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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.
January 31, 2008 at 6:45pm January 31, 2008 at 6:45pm January 29, 2008 at 4:34pm January 29, 2008 at 4:34pm
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I know at least one of you readers is a Counting Crows fan. The rest of you can safely skip this entry.
One of my employees, a guy whose taste in music is similar to mine (to the extent that he accompanied me to Meat Loaf and Bruce Springsteen concerts) wondered, today, "When's the new Counting Crows album supposed to be coming out?"
I frowned. "It was supposed to be last fall. I don't know. But I know how to find out."
I'll save you the suspense: it's set to be released March 25. My next goal is to get tickets for the tour I hope will follow.
In the course of discovering this information, I noticed that they have available for download (free) a "digital 45" of two songs from the upcoming release:
http://countingcrows.com/digital45.html
"When I Dream of Michaelangelo" is what I'd call a pretty typical Adam Duritz offering: slow, melancholy, lyrically poetic, self-referential (in this case, to a song from their second album) and musically intriguing -- all of which makes it better than the bulk of the crap out there that passes for music.
And I dream of Michelangelo when I'm lying in my bed
I see god upon the ceiling I see angels overhead
And he seems so close as he reaches out his hand
But we are never quite as close as we are led to understand
"1492", on the other hand...
All I can say is: wow. You just have to hear it. The lyrics alone couldn't possibly do it justice. Duritz reportedly called it "probably the hardest, darkest song we've ever played."
Into the dark Italian underground of disco lights and disco sound
And skinny girls who drink champagne
And take me on their knees again
Then pull me up and out the door
Past railway cars and tranny whores
And morning spreading out across the feathered thighs of angels...
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January 28, 2008 at 2:50pm January 28, 2008 at 2:50pm
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I hate to sound like a scratched CD, but this thing with my back is making me meshuggah. I can't seem to get away from the pain for very long. Hence my absence from this blog and anything I haven't absolutely had to do.
I did have time to find this:
http://www.alternativereel.com/includes/top-ten/display_review.php?id=00037
Which only makes me want to invest in more gin therapy.
So, rather than go on an angry tirade about things that would probably just slide past me if I weren't in pain, I'll leave it at that for now. |
January 24, 2008 at 4:54pm January 24, 2008 at 4:54pm
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I've been trying to think of something to say today; preferably, something innovative, honest, revealing, self-deprecating and more than a little funny, since that sort of thing seems to draw in blog readers - but I can't seem to pull any bumper-stickers out of my hat, these days.
I didn't want to resort to another day of weird news stories, though I have a couple I'd really like to post - only one of which involves Hello Kitty. They can wait.
Sadly, the big news today seems to be the "economy stimulating package" or some such from Washington, which apparently does to us what the government always does to us - stick their package to us in a stimulating (to them) manner, over and over again. If I were a politically-inclined blogger, I'd link a serious article on it from a serious news source, like this one:
http://www.washingtonpost.com/wp-dyn/content/article/2008/01/24/AR2008012400532....
In case you can't read it, I'll summarize:
Nancy Pelosi and John, A Boehner (a setter and a pointer, respectively) worked late into the night trying to find different means of stimulation, rejecting trickle-down schemes in favor of something similar to the Bush stimulation a few years back, wherein almost everyone gets some (unless you're wealthy, in which case you're already getting some). This isn't meant to shaft Americans so much as stroke them, convincing us to spend ourselves into exhaustion. Seems like quite the opposite of the trickle-down theory - I'll call it the "spurt" theory of economics where the flow is from the "bottom" of the economic frenzy to the "top," from which it just might drip back down again.
So it seems we can expect the package (which Bush said was "just the right size") to climax sometime in May. It'll most likely be spent quickly. Then the government can roll over and go back to sleep, leaving the people blinking at the ceiling, frustrated and wanting more despite the frenzied activity of mere moments before.
...But I decided that to comment at all upon such trivialities is beneath me; first, because I'm not a politically-inclined blogger; second, because you'll have heard all about it already and formed your own opinions; and, finally, because it lends itself too easily to parody, and I'd never stoop so low.
Then I thought that maybe I could present to you my latest forays into the philosophical world, especially as regards the meaning of life, the Universe and everything; the difference between reality and illusion, with an emphasis on why it is that so many people find deep comfort and meaning in the belief that reality is an illusion (with commentary on how difficult people like that are to deal with); and the general banality of things like economic stimulation packages. But when it comes to philosophy, I really don't know what I'm talking about. I mean, apparently, those things that I think are real - like trees, flowers, the past and concrete - are actually abstractions, illusions formed by my mind to distract me from the real, true reality, while those things that are illusions to me - like dreams, fantasies, the future and story ideas - are, to these same people, the true reality that I should be focusing on. Worse still are the "forget the past, ignore the future, live only for the present" types, most of whom have credit card debt that make many small countries jealous. But it's been made clear to me that I don't know what I'm talking about on that score, and besides, it takes too much effort to type anything on this illusory keyboard - especially anything about the past, which they've already established as illusion that can be disregarded, but to me makes for the most engaging writing (after all, you can't write about the present - because by the time you've written about it, it's the past).
I mean, seriously - how shitty does your past have to be for you to make like it's not real?
But I'm not going to go there.
I guess I'll have to post the Hello Kitty link after all.
But first, the Idiot Test. Take it and see how far you can go with it:
http://users.skynet.be/bk258512/idiot_test.swf
And now, the Nefarious Neko herself:
http://www.hellokittyuniverse.com/page/Indecent%20Hello%20Kitty%20Products?t=ano...
Oh. That's why people have to claim everything is an illusion. It makes the prospect of Hello Kitty Menstrual Pads that much easier to take if you can keep saying to yourself, "It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away...It's only an illusion... ignore it and it'll go away..." |
January 23, 2008 at 5:08pm January 23, 2008 at 5:08pm
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People ask me why I like to stay inside rather than "enjoying" "nature."
Here's one reason. Actually, here's FIVE reasons. Or, more precisely... here's ten quintillion reasons:
http://www.cracked.com/article_15816_5-most-horrifying-bugs-in-world.html
Now, granted, there are occasionally bugs in my house from time to time - usually for the time it takes for one of my cats to notice them - but to paraphrase the great philosopher Calvin, "The problem with nature is something's always stinging, biting, or oozing slime on you."
Hell... even Windows Vista doesn't have that many bugs.
Okay, maybe it does.
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January 21, 2008 at 4:44pm January 21, 2008 at 4:44pm January 19, 2008 at 7:05pm January 19, 2008 at 7:05pm
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For the first time in what seems like ages, I'm actually going out on a Saturday night.
It's an odd feeling. |
January 19, 2008 at 4:46pm January 19, 2008 at 4:46pm
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This was my Google Quote of the Day:
If your parents never had children, chances are you won't, either.
- Dick Cavett
Well, my parents never had children, and I don't plan on having any, either, so here's one data point of support.
And every time I state my intentions in the matter, some wag always says something like, "Whew! I'd hate to see another Waltz running around."
I have to think they just don't realize how offensive that is - because I can't believe anyone would be that insulting to me on purpose, even if my life choices are different than theirs. |
January 17, 2008 at 9:35pm January 17, 2008 at 9:35pm
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It finally snowed here. It was a brief but intense thing, lasting a few hours before turning to rain, which of course is very likely freezing the roads solid right now.
But I don't care - I'm already home.
When I came home, my wife had decorated the front yard.
Since I think the Calvin and Hobbes snowmen strips are the funniest things ever, I laughed my ass off at this.
But then I saw what she put on the back deck:
I hate wasting good gin on a snowman who's only using it to get slushed - those were my empties.
And I think he needs another bottle, so it's MARTINI TIME! |
January 16, 2008 at 6:04pm January 16, 2008 at 6:04pm
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...but it's pretty cool.
It's in Dutch, and you can't actually buy anything from this page, but just let it load and do its stuff.
http://producten.hema.nl/ |
January 15, 2008 at 7:44pm January 15, 2008 at 7:44pm
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Just not a lot going on besides work, the tournament and back pain, none of which any of you want to hear any more about, so instead I present - mostly for the guys out there - 11 Telltale Signs Your New Girlfriend May Be a Restraining Order Waiting to Happen
http://www.themishmash.com/2008/01/telltale-signs.html
(Girls, you might want to read it too. You know, kind of as a how-not-to)
Speaking of eleven, here's 11 Interesting Pictures That Look Photo Shopped But Aren't - unfortunately, it's also 11 Interesting Pictures That Should All Be Captioned But A Bunch Of Them Ain't. Still...
http://www.wallstreetfighter.com/2008/01/11-interesting-pictures-that-look-photo...
And, finally, one of those stupid damn which-one-are-you quizzes, which I wouldn't normally have even bothered with, except we're finally getting around to watching Season 3 of Lost:
http://www.liquidgeneration.com/Media/Games/Quizzes_Puzzles/Personality_Quizzes/...
(Me? I was Sawyer, of course.)
(Don't link me the equivalent Heroes quiz. I don't want to know.) |
January 13, 2008 at 7:42pm January 13, 2008 at 7:42pm
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I really hate to make excuses, but constant pain in my back and leg, alternating with numbness in my leg, is taking its toll on my patience and calm.
I'm sure this is coming through in forum posts, scroll and IMs - not to mention phone conversations with those few of you who have the honor of having my phone number - and I'm sorry if I've been short with you. Just remember: my wife's getting the brunt of it. (Sorry, dear.)
Bear with me. I hope to be "back" to normal sometime...
...in the next few months  |
January 12, 2008 at 9:19pm January 12, 2008 at 9:19pm
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I went to the gym today for the first time in over a year.
Mostly, I hate the gym because I never quite know what to do there. Yeah, "excercise," I know, but on what? I can't keep all the conflicting suggestions straight.
But with my back the way it is, it was pretty much "swimming." It helped - for a while.
Something's gotta work, and soon. |
January 11, 2008 at 8:49pm January 11, 2008 at 8:49pm
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With the solstice less than a month behind us, I can already tell the days are lenghtening. Not on the front end, of course - I make it a point to never rise before the sun - but at the end of the day, when it's actually still light when I leave work.
Between my back pain and the meds I'm taking for it, I was in a foul mood this evening, from the time I got off work until I got to Baja Bean, a local Cal/Mex restaurant.
The distinguishing feature of Baja Bean is its Tequila Club. You get a Green Card with 20 boxes on it. Each box contains the name of a tequila, from crap like Cuervo to nectar like Patron Silver. Each time you order a different tequila - shot, small margarita, or grande margarita - you get a punch on the card. When you're done, you get a t-shirt and $1 off any future tequila purchase.
Today's tequila punch was the aforementioned Patron Silver. I had it in a margarita. A fucking HUGE margarita that cost me $16, plus tip (that $1 off will come in handy when I achieve it). And then, everything was better. |
January 10, 2008 at 7:56pm January 10, 2008 at 7:56pm
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And sometimes, that's not a bad thing.
http://www.paleofuture.com/2008/01/will-war-drive-civilization-underground.html
The December 13, 1942 Montana Standard (Butte, MT) ran an interesting piece by Gardner Dane about the world of 1975, devastated by war, forcing people to move underground in order to survive.
People thing it's the job of the science fiction writer (or, in this case, prognosticator) to predict the future. Not so.
Their job is to prevent the future.
I still want my flying car, though, dammit! |
January 9, 2008 at 5:40pm January 9, 2008 at 5:40pm
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I picked up a couple of tangerines, today.
I've been eating those little bastards since I was a kid, but I never knew much about them. So I checked the internet, of course.
Skipping Wikipedia, I went to sources.
http://www.hort.purdue.edu/newcrop/morton/mandarin_orange.html
In 1965, the 'Dancy' tangerine was found to contain more of the decongestant synephrine than any other citrus fruit-97-152 mg/liter, plus 80 mg/100 g ascorbic acid.
Fascinating.
Yes, the article is about mandarin oranges. Turns out they're the same thing! Tangerines are varieties of mandarin orange.
http://mountainmandarins.com/documents/10Oct2005-MMGA.pdf
Leaving aside the questionable veracity of any document produced by someone named Fake, this is still pretty cool.
However, to quote one citrus expert, Lance Walheim, “The name tangerine has no botanical standing; rather it appears to have developed as a marketing term for bright colored (reddish-orange) varieties of common mandarin, such as Dancy”.
So... a tangerine isn't a tangerine. All my life, I'd been told it was a tangerine. My mother told me it was a tangerine. The store display today called them tangerines.
But wait! There's more!
Properly speaking, they are not mandarin oranges, but simply mandarins. However, since many Americans’ only acquaintance with mandarins is from a can labeled “mandarin oranges”, it may be helpful to call them mandarin oranges, even if it is not technically correct. Interestingly, DNA technology has revealed that the common or sweet orange is probably a hybrid of a pummelo, a large, thick-skinned citrus, and a mandarin. So, even your orange is part mandarin!
My orange is part mandarin?!  Well... at least I can find words that rhyme with "mandarin." "Hand 'em in." "Random win." That sort of thing. Not so, orange.
So I started to wonder: which came first, orange or the orange? In other words, was the fruit named after the color - or was the color named after the fruit?
http://m-w.com/dictionary/orange
Etymology: Middle English, from Anglo-French orrange, araunge, from Old Occitan auranja, from Arabic nāranj, from Persian nārang, from Sanskrit nāraṅga orange tree
Okay, so in Sanskrit, the orange tree was the root word for "orange." That tells me that, most likely, the color was named after the fruit. It still doesn't explain why the word has no rhymes, but I think I'll let that mystery sit for a while.
Just remember, though, next time you peel a juicy, succulent tangerine and pop its tart little sections into your mouth - you're actually eating a mandarin. |
January 8, 2008 at 7:59pm January 8, 2008 at 7:59pm
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Well, my creationism rant inspired some comments, but not nearly the shitstorm I feared. Thank you for that.
I did want to make clear, though, that my rant about creation "science" is not about Christians in general - in other words, I'm not attacking faith, but opinion.
I responded to someone in a private email a clarification that I'll paste here (in edited form):
I hope you don't think I'm painting all Christians with the same brush; I'm not. While it's true that the intolerant ones tarnish the image of the whole group, that's the case for every group. When it comes to people, I relate based on what I see of them, not their stated religion - because, too often, the two are contradictory.
Young-Earth Creationists, on the other hand, uniformly annoy me. Not because of their religion (technically, they don't have to be Christian, but I've never heard of a Jewish YEC, despite drawing from the same Book), but because they're willfully blind to evidence - or, worse, twist it to suit themselves.
The way I see it, it makes no difference in the grand scheme of things whether one believes that God directed evolution or whether it was the result of billions of years of environmental pressures. What does make a difference is the "billions of years" versus "a few thousand years" thing. The latter ignores centuries of rigorous intellectual study of, if you will, God's creation (or nature, if you won't), pretty much throwing most of science out the window.
And that offends me.
That's the last word on it from me - at least for now.
But let's see what Wired Magazine has to say:
http://blog.wired.com/wiredscience/2008/01/evolution-is-no.html
In science, being a "theory" is not a step below a "law." The "Theory of Relativity" by Albert Einstein is not waiting for its day in court when it graduates to "fact." |
January 7, 2008 at 6:33pm January 7, 2008 at 6:33pm
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First in our Web of Wrong today, we have this heartworming story about a couple denied their child due to their religion - or, specifically and just as chilling, lack thereof:
http://www.time.com/time/magazine/article/0,9171,877155,00.html
Inestimable Privilege. In an extraordinary decision, Judge Camarata denied the Burkes' right to the child because of their lack of belief in a Supreme Being. Despite the Burkes' "high moral and ethical standards," he said, the New Jersey state constitution declares that "no person shall be deprived of the inestimable privilege of worshiping Almighty God in a manner agreeable to the dictates of his own conscience."
This is especially appalling to me because my own parents had to wait until they were 50 to have a child - because no agency would adopt out a child to non-Christian parents.
I hereby begin my list of Candidates for Douchenozzle of the Year with Judge Camarata.
But it might not matter, because clearly, the End is Nigh, and it might come with the U.S. Presidential Election:
http://www.physorg.com/news118756781.html
Former Arkansas governor Huckabee said in a debate in May that he did not believe in evolution.
A poll conducted last year showed that 53 percent of Americans do believe that humans developed over millions of years from less advanced forms of life -- the theory of evolution -- while 47 percent do not.
Forty Fucking Seven Percent? That's it. We're doomed. 47% of Americans can't understand or accept the scientific reasoning that we developed out of a different form of life, despite the crushing weight of overwhelming evidence? Look, I don't care if you believe your Invisible Friend guided evolution; there was still evolution. I also don't care that the scientists can't agree on the precise mechanisms that drive evolution; that's called scientific debate and it goes on all the time. Come to think of it, I don't care what you believe, period - until it starts to affect public policy. 47%? No wonder judges are being douchenozzles about religion.
But, lest you think that the proof of Ragnarok's approach is purely religious, I give you People With More Time On Their Hands Than They Know What To Do With - so they post pictures of (admittedly interesting) automobile accidents:
http://www.quazen.com/News/Alternative/10-Freak-Car-Accidents-2.71373
And speaking of automobile accidents, I bet they go UP - at least among male drivers - when these become standard equipment. I give you: the Porn-Inspired Airbag (link's pretty safe):
http://boinkology.com/2008/01/04/first-ever-porn-inspired-automobile-airbag/
But in case you were wondering exactly what form the eschaton will take, well, there are at least five possibilities - depending upon one's religion. Here's Cracked's list of the "most kick-ass" ones:
http://www.cracked.com/article_14977_5-most-kick-ass-apocalyptic-prophecies.html...
My personal favorite is #3:
What to watch for:
The arrival of white men in the lands of the Hopi Indians, taking land that isn't theirs and killing their enemies with hand-held thunder.
Wait a minute.
Uh oh.
But, speaking of Hopi, all Hope is not lost, as long as we have people doing this:
http://www.snotr.com/video/789
I mean... that's just plane COOL. |
January 6, 2008 at 4:37pm January 6, 2008 at 4:37pm
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Wait, don't run away - there's no MATH involved.
What you do is draw shit in the green box, and the program applies a 2d analogue of physical laws to it.
http://www.enigmasand.com/games/nphys/
Things I've done:
-Created a bowl and dropped little "cherries" into it.
-Made a fulcrum (triangle) and lever (straight line), dropped a small object on one end and a large object on the other. Whee!
-Made irregular shapes slide down an inclined plane and pile up at the bottom.
It's cool. And slightly more useful than the virtual toilet paper roll. |
January 5, 2008 at 2:57pm January 5, 2008 at 2:57pm
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If you don't do anything productive all day, it's hard to think of something to write about.
I mean, I worked on "Invalid Item"  for a bit, talked to people, did some office work, took care of some piled-up mail, and got further along in my new project here on WDC (sadly, this doesn't involve actual fiction writing).
Later I'm probably going to watch a movie.
Saturdays can be kind of boring.
Not that I mind. |
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I'm more than happy with Carrion Luggage, however.
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