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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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April 2, 2023 at 10:25am
April 2, 2023 at 10:25am
#1047344
In the course of picking, at random, an older blog entry to revisit, I ignore anything less than a year old. I figure it needs time to become vintage, and one year is generally enough for that on the internet.

Today, I got my first result from 2022—but it was from early January, so it's more than a year old. As it turns out, I do have something to say about it. The entry was mostly the answer to a former prompt from "JAFBGOpen in new Window. [XGC]; if you're following along, you know I've been working through the current iteration of prompts there.

As for the entry itself, here's the link: "Judge, MentalOpen in new Window.

It starts off with a personal update:

Yesterday morning, we got a few inches of ugly, dense, watery sn*w which brought down branches, leaves, trees, and a nearby transformer (the electric kind, not the Michael Bay kind, though I did get to hear it explode). And my home generator picked yesterday to go on strike for higher wages and better working conditions. To be fair, any wage would be higher that what I'm paying it now, but come on, you only have to work like twice a year; get over yourself.

It took me several weeks, as I recall, to find someone to look at the generator. Fortunately, I didn't need it during that time. They did whatever they needed to do, and then, the next time the power went out... the generator failed again. Fortunately, that time wasn't during an intense cold snap.

I think it's finally back in shape, after I called out someone competent. Fortunately, or unfortunately (depending on your perception), it hasn't been fully tested under adverse field conditions, as this winter was mild.

If the power hadn't popped back on in the middle of the night, they'd have had to chip my corpsicle out of the solid block of ice that had once been a house.

I also have a vague recollection that, once I got the central heat working again that early morning, the thermometer on the thermostat said it had gotten all the way down to... 58F. Nowhere near literally freezing; just above, in fact, the ideal temperature for some darker beers and red wines. But enough for me to freeze my nads off.

In my last Comedy newsletter ("The WeatherOpen in new Window.), I described with only a little bit of hyperbole how cold my dad kept the house, which you might think prepared me for a life comfortable with persistent hypothermia (my dad certainly thought, mistakenly, that it would toughen me up), but, in fact, the opposite became true.

Look, I live in Virginia. I expect this kind of shit at least once per winter. It doesn't mean I have to like it.

And this year, I found out what I like even less: not having to put up with "this kind of shit" all winter. I mean, sure, it was nice to have only a couple of sub-freezing days, and no sn*w to speak of, but it ain't natural.

Hell, there was an extended period over the winter where it got up to the 70s (F again, of course) during the days. That's warmer than it's expected to be today. Not entirely unusual for that to happen occasionally in a Virginia winter, but the lack of sn*w beyond a few non-sticking flurries was out of the ordinary. It's April, now, obviously, and it's been known to sn*w in April here; we'll see if we get any.

The rest of the entry doesn't really need embellishment; it's all about a thing I'm judgemental about: beer. About the only thing I can say is: I've been working on it, and I think I'm fairly successful in, if not being less judgemental about it, at least being less of a prick.


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