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 |    Not for the faint of art. |
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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. ![Merit Badge in Quill Award
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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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I highly recommend your blog.](https://images.Writing.Com/imgs/writing.com/writers/badges/Kudos-Highly_Recommended.gif) ![Merit Badge in Opinion
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And so it ends.   PROMPT November 30th Wow, it's the end of the month! With Thanksgiving behind us (here in the States), and Christmas on the horizon, what, if any, are your Christmas traditions? If you have no holiday traditions, do you have any plans for this month? As we careen into December, I think it's of the utmost importance to remember the real reason for the season: Axial tilt. As the Earth orbits the Sun, the axis stays pointing in the same direction (roughly toward Polaris) (or away from it, depending on your perspective), which changes the apparent path of the Sun across the sky. In summer (assuming a location outside the Tropics), the Sun climbs higher, baking us with more direct rays for a longer stretch of time, while in winter, that bastard can barely get out of bed, and things cool down. And I'm still not sure which is worse: burning under the pitiless gaze of the accursed daystar, or freezing from its absence. Okay, I'm going to go with "freezing is worse" because I'd rather be too hot than too cold. In any case, axial tilt is the reason for the season, and, relative to the Sun, it'll be at its most tilted in about three weeks: The solstice this year (winter for me, summer for the folks hanging upside-down) will occur on December 21 at 10:59 am EST. Why it couldn't wait another minute for a nice, even 11:00 is beyond me. And now I'm tired of coddling the Down Under, so everything else here is going to be presented from an unashamed Northern Hemisphere perspective. I always celebrate that moment, because it marks the point when days begin to gradually get longer, when the light begins to conquer the dark. Not that there's anything wrong with dark, per se; it's just that, as I noted, less sunlight means lower temperatures, and fuck lower temperatures. Unfortunately, as weather tends to lag astronomy, the winter solstice isn't usually the coldest day. Obviously that's going to vary from year to year, but on average, around here, that doesn't occur until close to the end of January. Still, I'll take my victories where I can, which in this case means appreciating the solstice. And then, once I'm done appreciating the solstice, I remember that the next two months are going to be utter hell. The only month I hate worse than January is February. But at least for one moment, I can believe that, as they put it on an episode of Doctor Who, we're halfway out of the dark. As for other things in December, well, that remains to be seen. Literally. This is the month when I'm supposed to get my eyes worked on. I dread the operation, so I try to focus (pun intended) on the expected result instead. That's hard for me. I've never been one to endure temporary hardship for longer-term benefit. They do one eye, and then a week later, the other eye. Supposedly it has a solid success rate. I'm still absolutely not looking forward (pun also intended) to having them screw around with my eyeballs. Other things? In the Before Time, I used to go to California every year in December. Travel's a bitch now, though, because a lot of people are infected with weapons-grade ignorance. Perhaps I'll be able to do that again one day, but this year is not that day. Rather than inflict my presence on those who don't want me around (which as far as I can tell is everybody), a couple of years ago, I began a new tradition for myself on Christmas Day, a day which otherwise holds little significance for me: I walk over to the drafthouse cinema, get drunk, and watch a movie before staggering home. This year, I don't know if I'll be able to do that or not; my second surgery is scheduled for the 23rd. Probably I'll be able to. Unless they botch it, in which case my movie-watching days are over. Hey, it's important to expect the worst, so I can only be pleasantly surprised. For anyone else who's made it this far through 30DBC, thanks for reading. But I'm on a roll and I don't expect to stop blogging, so tune in next month for a whole lot more of the usual -- and maybe some things unusual. |
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