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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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| Sometimes I wonder if I've learned any life lessons at all. PROMPT September 17th What life lessons have you had to learn the hard way? Wait... there's an easy way? Dammit, I've been doing it wrong! I have a bit of a stubborn streak. While I'm flexible enough to change when new data comes in, I want to discover the information for myself. That is to say, hypothetically here, if I'd spent my childhood in an underground bunker, and people kept telling me the sky was blue, I'd only believe them provisionally -- better if I could escape and see it for myself. This has benefits as well as downsides. As a benefit, it keeps me curious, always wanting to know more. For instance, you might ask, as kids do, why said sky is blue. Turns out it's from preferential scattering of light in the atmosphere, the same effect that gives a rising or setting sun a more reddish hue. The details are important, but no need to get into them; the point is, I had to figure this out for myself by reading and learning about physics. But what's especially bad for me is that this means that some of life's unwritten rules, those social forces that guide behavior, don't really sit well with me. I prefer my rules to be written. To take a simple example, it turns out that when you're visiting someone, you bring a gift. There, now it's written down, and I can follow it. But it took me a while to figure that one out. All my life, I've wanted to know "why." When it comes to science, like the blue sky thing, that's actually pretty easy to figure out (and it was even B.I., before internet). But when it comes to social situations, the "why" almost always escapes me. This is probably why I don't get invited to parties. Well, this, and the puns. But mostly this. Like, in the Before Times, a handshake was considered a proper greeting. I thought I knew the rules: firm grip, eye contact, whatever. Not that eye contact is easy for me, but I fake it by looking at the person's nose. But then I went to shake someone's hand (as a teenager), and got corrected, "No, you wait for the female to invite the handshake." Okay, so it's different with men and women. Why? I don't get it. I try to follow the rules anyway, most of the time, to try to make a good impression. I just don't know all of them. There are science textbooks. There are no "being part of polite society" textbooks. Oh, sure, Miss Manners and all that, but most of what's in those texts makes no sense to me. Don't get me wrong; I try to be considerate of others' feelings. But subtle cues always seem to escape me. Anyway, some minor life lessons I've picked up the hard way:  Never go grocery shopping hungry. Money can't buy happiness, but it can buy just about everything else. Any internet argument that goes on long enough devolves into a discussion of epistemology. It's okay to suck. You get better. Making one's bed is a gigantic waste of time. Never choose lodging solely on the basis of proximity to the brewpub. Always carry a backup of essential items. Especially maps/GPS. When a cat displays the soft fur of its belly? It's a trap.I'm sure there are dozens more, if not hundreds, but that sampling should at least give you an idea of my mindset. I'm sure some people know some of these things intuitively, but like I said, I have to work on it. And I'll probably be working on it until the day I croak. |
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