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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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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 "You're Doing It Wrong" article is from, not Lifehacker for once, but Quartz. Hahaha. Yeah. Right. Eight hours a night isn't enough, whatever income you're making isn't enough, sex twice a day isn't enough, and one slice of pizza definitely isn't enough. I suspect this article was written by a cat. For something that we spend a third of our lives doing (if we’re lucky), sleep is something that we know relatively little about. “Sleep is actually a relatively recent discovery,” says Daniel Gartenberg, a sleep scientist who is currently an assistant adjunct professor in biobehavioral health at Penn State. "Discovery?" As anyone who has lay awake at night contemplating the complexities of the universe can attest, sleep is a slippery beast. Reminds me of the old joke about the dyslexic agnostic insomniac, who stayed up all night wondering if there is a dog. There are also many, many misconceptions about sleep: that you can “catch up” on the weekend for lost hours of shuteye. Oh? See "Sleeper Agent"  That you can get by on four hours’ sleep a night. You can, for a little while. Source: experience. That a nip of whiskey before bed helps you sleep better. Even I, with my alcohol-positive lifestyle, knew that. I just don't use it as an excuse NOT to drink. Even that eating cheese before snoozing causes nightmares. I rather enjoy eating just before bedtime. It usually results in the most vivid and memorable dreams. That could be a kind of placebo effect, but who cares, if it works? To set the record straight about being horizontal, Quartz spoke to one of the world’s most-talked-about sleep scientists. Yawn. He’s also an entrepreneur who has launched several cognitive-behavioral-therapy apps, including the Sonic Sleep Coach alarm clock. So this whole thing is an ad. A crummy commercial. Oh well, at least it's free, unlike most interesting stuff on the internet these days. Some topics we cover: why 8.5 hours of sleep is the new eight hours Spoiler: It's not, really. They're including time trying to get to sleep and wake up and coming up with "total bedtime." the genes that dictate if you’re a morning person or a night owl Like that's going to change anything, except that now you get to blame genetics for something. why you should take a nap instead of meditating Finally, an idea I can wholeheartedly support. how sleep deprivation can be a tool to fight depression Another spoiler: this is, to say the least, disputable. why sleep should be the new worker’s rights Right, like anyone has time to fight for worker's rights while holding down three jobs and a side hustle. and tips on how to get a better night’s rest (hint: it’s not your Fitbit) I'm going to go out on a limb here and say that the answer is the Sonic Sleep Coach Alarm Clock. The rest of the articleadvertisement is in interview form, and I won't reproduce much else from it. It's actually pretty interesting, and covers more than just the topics I just listed and snarked on. So reading it shouldn't put you to sleep. |
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