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Complex Numbers
Complex Numbers
A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.
The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.
Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.
Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.
March 30, 2007 at 12:25pm March 30, 2007 at 12:25pm
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... but you already knew that.
Specifically, I'm off to the BEACH for a couple days. Kirstin's birthday and all that. I'm not sure what the weather is going to do, but I need a weekend away, even if it rains.
Sunday night we're going to a Meat Loaf concert in DC. I've always wanted to see him in concert. Everyone around me hates Meat Loaf, and they do their best to make me feel like a dork for liking his music. Even my wife was like, "I'm only going because I want to see YOU have a good time. He sucks." (Actually, she's going because I threatened to take another woman.)
But I'm not caving in. Meat Loaf rocks. Oh, sure, he's not Bruce Springsteen, but then again, who is? And if everyone hates him so much, how come Bat Out Of Hell continues to sell 200,000 copies per year, making it one of the best selling albums of all time?
Sure, Steinman lyrics are overblown and melodramatic. My wife loved Phantom of the Opera, so what's the problem here?
The sirens are screaming and the fires are howling
Way down in the valley tonight
Theres a man in the shadows with a gun in his eye
And a blade shining oh so bright
Theres evil in the air and theres thunder in the sky
And a killers on the bloodshot streets
And down in the tunnel where the deadly are rising
Oh I swear I saw a young boy
Down in the gutter
He was starting to foam in the heat
-Meat Loaf,
Bat out of Hell |
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I got my truck's stereo fixed today! The tunage has returned!
Turns out my old tuner was defunct. FUBAR. Vermisched. So they yanked it [insert Beavis and Butthead remark here] out and installed the one that was in my wife's former car (her new car having its own, albeit shitty, stereo).
It makes me want to drive around this evening because a) the tunes are back and b) it's a mind-numbingly beautiful evening.
Correction: It was a beautiful evening. Now storm clouds are gathering, and I think we're doomed.
In other news - at the risk of freaking out the Thought Police by mentioning driving and beer in the same blog entry - I bring you:
THE RANDOM BEER NAME GENERATOR
http://www.strangebrew.ca/beername.php?Mode=Generate
Barney's Glutinous Gloworm Tripel
Smutty Fourth of July Golden Lambic
Ruby Portentious Gas Cloud Dubble
Achin' Stout
Evil Flying Squirrel Brown Ale (made special for darkin)
To pacify the Thought Police:
Don't drink and drive
(Edited because I forgot to say:)
Everyone needs to run subscribe to the Poetry Newsletter. terryjroo has featured Me in it. So even if you don't normally read it, don't miss this issue so you can see more of my nuggets of wisdom! |
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It's been a while since I've ranted about fiscal responsibility, and then I read this article today:
http://www.alternet.org/workplace/49676/
The federal government -- and the majority of Americans -- can no longer get by a single day without taking on additional debt. ... Eventually the higher levels of debt will lead to higher interest rates, which will lead to more debt, creating a cycle as vicious as it is inevitable.
I've heard doomsayers before. Most of the time, they're wrong. This time, though...
We're all building a house of glass cards, here. It might blow down, or it might shatter, or both. It is painfully obvious to me that this situation cannot continue for very long.
Inevitably, there will be finger pointing. There is already finger pointing with the mortgage situation. The Federal Reserve is being blamed for allowing the situation. The banks are blamed for providing subprime loans. People are being blamed for defaulting on them. Well, this latter has some basis in reality - they're the ones who signed the papers, and it's their own fault if they don't read the Ferengi print.
Ultimately, I see a society where desires turn into wants, and wants turn into needs, and needs are purchased on ever-expanding credit. Advertisers con us into needing things we never even knew we wanted, and we eat it up. Hell, half the people I know who watched the Superbowl didn't give a crap who was playing; they just wanted to see the commercials.
The idea that someone might watch television for the sole purpose of viewing the advertisements is so alien to me it might as well be someone telling me I really ought to try shoving my arm into a meat grinder, just for the experience.
There have to be alternatives to debt. Some of them might not be pleasant to contemplate - they involve things like living communally, going without certain things, and driving less than 100% reliable cars, and no one wants to hear that.
"Oh, but I need to have a brand-new car." "You've obviously never had hospital bills." "I just can't live with a roommate." I've never heard such absolutism as I hear from people who are in debt up to their ears. [I know I talked about "needing" a stereo in my ride in my last entry, but you'll note I still haven't done anything about it.]
Do I have debt? Yes. I owe money on my house, and I owe money for the business. Both loans are secured by real estate collateral. I don't have a car loan. I don't have credit card debt (I use a credit card for everything, and I pay it in full every month, on time). I have no student loans. Have I been in worse debt? Hell, yes; that's why I feel so strongly about it now. I'm not perfect; I don't have the retirement savings that I should, nor all the insurance normally recommended. And now I'm starting to think I don't have enough hedge against the coming doom.
Before you ask, no, I don't make a shitload of money. I make more than some, less than others - my personal income is below average for my age, and so is my wife's. It's not about what you make; it's about what you spend. And while I admit to many areas in my life in which I'm "lucky," there's no element of chance in this; I chose to have a small debt footprint. Anyone can do this. It takes time, patience, discipline. Less than it takes to lose weight, though - at least for me. More than it takes to quit smoking; again, personal experience.
It won't be enough to ride out the coming apocalypse, though - when the economy collapses, my income stream dries up. That's why I'm preaching. I couldn't give a crap if everyone else has debt, as long as it doesn't affect ME. |
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Yesterday was another "Drive around Virginia in my old pickup truck whose radio is broken" day. Having spent the last few weeks driving only from my house to my office and back, and little else besides, I hadn't been pushed to get the stereo fixed.
Yesterday, though, was the last straw. I borrowed my wife's boombox for the trip. (When she uses something of mine, it's not "borrowing," but it is when I use something of hers. Fortunately, I rarely want to "borrow" her clothes.) I grabbed the CDs that I made from the absolute best songs of my playlist, got in the truck and took off...
And discovered that the boombox won't play my CDs.
Shit.
I was able to tune in to a radio station sometimes on the box, but the land between Charlottesville and Fredericksburg is notably lacking in radio. Oh, there was some country stations, and some guy telling me all about Jesus (as if I'd never heard of Jesus in all my 41 years). When I did pick up something decent, it faded in and out every time I passed a large concentration of metal, such as a car, mailbox or Civil War battlefield (each of which is about as common as the others on this trip).
Sadly, I was running on a deadline, or I'd have stopped in Fredericksburg to pick up a new boombox, one which my wife could then take and maybe let me borrow it from time to time. Well, actually, I did stop, because Fredericksburg has become so choked with traffic that it makes the Long Island Expressway look like, well, an expressway.
But that was nothing compared to the trip back. Route 1 in Stafford County, going south into Fredericksburg, was backed up for - I'm not kidding or exaggerating here; I've driven that stretch enough to know - Five Fucking Miles.
I figured, wow, there must be some kind of accident up ahead. Occasionally, there'd be a car coming north, laughing at us poor fools in the southbound lanes. But as I inched - tunelessly - along down the road, it dawned on me that the source of the backup was...
The Falmouth light.
Yep, one single intersection - the one where Route 1 and Route 17 business converge - backed up traffic for five miles.
And they ask me why I don't live near Fredericksburg anymore.
Now, as it was Saturday, ordinarily this would have been at worst a minor annoyance. I wanted to be home, sure, but I could have dealt with it. If, that is, I had some tunes.
No. Instead, periodically, some snippet of the worst possible tune would come into my head. I don't even remember now, nor want to, what it was. Something from a commercial, or something. Or maybe it was some tune I knew when I was a kid, because that area would bring back memories like that - it was the route my parents used to drive me on to kindergarten. Hell, it might have been "if you're happy and you know it, clap your hands" - but then, if it were, you'd be reading about me in the paper right now instead of in my blog.
Today I went to Crutchfield, only to discover (though this didn't surprise me) that they don't have stereo people on Sundays.
Tomorrow, though. And I don't care if I have to take time off work to do it. |
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Here's a fun little link that is, perhaps, about as accurate a predictor as astrology:
http://blindcopy.blogspot.com/2007/03/what-is-your-favourite-colour.html
(My favorite color is black, incidentally. Make of that what you will.)
And here's a comic with a delicious, nutritious premise. The link is to the first one; scroll down to "Next" to continue. It's a short read (assuming you have high-speed access) and well worth it:
http://www.webcomicsnation.com/poyorick/botg/series.php?view=archive&chapter=109...
In other news, today is the four-year anniversary of the beginning our invasion liberation military action in Iraq.
Not very amusing, and not even very diverting.
Do you feel safer now than you did four years ago? I don't mean time-engendered relief just because 9/11 is four more years behind us, but as a direct result of the war action in Iraq?
I don't. Terrorism is the new Communism. They've given us something else to be afraid of. And if we're not afraid enough of Them, then we can turn our anger and rage on whatever political ideology we don't happen to subscribe to. Or we can just watch sports and pretend none of it is happening.
*pours myself another martini glass full of Liquid Fuck-it* |
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Guys: Whatever your wife / girlfriend / mother / sister / fuckbuddy / whatever may try to convince you of, DO NOT I repeat DO NOT under any circumstances watch the movie Marie Antoinette.
Ladies, if you love your men at all you won't force them to watch this.
It has ONE redeeming feature, which is the delicious Kirsten Dunst (who is, incidentally, a talented actress in addition to being tasty). But you can get pics of her from the Internet (or so I've heard) in less time than it takes to watch that movie, and there were only a few brief scenes where she wasn't wearing any clothes. It was PG-13, so you don't even get to see anything interesting. I'm sure if you look hard enough, you can find those scenes by themselves somewhere on the Net.
Probably the worst part about that movie was the soundtrack. I'm sure you can all imagine the sets and costumes necessary to pull off a movie about the last years of the French nobility. So you spend millions and millions of dollars on set and costume design, the result of which was, as far as I can tell, absolutely true to the period. Then, when you put together the soundtrack, you take extra care to make sure the music is just as realistic for the setting as the sets and costumes, right?
Wrong! You put together a mishmash of the most insipid contemporary pop music that you can find. Apparently, because that's what they did with this movie.
I thought when I saw Lost in Translation, "Boy, I bet I know how Sofia Coppola got her break in Hollywood!" This film proves it: if you're related to F. F. Coppola, you can pretty much get away with whatever you want and call it a "movie."
Now I'm off to Netflix to get the Mission: Impossible movies. I need an antidote. |
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I found out today that MIT has put its curriculum online:
http://ocw.mit.edu/OcwWeb/Global/all-courses.htm
In an alternate universe somewhere, I'm independently wealthy, and I can devote much of my time to learning this shit.
The civil engineering courses alone are making me drool. Plus there's advanced mathematics, physics, political science, writing, foreign languages, anthropology, linguistics and philosophy...
I've always said I wanted to learn everything about everything.
In this universe, though, I can only dream. |
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That's Pi as in the Greek letter standing for the mathematical concept, not the stuff you eat. As we all know, Pi 'r' squared? Nope, Pi 'r' round! Cornbread 'r' square!
So today (3.14) at 1:59, I celebrated by chanting:
Three point one four one five nine!
Mathematics is so fine!
Hey, everybody, come back! I was just kidding!
Today is also exactly one month from Valentine's Day. Since V-Day is all about chicks, it's been proposed by more important people than I that, since they invented Father's Day to balance out Mother's Day, to balance V-Day March 14 should be declared Steak and Blowjob Day.
*sigh*
Sadly, I had no steak today - dinner consisted of stuffed mushrooms. And here it is 9:15 pm. The forecast looks bleak.
Instead, my gift for YOU is this link that, along with House DVDs, has convinced me that if I'm sick I'm safer staying at home:
http://messybeast.com/dragonqueen/medical-acronyms.htm |
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Once again, I have too much going on and not enough time to do it in. It seems the days flash by now like telephone poles by the side of the road, and I never have enough time to do anything.
I need to find a way to do more and do less at the same time. Some people are going to be disappointed, but that might be better than me being insane.
Can't anyone stop this thing? |
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The antidote for the other day's "things to be happy about" entry:
http://www.amazon.com/Dark-Side-Thoughts-Futility-Ancient/dp/0806514817/ref=sr_1...
The philosophical antithesis of the 14,000 things book, this one has darkened my library for several years now. It's primarily a book of quotations, in loose chronological order, though sections are introduced by the author.
A few examples:
"To be ignorant is life's greatest joy!" -Ajax, c.441 BCE
"In the whole animal kingdom I recollect no family but man, steadily and systematically employed in the destruction of itself." -Jefferson, 1797
"One's real life is so often the life that one does not lead." -Wilde
This book is so mind-numbingly depressing that even I have to stop reading after less than an hour. It's beautiful in its nihilism, poetic in its embrace of oblivion.
And I guarantee you there's nothing cute in there. |
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... ever since my entry a couple days back about false accusations of rape.
I've been accused of "hating women" because of this and other attitudes I have.
Much as I'd like to say "so what?" the fact remains that I prefer the company and association of women to that of men, so if I do indeed hate women, that means I'm pretty much a broad-spectrum misanthrope, probably well on his way to becoming either a mental patient or a reclusive eccentric (depending on how much money I can accumulate before I finally snap).
Thing is, I just don't see it. Oh, sure, I've been known to objectify women, and I make no apology for that (seeing as we all objectify each other to one degree or another); but so what?
Is it that I point out gender inequalities, whether those inequalities seem biased in the favor of men or women? Because I have issues with how people think it's okay for women to joke about violence against men, but not vice versa? Because I've said that if they're going to draft men, they should draft an equal number of women to achieve parity? Because I feel that as the distribution of men and women in society is roughly equal, our representation in government should also be roughly equal? Because I don't like the idea of President Hillary Clinton? Because I think divorce laws are biased against men, especially fathers, and I don't hesitate to point out these inequalities when I see them? (Incidentally, this wasn't the case in my own divorce, so it's not a personal matter.)
Social issues are more complex than all this, of course, and the older I get the more I realize that there's not a damn thing I can do about them, and when I try, I just waste time I could be spending playing a video game. And as with the divorce inequity, it just doesn't affect me personally. And I'm not sure I can adjust my attitudes, or want to; I'm just getting a real dichotomy of opinion here.
Heinlein (who has also been variously accused of either hating women or pioneering the creation of strong, capable and independent female main characters in science fiction) once wrote that pursuit of equality for women does a disservice to women, because they are naturally superior. Much as I like Heinlein, I don't agree with that. I don't think any one demographic is superior to another (ideologies excepted). Is that where I've gone wrong?
I don't hate anyone, in truth. Not even Bush.
Aw, fuck this. I'm going to go find guy stuff to do. Whatever that is. As long as it involves beer. |
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My wife has a thick paperback book called, "14,000 Things to be Happy About."
http://www.amazon.com/14-000-Things-Happy-About/dp/0894803700/sr=8-1/qid=1172779...
All I can say is, " "
Fourteen thousand? If you contemplated ONE of those saccharine gems per day, you'd be using up 2/3 of your life. Or more, since doing so would certainly shorten your life by a significant amount. Me, I'd die of insulin poisoning long before I reached #13,999.
The book is in our Place of Excremeditation, so I have thumbed through it from time to time. The only saving grace it has is that a lot of things that seemed to make that author "happy" would disgust me:
Wet babies She probably meant "just bathed," but I read it differently.
Golden retrievers 
Naming your baby That would imply that I had a baby, which would cause me no happiness whatsoever.
On the plus side, the book might be a good source of Writer's Cramp prompts...
So I thought I'd come up with my own list of Things That Make Me Happy. Sadly, I don't have much time, so this'll just be a start. Feel free to add.
 Watching people make fools of themselves.
The Darwin Awards.
News stories about freak accidents.
Psychotic Flash animations.
Other peoples' misfortune.
Someone gets theirs.
Kittens.*
Ultraviolent movies.
Well-executed practical jokes.
Hanging up on telemarketers.
Signage mistakes, like the C falling off from "Now Hiring Closers."
*Well, I had to have SOMETHING legitimately cute in there. |
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I'm more than happy with Carrion Luggage, however.
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