Nothing much to say right now. I ate a MegaMac at McDonald's earlier. I'll try to upload the picture later once I've got it off my phone. I've gotta take a walk, though, to burn it off now. Thanks for the book, parental units!

Another Fine Day

I did basically nothing today, other than study a bit of kanji and read a chapter of This Side of Paradise. It seems pretty alright thus far. I am super hungry, though, and it's time to get out of here.

Workin' for the Something

Hey, I started real work again, which is sweet, because as much as I like doing nothing all day, I'd rather do it at home where it is less obvious that I am doing nothing and I don't have to change pants or anything. But, whatever, work has started out well and that is good.


This is completely unrelated, but I thought it was sweet. That was my lunch a couple days back, which consisted of miso soup, a salad I made out of vegetables that I'm not sure the translation of, kimchi flavored cucumber pickles and melon creme soda, which I bought out of a vending machine. It was in a 1.5 liter bottle. I couldn't figure out a way to combine those last two sentences without making it sound like either I or the vending machine was inside a bottle.

I was messing with continuity and compactness and whatnot, and I came upon a little claim that said that any continuous function mapping from a compact metric space to any old metric space is necessarily a uniformly continuous function. This result is called Heine-Cantor or something, I can't remember. As always, definitions because I know lots of people are reading this and just don't want to go all the way to wikipedia.

Metric space:
A topological space in which the topology is defined (or induced, or whatever you prefer) by a metric. Brilliant, so what is a metric, and what is a topology? A topology is just the set of subsets on the space that we call open sets. Open sets (and thus, topologies) need to meet certain criteria, but that doesn't matter right here. Just accept that metrics do a good job of setting them up, but aren't the only way to do it.

A metric is really just a distance function. That is, it takes in two points in the space and returns a non-negative real number. It has to meet these conditions, which if you think about for a second are really just what we mean when we say distance:

1. d(x, y) is non-negative, and d(x, y) = 0 iff x = y; This just says that distance is positive, unless it is the distance between a point and itself, which should be zero.

2. d(x, y) = d(y, x); it is nice if the distance between two points is the same regardless of direction.

3. d(x, y) + d(y, z) > or = d(x, z); the shortest distance between two points is going from one to the other. This is called the triangle inequality.

To make it a bit more concrete, just think of a metric as being absolute value of the difference, or really just how you would intuitively find distance given a picture.

Continuous: Remember your calculus here; a function f is continuous at x if for any real number r > 0, there exists a real number s > 0 such that if d(x, y) < s, d(f(x), f(y)) < t. If f is continuous at all x, then f is said to be continuous.

That's one that gets calculus students all the time. Since I don't have Greek character keys, I had to substitute for epsilon and delta, but if you've ever taken one of these courses, you should have recognized it. What does it really mean? It means that we can get arbitrarily close to the function value at x [that is, f(x)] and still be able to find a neighborhood around x that maps entirely closer to f(x) than whatever value we chose.

I'm sort of glossing over the fact that you can have different metrics on the domain and range spaces, but I figured you can figure that out and I don't have subscript buttons. Furthermore, we don't even need a metric space to define continuity, but it will do for right now.

Uniform continuous: Also usually throws people at first because it looks like continuity. So what is the difference? Delta, or s, as above is independent of x. What does that mean? It means that if we choose some arbitrarily small epsilon, or r, then we can find s as before, but that this s (some s that we can find will have this property anyway) is sufficient for any x. So we can move our s-neighborhood to some other point, say y, and it will map to within the r-neighborhood of f(y). Clear as mud?

Compact: A metric space is compact if any open cover of the space has a finite subcover. This just means that if we choose some of our open sets (possibly an infinite number of them), and that by "unioning" them, we cover the metric space, we are guaranteed to be able to keep only some finite number of these open sets and still be covering the space. I know, it's a little out there.

So, on to the problem. I am thinking this way might work. First, let's choose our arbitrarily small r. Now, assuming f is continuous, that means that at each x, we can find our s value that meets that nice condition. Of course, we don't know that f is uniformly continuous (as this is what we'd like to prove!), so we must assume that s depends on x, so let's write s = s(x).

Here I've got a little issue that I haven't bothered to work out all the details of. Since s is a real number, and number less than s is going to work too, so how do we properly define this function? Experience tells me we generally have a largest s that works for a given x, which makes sense if you think about real numbers, so I suggest choosing that number. Of course, it is possible that any s may work, but I think then we can just choose whatever number we want and it won't really matter.

Anyway, now let's consider a set we just created implicitly. That is, let's look at each of the s-neighborhoods of x (x can take any value in our original domain space, which we might as well call X). It's fairly obvious that x is an element of it's own s-neighborhood, and it also turns out that an s-neighborhood is necessarily open [this results from how we define the topology via the metric], so the set of s-neighborhoods of x forms an open cover for X. If we assume X is compact, as we are doing, then we know we can keep only a finite number of these s-neighborhoods and still cover X. Since the set of s's that we are considering is now finite, we know there's a smallest member, which I'm tempted to call s'.

It seems now to me that this s' should be sufficient for any x in X, but I haven't worked out the details. Feel free to work it out for yourself if you want. And congrats if you made it through this post.

Izumo Taisha part Two

I had practically forgotten that I didn't finish talking about Izumo Taisha, but I'm sure you all enjoyed my meanderings about language in the mean time. If the comments sections are any indication, than spammers certainly enjoy my blog, anyway.

So here's a cherry tree on the grounds of the taisha, the first one I saw in bloom. Cherry blossom viewing is a huge thing here, but since I just did that last week, I'll have a new update with pictures just for that later.


Here are some shots of some outlying buildings of the shrine.

And this is the main building. People were going up to it and praying and all. Some dudes even asked me to take their picture for them, so I did.

There were two statues, one of a horse and one of an ox, in a little building near the center. I don't know what significance they have, but I assume there's a reason.

Here's a neat little waterfall with some sort of mini-shrine.

And here's a thing that the shrine is famous for; a giant rope. I forget what the name for these rope things that shrines often have is, but the one at Izumo is gigantic, probably the biggest in the country. There is a tradition of throwing coins up at it, and if the coins stick, your marriage is supposed to be brought good luck. Or something.

And another shot of a doorway.

And some kind of artwork out front.

That about does it for Izumo Taisha.

Yesterday I went to a school entrance ceremony, because school is starting up again, which necessitated wearing a suit. Unfortunately, the snow tires are still on my car because they haven't given me back my normal tires yet, which has caused them to get worn down, which in turn caused one of them tires to go flat, so I had to put on the spare tire while wearing a suit. Awesome.

So, I was running a bit behind of schedule, though not really in danger of being late, so I decided to take the shorter route to school, which basically goes up and over a mountain, but I guess the car didn't like that with the spare on, because it completely died in the middle of the road and I couldn't get it to go forward, so I just backed it down the mountain in neutral until I could get to a spot off to the side, where I could presumably get help.

As it turns out, a lot of Japanese people are terrible drivers and were completely baffled that a car could die, I guess, as it generally took them a bit of waving to figure out to just go around. One dude driving a big truck even stopped behind me ( I stopped reversing when I saw people) and honked his horn. You would think it would be pretty obvious that I haven't just stopped my car in the middle of the road and put on my hazard lights and been waving you around for the last two minutes just for the fun of it. Eventually, he got the idea and decided to drive around me on the left (that is, in the lane I was in) instead of just using the right lane, avoiding running into my car by about an inch. Of course, the truck following him decided to do the exact same thing. It is amazing how stupid people can be.

Anyway, I got my car back to a spot off the road, but when I put it in drive this time, it didn't give me any warning lights or any trouble at all, so I ended up just turning the car around and driving to school the long but flat way. Ridiculous.

Kakokei

I've been learning Japanese for a while now, and I'd say I'm pretty decent at it. People who learn Japanese often complain about kanji and various other stuff. Admittedly, learning a ton of characters is not particularly easy, but it's really not that bad and you don't actually need to know any Chinese characters to write the language; your writing will just look like a kindergarteners if you don't use any. Other than kanji, Japanese is essentially an extremely simple language, which is compunded by the fact that Japanese people basically never really say anything in that Japanese culture is high-context compared to most other cultures. So you can basically get by with a couple nouns, a couple verbs and a lot of soo desu ne? and yoroshiku onegaishimasu.

So, I started spending some of my copious amount of time here at the BOE reviewing some French, which actually comes back pretty easily, and trying to pick up some German because why not. Actually, I looked at a couple other languages, but I decided after reading about it for about half an hour that Dutch is essentially impossible and best left to the Dutch.

French isn't so bad if you are an English speaker, and really not so bad if you knew it at one point, anyway. German is really just a hilarious sounding language, which is what keeps me going on it. I'd say it ranks just behind any of the languages in the Chinese language family for sheer weirdness of sounds, probably just ahead of the Nordic languages. Certain words are just awesome, like das Krankenhaus. I can also appreciate that nouns are capitalized regardless of what they are because at least that's consistent.

But let me get to my point. The past tense is a mess in European languages. I'm glad I'm not trying to learn English as a second language because it is pretty terrible, but I am going to highlight some of the weirdness.

Firstly, multiple past tenses. From what I can tell, French has three past tenses, though one is basically just used in writing and my guess would be will eventually cease to exist whatsoever, and another is for all intents and purposes useless. So, that leaves us with the passe compose (I can't add accents on a Japanese computer as it turns them into random Chinese characters), which is not amazingly hard to form, but has its own peculiarities.

German uses a past indefinite tense, which is essentially the same as passe compose. Both of these tenses are basically equivalent to English present perfect in construction, but translate into past perfect, (simple) past, or emphatic past, depending on the situation. English is probably the worst, but I'm not learning that! The tenses are formed by conjugating an auxillary verb, either to have (avoir, haben) or to be (etre, sein) to the subject, and adding a past participle, which is somehow formed from the original verb that you want to express. Whether it is to be or to have is something you basically just have to memorize, though they follow ridiculous rules. Forming the past participle for most verbs is rather simple:

French:
jouer -> joue (accent aigu over the e)
choisir -> choisi
appredre -> apprendu

(verbs in French all end in -er, -ir, or -re, so most change as above)

German:

sagen -> gesagt
arbeiten -> gearbeitet
studieren -> studiert

Unfortunately, Europeans seem to hate any form of regularity, so all the verbs that you'd ever want to use are irregular. My list of French verbs with irregular past participles has 40+ members, and I'm pretty sure doesn't list all of them, while my list of German verbs with irregular past participles is pretty close to a hundred. At least in French the irregularities tend to fall in nice little groups:

prendre -> pris
apprendre -> appris
comprendre -> compris

German past participles seem to be chosen essentially at random, as if to confuse non-native speakers. At least they sound funny.

fliegen -> geflogen.

Here's a thing that's nice about Japanese. There is one past tense. It works like this:

shimasu -> shimashita
kimasu -> kimashita
demasu -> demashita

Getting to the -masu form requires a little bit more work, but it's entirely regular excepting two verbs. I have to admire any Japanese person who can be bothered to gain a mastery of English because doing comparative lingustic stuff like this makes it apparent that European languages, English in particular, are ridiculous and almost mind-bogglingly complicated.