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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.
December 31, 2007 at 1:13pm December 31, 2007 at 1:13pm December 31, 2007 at 10:17am December 31, 2007 at 10:17am
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31,536,000 seconds.
By convention, that is - that's how many seconds are in a year of 365 days. Next year, of course, is a leap year of 366 days. And that means two things:
-The Olympics
-The U.S. Presidential Election
Looks like another year for me to stay the hell away from television.
Anyway, as 2007 draws to a close, I'm tempted to look back on it and recap the highlights - but I won't.
And as we approach 2008, I'm tempted to make predictions and resolutions - but I won't.
I'll turn 42 in 2008. 42, as all readers of Douglas Adams will know, is the Answer to the Ultimate Question of Life, the Universe, and Everything. 42 is also twice 21, which means I will have spent as much time being legally able to drink liquor as not.
Obviously, I will celebrate this anniversary by drinking liquor.
Speaking of which, we're doing the teppan yaki thing tonight - it's been our New Year's Eve tradition for some years now, and I see no reason to quit.
This year was pretty good - so I won't hope for a better next year. I'll be happy with the same old shit.
Here's to life. |
December 30, 2007 at 5:29pm December 30, 2007 at 5:29pm
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I used to think that this:
http://www.urban75.com/Mag/bubble.html
was the most useless webpage ever developed. I mean, it's a piece of BUBBLE WRAP that pops as you drag your mouse across it - and then the bubbles regenerate so you can keep doing it.
Useless.
But then I found this:
http://www.papertoilet.com/
It is as if a cat or a toddler designed the website.
To anyone BUT a cat or a toddler, it is utterly USELESS.
But funny as hell.
(Edited to add:)
And the runner-up contender:
http://www.virtualstapler.com/ |
December 29, 2007 at 9:46pm December 29, 2007 at 9:46pm
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The end of the year, that is.
It doesn't feel like the end of the year. In fact, it feels like 2007 has just gotten started. That may be because I'm still working toward the same goals, trying to get the same stuff done.
Whatever. Tuesday is just another day (except, of course, for certain writing.com activities). And just like always, first I have to make it through Sunday  |
December 28, 2007 at 8:34pm December 28, 2007 at 8:34pm
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I don't have very long, today. My back is causing me severe pain and I can't sit at the computer very long. It's become bad enough that I actually made a  doctor appointment.
BUT I wanted to remind everyone to enter
AND
 |
December 27, 2007 at 5:41pm December 27, 2007 at 5:41pm
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As we approach the end of the year, I find my time divided between three major activities:
1. Personal Finance (specifically, preparing for taxes).
2. Setting up "Invalid Item"  in preparation for its launch on January 1.
3. Trying to fix my wife's #$#%@ing laptop, which keeps giving us the BSOD.
I'm frustrated by #3 and I have Minions working on #2, so I'm going to talk about #1 for a bit. This is prompted by a conversation I had with CCWolf  here, but also by the reported incredulity of several of my wife's friends when she tells them about:
How to Beat Credit Card Companies at Their Own Game
By all reports, consumer debt is at an all-time high. People aren't saving; they're spending, and worse, they're spending money they don't have. Even worse, they're paying astronomical interest rates on the money they spend that they don't have. The principal enabler of this spending is a little plastic wafer with a magnetic stripe, that you can use at places like Sak's Fifth Avenue, the local grocery, and the McDonald's drive-thru. And when the bill comes due, if you don't have enough cash to cover the money you've spent, that's okay - you can just pay a small percentage of it and let the rest carry over!
With credit card interest rates (aka "finance charges") ranging anywhere from 9 to 31 percent or even higher, the cost of this money can be astronomical. I'm not going to give you headaches with math, but if you pay nothing but the minimum payment due every month, it can take years to pay off a balance - and meanwhile, accumulated finance charges can double or even triple the amount you paid for something!
Many people complain that they can't seem to get ahead. This is why.
To get ahead, you have to break the cycle, but you can't break the cycle because the debt keeps piling up.
Still, you can break the cycle, but that's not what I'm going on about today. Today I'm talking about how to make money from credit cards. But to do that, you have to start from a position of no credit card debt.
Not always easy to do, I know. We're trained to believe that debt is simply a fact of life, and we might as well deal with it. Well, it's not, and we shouldn't have to. Being in debt helps only one entity: the bank. So unless you also own the bank, you should do everything possible to minimize debt, and what debt you have should be in the form of low-interest loans, not carryover balances on credit cards.
What you need to make money from credit cards:
1. A credit card (duh) with a zero balance.
2. An interest-bearing savings account.
3. A budget or spending plan, in which expenses total less than your income.
4. Willpower.
Here's how it works:
1. Give me all your money.
Just kidding.
Here's how it really works:
1. Make a spending plan and stick to it (this is the "willpower" part).
2. Whenever possible, make purchases and payments by credit card, as long as it doesn't cost extra to do so.
3. Every time you make a purchase, or once every few days, take the amount that you have spent with the credit card and deposit it into the interest-bearing savings account.
4. When the credit card bill comes, ignore the "Minimum Payment" amount and pay attention to the "Balance" amount. If this "Balance" is paid in full, there will be no finance charges.
5. A few days before the bill is due - make sure you allow enough time for the payment to clear; I recommend electronic payments for speed and accountability - pay the Balance in full.
6. You will now have more money in the savings account than you did when you started, because it has earned interest over the month or so between the purchases and the due date. It's not much - but it's more than you would have had otherwise, and YOU are making the money, not the BANK.
You can keep this up indefinitely, as long as you pay off the entire statement balance in full. This is called a "grace period," and as far as I know, all credit cards in the US feature this grace period - but read your CC terms carefully or call them just to be sure.
This will affect your credit rating - but in a positive way. The credit reporting agencies see that you have a revolving credit account balance due - but they're not told that you're paying it off every month, or that you're not paying any interest on the borrowed money. Since you're paying something every month, they see that and your credit score goes up. Further, don't touch the balance in your savings account after you pay the Balance - and it will continue to earn interest.
This bank gives a high interest rate on savings; it's fully insured, and has no minimum balance. You can open an account with a buck fifty - or less:
http://home.ingdirect.com/
(I'm in no way affiliated with that bank. It's just where I stash my cash.)
The key, of course, is not to spend more than your income. But it doesn't matter what your income is; you can use this technique at any level.
Money is a good thing to have. Don't let anyone tell you otherwise. |
December 26, 2007 at 8:17pm December 26, 2007 at 8:17pm
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This drink recipe comes from the twisted mind of my brother-in-law, Erik:
Nagasaki
3 parts Eggnog
1 part Sake
(Get it? Nog-a-sake?)
Hello Kitty mushroom cloud stirrer is optional.
*Resists the urge to recite the Nagasaki Memorial Haiku* |
December 25, 2007 at 11:25am December 25, 2007 at 11:25am
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I have this intense back pain that's coloring everything I say or do. And it doesn't help that this computer keeps crashing, usually whenever I do something like try to figure out WHY it's crashing. So I'm grumpy - grumpier than usual, anyway.
But it's Christmas.
And though Christmas has never been my holiday, I think that on Christmas - whichever Christmas you observe, be it the commemoration of Jesus' birth, a time to make kids happy, a time to run up debt and keep stores in business, a day to be with family, a day of peace and contemplation, or even just a day when you don't have to be at work, or whatever - you should be nice to people. It's the one day when you can get away with that without other people thinking you want something in return.
There's not much I like when it comes to Christmas songs. I prefer the parodies and the fringe songs to the jingle bells and silent nights. But there's one Christmas song that I always like to hear and, fortunately, the rock station I listen to at home plays it from time to time in December.
Greg Lake, of Emerson Lake and Palmer fame, did the song, called "I Believe in Father Christmas." And even though its message - deploring the commercialization of what he feels should be a spiritual holiday is not one that I totally agree with, I like it anyway. You have to hear the song to get the full effect, but the lyrics pretty much stand on their own.
They said there'll be snow at Christmas,
They said there'll be peace on earth,
But instead it just kept on raining,
A veil of tears for the Virgin birth.
I remember one Christmas morning,
The Winter's light and a distant choir,
And the peal of a bell and that Christmas tree smell,
And eyes full of tinsel and fire.
They sold me a dream of Christmas,
They sold me a silent night,
They told me a fairy story,
'Til I believed in the Israelite.
And I believed in Father Christmas,
And I looked to the sky with excited eyes,
Then I woke with a yawn in the first light of dawn,
And I saw him and through his disguise.
I wish you a hopeful Christmas,
I wish you a brave New Year,
All anguish, pain and sadness,
Leave your heart and let your road be clear.
They said there'd be snow at Christmas,
They said there'd be peace on earth,
Hallelujah! Noel!, be it Heaven or Hell,
The Christmas we get, we deserve.
Have a great one. |
December 25, 2007 at 10:23am December 25, 2007 at 10:23am
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If you're not familiar with the idea, it goes something like this:
-Everybody brings a pressie, usually with a cost range involved
-Names are drawn one by one out of a hat.
-The first name drawn picks a wrapped pressie.
-The second name drawn decides whether to pick a wrapped pressie, or whisk the first person's pressie away, laughing hysterically.
-If your opened pressie is stolen, you can unwrap a new one.
-The third person likewise has a choice between a wrapped pressie or ANY of the previously opened pressies, whether they've been previously stolen or not.
-After the last person makes the choice, the first person gets one free pick from all the previously opened pressies.
Whoever thought of this "tradition" should be lowered inch by inch into concentrated hydrochloric acid. Whoever perpetrates this "tradition" onto anyone else should be shot. If the perpetratees are family, the person with the bright idea of perpetrating this "tradition" should be shot in the knees first.
That is all. |
December 24, 2007 at 9:52pm December 24, 2007 at 9:52pm
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Here I am back in Pittsburgh, where the Official Religion is Steelers.
The problem with traveling to Pittsburgh isn't the fact that it's Pittsburgh - it's actually kind of nice around here - but that there is NO direct route from my hometown of Charlottesville to here. This is because West Virginia is in the way, and nobody's bothered to cut a road through the mountains. Consequently, you have to start out going west - then kind of north-northeast - then north for a bit, though there's some zigzagging involved, and you leave the interstate for a while - then kinda west-northwest to Pittsburgh.
But the trip was easier than I expected, it being Christmas Eve and all. Five hours on the road, and we were done. Closer, even, than New York.
Now if I can get the laptop to quit crashing to the Blue Screen of Death, I might even have a good time visiting the in-laws. |
December 23, 2007 at 7:17pm December 23, 2007 at 7:17pm
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Someone asked me to explain my blog header some more. Sorry, but that's as simple as I can make it. However, I found this:
http://mathforum.org/johnandbetty/
while searching for a way to be simpler.
The drawings crack me up. |
December 23, 2007 at 7:06pm December 23, 2007 at 7:06pm
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What ain't no country I ever heard of. They speak English in What?
-Jules
http://www.timesonline.co.uk/tol/news/uk/health/article3087367.ece
DEAF parents should be allowed to screen their embryos so they can pick a deaf child over one that has all its senses intact, according to the chief executive of the Royal National Institute for Deaf and Hard of Hearing People...
Say what?
More:
In America a deaf couple deliberately created a baby with hearing difficulties by choosing a sperm donor with generations of deafness in his family.
WHAT??!
How about we stop breeding for stupid, huh? I mean, I know some people would love to select undesirable traits OUT of their offspring - the definition of "undesirable" being a key issue that I'm not going to touch - but what kind of parent purposely does something to their kid that gives them a disadvantage in life? Of course, lots of deaf people do just fine in life, and that's not the issue; the issue is where does it stop? Should retarded people (and yes, I'm using the R word) deliberately have Down's kids so they can all be retarded together? Come on!
I weep for the world. |
December 22, 2007 at 8:38pm December 22, 2007 at 8:38pm
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Shortest day of the year? Big fucking whoop. It was as cold, cloudy, dark and dreary as a Morrissey song.
I wasn't going to go anywhere today; I was just going to sit on my ass or lie in my bed and celebrate the first of many days off in a row - and, of course, put together next week's Comedy and Fantasy newsletters, which are now almost done.
But my cunning plan was foiled.
There was not a single can of Coke Zero in the entire house.
Now, given a choice, I'd be drinking real Coke. But since they started making it with corn syrup instead of sugar, it just hasn't been right. So as long as I can't get the real stuff, I might as well bow to the low-calorie ideal and get the Zero, which tastes a hell of a lot better than Diet Coke, which in turn is ambrosia compared to anything made by Pepsi.
But if there had been nothing in the fridge but a Pepsi, I'd have drank it, merely because it contains caffeine.
Oh, but Waltz... what about coffee? You ask. I know you're asking. I can hear you. Well, as lousy as that crap Pepsi is, it is sweet nectar compared to coffee. I've never developed a taste for coffee, and I've never yet been desperate enough to need some. Consequently, there's none in my house, which brings us back to my main point...
Caffeine addiction is a real thing. I don't know about anyone else, but upon withdrawal, I get irritable, cranky... okay, MORE irritable and cranky, and on top of that I get this headache that nothing can fix.
Nothing, that is, except drinking something with caffeine in it.
I did, briefly, contemplate making myself a cup of Earl Grey, but for me, the hotness of tea cancels out any caffeine molecules it might have. Nope, there was only one cure for my splitting headache, and that was to go get some soda.
So it was off to the Food Lion (sometimes known as Fool Dyin') to get some Coke Zero.
When I got there, the first thing I saw after all the bedraggled, harried customers and the tired, foaming at the mouth checkout people was that there was no Coke Zero in the refrigerated sections.
Okay, no problem. Diet Dr. Pepper works just fine. So it's a 20 oz DDP and two (on sale!) 12-packs of CZ. Oh, but while I'm here I'm also going to get a bag of pretzels and a box of nukable popcorn!
So much for the advantages of low-calorie soft drinks. This is why I usually get my wife to shop for me. Well, that and I'm lazy.
Anyway, the story ends well - I chugged the DDP and within minutes my headache had resolved into a low roar, once more taking second place to the sharp, stabbing, radiating, numbing, tingling, unbearable pain in my lower back. A pain, in short, that no amount of caffeine can fix, but at least I don't have that godawful damn headache anymore. |
December 21, 2007 at 5:34pm December 21, 2007 at 5:34pm
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Sat., Dec. 22, 2007, 1:08 A.M. EST (06:08 UT), marks the solsticeāthe beginning of winter in the Northern Hemisphere
http://www.infoplease.com/spot/wintersolstice1.html
For those of us situated to the north of the Earth's equator, tonight is the longest night of the year.
Where I am, the sun has already set and the Night has begun, and it will not end until 7:27 am tomorrow.
My life isn't particularly dark right now. It's a good life, and I wouldn't trade it for anything. Okay, I'd like my back pain to go away, but other than that I have no real complaints.
It hasn't always been like that. Like most people, I've had my ups and downs, and I fully expect I'll continue to have them. The ups are like summer: sunny, carefree, bright, cheerful. The downs? Well, there's a lot of fake "cheer" going around these days, usually bedecked in red and green with a price tag swinging from it in the snow-flecked breeze, but I don't find much cheerful about winter. I mean, in winter, through the longest nights, we have to make our own cheer, be it bright lights, dancing fires, the company of friends and lovers.
The ups and downs of the seasons are fairly predictable. Not so those of humans. I suppose many of us suffer from seasonal depression. Not me. I just get depressed at random times. Then I get, "What do you have to be depressed about? You have such a great life! Friends, family, people who care, and all the stuff you've ever wanted!" and so on. And so I feel guilty about feeling bad in the midst of all of that, which makes me feel even worse, which leads to more protestations on the part of well-meaning friends, which makes me want to go away from them, which makes things worse, until I, for no reason I can ever properly elucidate, feel like I'm living my own longest night.
See, people are always telling me to "count my blessings." It was one of my mother's favorite phrases. I never did fully understand it. "Count your blessings," she'd say. Like when you're lying awake at night and instead of fluffy white sheep hopping a fence, you see little blessings - whatever the fuck they look like - and you can fall right asleep. It's not that I can't count my blessings; it's not that I can't be thankful for all that I have.
It's that I'm scared shitless that I'll lose it all.
On the solstice, I have in the past had a personal tradition to remain awake all night in a kind of vigil, to force myself to endure Nature's longest night in hopes that it will, through some psychology or sympathetic magic, allow me to withstand my personal ones.
I don't know if I can do that tonight. I didn't sleep well last night, and I'm not sure I can stay awake. I'm not sure if I want to. I've done the vigil a few times, and I think I've gotten out of it what I need to.
The night is no darker than any other, really. In fact, tonight it should be even brighter than usual - it's almost a full moon, and even if it's cloudy, the clouds will shine from the reflected fake cheer hung from everyone's trees and houses. It's a bright enough night, but neither moon nor blinking red and green lights can hold a candle to the light of the Sun. As dawn approaches, the light intensifies, and its quality becomes crepuscular. I love that word - crepuscular - and I don't get to use it often enough. "Of or pertaining to twilight." For a while, the world hangs in the crepuscular balance between night and day and then - slowly, so slowly that you can no more detect it than you can detect the movement of the hour hand on an analog clock - the day begins.
Dawn doesn't break; it melts.
As it has done since before human history, the world wakes up from its long night as a sliver of sun peers over the horizon. In contrast to the steady melting of night into day, it takes a surprisingly short time for the solar disk to crest the horizon - at which point you're really not supposed to look at it anymore, but I figure the UV has been scattered away and I have just a few seconds to contemplate that which makes life possible here on this remote speck of a world, so small in the universe yet so large to us.
It's all a matter of perspective, isn't it?
Sunrise: one of the few things that we can say with certainty that it will happen tomorrow. Because it defines tomorrow.
It's not long before I have to look away. The light is only burned on my retinas for a few short moments, but it's burned into my memory forever: There will be a tomorrow, and things will cycle back to summer.
Mama always told me not to look into the sights of the sun.
Oh but Mama,
That's where the fun is. |
December 21, 2007 at 5:01pm December 21, 2007 at 5:01pm
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...because this made me laugh.
http://www.canada.com/reginaleaderpost/news/story.html?id=4e53b7c3-1200-4748-ab8...
"I told Maya: 'There's a letter from Santa just for you, let's read it'. We sat down on the couch, I opened the letter and began to read. My mouth dropped open. Oh, My God!"
Speaking of bad people, this quiz might help you choose from amongst the plethora of evils visited upon us by the Republicrats and Democans vying for the Presidential election. Why they'd actually want the job is beyond me - it's like volunteering to clean up a Superfund site without a biohazard suit.
Anyway,
http://www.wqad.com/Global/link.asp?L=259460
Answer the 11 questions below to find out which candidates are most aligned with your views and opinions. You may skip questions if you do not want them factored into the results. This quiz is not meant to pick your candidate for you. It is designed to inform the public of the various stances candidates make.
I ended up with Rudy Giuliani. You know... the guy Pat Robertson endorsed?
I think I'd rather write in Hello Kitty 
Speaking of disgusting things that are bad for you:
http://www.supersizedmeals.com/food/
Having a hard time deciding what to buy your friends or relatives this Christmas? Why not make them something instead! Everyone always says, "everything tastes better with bacon", why should chocolate be any different? |
December 20, 2007 at 5:38pm December 20, 2007 at 5:38pm
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I'm sure most of you have been to websites that list the top 5 or 10 "Most Viewed Articles."
Something always bugged me about that, and today, I finally realized what it was.
"Duh," I sez to meself. "If you're going to list 'Most Viewed,' it's a rather self-fulfilling thing, isn't it? People will click on them and they'll be Way More Viewed."
It would be difficult for lesser-viewed articles to rise to the top then, yes?
I think websites should have a list of their LEAST viewed articles, instead. Then, when enough people click on one, it starts to move up the list, making room for the next-least-viewed articles, which are then clicked on... etc. That way the site, whatever it is, will get more views overall.
Anyway, I found this from a "Most Viewed" list:
http://money.cnn.com/galleries/2007/fortune/0712/gallery.101_dumbest.fortune/8.h...
That particular URL points to #8 in a 101-item list, mainly because #s 1-7 are boring, but #8 is amusing: "hordes of rats" in a KFC/Taco Hell in NYC. Ratatouille, it ain't!
Everyone knows NYC has rats, both the two- and four-legged kind. What you may not know is that even the four-legged kind have opposable thumbs. Now, you see the rats in that picture? That is the actual color of a New York City rat. They're darker than your average gray rat and a LOT darker than your cute little lab rats.
Why is this, you wonder? Well, the New York subway track pits are all painted black. A black that, over time, fades to a kind of 85% - 90% gray. And other than in fast food outlets and the mayor's office, the single easiest place to find a rat in NYC is the subway. Now, the subway rats don't get up on the platforms - at least not when anyone's on them - but you often see them scampering along beside the third rail. But that's the ONLY time you see them - because when they stop, they blend into the background because their fur is 85% - 90% gray.
Natural Selection does work.
Anyway, here's the BEST part of that list, appropriately enough at #13:
http://money.cnn.com/galleries/2007/fortune/0712/gallery.101_dumbest.fortune/13....
Disneyland announces plans to close the "It's a Small World" attraction to deepen its water channel after the ride's boats start getting stuck under loads of heavy passengers. Employees ask larger passengers to disembark - and compensate them with coupons for free food.
Disney: Unclear on the Concept since 1939. |
December 19, 2007 at 5:34pm December 19, 2007 at 5:34pm December 19, 2007 at 12:37pm December 19, 2007 at 12:37pm
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The sad thing is that I still have to find gifts for some people.
The happy thing is they all know I'm a slacker and won't stop being my friends if they don't get them until, oh, around New Year's |
December 18, 2007 at 5:57pm December 18, 2007 at 5:57pm
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I just happened to come across this saliva-inducing headline from Reuters - I wonder if it was intentional or not.
Iraq Kurdish leader snubs Rice over Turkey raid
Mmmmm... turkey and rice... with Kurds. Is there a whey this could be real?
I suppose there was too much Grease and they found themselves Russian to the toilet...
The actual article, boring as it is: http://www.reuters.com/article/newsOne/idUSL1839316520071218 |
December 18, 2007 at 1:23pm December 18, 2007 at 1:23pm
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Just when you think you've seen the worst the internet has to offer...
Just when you believe you've plumbed the depths of darkness, and congratulated yourself on emerging unscathed...
Just when you think the worst POSSIBLE thing you can do with a certain pink-clad cat is paste her talking head on a dancing elf...
THIS comes along.
http://www.kittyhell.com/2007/12/15/hello-kitty-hotel-room-video/
If you view it several times, with the sound turned WAY up (especially if your computer has a sub-woofer), you will be vaccinated against everything the internet could ever dredge up.
Or, your head will explode. Same difference, really. |
© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.
|
I'm more than happy with Carrion Luggage, however.
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