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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, 2009 at 12:23am December 31, 2009 at 12:23am
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I don't like making resolutions.
Making a resolution, to me, is just setting me up for failure. I don't know why. It's like, as soon as I make a resolution, it becomes something I should be doing, and my inner child stamps his foot and goes NO!
I really need to kick that fucking brat's ass, you know?
Anyway, no resolutions.
But I'll make some goals. Maybe putting them here will shame me into keeping them.
Goal #1 for 2010: Fitness. Yeah, I know this is everybody's stupid resolution. The thing is, I've already been working on it, going to the gym and even sometimes watching what I eat. But my new goal is more specific: gym three times a week, and at least pay lip service to eating right. (Get it? Lip service? Eating? You'll note that "stop making puns" isn't anywhere near my goal list.)
Goal #2 for 2010: Organization. Keeping a to-do list on the computer instead of in my head; getting and keeping my work areas (home and office) clean and shit filed; all that may help me be less scattered.
Goal #3 for 2010: Publishing. I can't set a goal to "be published," because that's not in my power. But... okay... at least one submittal to a legitimate publication (that is, they pay me or at least give me a free magazine) per month.
To help with Goal #3 - which I suspect some of you share - I'm working on a group to help beat into submission each others' stories, poems, articles, chapters, and whatever you want to try to get published. (Get it? Beat into submission? Oh, I slay myself)
Join us if you want to get published, or even if you feel like helping out with reviews and whatnot. There are no obligations (except for me, to keep things going...)
So okay. I feel kind of dirty actually doing something as common as setting goals for the new year, but really, those have been my goals for some time now... I just haven't done as much as I could toward them.
And so it ends. Tomorrow - well, technically, later today - it's dinner, then Gogol Bordello concert (whoohoo!), and then it's next year.
It's too bad, really - I barely noticed 2009 go by. Maybe my goal should really be "don't let the year go by without you noticing it."
Yeah. Fat chance.
Thanks for reading, Happy New Year, and I'll be back in 2010 with more of what you come here for!  |
December 24, 2009 at 10:55pm December 24, 2009 at 10:55pm
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...because it's the last one.
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December 23, 2009 at 2:10pm December 23, 2009 at 2:10pm
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Okay, so apparently this dude's parents caught him with a 12er of beer and grounded him for three months.
The reason they caught him was that his sister ratted him out.
So he goes rooting in her room and posts what he finds on Facebook.
*sniff* This is.. so beautiful... I hope it's real and not fake like most things on the internet.
http://degenerasian.blogspot.com/2009/12/revenge-of-facebook.html
(you have to click on the image to read it, and even then it's kinda tough. But it's SO worth it. And the comments are the sweet, sweet crumbles on the streusel of WIN.) |
December 22, 2009 at 1:00am December 22, 2009 at 1:00am
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There's something about snow.
I mean, from one point of view, it's an utter pain in the ass. Like today... okay, actually yesterday, but you know what I mean. I didn't even bother waking up in time to go to work, because there was no way in hell I was getting out. I slept in, giving the sun time to come all the way up (knowing full well that of all the days of the year, it would be "up" for the shortest possible time).
Then I went out and shoveled the bastard stuff. From my front stoop, down the flagstone walk, up and down the sidewalk in both directions, to my truck's doors, and in front of the truck so I could maybe eventually leave. All the time, I was hacking up whatever's been in my lungs as I've been sick on and off all month.
All the people on my street were performing similar activities, with varying degrees of equanimity. My one neighbor (not the hateful bitch uphill, but the nice guy downhill) helped out a bit with the digging out.
It took about three hours.
That is the longest time I've been outdoors since the beach.
My cat, Ghost, kept walking on the fragile film of ice that had formed on top of the two feet of snow. Occasionally, a paw would break through the crust, and he'd shake it and keep walking - until the next paw broke through the crust.
Snow is transformative. I think that's why it's so closely associated with the Christmas season. I mean, in some parts of the US, snow in December may be commonplace, but not here. Here, when we get it at all, it's in January or February, when everyone hates it except for schoolkids. No, snow at Yuletide has the connotation of wiping a slate clean, shaking the Etch-a-Sketch.
I didn't like it, mind you. But it's still transformative. Friday night, everything became quiet, and all I could hear was the soft hiss of snowflakes piling up on the yard (and all I could think was, "Holy shit. I'm going to have to shovel this shit eventually.") Everything became white. Everything developed soft curves, like a supermodel.
I should be writing right now, by the way, and not in the blog. I have a story idea and everything. It's just not flowing. The snow didn't help that.
Perhaps tomorrow.
Anyway, snow. I managed to get out and take my wife to her workplace. I wasn't in any hurry to get to my own - not a lot of work, and it's not like my partner would make it in. Driving around, I was glad I had four wheel drive: bastards hadn't done much to clear the roads. In their defense, this is the most snow we've gotten since forever. In everyone else's defense, what the FUCK are they doing with our tax money?
Three bone-jarring hours later - when snow gets compacted into ice on the road, it develops a nasty washboard effect - I came back home.
I don't know if I'll go out tomorrow or not. I'm definitely waiting for the sun to melt some ice, first.
Still, the snow made things different, for a while.
But not as different as it made Times Square:
http://blog.ricecracker.net/2009/12/20/snowball-fight-times-square/ |
December 19, 2009 at 11:19pm December 19, 2009 at 11:19pm
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Ran across this website:
http://www.marcandangel.com/2009/07/13/50-questions-that-will-free-your-mind/
50 Questions That Will Free Your Mind
These questions have no right or wrong answers.
Because sometimes asking the right questions is the answer.
It's probably best if you go ahead and click on that link and look at the questions, before I do what I do.
Go ahead - click. I'll wait. I'll just watch a video while you're looking.
Ready?
Okay.
1. How old would you be if you didn’t know how old you are?
21. Because I never did learn how to be 21. Or 19 for that matter, but at 21 I can drink.
2. Which is worse, failing or never trying?
Failing, of course. But I wouldn't know; I've never tried.
3. If life is so short, why do we do so many things we don’t like and like so many things we don’t do?
Money.
4. When it’s all said and done, will you have said more than you’ve done?
Depends. Does blogging count as saying or doing? I'll put it in the doing column so it'll be longer.
5. What is the one thing you’d most like to change about the world?
The part where I'm not in charge.
6. If happiness was the national currency, what kind of work would make you rich?
Beer.
7. Are you doing what you believe in, or are you settling for what you are doing?
Making money is never settling.
8. If the average human life span was 40 years, how would you live your life differently?
Chances are, I'd be dead.
9. To what degree have you actually controlled the course your life has taken?
Ha!
10. Are you more worried about doing things right, or doing the right things?
Both.
11. You’re having lunch with three people you respect and admire. They all start criticizing a close friend of yours, not knowing she is your friend. The criticism is distasteful and unjustified. What do you do?
Depends. Is she cute?
12. If you could offer a newborn child only one piece of advice, what would it be?
GO BACK! GO BACK NOW WHILE THERE'S STILL TIME!
13. Would you break the law to save a loved one?
Misdemeanor, yeah. Felony, no.
14. Have you ever seen insanity where you later saw creativity?
I see insanity all the time.
15. What’s something you know you do differently than most people?
Putting my pants on. See, I heard a long time ago "He puts his pants on one leg at a time, like the rest of us." So I developed the simultaneous-leg pants-donning technique.
16. How come the things that make you happy don’t make everyone happy?
Because they're a bunch of idiots.
17. What one thing have you not done that you really want to do? What’s holding you back?
Gotten rich. Money.
18. Are you holding onto something you need to let go of?
Oops, okay, sorry; I'll type with both hands now.
19. If you had to move to a state or country besides the one you currently live in, where would you move and why?
You mean like if Palin gets elected President? Belize. Or maybe Russia. There'd be more freedom in Russia, but it'd be colder.
20. Do you push the elevator button more than once? Do you really believe it makes the elevator faster?
Yes; no, but it makes me feel better, like when I yell at the idiot in front of me on the road.
21. Would you rather be a worried genius or a joyful simpleton?
I dunno. I've always been the former. Seeing my father deteriorate into the latter, I'd say "worried genius" any day of the week.
22. Why are you, you?
Because I'm not you.
23. Have you been the kind of friend you want as a friend?
I don't know what I want as a friend so, no.
24. Which is worse, when a good friend moves away, or losing touch with a good friend who lives right near you?
The latter. Internet; duh.
25. What are you most grateful for?
Donuts.
26. Would you rather lose all of your old memories, or never be able to make new ones?
The former. It'd be like when you die in a video game and you can go back to your last saved game.
27. Is is possible to know the truth without challenging it first?
What?
28. Has your greatest fear ever come true?
No, I haven't been attacked by clowns wearing Hello Kitty earmuffs while Britney Spears sings and Sarah Palin is President in my sleep. Yet.
29. Do you remember that time 5 years ago when you were extremely upset? Does it really matter now?
Seems it does, actually. It pretty much destroyed my life. Oh, wait, I'm supposed to be funny. Sorry.
30. What is your happiest childhood memory? What makes it so special?
I don't know how to answer this one.
31. At what time in your recent past have you felt most passionate and alive?
Springsteen concert.
32. If not now, then when?
Look, bastard, don't go quoting the Talmud at me.
33. If you haven’t achieved it yet, what do you have to lose?
Everything.
34. Have you ever been with someone, said nothing, and walked away feeling like you just had the best conversation ever?
Um... no? Am I supposed to? What the hell?
35. Why do religions that support love cause so many wars?
Do you really want me to answer this? REALLY? Okay... it's because it is impossible to be moral and worship a god at the same time. Gods are necessarily divisive; at a minimum, religion divides the human race into people who believe in a particular religion, and people who don't. Or people who believe in it in the wrong way. And the only way to avoid war is to recognize that every other person in the world, regardless of race, creed, age, sexuality, or anything, is just as deserving of life as you are. You don't get that from religion. Religion doesn't teach morality; it perverts it. There, I finally said it. Okay, that's not funny either, but that's been festering inside me for a long time.
36. Is it possible to know, without a doubt, what is good and what is evil?
It is not possible to know anything without a doubt.
37. If you just won a million dollars, would you quit your job?
If I didn't OWN my job, yes, in a heartbeat.
38. Would you rather have less work to do, or more work you actually enjoy doing?
What's the difference?
39. Do you feel like you’ve lived this day a hundred times before?
What, stuck at home with three feet of snow on the ground, an empty house, and nothing to do but write and waste time on the internet? Sure, every freaking day.
40. When was the last time you marched into the dark with only the soft glow of an idea you strongly believed in?
What the hell? Is that a metaphor? Don't talk to me in metaphors. If you're going to make metaphors, write a goddamn poem.
41. If you knew that everyone you know was going to die tomorrow, who would you visit today?
My shrink.
42. Would you be willing to reduce your life expectancy by 10 years to become extremely attractive or famous?
Attractive? Sure. Then I'd be able to fit in an extra 10 years' experience. Famous? No.
43. What is the difference between being alive and truly living?
Sex.
44. When is it time to stop calculating risk and rewards, and just go ahead and do what you know is right?
If you know it's right, don't calculate. If you don't know if it's right, do the calculation. Jeeze, ask me a hard one.
45. If we learn from our mistakes, why are we always so afraid to make a mistake?
See "Logical Fallacies"
46. What would you do differently if you knew nobody would judge you?
Something involving leather, I'm sure.
47. When was the last time you noticed the sound of your own breathing?
The last time I had a goddamn COLD. Which was, lemme see... YESTERDAY.
48. What do you love? Have any of your recent actions openly expressed this love?
...
49. In 5 years from now, will you remember what you did yesterday? What about the day before that? Or the day before that?
No, because I have a horrible memory for day to day shit.
50. Decisions are being made right now. The question is: Are you making them for yourself, or are you letting others make them for you?
I've made the decision to not use the passive voice if I can at all avoid it.
-
So there you go. Things I do when I'm terminally bored.
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December 17, 2009 at 4:13pm December 17, 2009 at 4:13pm
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Does wrongness stack?
That is, if you have a wrong, and someone else has a wrong, and you put them together, are they only as bad as the worst wrong? Or are they as bad as both wrongs put together?
Or do they multiply?
Or... and I submit that this is the case with the link I am about to inflict upon you... do you take one and raise it to the exponent of the other?
http://www.kittyhell.com/2009/12/17/hello-kitty-snuggie/
The only thing I can think of that could possibly make that worse would be if Perez Hilton wore one.
Then the universe would have to collapse into a singularity to save itself from the suck. |
December 11, 2009 at 4:03pm December 11, 2009 at 4:03pm
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...this song which usually manages to crack me up.
Happy Hanukkah, whether you celebrate it or not! |
December 9, 2009 at 11:24pm December 9, 2009 at 11:24pm
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You know what else sucks about having a cold? Besides being unable to sleep, having a nose that runs faster than an illegal alien in Brownsville, displacing vertebrae every time I cough, screwing up my face like a prude viewing porn for the first time every time I get one of those sinus itches, blowing through three packages of tissues a day, and having everyone else treat you like a leper?
This:
"Are you taking anything for it?"
NO. I'm not taking anything for it. You know why? Because nothing will make it go away. The best I can do is moderately alleviate the symptoms, and the snake oil they sell over the counter is next to worthless, to me, for anything but parting me with my hard-earned cash.
But they don't listen. Everyone has his or her own favorite "remedy."
"You should take Sudafed." - not only will that get me put on a List faster than propositioning a 13-year-old (another thing I'm not going to do, by the way, just so you know), but it dries out my throat to the point where it's painful to swallow.
"Drink lots of that Emergen-C stuff." - placebo.
"Take 'Airborne'" - ditto.
"Mix up some sugar, lime juice, and honey." - Yeah, that's real scientific.
"Tea?" - Yeah, okay, that makes me feel better for a while, but I like tea anyway.
No one ever seems to mention how great it would be to chug an entire bottle of rum. I imagine that would knock the cold right out - along with me.
So, no, I'm not taking anything. Go back to treating me like a leper. That way I don't have to croak out why your patent concoction won't work, between spine-shattering coughing fits.
Looks like when this is over, I'll be visiting my chiropractor.
(Yes, I know they're quacks, too. But at least she's cute.)
Yes, I know this cold is turning me surly. Or maybe it's the Season of Greed again. It's like the poster I saw downtown yesterday: "Yes, the glass is half full - but sometimes, it's half full of CRAP."
Edited to add: Okay, chicken soup might work - but only if it were made by a Jewish mother. That's just how it is. |
December 7, 2009 at 2:37pm December 7, 2009 at 2:37pm
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It never fails.
Never.
Every damn time I get a cold, with the accompanying buckets of snot in my nose, I never have tissues at hand. So I have to use the nearest thing I can find - usually, asswipe.
By the time I get to the store to buy tissues and give the cashier the cold, my nose is as red as Rudolph's balls, and I have to get the lotion kind, which always feels like I'm blowing my nose with a moist towelette from the 60s.
You'd think that if it's soft enough to use on your ass, it'd be soft enough to use on your nose, but you'd be wrong.
It's almost enough to make me want to shave off my goatee, because I can never be sure of not having snot all in my mustache after an hour-long nose-blowing session - but then what happens is as soon as the stubble comes back, it collects tissue bits and then I end up looking like the rear end of one of those Charmin bears.
I hate having a cold.
But hey, at least I'm not oinking. |
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I'm more than happy with Carrion Luggage, however.
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