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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.
October 31, 2009 at 10:30pm October 31, 2009 at 10:30pm
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I don't like videos.
That's probably weird coming from a guy who keeps linking videos, but the only reason I link videos is because I can't link the songs. This is probably for copyright reasons, leading me to question: Why are the videos on a different copyright?
Whatever.
I don't like videos because I think the song should stand alone (as I've pointed out, some don't).
That said, this video is epic.
Happy Halloween and Spiffy Samhain to everyone!
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October 27, 2009 at 5:52pm October 27, 2009 at 5:52pm
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I fully admit that it's backwards, but it's the way I am, and I have to accept that, even if my friends and family don't understand - which they don't.
See, when it comes to music, as you've already figured out, I'm not normal. First of all, I don't either love or hate a song. For most people, it's like Beavis and Butthead: either it's cool, or it sucks. But as they once said, "If everything was cool, and nothing sucked, how would we know what was cool?" For me, there's a whole spectrum from "suck" to "cool." About some songs, I'm just indifferent.
Second... well, what's "cool" for me has a wide range of styles, including what some would call "depressing" songs and what some would call "happy" songs. I like 'em both - when they're done right. The thing is, "depressing" songs make me smile. They make me happy. I don't know if it's because of my finely-honed sense of schadenfreude, or because I just like a good sad song, or because I can say my situation is superior to that described in the song.
Meanwhile, "happy" songs make me want to cry. (I don't actually cry, of course; I'm a man, after all.) They show me a glimpse into a world from which I am forever barred from participating. It's not that my life sucks; it's just that joy has been elusive to me. I get a small taste of emotion from these songs, but I try not to overdo it.
So today's video is a song about what most would consider a depressing subject, but it's one that never fails to make me happy. It's from The Boomtown Rats, who were probably better known for their lovely, upbeat song about school shootings, "I Don't Like Mondays." I love that song, too, but for whatever reason, the one I link here is the one that sticks in my head as an all-time favorite. From the depths of 1979, I present:
(the Rats gave us Bob Geldof, who is now better known as the organizer of Band Aid and Live Aid, but I will always remember as the main character in the movie Pink Floyd: The Wall.)
Oh, and here's a more recent picture of Bob Geldof - ah, the ravages of time. http://prod.campuscruiser.com/news/22/1188826/91682/Bob+Geldof-w275-h344.JPG |
October 26, 2009 at 10:39pm October 26, 2009 at 10:39pm
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As voluntary penance for rickrolling everyone in the last entry (and for mocking the Eurythmics a while back, which I don't really apologize for, but it was rather negative), I'm going to use a few entries to link YouTube songs/videos that I like. They'll be embedded, so you'll be assured of not hearing Rick Astley (who, incidentally, was born just twelve days before I was).
We'll start with one that I promised to link a while back and overlooked. Written by Me and performed by our very own Brandiwyn🎶 v.2026  , it's not so much a video as a vehicle for the song. But Brandiwyn🎶 v.2026 is easy to look at, in addition to being talented, so don't mind the static "video." 
(Lyrics are linked in "It lives!"  )
(Edited to add this link I found about the subject of that song, Nikola Tesla. In 1931 Tesla announced to reporters at a press conference that he was on the verge of discovering an entirely new source of energy. Asked to explain the nature of the power, he replied, "The idea first came upon me as a tremendous shock... I can only say at this time that it will come from an entirely new and unsuspected source." - well, of course it came upon him as a tremendous shock. I daresay he had more than a few of those in his lifetime playing with electricity.) |
October 26, 2009 at 1:22am October 26, 2009 at 1:22am October 23, 2009 at 5:41pm October 23, 2009 at 5:41pm
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As most of you know, my Theory of Comedy states that adding a duck to anything makes it funnier.
Consequently, this is about the funniest thing I've seen all month:
http://failblog.org/2009/10/23/ad-placement-fail-4/
And now I'm convinced that a duck is watching me. |
October 14, 2009 at 6:53pm October 14, 2009 at 6:53pm
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Yesterday, Lorien  quoted a song, as she is wont to do on occasion, for a blog entry: "Invalid Entry" .
My first comment was "That song sucks."
Lynn McKenzie disagreed, even going so far as to impugn my favorite psychotherapist, Jung.
Well, we can argue about Jung, but there is no doubt whatsoever that the Eurythmics' song "Sweet Dreams (Are Made of This)" sucks massive rat turds.
And I can prove it.
First of all, I'm not saying the Eurythmics suck. Annie Lennox has a beautiful voice, and their music was polished and not too overproduced compared to some of the other crap the industry was pumping into a tone-deaf public in the early 1980s, pre-Born in the USA. I hear the video was pretty well done, too, but the video is not the song and I would no more judge the song by the video than say The Matrix was a good movie just because it had killer special effects.
That said, "Sweet Dreams (Are Made Of This)" sucks.
Let's start with the lyrics, because to be good, a song has to have good, meaningful lyrics. Otherwise, why bother making it a song? It can be an instrumental.
The lyrics:
Sweet dreams are made of this
Who am I to disagree?
I travel the world
And the seven seas--
Everybody's looking for something.
Some of them want to use you
Some of them want to get used by you
Some of them want to abuse you
Some of them want to be abused.
That's all. That's it for the lyrics. It's all chorus. Or, looked at another way, it's all verse. Oh, except for the almost-unintelligible part:
(Hold your head up--Keep your head up--MOVIN' ON)
Which before I could look up lyrics on the internet, I could swear went, "Powderhead (movin' on) Chowderhead (movin' on)" - but that's me, and that doesn't contribute to the song's massive vacuum pull. More, that was, in fact, the only saving grace of the song, and to find out that it was as much of a lie as "'scuze me while I kiss this guy" was a massive disappointment.
Okay. Okay. So the lyrics are spare. Haiku gets by with only 17 syllables; maybe they were going for that same kind of feel?
Well... No. Look at the lyrics again. Is there any imagery there? Is there a metaphor, an onomatopoeia, ANY kind of poetic trick?
Um... no.
In fact, the second line is a cliché: "Who am I to disagree?"
Oh, wait, I lied. There is one poetic device used: Rhyme.
But wait - what's the first line? "...this / ...disagree."
Do. WHAT?
They get around this by singing, "Sweet dreams are made of THESE."
That isn't a mishearing; that's no "There's a bathroom on the right." That's a LONG E and Z sound, when the lyrics - and the song title - and the album title all say THIS, which is a SHORT I and HARD S sound. You don't get those two mixed up, even if you are British.
If they'd said "Sweet dreams are made of CHEESE" and wrote that in the lyrics and song title and album title, then I'd change my opinion of the song. Really. Surrealism is always a good thing.
But it's not cheese - not even Wensleydale - it's THIS.
Okay, you say, you're wrong, idiot. "Disagree" is meant to rhyme with "seas." And yes, I'm willing to forgive the absence of the sibilant at the end of the first word. But my point remains - they don't say "this;" they say "these," creating an internal rhyme. So, no, I'm not wrong, especially if you consider "Sweet" through "seas" to be FOUR lines, which is how I've always seen it written.
Moving on: "Everybody's looking for something." So? You might as well say "Everybody needs air to breathe" or "My cat likes to lick her asshole."
I'm not even going to go into the next four lines, except to say that they'd make a set theory mathematician cry. The categories are neither overlapping nor mutually exclusive nor, as with the previous line, do they really mean anything.
As for "Hold your head up," well... Argent did it better, and first, with a song that's only marginally longer, lyrics-wise, than "Sweet Dreams:"
...And if they stare
Just let them burn their eyes on you moving
And if they shout
Don't let them change a thing what you're doing... Hold your head up, etc, etc.
Overall, if I encountered those Eurythmics lyrics written out here on WDC, I'd probably have to rate them   - assuming everything was spelled correctly.
Now, if you want a Eurythmics song that was popular AND good, you need to look no farther than "Here Comes The Rain Again."
But hey - at least it's not "Brass In Pocket" by the Pretenders. So "Sweet Dreams" does have one thing going for it. |
October 8, 2009 at 3:37pm October 8, 2009 at 3:37pm
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I just got tickets to go see these guys in Richmond.
http://gogolbordello.com/
It's been a LONG time since I've been to a punk show. I wonder if I can find my old combat boots and skull rings.
Here's the video that convinced me that this was a great band:
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October 5, 2009 at 9:40am October 5, 2009 at 9:40am
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http://www.lehighvalleylive.com/slate-belt/index.ssf/2009/10/woman_killed_by_pet...
A Ross Township woman who keeps exotic animals as pets was killed this evening after she was attacked by her pet black bear[WTF?]
But it gets better. This chick liked to live dangerously:
Also kept at the house are a Bengal tiger and an African lion.
Lions... and tigers... and BEARS? Oh. My.
While she was inside, the 350-pound bear turned on Walz [no relation] and killed her, officials said.
So, verily I say once again unto you, forsooth:
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I'm more than happy with Carrion Luggage, however.
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