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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 the "don't believe everything you hear" department (courtesy of The Guardian): Chocolate doesn’t cause acne – but carrots do help you see in the dark: the best and worst health myths and wisdom  True or false: cheese gives you bad dreams and oysters are aphrodisiacs? We investigate good, bad and mad health advice Folk "wisdom" usually isn't wisdom, but mythology. People have always had a problem confusing correlation with causation. Sometimes, though, like a sightless person throwing darts randomly and hitting a bullseye, it turns out to be right—at least provisionally. How do you tell the difference? Science, of course. I won't copy all of them here; there are quite a few. Just hitting some highlights that I wanted to comment on. Chicken soup helps cure colds and flu Works best if prepared by a Jewish mother. Okay, no, that's a joke. But I'm pretty sure the canned kind is going to be inferior to the homemade variety. I'm wary of the word "cure" in the title; however, this falls into the "can't hurt and might help" category. Unless you're vegan, in which case, good luck. Anyway, I've banged on about chicken soup in here before. The short version is, if it makes you feel better, and you like it, great. Chocolate causes acne This one's labeled "false." As with much of "nutrition science," the jury's still out. An apple a day keeps the doctor away Also labeled "false," but only on a technicality: you're going to get sick eventually, no matter what you do or don't do. But, as the article notes, it's not going to hurt you to eat a damn apple. And it's admittedly a catchy rhyme. Going out with wet hair gives you a cold "False." Duh. Colds are caused by viruses. Viruses that you pick up from *shudder* people. Carrots help you to see in the dark The article points to "true," but I have to say, not to the extent that mythology would indicate. This nonsense started, if I remember correctly, in England during WWII, when, not wanting "zee Germans" to know about the Allies' sophisticated (for the time) radar, they attributed early warning of aerial attacks to people eating carrots and therefore seeing the impending threat better in the dark. But again, as with apples, it's not like eating a few carrots is going to hurt. Cracking your knuckles will give you arthritis This one's false, and I've known that for some time, but goddamn, it's annoying. So if you use it to scare kids into not cracking their knuckles, I can understand that. I crack my knuckles all the time. It takes up to seven years to digest swallowed chewing gum Another false one intended to scare children straight. Garlic under your pillow aids sleep Labeled "false," but I'd call it true, if you're frightened of vampires; clearly, you're going to sleep easier if you know you're protected. It also keeps other people away because of the smell, so you get a better night's sleep. Still, when it comes to garlic, I'm too busy eating it to put it under my pillow. Urine relieves jellyfish stings I'm including this one in my commentary because I'm still hearing this nonsense sometimes. I suspect it got started by someone with a pee fetish, which is way more common than I ever realized. Oh, yeah, and it's false. Cheese gives you bad dreams I remember the first time I heard of this one. It was in Dickens' A Christmas Carol, as Scrooge attributed his nocturnal visitations to possibly having eaten cheese. As the article notes, dairy products might actually help with sleep. Again, good luck, vegans. Probiotics support your gut health This is the last one on the list, and it doesn't surprise me in the yeast—er, I mean, least—that it's not entirely true. The magical benefits of probiotics are mostly marketing gimmicks. Big surprise. |
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Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless. 
