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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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May 16, 2022 at 12:05am
May 16, 2022 at 12:05am
#1032463
It is a night of a lunar eclipse. The actual full moonination (I just made that up) occurs at 12:14 am (yes, I keep track of these things), which would be when the lunar orb is fully within the shadow of the Earth. That puts it way high up in the sky, to use a technical phrase from astronomy -- perfect for viewing. Usually, during a lunar eclipse, the moon takes on a deep red glow, the reflected light of every sunset and sunrise on our planet simultaneously. It's all really very cosmic.

It's not all that rare; a lunar eclipse happens every few years. I'd say "once in a blue moon," but that would only make the confusion surrounding the definition of a blue moon that much worse. I've ranted about that before. I'll rant about it again. But not today. Common or not, I like to look at these things, especially now since it's the first one since I got new eyeballs.

Naturally, the sky where I am is completely covered by a thick blanket of clouds.  Open in new Window.

I should probably be more frustrated by this than I actually am, but -- though I hate it when someone goes "well, it could be worse" -- it could be worse. I got the news yesterday (Sunday) that my last remaining aunt, who had a stroke back in February, died over the weekend. She was in her 90s, so it's not like it was totally unexpected or anything, but still sad.

My cousin told me the funeral would be on Wednesday. I went online and started looking for near-last-minute transportation, because I still don't have a car. "Oh, you have to travel in two days? You must be desperate. Here, let us give you the highest price we possibly can." Usually I take a train to NYC, because it's a lot less stressful even if it takes longer. But the trains were booked solid. Still, one cool thing about our little airport here in Charlottesville is that they have daily nonstop flights to La Guardia. That's flights, plural. No puddle-jumping to IAD and getting drunk in the airport bar while waiting for your connection, and lots of options to choose from -- all remarkably pricey on short notice.

Right after I booked the ticket, he called to inform me that, well, no, the funeral would be held in two weeks instead. On Memorial Day weekend.

To his credit, he offered to reimburse me for canceling my really very goddamned expensive booked flight. I mean, seriously, I've flown to Vegas for less. Shit, I've flown to bloody England for less, but that was over a decade ago so maybe it doesn't count. It's pretty close to what I paid for a trip to goddamned Maui.

Problem is -- setting aside for the moment the absolute joy that traveling on Memorial Day weekend is -- I just can't go that weekend. My housemate has her own family plans, and has had them for some time. We have pets. Finding a holiday weekend cat-sitter on short notice is harder than watching an eclipse through the clouds, and I'm not leaving the cats alone.

So it looks like I'll miss the funeral. Hopefully I can take the trip sometime in June or July, go visit my cousin, see the grave where she'll be buried with my mom, her other sister, her brother, and her parents.

Still mostly cloudy here, though I just looked up and saw a single star. It looks like Mars but it's in the wrong place, almost directly overhead. I don't think it's Antares, either; that should be closer to the moon. I can't really tell what it is, because I don't see any other stars to get my bearings.

The whole neighborhood is dark. I think everyone's trying to look at the sky.

Ah. The clouds parted, briefly, and I got a glimpse of the blood-red moon.

Mission accomplished.

Oh, incidentally, the airline completely refunded my ticket price. If I were a total asshole, I'd tell him it was nonrefundable and collect the money, but I'm only a partial asshole.

I'm not entirely in the shadow, you see. Or, well, technically, right now I am, but at least I'm looking at the stars.


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