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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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| It's unlikely that any individual is "an average human." To claim so would be mean. What does the average human do every day?  The Human Chronome Project finds that the average human sleeps for 9 hours but only works for 2.6 hours. Pun intended, of course, if a bit forced. While each of us has a decent conception of how we spend our own time, the actions of our fellow humans — from our next-door neighbors to people living in faraway countries — can seem quite mysterious. Do they watch as much TV? Work as many hours? Fiddle with their smartphones as frequently? Cook as often? Spend as much time watching their kids? Even some of those questions reveal a developed-world bias. First and foremost, the average human spends about 9.1 hours sleeping or resting. As the article notes, "human" includes everyone, including children. I usually manage something like that, but certainly did not when I was working full-time. While awake, the average person spends close to one-third of their day on passive, interactive, and social activities. These roughly 4.6 hours include reading, watching TV, making art, playing games, going to gatherings with friends or family, or simply doing nothing at all. The idea of "simply doing nothing at all" seems incomprehensible to most Americans. Eating and food preparation accounts for another 2.5 hours. Yes, fast food isn't universally available. Hygiene, including grooming, washing, and dressing, takes about 1.1 hours. Oh, that's what I'm missing. Cleaning and maintaining the spaces we inhabit costs us 0.8 hours of the day. And that. Though employment can be hugely time-consuming for working individuals, when looked at through the lens of the global human day, it appears as a mere sliver of time, just 2.6 hours. Coincidentally, that's about how much actual productive time most office drones achieve. Education also isn’t very demanding, only 1.1 hours. That's because a whole lot of 0s skew the average. The researchers were also curious about how average human time use changes with wealth. One big advantage of being rich is grasping more leisure time by paying others to have more working time. For instance, I (not really rich for an American, but close enough) pay people to mow my lawn. To be clear, though, it used to take me about 4 hours to do it, while they knock it out in 15 minutes. Additionally, people in the richest countries spend an average of just five minutes a day growing and harvesting food, while people in the poorest countries spend well over an hour doing so. As this illustrates, you do, too, if you go shopping at a grocery store instead of growing your own food and butchering your own hogs. By assembling the human chronome, the researchers say that we can compare ourselves to civilizations from the past. Right, because we know exactly how they used all of their days. Also, civilization itself changes its individuals' time utilization. More importantly, we can see from a high-level, empirical perspective what our species is doing on our planet and make more informed decisions about reallocating our collective time to change the world and society for the better. Like that's going to happen. Also, the worst excesses are perpetrated by a very small, average-skewing group with greater resources (aka "the Rich"). So, while this research may be useful (no such thing as useless knowledge), I don't think it has the lofty practical potential that they claim. Not to mention that just looking at an "average" (however that's computed) tells you enough about the range. It's just another way of manipulating with statistics. For example, "the average human" possesses fewer than 2 legs. Think about it, and you'll realize I'm right. But saying that can be misleading, as the vast majority of people have exactly 2 legs. Like me! I always knew I was above average at something. |
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