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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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Today's list, from Cracked, is way too short. It fails, for example, to tell the story of "Mad" Mike Hughes, the flat-earth rocket scientist who, in an effort to see for himself the flatness of the planet, built a steam-powered rocket in the wilderness of Southern California, and promptly died in a lithobraking maneuver. I wrote about him, last year, here: "Bad Advice"  So here's more of that sort of thing, albeit not nearly as steam-powered: Stubbornness isn’t a particularly delightful trait to interact with. It is also not a virtue, no matter how stubbornly people insist it is. Dealing with a bullheaded friend or acquaintance is likely to end with a prominent forehead vein and a conversation that concludes in “okay, whatever, I don’t even care anymore.” When a Gen-X meets a Taurus... Combine that same stubbornness with an incorrect belief that’s considerably higher stakes, and you’ve got a recipe for disaster. Like crashing your homemade rocket in the California desert. With you inside. Or like these items: 4. Franz Reichelt For whatever reason, I've seen this guy from multiple sources recently. Franz Reichelt was highly interested in the human power of flight, a hobby that, throughout history, has a pretty abysmal survival rate. Reichelt, however, lived at a time where airplanes already did exist and functioned — mostly. His interest took a slightly different slant, which was the development of a parachute suit that would allow pilots, or thrill-seekers, to jump from a great height and float down safely to the ground. To give you some idea of how this went, I can assure you that Reichelt is absolutely not the inventor of the parachute. Or, for that matter, the wingsuit. After what had to be an incredibly irritating back and forth with French police, Reichelt got permission to toss one of his dummies off the top of the Eiffel Tower. When he arrived at the top, though, he committed one of history’s most ill-advised and disastrous switcheroos, deciding he would wear the suit and jump himself. And that, mes amis, is why today we call it the I-Fell Tower. 3. Herman Cain As far as jokes about stubbornness go, politics is rather low-hanging fruit. But this guy was an entire branch of low-hanging fruits. No person became more of a grim figurehead of the health risks of being a huge asshole than ex-presidential candidate Herman Cain. I guess he wasn't Abel to let go of his stubbornness. 2. William J. Bailey Throughout history, humans have come up with no shortage of wackadoo medical treatments and various snake oils. Snake oil, it turns out, has legitimate uses. Most of the things we label "snake oil" are just useless. Some might actually do something, but no one's done studies. They don't make up for the ones that, you know, kill people. In the 1920s, for example, radium was all the rage. Yes, the radioactive kind. Looking back, you can find it casually included in all sorts of consumer products like makeup or the glowing numerals on a watch face. Maybe the most straightforward, and incredibly stupid application was invented by a man named William J. Bailey, who created and sold Radithor, an “energy tonic” that was created from the simple recipe of water plus radium. I'm not an expert on radioactivity (there are different kinds of radioactivity, and some of them are relatively harmless if their sources stay outside your body), but my understanding is that ingesting radium is particularly harmful because the body's chemical processes think it's calcium. So you end up with radioactive bones. Suddenly, those glow-in-the-dark skeletons you see around Halloween aren't so cute, are they? 1. The Titanic This one's so famous that I don't know why they even bothered including it on this list. It might not be a single person, but I don’t think we could really end this article without acknowledging one of the greatest acts of human overconfidence in history. This is true, but few of the people involved were directly, corporeally affected. The submersible that went to look at the wreckage earlier this year, though... |
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