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Science

Journal Journal: Beyond irrational numbers (continued fractions)

Lately, I've been casually trying my hand at learning some mathematics, especially number theory (my background is in electrical engineering). While doing some reading, I came across continued fractions, which are of the following form...

a/(b+1/(c+1/(d+1/...

...or in ASCII art...

Arrrgh. My ASCII-ART-fu isn't strong enought to defeat slashdot's lameness filter, see the link above to get a better idea of what a continued fraction looks like

So what I found interesting was that you can express any rational number as a continued fraction with a finite number number of terms (a,b,c,d,...) and any irrational number as a continued fraction with an infinite number of terms that repeat peroidically. For example...

sqrt(2) = 1+(1/(2+1/(2+1/(2+1/(2+...

Well it seems like the next question to ask is, "are there numbers that can't be expressed irrationally?" Or put in another sense, in the sequence: integers, rational numbers, irrational number, is there anything after irrational numbers? Let's make the terms of the continued fraction be the digits of pi...

3+1/(1+1/(4+1/(1+1/(5+1/(9+...

Can this number (is it a number?) be expressed as another continued fraction, but with terms that repeat periodiocally? Or is it a new kind of beast altogether? My quest continues...

The Matrix

Journal Journal: Matrix Reloaded Sucks

Arrrgh. It sucks. There I've said it. I was an unabashed fan-boy of the first Matrix. That's why it pained me so much to see the second. If I'd had no previous expectations, I still would have walked away disappointed. And $16 poorer. But not betrayed. The sad part is, I should have seen it coming, the signs were definitely there. Sequels, it seems, are never as good as the original. Especially when the first movie does a good job of coming to a final conclusion. After the first movie, I distinctly remember thinking, "how are they going to continue this?". Everything was wrapped up so nicely for us. In retrospect, this was Hint #1.

And we all know that great works of art are solitary achievements, right? DaVinci doesn't say to himself, "Hey, that first Mona Lisa didn't turn out too bad, maybe I'll crank out a couple more". I guess the sign of a true master is knowing when to leave it alone. Hint #2.

Of course I shouldn't discount the fact that I had high expectations going into the movie. Now it might be just me, but it seems like the best films I've seen are the ones I've had no preconceived notions about. Like where a friend says, "Hey let's go see if something good is on." That was my experience for _The Matrix_. This is in contrast to _Reloaded_, where I bought the tickets on-line, so I knew I would get a ticket on opening day. I think the reason for this is because I've become accustomed to being disapointed at the theater so often. I think psychiatrists call it the "defense mechanism". If any particular film I go to is a stinker, I shrug it off and swear I'm going to abstain from movies for a while. Just like most of the previous movies I'd been to. No sense in getting all worked up over it, after all, it's only a movie. So then, when a genuinely good motion picture comes along, I'm psychologically unprepared, and I'm blown away. How could I not have picked up on #3?

And then there's that commercial crassness swirling around this flick that should have tipped me off. TV advertisements in which the cast is endorsing crap *before* the actual release of the movie should have been a giant neon sign pointing out that we were well on our way to sucksville. So I really don't know why I was surprised that the creators sold out to Cadillac.

So that's why I should have know _Reloaded_ was going to be bad. Here's why it actually is. I don't know if I can explain exactly why the first one was so good. I think it had something to do with actually having to think during the film. Everything was new and exciting. There was the meta-physical aspect (i.e. "hey, how would we know if were not in the Matrix right now?!?"). Then there was the cool camera work, and the cool music, and the cool way the agents talked. You're mind was always occupied, always immersed in the film. I wouldn't call it a formula in any sense of the word. Of course I wouldn't have written all of that if I didn't think part II was the exact opposite. The movie just felt wrong. Like they were trying to hard. Or not hard enough. Or something. Maybe it just felt forced. As Yoda might say, "Immersed, not I". Like the first fight scene where Neo takes on all of the Agent Smiths, was it just me, or did that computer generated crap look like it was rendered on a Sony PlayStation? And for that matter, who cares what the inside of the Zion ship hanger looks like. Why are we devoting 5 minutes to watching the ship land in the hanger? How does that advance the story. It felt like I was watching the guys who run the computer graphics machines masturbate. Of course, we are also treated to the engineering level of Zion. A place so boring, that no one who lives there, goes there. So why am I there? Oh yeah, so the old man can say that we are all here for a reason. Like that wasn't repeated 5,000 times elsewhere.

And I guess it's comforting to know that some things stay the same no matter what circumstances humanity has to endure. The city council meetings in Zion are precisely as dull as the city council meetings in my home town. I almost expected them to vote on a zoning ordinance. The story just didn't seem as compelling this time around. It could have been. Why didn't we see Neo spend more time philosophizing with the architect, instead of flying around in the corn-ball Superman schtick? Oh, and am I wrong or did they lift part of the sound-track from a '70s Batman episode? We may never know the answers to those questions, but one thing we do know for certain is that the albino agents are designed by the architect to be superior to the ordinary agents in every way. Including how they shill for Detroit. And I think we can also determine that the original _Matrix_ wasn't a financial success for the Wachowski brothers, because I would have thought if they were millionaires, they wouldn't need to grub for money from Cadillac. This isn't your father's Matrix. And here's a piece of advice for all of the future film-makers out there, leaving a movie unresolved at the end doesn't make me want to see the next one more, it just make me respect the current one less.

But I digress. I'm probably being too harsh. The film was a piece of art in the twentieth-century-post-modern sense of the word. You know what I mean. Like how someone can make a video tape of themselves taking a dump in your front yard, and it gets lauded by the New Yorker *and* the rubes are lined up willing to pay to be insulted. But I can't say I'm above the fray. I'll probably even see part III. When its on the 99 cent rack.

The Courts

Journal Journal: Lawsuit Insurance

Hardly a day goes by without Slashdot posting a story about some coporation using the court system as a form of legal extortion. I was wondering what experience other /.'ers had concerning lawsuit insurance. Is it afforadable? Can you get a plan that just covers your attorney's costs? I'm assuming that would be cheaper than having a plan that covers any damages if you lose. Companies might think twice about filing some of these lawsuits if they knew they were up against a million dollar team of attorneys.

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