Bubble

What is this John and Kate thing? I have no idea actually. From what I can gather it is some sort of tv show about kids or people with kids or something. People keep referencing it on shows that I actually watch and there are news stories or opinion pieces or whatever about it that I don't read but see on news websites. I could just google search, I'm sure, but I actually don't want to know. One of the little known benefits of living overseas is that the effort it takes to stay in contact with the US makes you basically immune to whatever stupid culture stuff is going on there. Also, the effort of trying to figure out Japanese tv, etc., makes you basically immune to the stupid stuff here, too. It's fantastic and I'm going to miss the ease with which one can live in a bubble, protected from all the stupid, here. Actually, nobody tell me what it is because I don't want to know.

Eat, Drink, etc.

Check it out. New Fanta Cider, which is zero calories and somehow reminds me of Red Flash even though the taste is totally different. And, Pepsi Shiso! A good way to leave Japan since I apparently just missed Cucumber Pepsi on the way here. Shiso is some kind of leaf that appears in Japanese food. This was rockin' good. I basically never drink soda, so this was kind of weird, but I couldn't resist something green to drink. It's quite the opposite of ma, I guess.


Coffee-flavored jelly that you are supposed to drink. I don't know how, since I had to scoop it out of the bottle. This was part of my juice or not juice quiz for my English conversation class. Juice, or juusu, is a loanword into Japanese, but it's used for all sorts of non-juice things, so I was testing my students to see if they could tell what qualifies as juice in English. The answer is not really, but I expected that. Everyone here is surprised to hear that Calpis is not what an English speaker would consider juice.


New beer! Quoting, Kirin's KOKU NO JIKAN delivers you a great harmony of refreshing and full body taste.


Probably I already posted this, but that's actually donkey meat. Thanks, Italy.

Those last couple of pictures are dark because the light in my bedroom has been broken for a couple months, but the electrician just replaced it today at (hopefully) the taxpayers' expense.

Tonight I ran into the same little kid at the convenience store, and he again gave me a great recommendation on snacks, this time some rice crackers. Some other kids showed me the stag beetles they had just bought. This place is great.

Last but not least, congrats to Rayfro on his upcoming marriage.

Nice Piece

I came across this piece, which I thought some people in my regular audience might like. Read.

Robots

I recently finished the Philp K. Dick short story "Second Variety," which is about robots that take over the world and are trying to kill all the humans. It was somewhat amusing if fairly predictable. Then I went to see Terminator 4, which is basically about the same thing.

I'll say I went in with pretty low expectations because while almost everyone seemed to complain about how Terminator 3 didn't show us the promised war with the machines, I actually liked it and thought that it was a good idea not to show that. I also liked the ending about how the future can't be changed. The problem with a war against robots is that it is actually stupid, so it's best seen in the little glimpses that we got in the first couple movies. I should also add that I wasn't expecting much from Christian Bale, fresh off ruining every scene he was in in the latest Batman movie.

That said, this movie managed to be even dumber than I could have imagined, and I pretty much loved it. Don't get me wrong; it is a failure on basically every level, managing to undercut even my low expectations, but it is such a spectacular failure that it's hilarious. As I was saying, a war against robots in the future is basically on its face stupid, and Terminator 4 does a good job of showing us how stupid it is. In particular, it does a good job of making the robots so stupid as to be laughable in an attempt to make it believable that our protagonists could survive for more than about five minutes.

One glaring example is that there even is a human resistance. If you've seen the previous movies, or even if you haven't, because they remind us multiple times what happened here, you know that the supercomputer Skynet set off nuclear warheads all over the world, leaving only a few people alive, which it then hunts with Terminators, which are generally human-shaped robots. How stupid would this all-seeing military supercomputer have to be in order not to make sure all the military sites would have been taken care of? Yet the resistance is shown with fighter jets, helicopters, all manner of weaponry and even a freaking submarine. Where are they getting this stuff?

Then, after that, this brilliant computer decides that the best way to hunt down humans is by making absurdly slow humanoid robots that just kind of wander around until they find someone, then try to punch him to death. Seriously, they're basically like life-sized rock-em-sock-em robots. Of course it also builds giant robots that pick people up and put them in boxes (it is said that Skynet is doing experiments on people, but only briefly, and this is never explained) and robot motor cycles that are defeated by, I kid you not, putting a rope across the road in front of them WHILE THEY WATCH so that they clothesline theirselves.

Maybe the best part of this Skynet stupidity is that it has a crazy and convoluted plan to, big spoiler, kill John Connor. Here are some more spoilers for you. Skynet manages to use one of these big box robots to capture John's father, Kyle Reese (he is from the future if you haven't seen T1) and use him to lure John to Skynet's central complex thing. John is worried because if he doesn't send Kyle back in time, he himself will never exist, blah blah, Terminator is always about this stuff. At first, Skynet doesn't realize it is Kyle Reese, but then once it figures it out, it separates him because it also knows that Kyle is the key here. Then it proceeds to NOT EVEN TRY to kill him, just leaving him in a box for John. When John inevitably comes and rescues him, it tries to kill each of them with a single, unarmed terminator for each.

Beyond that, the script is mostly just ridiculous cliches and one dimensional-characters (given it is an action movie, but these characters are particularly egregious examples of hackneyed writing in the genre). Here are the ones I remember:

John Connor (Christian Bale) - angry. That's all. At least Bale doesn't do the stupid Batman voice.

John Connor's wife (?) - She is a doctor, I guess, and that's about it for her characteristics. Unless you can count the distractingly wooden performance of whoever it is that plays her as a character trait.

Kyle Reese - Young and inexperienced, but enthusiastic about the resistance. He's not that annoying other than you can pretty much determine his entire character within the first minute he is on screen.

Star - Little mute girl. This one amazed me as being the most cliched character I think I've ever seen, somehow. Can't blame the kid playing her for a character that literally could have been written out of the script by simply scratching out all of the million or so times somebody screamed her name.

Barnes (Common) - From rapper to basically worthless character, quite the stretch for him. He spends almost every second he is on screen scowling, and that is about it.

Marcus Wright - Spoiler, he is a robot. He's the tortured guy who just woke up in the future and has to discover why (he is a robot). He was on death row and feels guilty. This ultimately leads to some of the worst dialogue I have ever heard about hearts. If you see the movie, you will know immediately what I am talking about as soon as it starts. Unfortunately, the hearts theme continues to walk the line between annoyingly bad and laughably bad throughout the remainder of the movie.

Pilot Woman - I forgot this character's name, which goes to tell you how well developed she was. It's not like she's even a minor character; she's just that worthless. As soon as she appeared on the screen you could tell she was going to be a love interest for Marcus, and the writers seemed content to let your intuitions serve as backstory for her because they basically just throw her at him. She has some kind of weird eye paint, which is also kind of annoying.

Robots - hilarious. I should mention that probably the best acting in this movie is done by a computer generated Arnold Schwarzenegger. It is without a doubt the best part of the movie when he shows up, and it's made even better when you realize that Skynet has deemed that a single naked robot-man is the best way to kill John Connor when he is in the center of an entire army of robots and robot planes and robot motorcycles and probably other stupid robot stuff that actually have guns.

There are some other people in the movie, but they are basically even more worthless.

I just want to reiterate the point about how bad the hearts thing is before I end this post. If I hadn't heard it with my own ears, I would have thought it was a parody of action movie dialogue.

Short Story

I just finished my weekly local English conversation class, which this time featured heavily me running a sort of modified test for the Stroop effect. I actually want to repeat the test in an experiment to see if doing it in a second language has an effect, as well as to see if running the test in kanji or kana changes the result. So far there seems to be some effect, but my sample size is too small, etc. So I went to the store to pay a bill and to buy a beer for a reward, since I was teaching forever today it seemed. I ran into one of my favorite little second graders, who immediately ran up to me for a hug, and then came in the store with me and gave me advice on how he likes chu-hi better than beer, and which snack is delicious. Life here is at times hilarious.

Boring (or not) Math Post Ahead

Dan seems to have gone back to his roots with a post about lit, so I guess it wouldn't hurt me to go back to mine.

A few days back, I had to teach this lesson about numbers using our still somewhat infuriating new textbook, which contained a bit about counting the number of times you could find a certain shape within another shape. That is, there was an irregular shape made of square tiles, and you had to find how many 1 x 1 squares, how many 2 x 2 squares, how many 2 x 3 rectangles, etc. are contained in it. I didn't read the directions, though, because most of the activities are stupid I don't really care about them, especially if another teacher is going to do all the work, anyway. So, I thought at first that it was asking how many squares total were contained in each of the previous shapes. As in, a 1 x 1 square contains one sqaure, and that's it; a 2 x 2 square contains 4 1 x 1 sqaures and 1 2 x 2 sqaure, so it contains five squares total. That got me to a problem of finding the number of squares in a given shape, which is way too hard, so I decided to reduce it to how many squares are in an n x n sqaure. This is a combinatorics problem of a sort, for any of those who have forgotten about that post.

So, let's define our counting function, say f(n) for n = 0, 1, 2, ... A good way to start is just by looking for a pattern.

f(0) = 0
f(1) = 1
f(2) = 1 + 4 = 5
f(3) = 1 + 4 + 9 = 14

And thus, a pattern emerges! What we are really looking for, it seems is a sum of the squares of the integers up to n. Or maybe that is just the first few steps of the pattern and then it diverges somehow. Now we will need a proof. Can you work one out? Probably. Here is how I figure it.

If we have an n x n square, we can label each tile by coordinates like so:

(1, 1) (1, 2) (1, 3)... (1, n)
(2, 1) (2, 2) ...
...
(n, 1) ... (n, n)

Forgive me if that doesn't hold up to html, but you should be able to figure it out.

If we want to count 1 x 1 squares, we can start in the upper left corner at (1, 1). From there, we can move right one tile, then right another, etc. and down one tile, then again, etc. Leaving us with n x n places to put that square.

To count 2 x 2 squares, we can start again in the left corner and move right, but we aren't able to move the left column of our 2 x 2 square to the final column, so we have only (n -1) places that way. Similarly, we can't move it all the way to the bottom, so we only have (n -1) places that way, too. That means there are (n-1) x (n-1), 2 x 2 squares.

Following the pattern, we will end with exactly 1 n x n square, and we see that what we have done here is add the squares of the integers up to n, though in reverse. So, our formula is good!

Good in a sense, anyway. Anyone who has taken calculus (and probably anyone who has taken Algebra II) should be able to tell you that these summations, with their sigma forms and all, for those who remember, aren't particularly nice when your n gets anywhere even remotely considered "big." For us, "big" means probably around 4 or 5, but for John it's probably more like 13 or 29 or something. For the computer science-y people there, we can actually figure an operation count here. For some n, we are doing n multiplications and n additions (assuming we add 0, which seems stupid unless you want to make your program crash when it gets n=0). So, I suggest we pull an 8 year old Gauss maneuver and get us a nice fixed number of multiplications/additions.

When I say Gauss maneuver, I am referencing Carl Friedrich Gauss, who was possibly the smartest dude to have ever lived. There is a story about him that when he was still a wee lad, one of his teachers got annoyed with him being so smart and had him sum all the integers from 1 to 100, thinking it would take quite a bit of time. Gauss almost immediately came up with the formula for doing this. It was already known, but it's still pretty impressive since he was doing it at an age when people generally can't abstract whatsoever. That formula is actually pretty easy to prove for us adults if you think about it a bit. It's

g(n) = (1/2)n(n+1). If you can't get it, I'd suggest stacking up boxes like a staircase and noting how much easier it would be to count if you had a rectangle instead of a staircase.

Anyway, the point of that little sidebar is to note that when adding the first power of n, we get a quadratic polynomial as the closed form. It is intuitive, maybe, to think that if we add the squares of integers, our closed form will be a cubic. It is fortunate for us that our intuition is right. I don't actually know how intuitive it is, but we can come back to that with a later problem that should sort of bound our form here in a sense. I really just remembered that the powers need to go up, but could never remember what affine functions of n are the factors. I don't think anyone ever does, but that is why textbooks have appendices.

So, what do we do if we are looking for a cubic polynomial? You could always ask your graphing calculator, assuming it is TI-high enough. But why not do it the old fashioned way? Because it turns out that the way to do that is a system of equations, which nobody likes.

A cubic should look like this

f(x) = ax^3 + bx^2 + cx + d. Now we just need to plug in our values of x. I switched to x because that is what I am used to for algebra but it is the same as the n from before.

We are fortunate that f(0) = 0, since that means d = 0, so we have really only a system of three unknowns to deal with. What's the difference? You can look at operation counts for Gauss-Jordan elimination on matrices of size m x m if you are really curious. Suffice it to say that solving a system of even three variables is deemed computer work once you get out of Algebra II.

Our other points here are

f(1) = 1; f(2) = 5; f(3) = 14, if you forgot. Coupled with the handy zero, that gives us four points, just enough to define a cubic.

So, we have

a + b + c = 1
8a + 4 b + 2c = 5
27a + 9b + 3c = 14

That should be enough to send you running for the hills of Mathematica, but I didn't have that as an option at the time, so I brute forced a solution, which you are free to do if you want. Here is what you should get

(1/6)n(n+1)(2n+1). Lots of work for no reason. We don't yet actually know that this is the formula since we were just guessing that it is a cubic. If you want to prove it, you can apply mathematical induction, which I will post about doing if anyone asks for it, but this post is already long enough.

I will mention one last thing about intuiting the degree from before. If you look at the sum of the cube of the integers up to n, you will get

h(0) = 0
h(1) = 1
h(2) = 1 + 8 = 9
h(3) = 1 + 8 + 27 = 36
h(4) = 1 + 8 + 27 + 64 = 100

Those last number should set off a whistle in your math brain. They're all perfect squares, of 0, 1, 3, 6, and 10, in that order. Those numbers should set off another whistle if you were working on Gauss's problem from before. What you have here is that the sum of the cubes up to n is equal to the square of the sum up to n. You don't have to go through the whole algebra here to prove it or anything, just induct like before.

But here we see that we have a fourth degree polynomial. When we summed just the integers, we got a second degree polynomial. Since the sum of the squares should be in the middle of these two sums all the way, it makes sense to guess that we are looking for a third-degree polynomial.

Rock on!

梅干し

Sorry for the long wait between updates, if anyone was actually waiting. This should just be a short update about ume, a fruit called alternately Japanese apricot and Chinese plum. It originally came from China, but it's a lot more like an apricot than a plum, so take your choice of translations. They start out green, but if you give them time to ripen, they turn an orangish color, rather like apricots. Unfortunately, they don't taste particularly good, unlike their more familiar western relatives.


When they're still green, you can use them to flavor alcohol, I think shouchuu, but I'm not sure, to make umeshu, which means plum wine. It's really sweet and most people seem to like it. I didn't do that, however. I bought a bag of ume for 100 yen to see how they were and to see if I could make umeboshi. To do that, one needs salt (not pictured) and a bit of this:


This is called white liquor (howaito rikaa) and it tastes pretty bad on its own, but I guess it isn't really made for drinking. You basically just wash the Japanese apricots in it, then roll them around in a bunch of salt. Then you put them in a bag and put something heavy on top of them for a few days. A bunch of the juice comes out and they sort of pickle in it, getting soft and staying sour. Here's the result:



Normally they are red, but mine are more brown because I didn't put any akashiso, a red leaf in with them because I didn't want to buy a big bag of it for only using a little. They're still good, though. The only annoying part is that they still have the pits in them, so you have to spit those out. Beside the umeboshi, you'll notice a limited time brew from Yebisu which is one of the best beers I've had here. It's not quite as good as the other amber beer I had, though. I have to get that from a convenience store on the other side of town, sadly, because they don't have it at the one by my house. Well, that's it.

懐かしいな〜

Recently I was digging around on my computer for something to listen to and I rediscovered a couple tracks from the days of Nerd Bowl. Thanks to Mr. Link for a couple of these, which led me to another couple.

Maynard wails away revival style.

Andy would be proud.

The right CHS? No, they are way too good, but a man can dream...

Inexplicably fun to play, even if you don't exactly have Jaco with you.

I think only I liked this song, but thanks to Karen for the tape. It might still be the best birthday present I've ever gotten.

We never did quite get this one right, but it was always interesting.

This one never even resembled the original form, no matter how many times Mr. G would run through it with us note by note.

The intersection Kool 95 (maybe? help me out, John!) and CHS jazz band, although I always like this number better, for never having played it.

I've been messing with this song on piano for no reason and it still sounds terrible, probably in no small part to my refusing to arrange moving parts beforehand.

Which leads me to a non-pep band song (there is no real transition) which I've also been messing with. This is maybe the best band ever, by the way.

Anyway, good luck with therapy and thanks for the memories, buddy!