Monthly Archives: November 2009

Count von Count vs. Cantor

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A combination of an incidental argument over whether the cast of Sesame Street or the Muppet Show would win in a fight and reading about Internet crazy people refusing to believe the uncountability of the real numbers lead to this. I hope you like math.

So we know that Count von Count (colloquially known as The Count) loves counting. According to Wikipedia, he will count anything and everything, regardless of size, amount, or annoyance he causes everyone else. The logical question would be, what happens when we present The Count with an uncountable set like the set of real numbers, ℝ (unless you are a crazy person)? Can he count it?

The answer is of course he can, he’s the goddamn Count.

What are the implications? Basically, The Count can enumerate any set, whether it’s uncountable or not. This means that to The Count, every set is recursively enumerable. This means that for every set S, S and its complement S’ are recursively enumerable. But this means that every set S is recursive.

So, now we consider the halting set H = { (P, w) : program P halts on input w ∈ Σ* }. From above, we have that H is recursive (since H’ is recursively enumerable). But this means that H is decidable. This means that The Count can decide the Halting Problem, and thus, can decide any undecidable problem.

What we conclude is that The Count’s power isn’t to count, but is, in fact, to break logic.

Finale: GA Geijutsuka Art Design Class

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So while I am waiting for stuff to cook, it’s time to do something I haven’t had the chance to do and hammer out a post. This way I can keep up my monthly posting schedule in between hammering out Galois theory problems.

I remember looking at the season chart for GA and going MORE LIKE HIDAMARI SKETCH HURR and didn’t look at it for a few weeks. After all, I had a ton of other stuff to watch. I did give it a shot after a fairly positive reception from PA forumers.

The thing about GA is that its pace, direction, and style is a lot like Hidamari: quick, really SD and cute, and tons of SHAFT-like cuts and backgrounds. There weren’t any weird photos or text, though, which was a nice change. On the other hand, the content of the gags was more like Moyashimon in that they were grounded in the topic.

Both of Hidamari and GA are about a bunch of high school girls in a specialized art school. Where they differ is that Hidamari is about school life and the relationships between the main characters, while GA is entirely about art. We’ve got art history, art techniques, art tools, art design philosophy, and more. And since I’m interested in design, it was pretty neat seeing jokes about composition and colour theory.

The flipside to this is that I can’t remember the names of most of the characters. There are a lot of them and the time that they do spend time on characters is spent on exploring that particular character’s quirk. So there’s emotionless girl who likes black, hyper active girl, hyper cutesy girl, shy girl who likes cat, and the most normal out of the five girl.

I wouldn’t say that this is what would immediately come to mind if someone asks for a recommendation for this genre. That’s not to say this is anywhere near bad. It’s really good and fun and enjoyable. This can definitely get another season, and maybe next time they will talk about typography, please. ◔ ◡ ◔

When the seagulls cry… (III)

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…there is one survivor.

Bet you didn’t see that one coming.

So if it wasn’t clear enough from EP2, EP3 will definitely convince you that Umineko is a completely different beast from Higurashi. We begin with a look into the past with the revelation of the existence of Kuwadorian and someone who’s actually named Beatrice as well as Rosa’s confirmation of this fact. We also take a look inside Eva’s ambitions and how this plays a part in 1986 Rokkenjima.

The exciting parts of this episode during the actual twilights were decent. Both Beato vs. Virgilia and Rudolf/Kyrie vs. Stakes were a bit short. All of the important good parts were kept, of course, but the extra stuff that really sealed the deal was absent. The depiction of Evatrice’s carrying out of the second twilight was one of the more disappointing parts of EP3. The visual novel was able to render it much more nightmarish than in the anime. The anime’s offering was also a lot weaker than what we all imagined. When they said sea of jelly and mountain of cake, I think that was what we were expecting to see.

But the most important part of the Episode was the ending. How well did it do on that front?

I felt like the ambiguity of who died and who survived shouldn’t have been there (yes, Eva was the only who survived). The buildup from the beginning of the episode was fairly well done. From the looks of my feed reader, Beatrice did her job and masterfully trolled everyone. Ange’s introduction was pretty good, although it could have been foreshadowed better (like mentioned once in a while over the last three Episodes rather than have a flashback the episode before). I’m not sure about the choice of forgoing more EP3 Tea Party stuff for going straight into EP4 material. I suspect that they wanted to clear up who died and who the mysterious girl was, but from the discussions I’ve read, it seemed to make little difference.

The main problem with the adaptation is that it hasn’t managed to convey the depth and richness of the visual novel’s storytelling. This is for two reasons. The first is that there simply isn’t enough time. At the moment, I think that they’re doing the best that they can, leaving in all of the important stuff. That’s good, but it’s all of the small details that get paved over that really makes Umineko fantastic and I think that another twelve or thirteen episodes would have given enough time for the studio to include even small, incidental stuff. I’m not saying that it needs to be one-to-one, but the selection of material to adapt can definitely improve.

The other thing is that I just don’t think DEEN is good enough to render an adaptation that matches up to what we see in our heads when we read the VN. All of the awesome parts of the visual novel so far have been good in spite of the adaptation. However, for every single one of these moments, there’s always something lacking in the execution.

fffff – a tale of failures.

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Since I have a blog, I figure I should blog once in a while. Don’t worry, I’ll be back to blogging too much about animu and politics shortly. So this term has been not quite as keikaku as I’d have liked. This has been fairly enlightening as I try to figure out just wtf I’m going to be doing and how future terms are going to be affected.

Act I: Analysis

I’d already mentioned before that Complex Analysis was a crazy roadblock that put me on to the road to proposed and much easier plan requirements. This was clearly because I was insufficiently prepared for the material. Even though the lecture material made sense as we went through it and the textbook was pretty much the same thing, it was determined that I didn’t have the adequate foundational knowledge in analysis and the intuition that comes with solving those sorts of problems.

So, this was for the best, it seemed. After all, dropping one course wouldn’t be too bad.

Act II: First-Order Logic

Now this, this is failure. This is where we learn that the Rudy 08 strategy does not work when applied to coursework. After not having gotten a passing mark on any assignment, I decided to seek the advice of the TA before the midterm. It boiled down to understanding the solutions to the problems, which I felt like I had a pretty good handle on, especially after relearning everything.

As it turns out, it wasn’t good enough and I failed the midterm. I decided that the chances of my passing were very slim at this point and decided to abandon ship.

This course was a very interesting experience for me. Unlike Complex Analysis, where I was insufficiently prepared, this course should have been cake. I did well in my first logic course and I enjoyed computability theory in the CS context. It turns out that that would be my downfall, because it seems that that was some sort of mental block that made it impossible for me to solve the problems in such a way that it would satisfy the subject in a pure mathematical context.

I don’t think I’ve ever had a course baffle me like that before. I’d go do an assignment, feeling confident that I’d solved the problems fairly competently and find that I was doing it wrong. I’d look at the solutions and try and see what went wrong, internalized the mistakes, and took a stab at the next assignment and, again, felt confident. The cycle would repeat all the way to the midterm.

Epilogue

I walked away from this entire debacle understanding just where my interests in mathematics lie. The things that attracted me to pure math wasn’t exactly the purity and the theory. It was exactly the things in math that I found cool (algebra and number theory) and pure math was the only way I could study those things. And as much as I might want to think otherwise, I’m still much more of a computer scientist than any other kind of mathematician.