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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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| Anyone remember a couple months ago, during the depths of the holiday season, when people panicked over mysterious lights in the sky over New Jersey? We even had some sightings here in Virginia. No? Don't remember? Yeah, maybe a few other things have happened since then, and we generally have the memory of a... whatever that fish is that has a short memory. Or maybe we all got mem-wiped for our own protection. Still, here's a reminder of other lights-in-the-sky incidents, from Gizmodo: An Incomplete List of the Times We’ve Panicked Over Lights in the Sky  The planet has a not-so-proud tradition of getting scared about what it sees among the stars. And by "getting scared about what it sees among the stars," they don't mean an inauspicious horoscope. Hm. Inauspicious Horoscope should be the name of my Blue Öyster Cult cover band. We blotted out the stars and became frightened when we saw our own lights amidst the darkness. That's almost poetical. America is in the midst of a full-on drone panic and it’s gotten very stupid. People in the northeast part of the U.S. are freaking out about strange lights in the sky and spinning all kinds of conspiracy theories. Yeah, the article was timely when it came out. And to be fair, people are going to spin conspiracy theories no matter what happens. I think there's an official competition now, run by a shadowy worldwide cabal, to see how fast a conspiracy theory can go around the disc. I mean, study it out. We have been here before. Recently. And what’s frustrating, to me, about this is that we’ll do it all again in a few years. And when it happens, we don’t remember all the sky panics that have come before. Clearly, that's because there's a government agency tasked with removing our memories of certain encounters. It’s natural to be afraid of things we see in the sky and don’t understand. It’s been happening for hundreds of years. Try thousands. The only thing that changes, from century to century, is the explanation for the fear. The answer to that question tells you about the society that’s afraid, but it may not give you an explanation of what actually happened. There are only three possible explanations: supernatural entities such as angels or gods; extraterrestrial entities such as space aliens; or inimical foreign actors showing off their technological superiority. Okay, four: Maybe it's a helicopter. “We know for a fact that drones can sometimes be used to do harm, and we probably shouldn’t lose sight of that fact just because a bunch of people see drones in the sky that do not, in fact, exist.” Sure, and if we keep mocking the people who cry "drone!" the panic will lose its edge an no one will believe them when it actually is a drone. I believe there's an ancient fable warning us of that effect. In the last month of 2019 and the first month of 2020, people in Colorado were convinced they’d seen unexplained lights in the sky. So, did they not actually see the lights? The cases that could be verified and chased down had mundane answers. They were planes, commercial drones, and other common objects. And swamp gas. And weather balloons. In 2016, a passenger plane was landing at Heathrow International Airport when it collided with what it thought was a drone. I'm way more concerned that passenger planes have achieved sentience, which that sentence clearly implies. One of the first great panics about lights in the sky happened in Canada, not the U.S. Thus shoring up my hypothesis that people are easily spooked everywhere, not just in the US where we're used to the sound of random gunfire. No attack came and later some kids admitted to sending up balloons loaded with fireworks in a village near Brockville. They wanted to scare people. Well, mission accomplished, my poutine-munching friends! During World War II, America trained its citizens to be paranoid about what it saw in the sky. That was probably about as hard as training a cat to shit in a litter box. In 1947, a military balloon crashed in Roswell, New Mexico, and it kicked off the first great sky-watching panic of the post-war years. I see that They have gotten to this article's author and publisher already. Anyway, the article does end up giving a passing nod to pre-airplane sky sightings, because while the technology has changed over the years, the people really haven't. It is, as the author points out, perfectly natural for humans to fear what we don't understand or can't identify. But what really makes us human, I think, is to get over that fear, and work to understand and identify. Or make up conspiracies about it. That's human, too. |
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