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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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July 31, 2007 at 6:32pm
July 31, 2007 at 6:32pm
#524977
Yeah, so I've been trying to think of something to blog about that doesn't involve work stress, road rage, my ex-wife, writing, boobs or people who light themselves on fire.

I got nothing.

Nothing, that is, but this compendium of what would have REALLY happened to those superheroes:

http://www.cracked.com/index.php?name=News&sid=2277

And just because I like you, some helpful tips:

http://radaronline.com/features/2007/07/narcotics_drug_arrest_tips_gladewater_po...

No Hello Kitty stuff this time... thank gods.
July 28, 2007 at 11:38pm
July 28, 2007 at 11:38pm
#524311
I've seen some Wrong things in my time on the Web. I've posted many of them here to share with you, because I believe that while shared joy is multiplied, shared misery turns to laughter at your reactions.

This, though... this comes from the deepest, darkest depths of a culture that has produced some deep, dark depths.

http://gizmodo.com/gadgets/animal-abuse/japans-hello-kitty-cat-humiliation-syste...

Enjoy. And don't send me the therapy bills.
July 27, 2007 at 6:12pm
July 27, 2007 at 6:12pm
#524109
You know, when you and your buddy can't agree on a course of action, and talking won't get you anywhere, you end up glaring at each other... one of you will say, "Let's settle this like MEN!" You both roll up your sleeves, clench your right hands into fists...

Smack them three times against your left palms, and come up with rock, paper, or scissors.

Well, that's old school now. I give you...

RPS25

http://www.umop.com/rps25.htm
July 26, 2007 at 7:07pm
July 26, 2007 at 7:07pm
#523916
WARNING: This post contains Harry Potter and the Deathly Hallows spoilers!
Good god, the book's been out nearly a week. Finish it already.

Critic sniping at Rowling:
http://news.yahoo.com/s/csm/20070725/cm_csm/ysawyer;_ylt=Ai2wauD9Mc0r6j5rhVyg0y2...

My commentary:

I call bullshit.

If literature truly reflects society, then the end of the Harry Potter series spells trouble for us all.

Oh, right, yes, like the current political climate coupled with the public's demand for cheap, mindless entertainment and schadenfreude hasn't already trumped our doom.

Plus: "Literature?" Come on. See a few posts down.

J.K. Rowling's towering achievement lacks the cornerstone of almost all great children's literature: the hero's moral journey. Without that foundation, her story – for all its epic trappings of good versus evil – is stuck in a moral no man's land.

1. So what?
2. Over the course of seven books, Harry grows up. That's more than we can say for Luke Skywalker. Even as a full-fledged Jedi, he was still a whiny brat.
3. I'll get into (3) later.

Good always prevails. It's the hero's struggle – and costly redemption – that matters.

If I'm reading this right, the author is arguing that Harry should have started out as a whiny, self-centered brat just so Rowling could show "character development." Again, I give you Lucas.

A story is about someone who changes, who grows through a moral struggle. What is Harry's struggle? Exactly

Here's the real spoiler, so if you're still reading and don't want spoilers, leave.

What is Harry's struggle?

Let's see... you're a 17 year old kid, you've just been through months of being on the run, pursued by the forces of EEEvil, and you find out that to defeat said EEEvil, you have to die. Not, face EEEvil and possibly win, but lay down your seventeen year old life to save the world (or at least the only world you know). As Spock said, "The needs of the many outweigh the needs of the one," but of course Spock came from a morally advanced race. Going back to Luke, even that whiny prat had a chance (albeit slim) at defeating Vader the first time he went up against him. Harry had NO chance, and he knew it. How's that for a moral choice?

Me, I'd have grabbed Ginny (and Hermione, but that's just me) and taken my broomstick off to Belize.
July 25, 2007 at 7:38pm
July 25, 2007 at 7:38pm
#523717
YES!

We're finally entering the 21st century! At last, behold:

http://jalopnik.com/cars/jalopnik-loves-flying-cars/worlds-first-flying-car-ente...

The Flying Car!

Damn... now I have to buy my wife a Roomba.
July 25, 2007 at 7:20pm
July 25, 2007 at 7:20pm
#523711
This is actually kinda cool.

http://cbs13.com/watercooler/watercooler_story_206171558.html

Oscar the cat seems to have an uncanny knack for predicting when nursing home patients are going to die, by curling up next to them during their final hours.

Cool, that is, unless you're one of the unfortunates who don't like cats. Me, I think it'd be good to have a psychopomp by my side as I kick the final bucket - even though I don't believe in an afterlife.
July 24, 2007 at 11:51pm
July 24, 2007 at 11:51pm
#523571
I'm probably going to get flamed for this, but:

http://www.timesonline.com/site/news.cfm?newsid=18619298&BRD=2305&PAG=461&dept_i...

To me it's simple. Rather than discouraging behavior such as this, we need to - well, not encourage it, exactly - but look the other way and let Nature take her course. It's obviously not enough to tell people, "Hey, you know, it's a Bad Idea to play with gasoline and matches." It's not enough to have news stories like this, in spite of which other people will try this again.

No.

It's time to let the stupid weed itself out. Chlorinate the gene pool. Between this and the practice of dancing on top of your car when it's in motion - forget the name of it, but it was apparently popularized in some rap video and copycatted by people across the country - and a host of other activities with potential gene pool cleaning, we have the potential to not just make social progress, but thin the herd of idiots who don't seem to understand that stupid things are stupid.

And by "idiots," I mean "people with no common sense," like this literal genius:

http://www.nypost.com/seven/07242007/news/regionalnews/genius_dies_in_plunge_reg...

Don't get me wrong - I feel for the family and friends of people who Darwinize themselves. BUT I'd have to say that eventually, they'll realize that life is better without idiots around.

The world is too safe as it is. Protect people from other people, predators, and weapons of mass destruction, sure - but there's no damn point trying to protect people from their own bad judgement.

Okay, I'm mostly kidding about this one. Still, I read about someone doing something stupid just about every damn day, and it's not slowing down any.
July 22, 2007 at 8:11pm
July 22, 2007 at 8:11pm
#522982
Lorien Author Icon, commenting on us finding something else to obsess upon now that the last HP book is out: "Preferably something with literary merit."

While I agree with the sentiment to some extent - as good as Rowling is at capturing and engaging the reader, she's not the world's greatest writer (Richest, maybe, but the two are not synonyms) - I have issues with literary writing. Now, I'm not sure exactly how Lorien meant it, but to me,"literary merit" is code for "a dense, impenetrable force field of twisted allegory, obscure allusions, and other ways an author can demonstrate how clever she is without resorting to plot or characterization"

Ann Beattie is a great example of this. So is pretty much anything in The New Yorker (at least, it used to be that way - I haven't even tried to read that in a while). When I was younger and I picked up mags like that, and tried to read the stories, I found them dense, impenetrable and impossible to understand. I figured, "I'm a smart guy. One day, perhaps after college has warped my mind to a sufficient degree, I'll understand and appreciate the rarefied subtleties of literary fiction."

Well, here it is a quarter-century later. I'm still a smart guy, and I still find that sort of thing dense, impenetrable and impossible to understand. Granted, I took very few liberal arts courses in college - being an engineer and all - but I don't think I'm ignorant about writing.

As with a lot of modern art - an exhibit showing an overflowing trash can and a canvas painted red with a purple stripe down the middle come to mind - a lot of it is, as I mentioned above, artists (painters, sculptors, writers, whatever) having stopped trying to be accessible to ordinary people and merely trying to outdo each other using rules created BY the field FOR the field.

I shouldn't need a degree in art history to appreciate fine art. I shouldn't need a degree in literature to appreciate reading. And writers (I'll leave artists alone from now on, because this is writing.com and not deviantart.com) need to decide whether they're writing for other writers - or for general consumption.

If you're writing for other writers, hey, that's great. Don't expect to become rich, but then, that would be "selling out," wouldn't it? If you're writing for the general population, of course, don't expect to get rich doing that, either. I don't. I expect to get rich (well, at least earn enough to retire) doing engineering. You've as good a chance at winning the lottery, the only difference being that with writing there is some element of skill involved.

If you can string a sentence together, turn a few phrases, stand some clichés on their heads, create interesting characters, put them in interesting situations, and bribe a few publishers, you can get readers. Who cares if it's a rehashed plot? At least it's a plot. The romance industry makes a living cloning plots - or at least I've heard they do.

So... essence of rant: the same people who would rather find out what's going on in Paris Hilton than in Paris aren't going to read "literary" writings. They're going to read Stephen King and Patricia Cornwell - and J.K. Rowling, if they read at all. I'm not writing to impress professors and black-wearing, clove-smoking elitists*; I'm writing to (try to) impress guys in Ford pickup trucks and single mothers.

Not ragging on you, Lorien Author Icon - I agree with you to a point. It just ain't going to happen.

*Incidentally, I wear black and I used to smoke cloves.
July 22, 2007 at 1:28am
July 22, 2007 at 1:28am
#522837
There's a subset of people on the internet who like lolcats.

There's another subset of people on the internet who like to take quizzes.

At the intersection of these subsets, I present:

http://www.okcupid.com/tests/6348388576689378978/Which-Lolcat-Are-You-

In cyberspace, no one can hear you squee.
July 22, 2007 at 12:57am
July 22, 2007 at 12:57am
#522830
So the postman knocks on the door and hands me my copy of Deathly Hallows, which Amazon had oh-so-kindly labeled as such right there on the packaging. "People have been stealing these from mailboxes," he explains. "Thought I'd see if you were home."

Someone's getting a tip this year.

I spent the next eight hours straight reading the thing. Right now some of you are going, "Eight hours?! That's slow! It took me four and a half!" Shut the fuck up, okay?

All I can say is, there were a few things that surprised me, and at least two major plot points that I had nailed on the head. Plus, the ending was pretty much exactly what I expected - before I saw the god-be-damned Internet spoiler brigade. Did this disappoint me? Far from it. Just as with the ending to The Dark Tower, the prediction coming to fruition increased my enjoyment.

Sadly, however, Snape does not take McGonnagal to the dungeons.

And boy, am I glad that series is over. Move along, folks - let's all find something else to obsess upon.
July 19, 2007 at 5:02pm
July 19, 2007 at 5:02pm
#522388
Yes, folks, it's Poker Night.

Work has been kicking my ass, my constitutional rights have been eroded to frostbitten nubs, and I've been kicked out of the poetry challenge. The last Harry Potter book comes out in a matter of hours (more than 24, but still, hours), and thanks to the goddamn Internet, I already know how it ends (and I wish all of the spoiler people could be declared unlawful enemy combatants and shipped to Gitmo). I've become addicted to lolcats (http://icanhascheezburger.com/) against all reason and good sense, and I can't seem to bring myself to clean off my desk so I'll feel better.

But none of that matters, because they still haven't negated the 21st Amendment, and tonight I'll be at my house, enjoying large quantities of liquid fuck-it.
July 17, 2007 at 10:18pm
July 17, 2007 at 10:18pm
#521988
...it's how you see it.

I meant to link this here a while back, socked it into my favorites and promptly forgot about it until now.

Some people with epilepsy might have trouble viewing this site - but then, maybe not. I don't know.

The rest of us might just find the eyes that follow us around everywhere creepy.

http://www.michaelbach.de/ot/index.html

One of the cool things about the site is he gives (relatively) simple explanations for why the visual illusions work. So if you have some time, check it out - while some of the illusions are old hat for many of us, there are some I'd never "seen" before!
July 16, 2007 at 8:41pm
July 16, 2007 at 8:41pm
#521723
The Secret Life of Snape and McGonagall

Snape: "Minerva. Meet me... in the dungeons."

McGonagall: "Ooh."

(Snape bends McGonagall over a rack and withdraws a wand-shaped crop)

McGonagall: "Ten points from Gryffindor! OOOh! Twenty points from Gryffindor! OH! OH! FIFTY POINTS FROM GRYFFINDOOOOOOOOOORRRRRR!"

Snape: "Oh, stop it, Minerva. Now Transfigurate so I can get some... pussy."

Bet you didn't want that image in your minds, did you? Well, neither did I, but it got in there anyway, so now you get to share!

Don't ask.

I'll be glad when the series is over.
July 15, 2007 at 11:35pm
July 15, 2007 at 11:35pm
#521483
Because I'm tired and can't think of anything original.

This has gotta hurt:

http://news.yahoo.com/photo/070713/481/ef5af798074f4a4e8070577d110017a8

We don't need no edjacashun:

http://news.bbc.co.uk/1/hi/scotland/tayside_and_central/6898244.stm

And now I present these two stories - and let you judge for yourself:

http://www.redding.com/news/2007/jul/13/drug-czar-gives-warning/

and

http://www.cbc.ca/canada/story/2007/07/13/pot-toronto.html

And finally, this one's for all of you hopelessly addicted to World of Warcrack - or Writing.com:

http://www.usatoday.com/news/nation/2007-07-14-internet-neglect_N.htm
July 14, 2007 at 8:24pm
July 14, 2007 at 8:24pm
#521266
Remember, I warned you.

I signed up for

 Invalid Item Open in new Window.
This item number is not valid.
#1286424 by Not Available.


I can't believe terryjroo has committed to reading as many as 50 poems in a day, and checking them for disqualifications. You go girl. Of course, if she finds disqualifications, the number will diminish - so she has some motivation! *Bigsmile*

Anyway, for those who might be interested, my entries into the Challenge will reside in:

 Comedy Collection Open in new Window. (18+)
Can I make lemons into lemonade? Nah - gimme a Coke.
#1289594 by Robert Waltz Author IconMail Icon


I hope I make it through the 20 more days - poetry is a lot harder than it looks - but at least it encourages me to create something other than blog entries and horrible puns.
July 11, 2007 at 7:18pm
July 11, 2007 at 7:18pm
#520624
This might just be the second most beautiful thing I have ever seen in my entire existence.

http://www.pink-floyd.wz.cz/bodypaint.jpg

Second after my wife, of course.

Yes, she reads this.
July 9, 2007 at 9:53pm
July 9, 2007 at 9:53pm
#520219
This is quite possibly the most important scientific research of the 21st century, and beyond:

http://news.bbc.co.uk/2/hi/health/6283444.stm

Support stem cell research now!!!
July 9, 2007 at 6:06pm
July 9, 2007 at 6:06pm
#520166
Well, some of them, anyway.

Maybe.

Ten Politically Incorrect Truths About Human Nature

http://www.psychologytoday.com/articles/pto-20070622-000002.xml

Human behavior is a product both of our innate human nature and of our individual experience and environment. In this article, however, we emphasize biological influences on human behavior


While I have issues with some of the basic assumptions of this article - specifically, I have a hard time accepting that reproductive urges are the sole, or even a majority shareholder, driving force of human destiny - it does provide food for thought.

I completely don't "get" #6 though - it seems to be saying on the one hand that possession of desirable reproductive traits lead to a greater chance of producing daughters; while on the other hand, saying that more powerful people have more sons than daughters. Do not grok.

#9, I'm in total agreement with in principle if not in detail.

As for #10, I have entirely too many female readers to weigh in with one opinion or another *Bigsmile*
July 8, 2007 at 12:20pm
July 8, 2007 at 12:20pm
#519872
This week is another great milestone: the 50th anniversary of the release of the greatest cartoon EVER:

What's Opera, Doc?

http://www.youtube.com/watch?v=OyxPxpSvXQ8

Kill da wabbit, kill da WABBIT!

(though Duck Amuck may be a contender)
July 7, 2007 at 8:13pm
July 7, 2007 at 8:13pm
#519717
We are all in the gutter, but some of us are looking at the stars.
-Oscar Wilde

I've been trying all day to come up with the right words, but without much luck.

I want to say something to commemorate the life and work of Robert A. Heinlein, born 100 years ago today, but I find that everything I think of has either been said before, or doesn't do the subject justice, or both.

Thing is, if you've read Heinlein, you already have your opinion - and if you haven't, nothing I say is going to make a difference.

It's not that I agree with everything he wrote, or aspire to be just like him, or consider him to be the "best" writer - there have certainly been better, both within science fiction and without. It's more that what he wrote influenced my thinking more than any other author.

He had a way of taking your assumptions, your dearly-held basic ideas about the way the world and society work, and stripping them down to the practical. Taboos are exposed as mere hoary tradition, and traditions venerated only to the point where they continue to make sense to an evolving society. As any good science fiction writer will, he came up with alternative societies - with alternative taboos, neither better nor worse than his own society's, just different.

Take a scientist's scalpel to all of your basic assumptions, be it the nature of family, the inviolability of the laws of physics, the definition of "love," everything your priests and shamans have told you, even what you think you know about yourself. Pare it back like a corn on your big toe. It can be painful, and there's no anesthetic, but when you're done there can be this immense sense of relief and accomplishment. For a while it's like there's something missing, but you quickly get used to it.

I think the best I can do now is let the Master speak for himself.

Always listen to experts. They'll tell you what can't be done and why. Then do it.

Writing is not necessarily something to be ashamed of, but do it in private and wash your hands afterwards.

There is no such thing as luck. There is only adequate or inadequate preparation to cope with a statistical universe.

Progress isn't made by early risers. It's made by lazy men trying to find easier ways to do something.

Thou art God, and I am God and all that groks is God.

History does not record anywhere at any time a religion that has any rational basis. Religion is a crutch for people not strong enough to stand up to the unknown without help. But, like dandruff, most people do have a religion and spend time and money on it and seem to derive considerable pleasure from fiddling with it.

One man's "magic" is another man's engineering. "Supernatural" is a null word.

The truth of a proposition has nothing to do with its credibility. And vice versa.

What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what "the stars fortell", avoid opinion, care not what the neighbors think, never mind the unguessable "verdict of history" - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your single clue. Get the facts!

One man's theology is another man's belly laugh.

Everything in excess! To enjoy the flavor of life, take big bites. Moderation is for monks.

Theology is never any help; it is searching in a dark cellar at midnight for a black cat that isn't there. Theologians can persuade themselves of anything.

How you behave toward cats here below determines your status in Heaven.

Never attempt to teach a pig to sing; it wastes your time and annoys the pig.

The United States has become a place where entertainers and professional athletes are mistaken for people of importance.

Nobody has ever seen an electron. Nor a thought. You can't see a thought, you can't measure, weigh, nor taste it- but thoughts are the most real things in the Galaxy.

Love is the condition in which the happiness of another person is essential to your own.... Jealousy is a disease, love is a healthy condition. The immature mind often mistakes one for the other, or assumes that the greater the love the greater the jealousy.

The more you love, the more you can love, and the more intensely you love. Nor is there any limit on how many you can love. If a person had time enough, he could love all of that majority who are decent and just.

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