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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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From "JAFBG"  [XGC]:Make a list of all the things you've learned about the world during the pandemic in the last couple years. 1. If there is ever a worldwide crisis that requires human cooperation to solve, we won't do it. ...and that's all. Yes, I should have already known that, but this, the last vestige of hope and optimism in me, poured out of me like puke after a drinking binge, leaving me with that sour taste in my mouth, a headache, and the knowledge that yes, I will totally do that again, and telling myself I wouldn't would be lying to myself. As I'm sure you already know, we started the week off with a nasty snowstorm that knocked out power and toppled trees. I mentioned this a few days ago. Well, on Wednesday, I had two doctor appointments scheduled. Just routine stuff. Both were within two miles, so as is my custom in such situations, I walked, allowing myself extra time because there's still nasty frozen crap everywhere; the temperature was technically above freezing, but not enough to actually melt the slush that had, overnight, refrozen into ice. Now, it's important to note that our city has a law: while the city is responsible for salting and plowing the roads, it is required for each property owner to clear ice/snow off of the sidewalk adjacent to the property within 12 hours (or something like that, whatever) after the end of a snow or ice storm. I don't really care what you think of that law; that's not the point. The point is that it's on the books. After 12 hours, the city can levy fines. Naturally, it's not always enforced. But law or not, it's obvious that a) the city doesn't take responsibility for the sidewalks and b) therefore, clearing the sidewalk so people can walk on it is the Right Thing to Do. Most people do the Right Thing and clear the sidewalk. Maybe it's because of the possible fine, and maybe because it's Right, whatever, doesn't matter. But say you're a pedestrian trying to, I don't know, get to a doctor's office shortly after a storm leaves the pavement icy. Walking on cleared sidewalk is safe enough. But then you get to the sidewalk of a person to whom rules don't apply, who does whatever they want because FREEDOM, or maybe who insists that because the sidewalk is in the city right-of-way then they can fucking clear it if they want it cleared so bad (but who would object to raising taxes to do it). The sidewalk in front of this holdout's property is thus compacted into pure ice, maybe with a sheen of water to make it extra-slippery, so you have to either walk really, really carefully, or, if it's on a steep stretch, maybe hop the dirty slush drift the plows have kicked up so you're walking in the street where there's some traction, but also cars going by at 40 mph because it's a 25 zone. With narrowed lanes because of the aforementioned drifts. Honestly, if you have to do this maybe once or twice, okay, fine. But when one out of every three properties' sidewalks is a sheet of ice, hopping over the slush piles gets old and you're tempted to just walk in the street the whole way. But if you're a property owner, and you do what you're supposed to do, but then you see that your neighbor not only didn't do it but gets away with it, well, why are you doing all that extra work if the neighbor is just going to keep the sidewalk slippery? Point being that it only takes a few holdouts ruin the entire experience for everyone else. And this whole narrative is a metaphor for any kind of global crisis, whether it's a pandemic, global warming, or the inevitable asteroid strike (by the way, do not tell me to watch Don't Look Up. I will not do it.) "Just get a car already." I shouldn't have to have a car to go two miles; people should do what they're supposed to do to accommodate pedestrians. "Take an Uber." I shouldn't have to have a car to go two miles; people should do what they're supposed to do to accommodate pedestrians. It takes fewer people to ruin things than it does to create something. This is axiomatic. I have called it Lone Asshole Theory. For example, probably you lock your car when you go somewhere. Why? Is it because everyone who walks past will certainly try the handle and, finding it unlocked, steal the change from your console? No. Most -- the vast majority of -- people will walk by and respect that it's not their property, leaving it alone. But that doesn't matter, because all it takes is one person to steal all your spare change. (Yes, I know that even locking won't stop a determined thief, but that's irrelevant.) It took thousands of people several years to build the World Trade Center, and only a few religious fanatics to destroy them in hours. Most people are decent, or at least neutral. You'll meet thousands of them without being harmed. But all it takes is one asshole to kidnap, rape, murder, steal, stand on the left on an escalator, whatever. One accident on a road can tie up traffic for hours. And so on. Lone Asshole Theory asserts that no matter how good you are at following the rules and doing the Right Thing, all it takes is one asshole not playing along for everything to descend into chaos. Does this mean that you should be that asshole? Well, tempting as it might be, I don't think so. But it is tempting, because usually the assholes don't face any actual consequences, so why shouldn't you join them? So there it is. My list of one thing, and a rant to back it up. |
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