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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.




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January 31, 2009 at 9:45pm
January 31, 2009 at 9:45pm
#633188
I rarely get bored. Even when I have nothing to do, I always have something to do.

But as a resource for those of my readers who DO get bored, I present:

http://www.cardtoss.com/

and

http://www.zefrank.com/byokal/kal2.html

and

http://www.rafcareers.com/altitude/games/dz_game/dzgame.cfm

Not *quite* as useless as, say, the virtual bubblewrap or virtual toilet paper roll. Still... bloody damn useless.
January 27, 2009 at 1:06pm
January 27, 2009 at 1:06pm
#632327
http://progressiveboink.com/archive/calvinhobbes.htm

Every time I find something else about Calvin and Hobbes, I laugh all over again. This one's got some great commentary on it.

It's also an excuse to link my one and only fanfiction again, for anyone who might have missed it.

Home Again Open in new Window. (13+)
A middle-aged man rediscovers his childhood.
#1192516 by Robert Waltz Author IconMail Icon


What a stupid world.
-Calvin
January 25, 2009 at 8:06pm
January 25, 2009 at 8:06pm
#631955
A challenge to writers: true stories, told in one sentence.

http://www.onesentence.org/
January 22, 2009 at 4:49pm
January 22, 2009 at 4:49pm
#631343
My computer is (mostly) up and running again, and I was even able to restore a lot of stuff from an old backup.

One thing I wasn't able to restore was my long list of blog fodder links. Those are gone forever, I think. Well, most of them were one-shots anyway.

But I did find the time to begin a whole new list of blog fodder, and now I shall begin to inflict them on YOU.

Let us begin with this classic Top Ten List:

http://www.evilbible.com/Top_Ten_List.htm

Top Ten Signs You're a Fundamentalist Christian

Example:

5 - You are willing to spend your life looking for little loopholes in the scientifically established age of Earth (few billion years), but you find nothing wrong with believing dates recorded by Bronze Age tribesmen sitting in their tents and guessing that Earth is a few generations old.

Good stuff, good stuff. I can only add that, contrary to popular belief, there are not two sides to every issue. Some issues have multiple sides. Most, however, aren't even "issues" at all, and thus only have one side. These include: The Earth is round, humans have walked upon the moon, the Holocaust happened, and dinosaurs disappeared an unimaginably long time before the first human picked up a wrench.

Okay, off the soapbox and on to the next link.

While we're talking about religion, I might as well also decry the excesses of Barack-is-my-redeemer-ism. Hey, guys? Chill. It's not like we elected Bruce Springsteen.

http://www.holytaco.com/guest-column-barack-obama

Now that I'm president, here's four things I want you people to stop doing...

Seriously, when I walk up to a podium, stop f*&king chanting my name like I just shredded on a three and a half minute guitar solo.

Here's a site anyone with a cat will appreciate. Hell, dog people will probably get a chuckle out of it, too, as in "Lawdy, those cat people are weird." Hey, dog people, we're not the ones following around behind our lords and masters with plastic pooper scooper bags.

Guidelines for Cats

Doors
Do not allow closed doors in any room. To get door opened, stand on hind legs and hammer with forepaws. Once door is opened, it is not necessary to use it. After you have ordered an "outside" door opened, stand halfway in and out and think about several things. This is particularly important during very cold weather, rain, snow, or mosquito season...


http://www.jamesshuggins.com/h/hum1/guidelines_for_cats.htm

And I'll finish today's crop of websites you never would have otherwise found with this little offering, which will make you waste time whether you're a human or a cat. Dogs need not apply; go make your human pick up your poop now.

http://www.zefrank.com/memory/stringspin/spin_1.html

January 21, 2009 at 3:58pm
January 21, 2009 at 3:58pm
#631131
Still lazy today, so another short entry.

(Okay, actually, I'm not lazy. I'm just finishing up restoring my computer after I came into work on Monday morning and discovered that the hard drive had crashed. Completely. All my work files are on a network drive, but it was STILL a royal pain in the ass to reinstall everything. Pleh.)

So on to the entry: We all know that the painting known as the "Mona Lisa" was da Vinci's masterpiece, and is doubtless the most famous portrait, if not the most famous work of art, ever... right?

Well, what if some other famous artist had painted it instead:

http://damncoolpics.blogspot.com/2008/12/if-other-artists-drew-mona-lisa.html

Go ahead. There's a great punchline.
January 20, 2009 at 1:02pm
January 20, 2009 at 1:02pm
#630886
It's better without the W.
January 18, 2009 at 3:40pm
January 18, 2009 at 3:40pm
#630531
Well, I'm sure we all knew that someone would come up with a) Inauguration Bingo b) an Inauguration drinking game or c) both at the same time.

I'm still working on (c), but someone beat me to the punch with (a):

http://www.holytaco.com/barack-obamas-2009-inauguration-bingo

Watching the inauguration on TV is probably going to be a lot like Super Bowl Sunday. Coverage will start hours beforehand and the reporters are going to say the same things over and over again to fill airtime. So we made this bingo game, to make it a little more interesting. To play, just put a flag pin in the square whenever you hear a TV anchor say one of these phrases. When you complete a row, yell Bingo! (If you don't know how to play, ask your grandmother.) Good luck!

(Yes, I know the inauguration is in the middle of the day, on a weekday. That wouldn't stop ME from drinking. Go for it.)
January 17, 2009 at 4:40pm
January 17, 2009 at 4:40pm
#630316
I've said it all along: If you want to make something funny, throw in a duck.

http://www.nbcchicago.com/news/weird/Trucking_Duck_All__National_.html

I'll spare you the obvious puns. The announcer in the video in that link made enough to last for a good long time.
January 15, 2009 at 3:55pm
January 15, 2009 at 3:55pm
#629863
Tonight is poker night for me, so as a cautionary tale, I present:

http://www.holytaco.com/10-worst-types-drunks

The 10 Worst Types Of Drunks

Alcohol is a wonderful thing, but it can also turn your friends into those people that take a fun night of drinking and turn it into a sobfest, a fight or an uncomfortable conversation. Here are the 10 worst types of drunk people.


Now, of course, I'm not any of these people. Not me. Never.
January 13, 2009 at 3:57pm
January 13, 2009 at 3:57pm
#629469
I like science. Science is good. Science leads to a rational worldview and technological advances, and a better understanding of the universe.

However, things like this make me want to kick something.

10 Things Science Says Will Make You Happy

http://www.alternet.org/healthwellness/111138/10_things_science_says_will_make_y...

1. Savor Everyday Moments
Pause now and then to smell a rose or watch children at play...


Look, the last time I stopped to smell a rose, a bee came out and stung me on my damn nose. And the last time I was watching children at play, a couple of big, beefy cops came up and took me away. Now I'm on a List.


2. Avoid Comparisons
...Instead of comparing ourselves to others, focusing on our own personal achievement leads to greater satisfaction...


My personal achievement needs to include doing better than the Joneses.


3. Put Money Low on the List
...“The more we seek satisfactions in material goods, the less we find them there...”


I don't want material goods. I just want money. Enough money so I don't have to work anymore. Keep the "material goods." Just give me money.


4. Have Meaningful Goals
“As humans, we actually require a sense of meaning to thrive.”


My goal is to have money. That's meaningful.


5. Take Initiative at Work
...when we express creativity, help others, suggest improvements, or do additional tasks on the job, we make our work more rewarding...


BFPPPHHHAHAHAHAHA! When you do all THAT shit at work, most places, they'll either fire you or look at you like you're weird.


6. Make Friends, Treasure Family
Happier people tend to have good families, friends, and supportive relationships


Whereas everyone I know has a dysfunctional family, and talking about it makes them happy (see this week's Comedy newsletter for more details).


7. Smile Even When You Don’t Feel Like It
...Even if you weren’t born looking at the glass as half-full, with practice, a positive outlook can become a habit.


I'm positive. I'm positive this article is a crock of horsepuckey.


8. Say Thank You Like You Mean It
...people who write “gratitude letters” to someone who made a difference in their lives score higher on happiness, and lower on depression...


I want to thank you all for reading my blog. It really makes a difference to me. There - I'm going to be positively GLOWING for the next month.


9. Get Out and Exercise
...regular exercise offers a sense of accomplishment and opportunity for social interaction, releases feel-good endorphins, and boosts self-esteem.


The last time I went to the gym, there in the locker room was the elderly judge who presides over the Federal Grand Jury on which I've been serving for most of a year now. He was completely starkers, bent over and toweling off his leg. I will never, ever be able to get that image out of my mind, even with a 55-gallon drum of eyebleach. If this is what regular exercise has to offer, you can freaking KEEP it.


10. Give It Away, Give It Away Now!
...you get more health benefits than you would from exercise or quitting smoking...


Oh good; that means I don't have to exercise or quit smoking. Provided I don't have to see any naked judges, that's Just Fine With Me. Oh, and that song you quoted? One of the stupidest ever.

This list sucks. I need a Cracked list as an antidote.

Here:

6 Obnoxious Old People Habits (Explained by Science)

See? We're still talking about science here, but this one's going to be GREAT.

http://www.cracked.com/article_16952_6-obnoxious-old-people-habits-explained-by-...

How many times have you gotten behind some large sedan going 30 mph on the highway, only to notice it's being driven by someone born during the Great Depression? Do you stop to say, "One day, that'll be me!"

Because it will.


Now I'm happy.
January 12, 2009 at 6:19pm
January 12, 2009 at 6:19pm
#629304
DO YOU EVER want to change the way you see the world? Wouldn't it be fun to hallucinate on your lunch break? Although we typically associate such phenomena with powerful drugs like LSD or mescaline, it's easy to fling open the doors of perception without them: All it takes is a basic understanding of how the mind works.

http://www.boston.com/bostonglobe/ideas/graphics/011109_hacking_your_brain/

Now, look. Is it just me, or does fucking around with your mind sound like a Bad Idea to anyone else?

This is how people become headlines, folks. "The magical horse in the clouds told me to do it."

No. I'll leave the brain-hacking to zombies.
January 11, 2009 at 6:26pm
January 11, 2009 at 6:26pm
#629112
Walking sixty blocks of Broadway at 2 am, in the freezing rain, with the sidewalks just on the edge of becoming hockey rinks.

I gave up halfway and hailed a cab. It took exactly 1.2 seconds to get one.
January 10, 2009 at 1:47am
January 10, 2009 at 1:47am
#628842
The word "civilization" can be interpreted as "the art of living in cities."

The hotel I'm overnighting in doesn't have a fourth floor.

The elevator numbers go from SC (sub-cellar) to C to L to 2, then 3, then 5-9. I'm on the ninth floor. I'll call it the penthouse suite although it's about the size of my bedroom at home (which is to say: the size of the closet in many modern homes).

The hotel is in downtown Flushing, which is in Queens, which is in New York City. Nearby are the grounds where two World's Fairs were held - one significantly more famous than the other.

One of the great paradoxes of a city is how cramped everything is, and yet they leave room (at least, here) for wide, open spaces - after all, we've been evolving for billions of years (yes, billions; I hope I've scared all the young-earth creationists away from this blog by now) and have only had "civilization" for a paltry few thousand. I guess we haven't quite perfected the art.

The dominant local culture is of Chinese origin. Most of the shops are signed in what I assume to be Chinese characters. This hotel boasts multilingual hospitality: English, Chinese, Spanish, a few others; it appears to be owned and run by ethnic Chinese.

Perhaps there's a cultural aversion to the number four, just as many high-rises built by European-Americans skip the 13th floor. I wanted to ask at the desk about it, but didn't want to be rude or seem like a Bad American. Bad enough I wasn't thinking and put on my Serenity t-shirt for the trip - has what I sincerely hope is the actual Chinese ideograph meaning "Serenity" on it, and not "I am a Bad American."

The drink machine doesn't chill properly, and I ended up with a warm Sprite. I'm pretty sure that's a maintenance fault and not a cultural superstition.

I spent a few minutes walking around the center of town. You hear stories about how dangerous it is in a city, but who's going to fuck with a big guy in a trench coat? Nice place. Interesting shops. Starbuck's on one corner; I didn't go in.

Tomorrow - that is, later today, after I get some sleep - I'll go see my aunt. But I'm only here for one night; the only train I could catch going home leaves at 3am on Sunday morning. Turns out UVA classes restart on Monday, which explains why everything else was booked. I'll be spending tomorrow night in Penn Station and in transit.

Long weekend. Probably won't be back on until Sunday evening.

(Edited to add: after I wrote this I did remember something involving the number four in some Asian cultures and finally hit on the right Google search to confirm it. Apparently, the word for "four" is very similar to the word for "death" in at least China, and so there's a cultural aversion to it. Makes me wonder why they don't just come up with a different word for "four," but I suppose it'd be kind of difficult selling it to the over one billion speakers of some dialect of Chinese.)
January 8, 2009 at 4:43pm
January 8, 2009 at 4:43pm
#628580
I got a call Monday that my elderly aunt, whom I've always been close to, fell outside her house in NYC. They took her to the hospital - turns out she's pretty much okay from the fall, but they found some heart problem, so they're keeping her for observation.

My other aunt, her sister, acted weird on the phone while trying to tell me everything's fine.

Consequently, I feel the need to see for myself.

I decided to take a train - it's not worth the hassle of an airplane, and I can get everywhere I need to go by bus or subway. Downside is the return train leaves at three in the morning. Best I could do at short notice. At least I can maybe sleep on the train.

Well, perhaps I can treat myself to a late dinner in Manhattan. I don't get there nearly enough, and it's remarkably inexpensive to go to NYC from here by train. Not something I could do every month or anything, but still...
January 7, 2009 at 4:54pm
January 7, 2009 at 4:54pm
#628363
This will be mind-numbingly boring to many people, so feel free to skip it.

http://www.reuters.com/article/marketsNews/idINBOM36807220090107

BANGALORE, Jan 7 (Reuters) - The chairman of India's Satyam Computer Services (SATY.BO) (SAY.N) resigned on Wednesday, saying profits had been inflated over the last several years.

Summary: This outsourcing company in India didn't just cook the books, they covered up the stink of the rotting accounting meat with liberal quantities of the financial equivalent of hot curry, ginger and garlic. The result was, like some Indian food, outwardly palatable but inwardly... disturbing. As in, it disturbs your innards.

1. The Balance Sheet carries as of September 30, 2008

[a lot of numbers, which when translated from Hindi to Accountese to English amounts to "You know all that money we said we had? Well, about that...]


Basically, they tried to cover this up by "buying" with their "cash" a bunch of companies with the name "Maytas" (yes, Satyam spelled backwards) - all of which were owned by the owner's family - at overinflated prices. This would put a bunch of assets on the books to replace the cash that wasn't there. Confused? You're supposed to be.

I am also taking the liberty to recommend the following steps:

1. A Task Force has been formed in the last few days to address the situation arising out of the failed Maytas acquisition attempt. ...


In other words, these foxes can now guard the henhouse.

2. Merrill Lynch can be entrusted with the task of quickly exploring some Merger opportunities.

I wouldn't trust Merrill Lynch to tie my shoes. And I wear slip-ons.

3. You may have a restatement of accounts' prepared by the auditors in light of the facts that I have placed before you.

Translation: We lied. We can lie again.

l am now prepared to subject myself to the laws of the land and face consequences thereof.

Translation: I am willing to accept the consequences of my actions, unlike those weasels over at Enron, or that Madoff schmuck, who screwed you and then didn't own up to it. But you're still screwed.

The ultimate irony in all this?

I'm told that in the local dialects, "Satyam" means "Truth."

A slightly less confusing article:

http://www.reuters.com/article/companyNews/idUKTRE5061W020090107?symbol=SAY.N
January 6, 2009 at 2:15pm
January 6, 2009 at 2:15pm
#628142
While I don't have cable TV, sometimes I end up at a fashion-obsessed friend's house when the show "What Not To Wear" comes on. It annoys me more than most TV shows, but it was the first thing I thought of when I found the site I'm about to link.

In these trying economic times, lots of people become unemployed, some even through no fault of their own. When that happens, they usually polish their résumés and go looking for another job (that is, if they don't fall into the dark pit of homelessness and cheap wine). Often overlooked, though, is the cover letter. While I know that nobody reading this would have any problem writing, perhaps you have friends who would benefit.

Being an employer myself, I've seen a few résumés, and while I'm willing to forgive a few typos and misstatements - we are, after all, dealing with engineers, not copy writers - there are limits.

This site provides some examples of going WAY over those limits.

(Bonus: geeky reference in the first paragraph)

http://www.killianadvertising.com/coverletters.html

Attached to every résumé is the obligatory cover letter. Composing one, it seems, has a Difficulty Rating of 11, since that's where we find the most tortured prose ever set to paper. For example:

"I expect the position to pay commissary to that of its value, as well as to the performance completed."

...

Imagine, if you will, two roommates at Thesaurus U.:
"I aspire to obtain a beverage. The vending machine is where my path leads."
"I wish to accompany you, since I have assembled a myriad of coins."
"I possess coins, as well. Let's embark."


And I couldn't even read the whole "Twas 4 weeks after Christmas" poem. It made my teeth hurt. If I ever saw that posted on this site, it might just earn the author my very first one-star rating.

So, examples of What Not To Wear - résumé edition.
January 5, 2009 at 2:49pm
January 5, 2009 at 2:49pm
#627979
...at least, until you consider the alternative.

There's this girl, Amy, whom I dated in high school. She didn't live near me; she lived outside of Baltimore, a couple hours away. Long story for another time. We weren't all that serious, and the usual teen crap happened and we fell out of touch.

Yesterday, her best friend found me on Facebook - my rarely-used real-name account, which I only keep up because it's easier for old friends with names like "Bill Smith" to find ME with my unique name than it is for me to find THEM. So we exchanged the usual "oh my god has it been 25 years?" catching up emails, and she gave me updates on a lot of people we used to know - all of them, of course, married, in stable careers, 1-6 kids, happy, that sort of thing, including my former girlfriend's twin brother. She notably avoided talking about Amy, so I asked.

Turns out Amy died in late 1999, at 31, dropped from some rare and undetected heart condition. She'd just gotten back from her honeymoon.

So yeah, getting old sucks, but it beats the hell out of the alternative.

Most of the time.
January 4, 2009 at 2:42pm
January 4, 2009 at 2:42pm
#627763
We are people of this generation, bred in the most hedonistic society the world has ever known, housed now in over-mortgaged tract homes, and looking uncomfortably to the world we leave to our children. We were born in the days when the Soviet Union was the Evil Empire, a college degree was the ticket to the middle class, and being born American meant that unlimited opportunity was your birthright.

http://corporatemofo.com/society_and_antisocial_tendenc/reality_bites.html

You know, I follow financial discussion boards and websites, and you can probably imagine the kind of freaking-out that's going on at said boards these days. People with portfolios down 30, 40, 50%. People who have lost or are about to lose their jobs. People wondering why they should keep their home when it's worth 3/4 of what they paid for it - without interest...

[Allow me a venture into digression; as this is my blog, I don't feel too out of line doing this: I don't understand the "We're upside-down on our mortgage, so we're just going to default and let the bank foreclose" kind of mentality. You bought a house, you signed the papers - whether you fully understood all the Ferengi print is another discussion entirely, but let's assume "yes" - and you entered into an agreement to faithfully pay off the mortgage under the terms provided. Not ONE of those terms included a clause guaranteeing that your house would always appreciate in value; you just assumed that it was despite all historical evidence to the contrary. And now you want to default on a contractual obligation? There's a word for you, dude, and it's not a nice one.

[To continue my digression, consider a house that you may have purchased for, say, $300,000 - "modest" by the standards of the real estate boom, depending upon your area. Assuming a $50,000 down-payment and a 6.5% fixed interest rate on a 30 year loan, you're going to pay the bank a total of $568,861.22 over 30 years. (That's in today's dollars. Since you got a fixed rate mortgage, your monthly payment of $1580.17 is effectively less in 2039 dollars, when the mortgage will be paid off) (I never said there would be no math; quite the contrary). Anyway, the point is, you're already upside-down to the tune of $568,861.22 - $300,000 = $268,861.22 right from the get-go. So if your home value drops to $225,000 because of the current housing crisis, your upside-downedness is $343,861.22 instead of $268,861.22. Big effing deal.

[Besides, what are you going to do, rent? Fixed-rate mortgages never increase, except for any escrow portion. Rent will go up ever year. End of digression.]

Getting back to the essay at hand,

We grow into middle age not surrounded by prosperity and security, but by our doubts and fears. Even as the rich have gotten richer, we have seen our standard of living fall. The middle class is barely reproducing itself, bifurcated into those barely treading water and those on an endless paper chase after useless honors. Our hopes have been dashed, our dreams sold for firewood to keep warm and hold back the wolves for one more night.

That, fellow writers, is how to mix metaphors. This guy uses a Cuisinart.

Somewhere along the way, someone might have tricked us into caring or having hope, but we have come to realize that the current "crisis" is not the result of a great country hijacked by a cabal of free-market capitalists: It is, in fact, the new baseline.

In other words, in the immortal spirit of Queen Victoria, perform your duties faithfully. It will be unpleasant, but just lie back and think of England.
January 3, 2009 at 5:54pm
January 3, 2009 at 5:54pm
#627635
We got this flier in the mail a while back from a lawn care company - it was full of awful puns and clever jokes about the economy, relating it to lawn care. Things like, "We can dump the leaves onto your neighbor's foreclosed-upon driveway - who'd know?" I'd quote from it some more, but I'm too lazy to go to the fridge and get it. Yes, we tacked it onto the fridge - anyone that funny gets my business. If, that is, we actually have a freaking LAWN in the spring.

So someone found this ad in an Illinois newspaper:

http://i43.tinypic.com/27xezpi.jpg

Hey, if I lived in Illinois I'd buy from them.

Too bad I didn't notice anything like this around the time of the Clinton / Lewinsky thing.
January 2, 2009 at 3:41pm
January 2, 2009 at 3:41pm
#627456
http://www.reuters.com/article/newsOne/idUSL0910395120080109

WARSAW (Reuters) - A Polish man got the shock of his life when he visited a brothel and spotted his wife among the establishment's employees...

Okay, so this guy walks into a brothel and sees his wife working there.

Sounds like the start to a joke, right?

Of course, he'd never have known unless he went in there to... um, just to see what the inside of one was like, you know, because he'd never been inside one and... er... okay, EPIC FAIL.

The couple, married for 14 years, are now divorcing, the newspaper reported.

Sounds like a good plan. Maybe he can still hire her from time to time.

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