Complex Numbers (Book)

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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.

http://www.ddewey.net/mandelbrot/

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December 4, 2022 at 12:02am

#1041364

Revisited: "Aren't you a little short for a stormtrooper?"

In my ongoing quest to find random old blog entries so I can express how I might have changed over time (among other reasons), I hit on this one from almost exactly 15 years ago: "Aren't you a little short for a stormtrooper?"

The entry contains two links and, remarkably, the first one hasn't rotted away. For your amusement, in case you can't be arsed to visit the original post, I present it as an xlink here.

I'm pretty sure those are the original images from over 15 years ago.

So, what's changed? Well, back then, I wrote, by way of introducing the link:

These days, it's hard to find just one, solitary thing that you can point to and say, "There it is. There is the Sign that the end is near; that we've reached the Cosmic Cul-de-sac and some asshole's U-Haul is blocking the turnaround." But here's a candidate

And oh, my, I bet I thought I was clever as hell when I wrote that. The photos are now mildly amusing to me and in no way a sign of the impending apocalypse. We've been through so much in the last 15 years that I guess the needle moved further in the direction of Armageddon, making these pictures of a couple of young people doing stuff in Stormtrooper helmets a refreshing chunk of normal. And maybe even slightly day-brightening.

Worse, though: Okay, so I spent my career designing, among other things, subdivisions, and most of those subdivisions included roads with a cul-de-sac. Not once in the 20 or so years I spent doing that did I ever bother to find out what the English translation of cul-de-sac is. It's "ass of the bag." Okay, no, not really, but 'cul' is, from what I hear, slang for ass (buttocks, not animal); the more polite translation would be "bottom of the bag." The point being that these days, I wouldn't have juxtaposed it with the English word "asshole" meaning "unbearable person."

Worser and worser, it turns out that the French translation of "cul-de-sac" is "voie sans issue," probably because 'cul' has that slang meaning.

Okay. Anyway.

The second link in the original entry has, unfortunately, expired, surviving only in a couple of lines I quoted back then. Here they are again:

A man who called himself "Papa Pilgrim" and took his family far from civilization to raise them according to his interpretation of the Bible was sentenced to 14 years in prison for sexually assaulting a daughter.

...

Hale insisted that he had a perfect spiritual understanding, his wife, Kurina Rose Hale, testified Monday.

Which was fucked up enough that I had to do a search on this fine, upstanding gentleman, and I almost wish I hadn't, but since I did, here it is.

I won't paste stuff from that link here. It's dark as shit. It details charges against a man who tortured and abused his family on religious principles. I'm not too worried about that link going invalid at some point, because this good Christian man has his own Wikipedia page too—according to which, fortunately for everyone involved, this outstanding specimen of humanity croaked just a few months later.

Back then, I discussed at moderate length how there are decent people and horrible people in every religion, and ended with "judge by the deed, not by the creed."

Today, I'd add:

There are none so evil as those who proclaim themselves righteous.

Not even Stormtroopers.

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