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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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September 12, 2007 at 8:09pm
September 12, 2007 at 8:09pm
#534793
... I drank the entire bottle of wine.

I do that sometimes.

If you think that's bad, wait 'til next week...
September 12, 2007 at 6:22pm
September 12, 2007 at 6:22pm
#534774
When panic grips your body and your heart's a hummingbird
Raven thoughts blacken your mind 'til you're breathing in reverse
All your friends and sedatives mean well but make it worse
Every reassurance just magnifies the doubt
Better find yourself a place to level out


I haven't been feeling much like myself lately - whatever that means. It's more like there's someone where I'm supposed to be and I'm where someone else is supposed to be. I've switched places, somehow.

How do we know who we are, anyway? Am I supposed to just keep on being the way I've been, because that's what all my friends, and my wife, expect? When am I allowed to change? I can't exactly tell them that's what I want. Perhaps I fear their expectations will then be too high, like when I try to lose weight and I manage to shed a few pounds, and that's where it stops, and they were maybe expecting me to keep going. Hell, I was expecting me to keep going.

But hell, it's not like there's anything wrong with my life. Far from it. In most respects, I'm exactly where I want to be.

Most. Is that last 20% worth the hassle?

Got a cricket for a conscience always looks the other way
A cocaine soul starts seeming like an empty cabaret
Hey, where have all the dancers gone? Now the music doesn't play
Tried to listen to the river but you couldn't shut your mouth
Better take a little time to level out


So I thought I'd try something different tonight. My wife is at her dance thing, and usually I'd be on my computer playing video games or maybe even blogging. Instead, I grabbed a few of my vices - bread, cheese, wine, a cigar and the laptop - and went out on my deck. I don't use our deck enough. It's not the greatest, but it's big enough, and just the right combination of bright and shade, being on the north side of the house.

In the backyard, a tangle of scrub and viny trees drops down to a swale - a little piece of the country here in the city.

Sometimes, it helps me to level out.

The wine's a Cab/Shiraz blend from Oz. The cigar is from somewhere in Central America - not Belize, unfortunately. The cheese is from Switzerland - which leaves only the bread local. Oh, wait, I just read the label - it's got components from the Mediterranean area.

I suppose that all says something, but I'm not quite sure what.

I never thought of running
My feet just led the way

Mixed up Signals
Bullet Train
Cars are switched out in the crazy rain
I could meet you any place
If the Brakeman turns my way


Sunday, we leave to go to the beach. A week at the Outer Banks might help - or maybe it won't, seeing as my attempts at ersatz escapism don't seem to be doing much.

But I keep thinking that this is all I need - a week at the beach; a long weekend in New York City in December (when did I decide that NYC in December was a desirable vacation?); just... something different. It doesn't even have to be the beach. A mountain would do. A lake. The edge of a desert; maybe a whale-watching cruise near Alaska.

Just somewhere to level out...

(lyrics by Bright Eyes
"If the Brakeman Turns My Way")


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