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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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   PROMPT May 7th In your entry today, write about dreams. Do you dream often, or do you rarely remember your dreams? What is the strangest or most memorable dream you have ever had? Many trees have been murdered, ink wasted, and electrons annihilated on the subject of "dream interpretation." I can't claim that all of it is bullshit, but enough is that the whole idea is, at best, suspect. I've written about dreams in here before. Not necessarily specific ones, but about dreaming in general. Last I heard, the best scientific approach to figuring out why we dream is tied up with some of the physiological effects of sleep  on our brains.Dreams are, I think, a byproduct of these physiological effects. The brain is very, very good at drawing conclusions from inadequate data. Random firing of neurons, or whatever's actually happening in there, produces semi-random data and there's a part of the brain that insists on interpreting it. It usually does so in relation to events in one's life, whether those events seem meaningful in our waking consciousness or not. One odd side-effect I've noted from getting the Covfefe vaccine is especially vivid dreams. It happened to me, and I've heard of it happening to other people as well. These aren't necessarily bad dreams, just particularly realistic ones. Whether it's related to something in the vaccine, or (more likely) the psychological aspects of getting it at all, I don't know. Unfortunately, I don't remember them, just the fact that they existed and were particularly vivid. Memory works that way for me sometimes; I can more easily remember the feelings caused by something than the cause of the feelings themselves. There are, however, a few dreams that I remember, at least in part. Relating them risks opening myself to one of those silly interpretation things I mentioned above, but I do vaguely recall discussing some recurring themes in here before. Like, often, my dreams are dark. I don't mean like nightmares -- I have suffered from sleep paralysis and I know what a nightmare is, thanks -- but literally, visually, dark. Which I find odd because, like most sighted people, vision is my primary way of interpreting the world around me. It's really hard to describe, but it's like walking (or, more interestingly, driving or biking) down a black road on a moonless night with black trees all around. I can't see the road or the sky or the trees, or rather, they all blend into each other visually, and yet there is some other sense entirely that is able to distinguish, with perfect clarity, what is road and what is tree. That's just one example. Sometimes it's a wall that I just know is there, or people moving around in the darkness that I can easily avoid even though I can't see them. On one level this makes sense because my physical body is lying in a dark room with its eyes closed, so I'm literally in darkness. On another level, at other times the dreams are in brilliant Technicolor, so what the hell, brain? I should note that I had dreams of this sort even before I found out I will probably need eye surgery, so it's not just a matter of the phobia I attach to anything touching, let alone cutting into, my eyeballs (other than my eyelids; they get a pass), or any concerns about going blind. But yeah, they're worse now. For me, anyway, dreams seem to be about practicing emotions. Nightmares practice fear. Pleasant dreams practice contentment. The one where you walk into an exam late and then you realize you're naked practices the feeling of being in an uncomfortable situation. That sort of thing. Emotions are, at base, chemical reactions and electrical nerve firings, or whatever, and the brain seems to like rehearsing them in your sleep. Or perhaps the emotions come first (random neuron signals, like I said above) and the brain provides scenarios that fit them. You know, I kind of like the second hypothesis better; it makes more sense. I'll tell you what I hate more than nightmares, though. I mean, nightmares can be scary, by definition, but then they're over and you maybe have some story ideas. So while they're scary, they're still just dreams. What I hate is when you wake up and go about your day, but then you notice something's off, like the stairs have turned into a slide or whatever. So you realize that you're actually still asleep. So the alarm goes off and you wake up and go about your business, but the front door is in the wrong place, so you realize that you're actually still asleep. Then you wake up and do your usual thing, but when you open the refrigerator, it's full of cabbage. So you realize that you're actually still asleep... Or hey, maybe that's just me. |
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