chi$ is called the Euler characteristic. That makes $x=v$, $y=e$, $f=z$ and $D-1=\chi$. Now, the only thing here that we haven’t seen defined yet is a face. Intuitively, we can see that’s just the space that’s bounded by the edges.

What I find strange is the explanation in the novel that $D$ stands for the dimension of the polyhedra. As far as I know, this only works in the three-dimensional case for platonic solids. Once we generalize the structures to other kinds of polyhedra and topological surfaces, that analogy breaks down.

Anyhow, the way the formula is applied in the book is the use that I’m most familiar with, which is as a property of a planar graph. For planar graphs, $\chi=2$. In the novel, they deduce that $\chi=1$ since $D=2$ and that only works because they didn’t count the large face outside of the edges as a face, which we usually do.

But what is a planar graph? Well, if you go back to our definition of a graph, you might notice that all we’ve done is said that it’s a bunch of vertices and edges. We’ve said nothing about how to draw a graph. Usually, we represent vertices as circles and edges as lines in between those circles, but other than that, there’s really nothing telling you what order to draw your circles in or whether your lines have to be completely straight or not or how far apart everything has to be. How you choose to represent your graph is up to you, although if you draw your graph weirdly, you might make the people trying to read it angry.

Informally, a planar graph is a graph that you can draw with none of the edges crossing each other. This seems like a kind of silly thing to be worried about, because it seems like you could just keep on drawing a graph until it works out. Well, for edges with a lot of vertices and edges, it’s not obvious and even for really small graphs. For instance:

At a glance, it doesn’t look like the drawing on the right is planar, but all we have to do is drag one of the vertices into the middle to get the drawing on the left and it turns out they’re both the same graph, $K_4$, the complete graph of order 4.

That’s where Euler’s formula comes in really handy. It gives us a way of figuring out whether or not our graph is planar or not without having to fiddle around with placing edges properly and stuff. You already know how many vertices and edges you’ve got, so all you need to do is make sure you’ve got the right number of faces.

So it’s probably pretty clear at this point that you can’t draw every graph without the edges crossing. We can say something interesting about those graphs too, which just turns out to be another characterization of planar graphs, but oh well. But first, we have to introduce the concept of graph minors.

Suppose we have a graph $G=(V,E)$ and an edge $e=(u,v) \in E(G)$. If we contract the edge $e$, we essentially merge the two vertices into a new vertex, let’s call it $w$, and every edge that had an endpoint at $u$ or $v$ now has $w$ as the corresponding endpoint. Then a graph $H$ is a graph minor of $G$ if we can delete and contract a bunch of edges in $G$ to get $H$ (or a graph that’s isomorphic to $H$).

It turns out that every non-planar graph can be reduced to a minor of one of two graphs. The first is $K_5$, the complete graph of order 5:

The second is $K_{3,3}$, the complete bipartite graph 3,3:

These two graphs are the smallest non-planar graphs, otherwise we’d be able to reduce them further to get another non-planar graph. Like I mentioned before, this is a characterization for planar graphs too, since a planar graph can’t contain a $K_5$ or $K_{3,3}$ minor.

I guess I’ll end by saying that graphs are hella useful, especially in computer science. A lot of people complain about never using math like calc ever. If you’re a developer, you’ll run into graphs everywhere. It’s pretty amazing how many structures and concepts can be represented by a bunch of circles and lines.

THE MOST ANTICIPATED GAME IN HISTORY

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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

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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.

Ordinary boy who experienced extraordinary youth

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「正月２０１２」/「ZEN」

So my predictions have been a bit off, but there’s still plenty of time for Little Busters to get a KyoAni anime on that timeline! What I think is more surprising (other than Haruhi getting more anime before LB) is that the translation for the visual novel is finished and I’ve played through it, long before a Little Busters anime has even been announced.

Little Busters is an interesting experience for me, because it’s the first “real” Key visual novel I’ve played without knowing much going into it. Sure, there’s Planetarian, but that’s relatively short, so I don’t count it. Sure, there’s Angel Beats, but that’s not a visual novel. And sure, I’ve played Clannad, but it’s Clannad and I know everything about Clannad.

I mentioned before that Angel Beats made me wonder whether I really like Key or if I just really liked Clannad. Even better than an anime, I think the Little Busters visual novel is a perfect opportunity to see where my tastes lie.

Like any good Key work, Little Busters has to have a theme. That theme happens to be adolescence or childhood. Alright, then. From this, there are a bunch of things that are pretty similar to Angel Beats. We’ve got the setting down and there’s a good chunk of the game that’s spent on trying to put together a baseball team. At a glance it seems like it’s all about living out your youth and all that. The common route mostly just made me wonder why they bothered to create Angel Beats when they had this lying around.

You’ve got your usual suspects in the cast: socially awkward childhood friend who likes cats, disgustingly cheerful nice girl, shit-stirring genki girl, suspiciously combat-hardened and cool onee-sama, quiet book girl, and dojikko with verbal tic. But, the main character isn’t the usual Key template blank but mildly snarky dude. Instead, you’re a Hayate (from Hayate the Combat Butler) except you’re kind of weak instead of absurdly competent. You’ve also got a bunch of childhood friend bros, the Little Busters, who watch your back and are actually pretty important to the main story. Obviously, every important character ends up on the Little Busters baseball team.

Structurally, the whole thing is pretty similar to Clannad. You’ve got all of your routes that you have to do before you get a swing at the route that ties everything together. What’s different is the common route, where you’re building up stats and rounding up people and comedy happens. I actually like the common route, if I ignore being put through it about six times.

Where I’m pretty dissatisfied is with the side routes. I went in expecting the usual Key stuff with fatal sickness and astral projections. I think the main problem with this stuff in Little Busters is that the writers realized that they couldn’t fall back on the same old stuff again, so they tried to spin up some new awful tragedy for each character.

Before, the tragedies were pretty grounded. Someone lost a family member or someone is terminally ill. That stuff is easy to empathize with. The most outlandish stuff is the astral projection or animal spirit stuff, but even then, that stuff is sort of left to mystery.

In Little Busters, they take something simple and try to add another layer to it to try to make it new. So someone loses a family member, but they also regress into a catatonic state whenever they remember. Or someone is feeling out of place because they’re half-Japanese and struggling with their cultural identity, which is a real thing and you can empathize with that. But then they add this crazy backstory about their homeland under civil unrest and it’s like what.

And it’s not like they succeeded in making these developments new. I’ve watched and played almost all of the Key anime and visual novels and that basically let me SEE THE ENDING, so to speak (not that they weren’t making it extremely obvious). When I didn’t predict how a route would go when I got halfway through it, it was because there was the aforementioned ridiculous thing that was bolted on.

The “real” story, as in the right girl’s path together with the final route, is better in that the twists were actually kind of interesting instead of dumb and it’s where it differentiates itself from Angel Beats. How the story unfolds is a bit more clever than Clannad’s handling of the After Story route.

It’s definitely not as great as Clannad and I don’t think even the main route came together all that well. Even though it was better and actually interesting, a lot of it was still kind of ridiculous. I’ll let light orbs go, but this was kind of pushing it.

This all makes me kind of worried about Rewrite, but that has a trailer where a guy fights a dinosaur, so who knows?