「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?

He will use this knowledge in less than 24 hours.

So back when I was moving in at the start of the school year, I decided to try out my BD player on my hot new Dell monitor. Since I didn’t want to take out my Kara no Kyoukai BDs from their box, I opted to crack open the cheap flimsy Summer Wars case and throw in the disc. I hadn’t actually tried playing it yet anyway. I opted to skip the OZ introduction and go straight to the opening. First of all, I was disappointed that Funimation set the credits in goddamn Arial. Seriously, what? I find it difficult to believe they didn’t have Helvetica already from one of countless projects they could’ve used it on already.

More importantly, Funimation translated the chapter title of the book that Kenji was reading on the train. It turns out he was reading about Shor’s Algorithm. Shor’s Algorithm is the quantum algorithm that can factor integers in polynomial time. I alluded to it when I talked about Summer Wars and cryptography a while back and now’s as good a time as ever to get into it, since, you know, this means Kenji really is a quantum computer and all.

In quantum computing, instead of dealing with bits that are 1s and 0s, we deal with quantum bits, or qubits, that are denoted $|1\rangle$ and $|0\rangle$. These are really just quantum states. Quantum states have interesting properties, the most famous of which is being in superposition. Essentially, what this means is that we can have qubits that are in a state where it represents 1 and 0 simultaneously.

This turns out to be a very neat property to have. If we’ve got $n$ qubits, then we’ve got like $2^n$ inputs simultaneously. That’s great, right? We can compute things exponentially fast now! Well, it turns out it isn’t that simple.

Suppose that we do end up running an algorithm or something on our $2^n$ states. What happens when we want an answer? Well, we measure the state. The problem with that is that on measuring a quantum state, you won’t get all $2^n$ results. You’ll only get one of those results with a certain probability. What’s more is that once you measure a quantum state, you’re stuck with whatever it gave you and you can’t go back and check for another result.

That is obviously no good, because we want not just any answer, but, you know, the right answer. So it looks like approaching our problem from the naive interpretation doesn’t seem to work. And in fact, that immediately tells us that quantum computers aren’t a magic bullet that can help us solve SAT in a reasonable amount of time.

What we can do is manipulate our resultant quantum state so that the actual correct result we want is the one with very, very high probability and reduce the probability of getting any of the other results to near-zero. Of course, the problem is that we don’t know which result is the correct one to begin with. It’s actually this exact hitch that prevents us from efficiently solving general NP-complete problems.

Luckily, if we want to factor some numbers, we can take advantage of this. We can reduce the problem of factoring any old number into prime factors to the problem of order finding, which I’d mentioned before. For an integer $N$, there’s another integer $m$ such that $k^m=1\bmod N$ and we call $m$ the order of $k$ in the integers modulo $N$.

So suppose we have $k\bmod N$ with order $m$ and we decide to keep on taking powers of it, like $k\bmod N,k^2\bmod N, k^3\bmod N$ and so on. Eventually, we’ll get up to $k^m\bmod N$, at which point, that’s just $1$ and we start our cycle over again. The thing to note here is that this sequence is finite and periodic, which narrows down what we have to search through.

So what do we do? We create a quantum state for our period that’s in a superposition over all the powers of $k$ in $\bmod N$. We don’t know what our period is (that’s what we’re trying to find), so we just choose a large enough one that our order will be in the period. Now, in order to find this order, we do some magic with a Quantum Fourier Transform.

What?

So I mentioned at the beginning that when we look at a quantum state in superposition, we can think of it as returning one of the possible states with a certain amount of probability. How the probabilities for these quantum states work is actually more complicated and it’s from this that we can massage an answer out of our magic quantum algorithm.

Quantum states have something called amplitudes, which are kind of like probabilities, except that amplitudes can be basically any complex number as long as all of the amplitudes $a_i$ for a quantum state satisfy $\sum|a_i|^2=1$. If we’re just measuring a quantum state, this really doesn’t change anything, we just get state $|i\rangle$ back with probability $|a_i|^2$. But when we’re manipulating quantum states, there’s more to the amplitudes to consider.

If we think about amplitudes in terms of waves, we can see that we can cancel waves out. For instance, the states $\alpha|1\rangle$ and $-\alpha|1\rangle$ have the same probability if we were to measure them (since $|\alpha|^2=|-\alpha|^2$), but if we put them together and add them, they’d cancel each other out. What’s more is that since amplitudes are complex numbers, so we can think of them as having a direction (like a vector on the complex plane) and we end up with weird stuff like having things partially cancel out.

So just like a regular Fourier transform extracts some information about frequencies from a sequence, we can use the Quantum Fourier Transform to extract some information about all of this amplitude stuff that we can’t see just by measuring the state. And this is exactly how we can manipulate our state so that it increases the probability of the answer we want when we go to measure it and depress the probabilities of all the other answers.

Now after rambling about amplitudes and Fourier transforms and orders, we should probably step back and see what we’ve done in perspective. What we have is a way to find the order $m$ of an element $k \bmod N$. Well, actually, we don’t even have that quite yet. What we get out of all of that quantum stuff is just some information about $m$ that we have to manipulate further, except we just do that with plain old number theory instead of quantum computation. But, what we’ve kind of stumbled through is kind of a vague description of Shor’s algorithm.

Like I mentioned in the first Summer Wars post, this is the only way we know of so far that lets us factor large numbers (especially the ones that are used in cryptography) within a feasible amount of time. Again, Kenji (or at least his brain) is basically a quantum computer. Coincidentally, I played around a bit with what the implications could be if our brains were quantum computers in an earlier post on Kaiba.

But even if Kenji isn’t a quantum computer, he’s goddamn smart for a high school student. The theory behind the computing part of quantum computing is really just a ton of linear algebra, so an understanding of quantum mechanics isn’t really necessary (which is great, because I don’t know any of that crap). The quantum computing course that I took in my undergrad only had second year linear algebra as a formal prerequisite, but that was mainly to allow students from different departments to take it and also implies that you’ve got first and second year math down at the very least.

「魔法少女まどか☆マギカ」/「ゆーげん」

This show was made for me.

I think that should be your sign that you won’t find a paean to the greatness of Madoka and why it is man’s greatest work.

I mean, I was sold on the show already back when it was just “Shinbo makes an original anime”. That’s all it took.

And then it became “Shinbo makes an original magical girl anime” and I’m like, whoa, even better. I mean, I liked Nanoha. More of that? Yes, please.

And then it became “Shinbo makes an original magical girl anime with character designs by Ume Aoki, music by Yuki Kajiura, and script by Urobuchi Gen”. By this point I’d gone nuts. Magical girls! Designed by Ume-tentei! I mean, yeah, Kajiura and Urobuchi were kinda weird choices for a wide face magical girl show, but still, they’re great too. This will be amazing!

And then the characters! The character designs! Aoi Yuuki! Friggin Chiwa Saitou voicing mahou shoujo Senjougahara. Mizuhashi Kaori voicing a magical girl WITH GUNS. KitaEri voicing swords girl. An adorable mascot character!

If the anime that we got was the anime that was presented through only these CMs, I would have been ready to call it anime of the year already.

And then the actual first episode happened. I watched most of the episode going THIS IS AMAZING and then we get to the witch barrier.

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

And then Mami comes with her Gate of Babylon and her GUNS.

I mean, you can probably imagine my mental state as I wait for each week of this cartoon. And so this goes on and I flip out each week and once episode 3 rolls around I go, screw this, I’ll just watch the live stream.

Yes, I watched episode 3 raw when it aired.

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

And of course, each week while I’m watching this, I just send my friend a series of FFFFFFFFFFFFFFFFFFFFs.

And then we get to episode 10. I don’t know if it was apparent, but my favourite character is Homura, probably largely because Senjougahara is one of my favouritest characters. So yeah, we get to episode 10 and this is the best anime of the year and possibly of all years.

The end.

Yes, I know a lot of people have problems with it and a lot of what people have said about the show is pretty hyperbolic. Maybe there it does strain itself in trying to be deep and all. Maybe the characters weren’t amazing. I will admit that it very likely is not the best anime ever.

But I don’t think there’s been an anime that has been quite so attuned to my brain. And that is why I love it so.

「little world」/「momoc」

Yeah, I made the same joke last year. But who would’ve thought that we’d get two Utena derived shows within a year? Certainly not me.

But yes, Mawaru Penguindrum is a show that has penguins in it.

It’s fascinating how different Penguindrum is from Star Driver but still manage to be so heavily evocative of Utena. Having Penguindrum as a comparison, I realized that there really was no reason to expect that Star Driver would make as many callbacks to Utena as it does. I mean, it’s not like Igarashi and Enokido hadn’t worked on stuff together before.

Like Star Driver, Penguindrum exudes its own sense of style. In Star Driver, a lot of that is constrained to the more fantastical parts of the show, like whenever we’re dealing with Cybodies and the Glittering Crux. There’s no such separation in Penguindrum. Even in the real world, the architecture and shots of the locations are still really surreal. So while in Star Driver, there’s a clear delineation between real and fantasy, we’re often left wondering which is which in Penguindrum.

And the penguins don’t help very much in this department either.

Looking back at Star Driver, there actually isn’t that much weird stuff going on during the school life section of each episode. I mean, yes, weird events happen and all, but what you saw was pretty much what happened. In Utena, weird things where we’re not really sure how to take happen in the school life parts, which is the route that Penguindrum takes.

Structurally, Star Driver resembles Utena much more because of the clearly defined events that take place in each episode. On occasion, we’ll be missing, say, a song or something but for the most part, we know how each episode goes down. Penguindrum is not very repetitive at all, at least not in how each episode goes. Yeah, there’s SEIZON SENRYAKU, but those are really more diversions than a shadow play and then ZETTAI UNMEI MOKUSHIROKU followed by a substantial duel or APPRIVOISE followed by GINGA BISHOUNEN and a substantial duel.

Of course, all three still make use of visual symbols and phrases and keep on repeating them a lot. The obvious messages are pretty obvious because they’re shoved in front of you, but it just sort of piles on to you to the point that there are probably some other messages hidden under this mound of symbols you’ve suddenly got. I mean, every goddamn thing that shows up on the screen or uttered by anyone is probably a symbol. Has anyone dissected the Triple-H/ARB songs yet?

Penguindrum also differs from Utena and Star Driver by not being about a prince who strolls into town and upsets the establishment trying to revolutionize the world. Certainly, we’ve got our shadowy cabal trying to revolutionize the world, but it’s really more about two brothers trying to save their sister, which is much less grand. Of course, the penguins would probably deflate any sense of awe pretty quickly.

Not that I don’t appreciate the penguins. I think they’re an awesome part of the show. It’s an interesting way of adding another layer to all of those symbols we’re buried under, in that they supposedly are reflective of the state of mind of the characters they shadow. More importantly, their antics are just plain enjoyable and the show would be much more depressing without them.

Does the choice of penguins mean anything or does Ikuhara just really, really like them? It is a mystery.

Man, I wish I had a penguin that mirrored my internal thoughts and did errands for me and was invisible to everyone except me.

「FF系　マブラヴタイトル」/「ぽかり＠ぴくしぶ」

Muv-Luv is a journey.

Maybe saying it’s the longest visual novel I’ve played is a bit unfair because it’s really two or three games, depending on how you see Extra and Unlimited, and there was a good two or three years until Alternative was released. Still, going through the entire thing takes a ton of time.

The way I like to think about Muv-Luv’s unique structure is by comparing it to Clannad, where the really good stuff, Alternative and After Story, requires a lot of time invested beforehand in the content that comes before it. That’s not to say that the non-Alt/AS stuff is bad, but it’s definitely not earthshattering. And in the case of the Clannad visual novel, it’s probably not as important.

This isn’t true for Muv-Luv. If you’re only in Muv-Luv for the sci-fi, going through the school life hijinks of Extra is going to seem torturous but it is absolutely vital. This isn’t the same as Clannad’s school life routes or Fate/stay night’s Fate route. Extra matters, possibly even more than Unlimited does.

So when I say school life, I mean Muv-Luv Extra is basically your standard school life harem thing. Unremarkable guy goes to school and all of the girls he knows is inexplicably attracted to him. You’ve got childhood friend, mysterious rich transfer student, kuudere, and class president. Other characters include a bro and two teachers. And comedic and romantic things happen in this part and by the end of it, you’ll have a girlfriend. Congratulations!

So you finish Extra and suddenly the title screen changes and all of the heroines are wearing different uniforms. Here is where I’d really like to have been around for when this thing first came out because I have no idea if anyone expected this and what the reaction was. Even more so once you start a new game and find something called Unlimited. Now in Muv-Luv Unlimited, we start with some scenes from Extra. See, because you’re the same guy from Extra. Except now you wake up, walk outside your house and find that the city has been destroyed. HMMMMMMMMMMMMM.

Essentially, this entire thing is about Shirogane Takeru, a normal guy who gets thrown in to an alternate universe in which humanity is under attack by aliens and are losing. How does he deal with this? By breaking into a military base to steal a mecha and save the day, of course. Except that he can’t because he’s a high school student from 2000s Japan and doesn’t know about anything and knows no one.

That last thing pretty much guarantees he’s dead, but with some luck, he ends up becoming a trainee at the local UN military base and he gets a chance to show off his chops. Except, again, he’s a high school student so he fails miserably and holds his entire squad back because of his ineptitude. Unlimited is basically him learning the ropes and somehow getting it. This part ends fairly uneventfully, which brings us to Alternative.

In Alternative, Takeru mysteriously starts over at the beginning of where he was in Unlimited, except he’s retained all of his memories and experiences from Unlimited. This time, he’s going to do it right, which, as it turns out, is quite difficult even if he’s not the complete failure from before. It turns out saving the humanity is hard!

Here’s where everything exciting happens. Political intrigue! Mecha combat! Alien horrors! Military briefings! We finally get to see the mecha in action and there are some really fantastic action sequences. Yes, this is a visual novel and yes, it relies on tricks similar to Fate/stay night that use sprites and the visual novel engine to create a sense of dynamism to the combat. The other thing that adds to it is how the characters work together. Good squad combat is not something you see a lot of in mecha anime, but it’s here and I’d say it’s plays a pretty big part in the story’s themes.

This is also where all of the emotional payoff (read: gutpunches) is. And this is where all of the time you spent with Extra comes in, as the nature of the world you’re in is revealed and casualties mount. While Unlimited and Alternative take place in the same world, Unlimited doesn’t have quite the sense of danger that Alternative does because the aliens do not mess around when they show up. Sometimes we kind of forget that there’s a reason that humanity’s losing. All of this causes a number of oh, shit moments.

As we move from Unlimited to Alternative, the goal changes from trying to get the hell out of crazy apocalyptic world and get back to fun times high school to trying to save that world and the people in it. So now, he’s invested in that place, except that’s a scary place to have people to care for, especially if they’re fighting aliens bent on their destruction. What’s more is that even if he does end up finding a way to gtfo, can he bring himself to abandon everyone so he can chillax with his harem back in Extra?

Muv-Luv is not really about saving the world. It’s a lot more personal than that. How else would you explain Extra? It’s about Takeru coming to terms with this incredible situation he’s been thrown into and rising to the challenge of dealing with it. And it’s something that’s true for all the characters in Alternative. Everyone has things they would rather be doing, but instead, they have to deal with this terrible world filled with aliens and loss and it’s up to them to deal with it and decide to do something about it.

The game’s genre is “a tale of love and courage” for good reason.

「現象数式使い」/「あや波平」

I don’t remember where I heard about Sekien no Inganock, but when I was trying to figure out which visual novel to play next, Inganock jumped out because of how different its premise was. I mean, the last few visual novels I read before it were Cross Channel, Tsukihime, Sharin no Kuni, and Muv-Luv and all of those started off with high school shenanigans and even if they did end up in very different places, all of the principal characters were a guy in high school and other high school students.

Sekien no Inganock is set in a steampunk city inhabited by half-human, half-animal people and is about a travelling doctor. He goes around healing people with, uh, math, I guess? So you can tell that I like this guy a lot already. Besides that, he’s fairly calm and unmoved and his brand of snark is pretty deadpan.

Anyhow, I really love everything about this visual novel. Yeah, the story is kind of obtuse, especially once it gets close to the end. And yeah, that internal monologue system is convoluted and impossible to beat without a walkthrough. But everything else? Fantastic.

The art is stunningly gorgeous, even the character sprites. All of the landscapes are great, but it’s the monster event CGs that are amazing. It’s one of those games that I probably don’t want to see as an anime because an anime will never be able to capture the art (kind of like how the Steins;Gate anime can’t retain huke’s texturing). The music is really fantastic. I really liked the voices, whenever they were present. All of this adds to the great atmosphere and setting. This is something that’s shared amongst all of the games in the What a Beautiful series and this alone is enough to get me to pounce on the rest of them if I ever get the chance.

What separated Inganock from Sharnoth was the characters. I already mentioned our travelling doctor main character Gii. He’s great. But the other character that I thought was awesome was Ati. She’s a catgirl tsundere bro, kind of like Ami from Toradora. Regarding Gii, she waffles between the line of friendship and romance. They help each other out in various business ventures and get drinks at the pub. She’s more of the street smart one, since Gii is kind of a nerd, being a doctor and all. These two really made the game for me and when I got to the end of Ati’s story, well, I mad.

A lot of people complain about the repetitiveness of the story. I guess that aspect of it reminded me of Star Driver because it wasn’t too long after it had finished and we all remember all of the people complaining about how Takuto always wins. Well, it’s the same thing here. We get an encounter and Gii figures the monster out, so he stretches out his right hand. And then after Porshion, who we are assured is not human, burns the monster up, we cut to some dudes with a clock or watch trying to climb some stairs. This is the sort of stuff I enjoy.

I didn’t go in with the expectation that it would answer every question I had and I didn’t really have a desire to understand everything I didn’t get. It was just a really nice thing to experience and I was quite satisfied with having gone through it once I got to the end of it. Well, not quite satisfied in that I’ll be jumping at every bit of news of more WAB games getting translated.

「うさぎドロップ」/「ゆーた」

Single dad manga? Why not? Yotsuba&!’s great!

I don’t know whether there’s much I can add about Usagi Drop. The whole thing is fairly straightforward. It’s a great story about a guy who ends up having to look after a kid all of a sudden and gets into the ups and downs and details of it. I’m sure we’ve all been told that raising a kid is hard and doubly so if you’re the only doing it. Although I guess Daikichi lucked the hell out because Rin is probably the best kid you could hope for.

Okay, maybe I can say something about the much more contentious second half of the story, in which Rin is no longer an adorable child but is a teenager. The immediate reaction is “NOOOO why can’t Usagi Drop be about Daikichi taking care of little Rin forever?” but you know, it doesn’t work like that. Kids grow up and parents should get a chance to feel proud if their kids turn out to be decent human beings, which Rin is in spades.

But also important is that it has some loose threads that need to be resolved. Does anything end up happening between Rin and her mother? Do Daikichi and Kouki’s mom get together? Or do Rin and Kouki get together? I’d imagine a ton of people were interested in seeing how the last two questions get answered. Which of course leads us to the ending.

I’ve already talked about the ending and I’ve tried to understand where it came from. So a lot of people are pissed at the ending because it’s weird as hell and came out of nowhere. But more importantly, it was basically a punch in the gut for everyone who was waiting on those last two questions because it basically resolved the “problem” (because if you think about it, you can’t really have both happen) in the worst way imaginable.

Really, that’s the only snag of the entire thing and I’ll admit it’s a pretty big one. One of the great things about Usagi Drop is its realism and believability, which this development was not. Of course, this is only a concern if you’re at all interested in the manga. If your only desire is to remain in bliss solely in the realm of a guy tries to raise a kid without knowing how, then stick to the anime and the first half of the manga, which is the most adorable thing.

「Mage Killer」/「三輪」

The first time I read Fate/Zero, I got through about half of the prologue before forgetting about it. That was before I read Fate/stay night.

One of the great things about Fate/Zero is that the particular Holy Grail War it covers is serious business. Instead of having a bunch of high school students kind of flail about, you have some powerful magi all scheming against each other. These dudes know what they’re doing. And actually, that all of these guys basically off each other one way or another kind of explains why we’re left with high school students ten years later.

The main draw of Fate/zero for me has always been that I’d heard it’s particularly brutal and that there was a magus going around ruining everyone with the help of modern technology. After reading Fate/stay night, Kiritsugu’s character became much, much more interesting. As much as people seem to think that Rider is the best (and I’ll admit he is pretty fantastic), Kiritsugu has always been the most compelling character to me.

Those who are familiar with Fate/ will know that it’s all about dealing with ideals, whether it’s defending your ideals, sorting out your ideals, or having your ideals challenged. It’s kind of an easy subject to bring up when fighting for the Holy Grail. Fate/stay night is essentially about Shirou sorting out his ideals. In Fate/zero, we have Kiritsugu, who has the same ideals as Shirou, but ends up choosing a vastly different way of realizing them.

This combined with the high calibre of opponents means that there is a ton of cool stuff that goes down in this story. The fact that these are people prepared for the Grail War and not high school students not only means that their fights are better just because they’re better, but they’re also much better prepared. Calling the Grail War a war in Fate/stay night always seemed a bit silly to me, but in Fate/zero, I think there are enough casualties and heavy weaponry to justify it.

Of course, that’s all after I went through Fate/stay night. So what drove me to try and read the books the first time? Well, I’d just finished playing Saya no Uta at the time. Saya no Uta probably remains one of the most horrifying and disturbing things I’ve read. So obviously, I was looking for more in that vein and found this light novel that the same guy wrote.

On the physical horror front, I think Team Caster’s got it covered. In terms of emotional despair, we’ve got everyone else who’s connected to the events of Fate/stay night. It’s mentioned somewhere in the notes of the first volume that there is basically no happy ending for Fate/zero given what we know plays out in Fate/stay night. Basically, everyone involved bets the house on winning the Grail and ends up ruining their childrens’ lives in the process.

It’s going to be a long three months once the first half of Fate/zero is finished. I guess there’s uncensored Team Caster fun times to look forward to in March, though.

「シュタインズゲート・瓦礫と助手」/「huke」

Even though the track record for anime adaptations of Nitro+ games has been abysmal, I couldn’t help but hope that Steins;Gate would turn out well. After all, it’s the best visual novel ever or something according to Japan. And if it didn’t pan out, I guess I’d just fall back on the visual novel with huke’s pretty art.

And as I was watching it, I thought it was pretty funny and all. I was still trying to figure out why Japan loved this thing so much. It wasn’t until someone mentioned something about 2ch jokes that I think I got it.

So I’d known that Steins;Gate was about time travel, based on the synopsis. What I didn’t know was that the story was basically based on the John Titor story. And it the connection wasn’t superficial either. It wasn’t just, there’s a guy calling himself John Titor from the future on 2ch. A lot of details, like the IBM 5100 and the mechanics of time travel and divergence numbers, are taken straight from the story. You can think of Steins;Gate as one giant John Titor reference.

This is fascinating to me, because even though I’m not intimately familiar with the details of the John Titor story, I’ve been on the Internet long enough to remember this whole thing. It’s kind of weird to see something that was sort of the early-web version of an internet meme be used as the skeleton of a more fleshed-out story. I guess something like Densha Otoko would qualify as well, but I think there’s a lot less you can do with it to make something unique like Steins;Gate.

This whole aspect of Steins;Gate got me because I am a nerd and nerds friggin love references. I mean, look at any Shaft anime. But yes, Steins;Gate has tons of references and where there aren’t any, it’ll just create memes. For the most part, these references are all internet memes. If it’s not part of the John Titor mythos, they’ll be working in a 2ch meme. And then there’s stuff like EL PSY CONGROO and tutturu~ which seems like it was designed to be spammed across the internet.

The characters themselves are exactly the same kinds of people. After all, they encounter John Titor on 2ch. What kind of people read and post on 2ch? Daru and Okarin are really obvious otaku. But Mayuri seems relatively normal, except that she works at a maid cafe in Akiba and buys doujin at Toranoana. Okay. Even the most respectable and well-adjusted of the cast, Kurisu-TINA, is a closet VIPPER.

So I guess what’s special about Steins;Gate isn’t that it’s just a good story about a bunch of friends who fall into some time travel conspiracy. It’s that it’s a good story about a bunch of friends who are just like the people watching it who fall into a time travel conspiracy based on an internet urban legend.

「一面の花」/「k野」

I’d been hearing about how awesome Heartcatch Precure was so I’d always intended to eventually watch it. The art was fantastic and I’d seen some great clips of the fights. The problem is that when I found out about it, it was already really far into the 50 or so episodes. So once I got a ton of time after I graduated and was looking for a show to watch, I figured it was time. After all, I rolled through Cardcaptor Sakura pretty quickly.

I’ve been thinking about whether I’d put Heartcatch at the top of my magical girl list, but I think it ends up coming second to Cardcaptor Sakura. Still, this means I think that Heartcatch is pretty damned good. I think it’s a better magical girl show than Madoka or Nanoha and I friggin love those two shows.

What makes Heartcatch so great is that it’s just good. It has a great cast of characters, the story is wonderful, and the production is stellar. Most importantly, it’s just a magical girl show. It isn’t magical girl with lasers. It isn’t magical girl with zombies. It is what it is and it stands toe to toe with all of those magical girl and x shows, where x is something that makes it more palatable to people who need an excuse for why they’re watching shows for little girls.

And Heartcatch is girly as hell. Yeah, the Cures might be throwing some punches around, but the show is tripping flowers and fashion. You can attempt to reframe Nanoha as scifi and talk about intelligent devices and stuff, but the Cures spray perfume to transform. At this point, Nanoha’s pretty much decked out in mecha gear in Force. Meanwhile, this is a show with tambourines and those spinny things that look way too much like their only function is to sell toys.

There’s also the characters’ boundless optimism and energy. There isn’t anything that’s especially dark about is show, even the villains are kind of goofy. Everyone’s got dreams and everyone’s fighting to protect their dreams and it’s terrible that villains use the uncertainty in people’s hearts against them. Here, the objective isn’t to seal away some rogue magics or befriend the opposition with lasers, but to restore people’s hearts.

The other Precure series are going to have a tough time measuring up to the Heartcatch bar, but I hope they do.

「ガンバスター」/「タガナー」

It’s quite illuminating to watch Gunbuster and recognize things that I’ve seen before scattered throughout so many shows just because they decided to pay an homage to this. The obvious case is Gurren Lagann, where certain little things are straight up ripped out from this show. Another case would be Lucky Star’s Bun Guster track. At many of these points, it was like a light flipped on in my head and I went ohhhhhhhhhhhh.

What’s more impressive is that even though this is one of the oldest shows I’ve watched, it still felt new. It was kind of like when I watched Utena for the first time. In this case, the time dilation stuff added a really interesting dimension to the entire plot. While Gurren Lagann relies on physical size alone to give it that grand sense of scale, here, time and distance are used as well. It’s not on the same scale physically, but it definitely matches in the sort of awe you feel when you watch it.

This all makes Diebuster quite interesting as well. While it’s a “sequel”, it feels very different. There are some callbacks and some of the same themes, but it’s largely doing its own thing. I spent a lot of time trying to figure it out and how it connected to Gunbuster but it just ended up giving me all the answers I was looking for. I don’t think there was the same sort of awe as when I watched Gunbuster, but it was more like ‘wow, that’s pretty neat’.

But comparing these two to Gurren Lagann makes their similarities a lot more apparent. Both are about a girl who look up to a girl who’s very successful as their role model. Both of them eventually surpass their role model and achieve their dreams through hard work and guts. And then both of them save the world together with the mentor they’ve surpassed.

Watching these was kind of exciting because everyone loves Gurren Lagann and the question is whether Gainax will be able to top it. I imagine everyone who watched Gunbuster and Diebuster must’ve thought the same thing, that surely they can’t top THIS. I’m glad that they’ve proven us wrong twice now.

「静雄無双」/「巖本英利/旧PNス・タンリー」

I’d planned to write about Durarara!! during the whole twelve days of anime thing, but I dropped it at the last minute to make room for Utena and Star Driver. But now, you’re going, wait a second, there was no Durarararararara!! this year, how can it be a special moment in anime for this year?

Well, you see, it turns out a chunk of the light novels was decently far along. I went through books four through six, which, if we allow ourselves to dream a bit, would correspond to the second season. I liked the anime, but I think everyone is in agreement that the second half is weaker, although whether it was still good or terrible is up for debate. The nice thing about the three books immediately after is that the focus is not on Anri or Kida, so you won’t have to worry about them being a downer in your anime about crazy and exciting things in the big city.

So it should please everyone that a second season of the anime focuses much, much more heavily on everyone’s favourite really angry guy, Heiwajima Shizuo. The fourth book goes back to the Durarara/Baccano standard of telling a story with about a thousand different threads somehow coming together at the end. The fifth and sixth books form one story in which Shizuo is the focus in the same way that Mikado, Anri, and Kida were the main characters of their respective arcs. We’ll also see some familiar faces. An interesting thing about the fourth book is the return of some characters that you may or may not remember and the introduction of several new ones.

Shizuo was a really great side character before. He shows up, gets trolled by Izaya, and proceeds to destroy things, usually with other things. The focus that books 5 and 6 puts on him is great because it develops him from the guy that can be described by the previous sentence into a legitimate badass. I feel like he’s always been thoughtful and that his only real problem is getting pissed off really easily, so I enjoyed watching him put his talents to use in a more focused way.

The thing that I enjoy about Ryohgo Narita’s stuff is his ability to launch a million seemingly unrelated characters and plot threads and be able to tie them together. The one-volume version of that is very neat to read through, but I have a feeling that there’s some longer term stuff that he’s set up in the early books that will come back in a big way and there are already hints of that at the end of the sixth book. This isn’t unlike the Haruhi series, where seemingly inconsequential details come back later in an earthshattering way, although, here the pieces are bigger, I guess.

Really looking forward to that second season.

「ありがとう放浪息子」/「神田川」

The main problem for the characters is some variation of that, isn’t it?

Anime is full of traps and when you sit back and think about it, it’s kind of like, wow, they’re everywhere, aren’t they? Which, if you think about it, is kind of strange that Hourou Musuko feels so different from everything else. I mean, it’s an anime about traps.

An easy description of Hourou Musuko would be that it’s about gender and sexual identity and it does it realistically, unlike the usual fetish or comedy treatment. But what’s more interesting isn’t just that it examines these things in a realistic and mature manner, but that it starts from square one. These are children that are dealing with these things.

So we have these kids and we’re watching them struggle with it on their own. If they’re lucky, they meet someone to struggle along with. Maybe they’re doing okay for a while. Suddenly, things change, and they’re in middle school and have a whole new slew of bullshit to worry about. There’s never really any rest from these things, there are no answers and the kids just have to keep on growing up and dealing with crap that comes their way.

That the anime chose to focus on the middle school parts was something I found kind of unfortunate. Yeah, it’s really exciting that there’s a ton of relationship drama here, but I thought a nice thing about Hourou Musuko was that it took the time to take a look at the slower parts of the characters’ lives as well. Of course, it worked out that the particular slice that they chose to animate has some sort of closure, so that was nice. But just like how the manga starts long before the anime does, now the manga has gone beyond where the anime ends and everyone’s in high school.

Just like with Usagi Drop, we’ve had our fun times watching these kids grow up, but that’s not going to last forever. I don’t know whether this mangaka typically focuses on long term things, but I’d really like to see where this crew ends up in five, ten, or more years down the road.

「闇の力を秘めし鍵よ」/「hatsuko」

I don’t think it’s that much of a surprise if I tell you that Madoka made me watch Cardcaptor Sakura. Well, that’s not entirely true. A more accurate phrasing of that statement would be, I watched Cardcaptor Sakura in anticipation of Madoka. Yep, I spent a good chunk of the Christmas break just before Madoka aired watching the entirety of Cardcaptor Sakura.

Cardcaptor Sakura seems to be one of those childhood anime that sits alongside the likes of Dragon Ball or Sailor Moon. I actually had no idea it was dubbed in English and aired here until when I was way too old and cool for that crap. More recently, it went from ‘that show that a few of my friends watched that seemed lame’ to ‘that show that people cite as the epitome of its genre’.

CCS is a pretty lengthy show, at about 70 episodes. After I got into the whole magical girl thing, I’d planned to watch it eventually, but never really had the time or motivation to do so (which is fairly common for shows that I plan to watch because I “should”). But with 2011 and Madoka quickly approaching and having finished all of my grad school applications, I convinced myself to finally start.

Up until then, my benchmark for magical girl shows was Nanoha. As far as Sakura and Nanoha go, they’re pretty similar. For a while, before I watched either of them, I’d get them confused sometimes. Obviously, I knew that CCS wasn’t going to have huge explosions or funnels, but it was sort of surprising because I’d forgotten that magic doesn’t necessarily manifest itself as a giant pink beam of death. It turns out magic has a wide array of uses.

Speaking of magic, I was surprised to learn that Sakura’s magical girl outfit was not and that there wasn’t even a default outfit. I don’t even know if she actually ever wears the one that she’s seen wearing in most promotional art in the show. The only constant in her magical girl wardrobe is her staff. But nope, Sakura’s eclectic fashion is thanks to Tomoyo.

And I’m not entirely sure when it happened but the focus of the show seemed to shift slightly from Sakura learning to be a magical girl to include falling in love. She basically spends the entire show tracking down the Clow Cards in some way, but somewhere along the line we also get scenes of her and Syaoran sorting their feelings out. Something that I didn’t expect was for the entire show to basically consist of Sakura dealing with the Clow Cards. But even then, the last thing that Sakura had to do before everything ended wasn’t to save the world, it was to tell Syaoran that she loved him.

This love thing was new to me, especially coming from Nanoha, where at best, we have some best friends forever stuff crossing the line occasionally with undertones. Girls and boys interested in each other? Why I never! But it was interesting because it actually went there instead of dancing around it. And it was quite nice seeing Sakura and Syaoran growing in that way.

I think this show made me realize it’s okay to watch shows made for little girls even if they’re not wrapped in a layer of beam weaponry and sci-fi military trappings.

P.S. despite this post’s title, the best OP is Platinum

「キャスターと龍之介」/「ラク」

It’s that time of year again, in which I brush off a bunch of drafts that I’d hoped to post over the course of the year but didn’t get around to finishing on time. A funny thing happened on the way here, which is that I was expecting to not have enough to post about. The reason is that I would have been posting consistently about all the things I wanted to post about all this time. But as it turns out, well, “@blkmage ha ha haaaaa”.

Look forward to twelve days of quality handcrafted posts about some japtoons.

An introduction to mathematical writing

In chapter 2 of Suugaku Girl, we’re introduced to the third component of the little love triangle that’s forming. Tetra is the underclassman that the main character is tutoring and she’s one of the many people who think they might like math but school eventually beats that silly thought out of them.

Anyone who’s taken a real math class will know that by the end of it, your notes are essentially a giant list of definitions, theorems, and proofs along with an example thrown in once in a while. By a real math class, I mean a math class that’s actually concerned about reasoning about how we get our theorems instead of focusing on how to use them for practical applications. I did my undergrad at a school where math has its own faculty and where there’s a lot of rivalry between the various faculties. Everyone in math often jokes about how an example suffices as a proof for engineers and their ilk.

I checked your textbook for a proof and it said that we’ve done enough examples for it to be plausible. Must have been written by engineers.
— Vanderburg, PMATH 340 (F09)

Here, Tetra falls into the same trap when the main character asks her to define what prime numbers are. So MC-kun has to explain how definitions work. First of all, definitions have to be precise, just like theorems. It’s pretty easy to lose marks for misstating theorems and definitions by leaving off an edge case for 0 or 1 or something silly like that. Of course, that leads Tetra to question why these things need to be so precise and arbitrary.

One of the things I realized about math is that it’s all about trying to do things with the definitions you start out with. You can kind of see that in how the number system is built up. We can start with plain old numbers that we use to count things. And then we can add things to it. Like, what happens if we have less of a thing, how would we represent that? Tada, we’ve got negative numbers. Okay, now what if we have a part of a thing? Now we’ve got fractions. And so on and so forth. We realize that not every number can be written as a fraction and suddenly we’ve defined real numbers.

I’m sure we’ve all wondered why complex numbers work out the way they do. It’s because we’ve defined everything to work out like that. Some guy tried to take the square root of a negative number and found that it didn’t work out very well, so we defined the square root of -1 to be $i$. Now we have this $i$ thing, what can we do with it? Well, we can just start writing crazy things like $3 + i + 4i^2 + 5i^3 + 9i^4 + 2i^5 + 6i^6$, but then we realize that it just becomes $2-2i$. Well, okay that’s kind of neat.

But now we know that all complex numbers can be written as $a+bi$ with $a,b\in\mathbb{R}$. So someone along the line must’ve been like, what would happen if we tried to graph these things? So we treat $a$ as the $x$ component and $b$ as the $y$ component and it turns out we can think of complex numbers as other structures like a vector or just a 2-tuple or something. And suddenly, this gives us a way to compare complex numbers, by taking the length of the vector that they define. And now that we have vectors, we can do some weird geometry stuff with them. We can think of these things as the length of the vector and the angle that they form. And then you can go crazy and talk about roots of unity or what multiplication of complex numbers might mean.

The point is that all of mathematics is built up like this. You start off with some definitions or premises and you go nuts. Of course, you don’t have to use the same definitions as everyone else. The problem with doing that is you might not end up with anything interesting. Like, what if we did something nuts and defined 1 to be a prime number like so many people do when they leave off that condition? Well, not much, we’d probably just rephrase all of our theorems to exclude 1.

On the other hand, sometimes when we play around with definitions, we do end up with something interesting. For instance, we can define something called the extended complex numbers, which is just the set $\mathbb{C}\cup\{\infty\}$. Yep, we just say okay, infinity is a number now, deal with it. So what can we do now?

Well, we can divide by 0 now.

I imagine there might be a few people who might flip out at this notion, but yes, since $\infty$ is included in our number system, we can define $\frac{1}{0}=\infty$. Of course, we can’t do everything — $0\times\infty$ and $\infty-\infty$ still don’t mean anything. But if you’ve been paying attention, you might be going, okay well, we can divide by 0, but what else can we do? Dividing by 0 is kinda meaningless if there’s nothing new we can do.

As it turns out, the extended complex numbers defines a very different geometric object. If we remember from the example of the complex numbers, we can basically define every complex number as a vector over a two-dimensional plane. Here, with the extended complex numbers, we can define every number as a line passing through something called the Riemann sphere. And like the complex plane, this sphere lets us create weird relationships between numbers and angles and stuff. This turns out to have interesting properties in complex analysis and quantum mechanics.

So yes, definitions are often arbitrary. Why? Because it’s just useful and interesting that way. You could argue that it’s because nature forces us to define things a certain way. Kind of like, of course you can’t take a square root of a negative number, you just can’t do it! What happens, though, is that we always seem to end up finding useful things that line up with our mathematics rather than inventing our mathematics to do useful things with. After all, mathematicians have been playing around with imaginary numbers for at least a few decades before electromagnetism was even discovered.

「希望」/「niuya」

I’d been rewatching Kaiba with a bunch of people a while ago. Kaiba’s a great show to watch if you want to talk about things, especially if you like dealing with the sorts of moral and ethical issues that come about in a world that’s so starkly different from ours. The obvious things to talk about revolve around identity and existence. Being the computer scientist and the guy who likes to make laboured analogies to things I like, I began to think about memories and cognition from a CS point of view.

Kaiba’s already done a lot of the “what if” in exploring the idea of memories that are as easy to work with as data on today’s computers. There was an observation in one of the episodes that it seemed like one of the characters’ had too many memories and seemed to be unable to create anymore since there was no more room to store them. The obvious answer to me seemed to be just to throw in another disk or something. Of course, another thing we can do, since we can manipulate memories like data, is to selectively choose less important things to throw onto that extra “disk”. In a way, that’s kind of like what we do already, except instead of having a machine suck out our memories, we do things like write them down or take pictures of them. And in the case of photos, it kind of is like having a machine suck a memory out. In either case, that relieves us of the burden of having to keep it in our brain.

In light of this, it’s kind of a good thing that our brain cells do decay eventually and we do forget things. Otherwise, without a way to manipulate our memories like they do in Kaiba, we’d actually run out of room. Usually, we like to think of data or information as this ethereal sort of thing, but realistically, it’s constrained by the physical world. Those bits have to be written down somewhere, whether it’s on a magnetic platter on a hard disk or in a cell in our brains or in a photon in a quantum computer or in a weird capsule like it is in Kaiba.

Recently, someone linked to something about solving NP-complete problems in polynomial time by taking advantage of the many-worlds interpretation of quantum mechanics. This lead me to some of Scott Aaronson’s papers. Scott Aaronson is a complexity theorist who does quantum stuff at MIT and writes a neat blog. I read through the lecture notes for this course he did while he was a postdoc at Waterloo called Quantum Computing Since Democritus and a paper called Why Philosophers Should Care About Computational Complexity. These two things attempt to tie computational complexity and quantum computing with philosophy (duh). The Democritus stuff is pretty accessible if you have a bit of mathematical background and it introduces concepts like computability, complexity, and quantum computation if you’re not familiar with them. The complexity for philosophers paper assumes you’ve done some computational complexity.

So in Kaiba, we can send our minds around and stick them in other bodies or even in machines. But if we can stick them in machines, what’s running it? We’re not sure, but if we can build machines to interface with our minds or run those processes, then we’ve got a computer that can simulate our brains. This is where computational complexity comes into play.

Aaronson notes that a lot of people who think they consider AI a metaphysical impossibility really haven’t thought it through that far and are only considering the practical impossibility. For instance, what can we extract from the fact that Kaiba has computers that can simulate brains? One thing is that simulating a brain can be done efficiently, presumably in polynomial time.

See, in computer science, a lot of things (like simulating a brain) are possible if you just hardcode everything into a lookup table. Luckily, like I mentioned before, there’s a finite amount of stuff we can hold in our heads. So yeah, you could simulate a brain like that and it’ll work because the table’s finite, but you’d probably run out of atoms in the universe to hold all of that data and the possible choices that would branch out that the computer could make as it went along. Of course, that’s only a practical concern.

Which is why Kaiba’s brain simulating must be efficient, otherwise it wouldn’t be physically feasible. This would seem to imply that simulating a brain didn’t turn out to be that hard. Of course, this means that we’ve got a way to formally describe and model the way brains work too. Anyhow, this is all to ask, if we did have a way of doing this, would a computer simulating a person be that person? And then, we can go a bit further and ask whether a person that we’ve fabricated the data for and is simulated by the computer also constitutes a person.

It’s kind of the same question as whether clones would be people, isn’t it? Except instead of creating perfect copies of the entire person, we can just create perfect copies of the person’s memories and throw it into a computer. Of course, this leads us to the implication that brains are deterministic. Otherwise, this entire memory transfer thing wouldn’t work. You wouldn’t be able to designate a person as their memories if how they behaved changed with the brain that they occupied.

We do have some indication that the brains seem to function differently based on the body that they’re controlling. When Kaiba is in Chroniko’s body and meets the girl who’s in the huge guy’s body, they mention something about getting used to the body. It does make sense that biological processes are governed by the brain and isn’t tied to the person’s identity, but then we see how the body interacts with the person when they start to have ~feelings~ for each other. Of course we can consider the body as another part of the input into the brain and then that discrepancy goes away.

So the thing is that in Kaiba, we’ve got a way of creating something that’s literally indistinguishable from a person. Well, okay, we did start with the premise that it’s possible to simulate a person’s brain, which is kind of a stretch in the real world. But now we ask, what properties would human consciousness need to have in order for a computer to be unable to efficiently simulate it?

It turns out there are some possible ways for this to happen. For instance, if we could solve NP-complete problems or do quantum computations, then a classical computer wouldn’t be able to simulate our brains. Of course, that’s assuming P≠NP, so if it turns out that P=NP, then we might have to rethink this condition, and a quantum computer will be able to do quantum computations, so if we ever built one of those, then that also reduces our options. And of course, the bigger problem is that it assumes we can solve NP-complete problems or do quantum computations in our head.

On a slight tangent, this idea of quantum computations in our head leads to the question of what happens if our brains stored quantum information. That would make it very difficult to make perfect copies of our memories because of the no-cloning theorem in quantum information. The theorem is exactly what it sounds like: it’s impossible to make a perfect copy of an unknown quantum state. What this would imply is that if you tried to make a copy of yourself, it would not be 100% identical to you. Admittedly, it’s pretty unlikely that our brains can store any quantum information.

To close, something that’s slightly related, since it happened around the same time as I was watching, was a department seminar I went to where the guy was talking about neuroscience and brain imaging and tying it into graph theory. Essentially, what he did was he took a bunch of MRI scans of someone’s brain and created some graphs on them somehow. He then ran a bunch of algorithms on the graphs for a bunch of metrics to see if graph theory were any use for neuroscience purposes.

What he found was that the brain activity that could be seen from the scans translated to changes on the graph. Those graph transformations acted on the graphs in a predictable way from the metrics. He raised the possibility of linking thought or computations in the brain with graph transformations. The nice thing about graphs is that, even though there are plenty of problems that are hard, we still know a lot about them and we’ve got a ton of graph algorithms already.

Who knows, maybe we’re further along in figuring this brain thing out than we might think.

Green Party of Ontario

The Green Party of Ontario is lead by Mike Schreiner. Unlike the Green Party of Canada, there is nowhere near as much cohesive support for the Greens. They also don’t seem to be doing the all-in strategy like the GPC did for Elizabeth May, so their chances of success are near zero. I don’t know much else about them except that they may or may not be quasi-lolbertarians.

Ontario Liberal Party

The Ontario Liberal Party is lead by The Honourable Dalton McGuinty, Premier of Ontario and MPP for Ottawa South. He will be having a difficult time holding on to power because of a combination of unpopular initiatives, perceived rising cost of living, and the natural tendency for unpopularity to grow the longer you’re in office. Like the other major parties, he has some populist crap thrown in there like the tuition reduction and new citizen tax credit, but he also seems to actually have a vision in green energy and the educated workforce, which is more than I can say for the others.

For most of the months leading up to the campaign period, it looked like he was screwed and we’d get a Tory majority. Luckily, once we entered the campaign period, he seems to have caught up and is in a position to at least attempt to form a government. Unlike the others, his strategy is less clear and will involve trying to mitigate his losses as best as he can and possibly causing the others to stumble.

Ontario New Democratic Party

The Ontario New Democrats are lead by Andrea Horwath, MPP for Hamilton East. She seems to be trying to have the same disposition as Jack Layton in connecting with working families and such. The ONDP seems to be taking a leaf out of the BCNDP handbook and going for a set of piecemeal populist proposals rather than any coherent social democratic vision and leaving urban issues and the environment out.

That probably has a lot to do with their strategy. Andrew Steele had written about Ontario electoral strategy, where you can split seats up into urban, suburban, and rural and go for two of the three. The ONDP, in choosing Horwath, was going with the classic NDP working class and northern rural ridings. This is pretty unfortunate, because with Jack Layton’s passing, there was an opportunity to grab some of those urban seats.

Progressive Conservative Party of Ontario

The Progressive Conservative Party of Ontario is lead by Tim Hudak, MPP for Niagara South. This election should have been a cakewalk for Hudak. He was going to end up with a million seats and complete the conservative hat trick. Of course, John Tory was supposed to do that last time, and, well. Hudak’s strategy has largely been to remind everyone how bad McGuinty is, which is all well and fine, but he hasn’t really told us what he’s going to do other than TAXES BAD.

Like the ONDP, the PCPO largely set their strategy in choosing their leader. What they’re hoping to do is to repeat Mike Harris’ electoral success in going for rural and suburban seats after the failed experiment in trying to go for urban seats with under John Tory. In a way, this is also the Conservative Party of Canada strategy. The problem here is that I don’t think Hudak has done enough to cement his victory among suburban ridings. Certainly, his railing against foreign workers and foreign students isn’t going to help in that demographic.

Basically

The OLP and PCPO are neck-in-neck with no one in clear majority territory. The next parliament could very well be a hung parliament. Ontario’s history indicates that we could end up with a minority government or a coalition or some kind of deal. And polling seems to indicate that a ton of ridings will be flipping, so really, this is going to be pretty messy.

That really isn't enough terms to identify as Fibonacci

Suugaku Girl is a manga about people who really like math. The great thing about it is that it contains a substantial amount of math. This is also great because it will give me plenty to blog about.

The first chapter of Suugaku Girl is about the main character’s initial meeting with Milka, our socially retarded genius meganekko. She just starts spouting out numbers and, for whatever reason, he feels compelled to guess what comes next. And that is apparently the beginning of this love story.

In the chapter, we’re introduced to a few sequences, some of which are famous and some of which you might not have considered a sequence. It’ll probably help to understand what a sequence is beyond just being a bunch of numbers in a prescribed order.

Formally, we define a sequence as a function $a:S\to R$. The set $S$ is basically our index and is $\{1,2,…,n\}$ if $a$ is a finite sequence or the set of natural numbers $\mathbb{N}$ if we’re dealing with an infinite sequence. Normally, functions are written as $a(n)$, but, as was alluded to before, we refer to terms by index as in $a_n$.

However, $R$ can be any set. In the case of Suugaku Girl, it seems to be sticking with integers, but we can have sequences of bitstrings, vectors, complex numbers, functions, or whatever. What this also means is that a sequence doesn’t necessarily need to have a “pattern”, but can really be any ordered list of numbers (or functions or vectors or…).

Milka also brings up the idea of infinite sequences. A lot of the time, people will try to “solve” a sequence by completing it when they’re given only the first few terms. But, like Milka suggests, what they’re doing in that case is assuming that the rest of the sequence goes on as initially implied. Really, we can define any sequence we like with any behaviour we like. Again, remember that a sequence can be anything we want it to be. In fact, the sequence that Milka defines using the digits of π is kind of like that in that it’s completely arbitrary and doesn’t really have the kind of sequence definitions we’re used to seeing.

For finite sequences, we can just list all of the terms of our sequence like $(1,1,1,1,1,1000000,1)$. Obviously, we can’t do that for an infinite sequence. Luckily, a lot of the time we define sequences that have some sort of useful pattern that we can represent in a succinct way. Sometimes, like the digits of π sequence, this is harder.

We can try to formally define all of the sequences that were given in the manga. For instance, the Fibonacci sequence $(a_n)_{n=1}^\infty$ is commonly defined as $a_n = a_{n-2} + a_{n-1}$, but we have to give the first two terms $a_1 = 1, a_2 = 1$. The second sequence (which we’ll call $(b_n)_{n=1}^\infty$) takes a bit more work to define. We’ll need to define $p_n$ to be the $n$th prime number and then we can define $b_n = p_n \times p_{n+1}$. The third sequence $(c_n)_{n=1}^\infty$ is easy, it’s just $c_n = n^n$. And we can formalize the last one, which I’ll call $(d_n)_{n=1}^\infty$, just like the first two with a few more words. We let $\pi = q_1q_2q_3\cdots$ be the decimal expansion of π. Then $d_n = 2\cdot q_n$.

So that’s all fine, but what exactly are sequences used for? I’m pretty sure everyone’s learned about arithmetic and geometric sequences in grade school. Obviously, we can study sequences and their behaviour on their own. We can talk about whether they increase or decrease or how fast they grow or whether they converge. Apart from that, I don’t remember seeing sequences used for something besides sequences until analysis.

Analysis is basically the field of pure math that formalizes the concepts that we’re introduced to in calculus and generalizes them to spaces. Limits are a fundamental idea in calculus and analysis and these are defined by how a sequence converges. And this is where those weird sequences of vectors or functions comes into play, since we can talk about the convergence of a sequence of vectors or a sequence of functions in these other spaces that we want to do analysis in.

That’s probably the easiest example of an “application” of sequences. For myself, over the last few months I’ve read about automatic sequences, which are sequences that can be generated by a deterministic finite automaton. This gives us a way to relate automata theory to number theory and algebra. For instance, once we have k-automatic sequences, we can talk about k-regular sequences and come up with power series with respect to certain rings and fields and bla bla bla.

If you ever want to find out what crazy sequence you might have a part of, check out the Online Encyclopedia of Integer Sequences.

「うさぎドロップ」/「 LC斐爾 」

One of the few famous quotes in Canadian politics is one by Brian Mulroney, leader of the Progressive Conservative Party of Canada and the 18th Prime Minister of Canada, during the 1984 campaign. As the leader of the Liberal Party of Canada that took over after Pierre Trudeau resigned, John Turner inherited Trudeau’s premiership (yes, we can swap prime ministers without elections) and government in the latter part of his term. Just before resigning, Trudeau had appointed a ton of loyalists to various positions.

Technically, it is the Governor General of Canada (who acts as the representative the Crown) who makes these appointments, but he or she only does so on the advice of the prime minister. In this case, the appointments had only been recommended by Trudeau but weren’t finalized by the governor general when Turner became prime minister, so he could have stopped them. During the 1984 leaders’ debate, Mulroney attacked Turner for allowing these appointments and Turner replied that he had no option. This was the lead-in to Mulroney’s famous line:

You had an option, sir. You could have said, ‘I am not going to do it. This is wrong for Canada, and I am not going to ask Canadians to pay the price.’ You had an option, sir — to say ‘no’ — and you chose to say ‘yes’ to the old attitudes and the old stories of the Liberal Party. That sir, if I may say respectfully, that is not good enough for Canadians.

This left Turner shattered in the debate and pretty much won the election for Mulroney. Unfortunately, ever since then, media coverage of electoral debates has always focused on finding that snappy equivalent knockout line, but no one has produced one since.

I like Usagi Drop. Yes, I have read the entire thing. No, the ending was not what I would have liked, but I’m not particularly angry about it. I mean, 95% of it was great, which is a far better ratio than most stuff out there. What’s more is that I think the initial reaction absent the surrounding context made it seem much worse than it actually was, especially with the important reveal that Rin isn’t actually Grandpa’s biological kid.

In fact, I’d say that I don’t really have a problem with most of the ending “arc” and it’s only the very last chapter that makes me raise an eyebrow. I can buy that Rin could have developed romantic feelings for Daikichi. After all, I think it’s an important note that she sees him as a guardian and not her father. He’s always simply been Daikichi to her.

The problem, then, and the part I find hard to believe is Daikichi’s response, which pretty much amounts to a ‘welp, guess I have no choice’. It’s really strange because, even though he was clearly uncomfortable the idea, he didn’t put up that much resistance. It’s strange enough that he offers to wait two years and hopes the problem might go away. After the two year wait period, Rin kind of goes ‘hey, it’s been two years’ and he’s sort of resigned to the whole thing.

What I’m struck by with Usagi Drop’s ending is that Daikichi had an option: he could have said no, but he chose to say yes. It would have been perfectly fine for him to say no. Rin couldn’t have seriously been expecting Daikichi to reciprocate. She would’ve been fine if things continued the way they were. She was prepared to have things stay the same. Things might’ve been awkward for a while, but a ‘no’ would have closed the matter. Instead, we’re left with, well, whatever it is that we have now.

I’d like to stress again that I still think the manga is excellent, even the second half of it. However, Daikichi’s response is baffling and his rationale is unconvincing. Quite frankly, it’s not good enough, especially for such an otherwise great manga. I’ll defend it, but I’ll concede that the end is not at all what I wanted.