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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
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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November 27, 2024 at 8:41am
November 27, 2024 at 8:41am
#1080556
I'll admit it: I'm only linking this NPR article because the headline is glorious.



I mean, I come up with good puns sometimes, sure. But that one nailed it. (Nail? Scratch?... No? Okay.)

We've all had bug bites, or dry scalp, or a sunburn that causes itch. But what if you felt itchy all the time — and there was no relief?

Well, then you know you've truly sinned in the eyes of the Lord.

Seriously, though, that happened to me. Not, like, permanent, the way these unforgivable souls suffer, but a side-effect of some medication I had to take for a few weeks.

Journalist Annie Lowrey suffers from primary biliary cholangitis (PBC), a degenerative liver disease in which the body mistakenly attacks cells lining the bile ducts, causing them to inflame. The result is a severe itch that doesn't respond to antihistamines or steroids.

Yeah, that's gotta suck.

PBC is impacts approximately 80,000 people in the U.S., the majority of whom are women. At its worst, Lowrey says, the itch caused her to dig holes in her skin and scalp. She's even fantasized about having limbs amputated to escape the itch.

"PBC is impacts?" NPR, you used to be better than this.

Also, while I totally get the limb-amputation fantasy, seems to me that would just make the itching worse, what with phantom limb syndrome and all.

And finally, 80 thousand? I know that's not much on a percentage basis, but my whole city doesn't have 80,000 people in it.

There's a bit more at the link, mostly going into some detail about the phenomenon of itch. Some of it is accepted science, and some of it isn't (the evo-psych bits, I mean). I managed to read the whole thing without experiencing the sympathetic itch the article talks about, which is more than I can say for when there's an article about yawning.

But mostly, I linked it for the absolutely stellar headline.


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