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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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| Samhain, and the temperature is supposed to get up into the 80s (Freedom Units) today. Not that I'm unhappy about that, but it is somewhat unnerving for the end of October. This Halloween night coincides closely with a new moon (8:47 Eastern tomorrow), so it's not nearly as cool as when it coincides with a full moon. So I'm doing... absolutely nothing for the occasion. Except, of course, trying to keep both of the black cats indoors, because some people are idiots. Speaking of the moon, though, here's a lunar mythology article from Discover: Myths of the Moon Shaped Ancient Cultures and Modern Cultures of Today  From ancient myths to modern superstitions, all cultures — even modern ones — tell stories about the moon. The moon is something all people on Earth, no matter where or when they’ve lived, have in common. Unless, I suppose, you spend your entire life underground. That we all share the moon does not mean that we imagine it the same way, however. In our myths and stories, the moon plays many different roles. We know more about the moon than ever before, and we continue to learn more. That dead hunk of rock in the sky still has secrets to give up. Myths and legends don't tell us much about the moon, but they do reveal a lot about us. The relationship between the moon and the tides, for example, was clear to early peoples who lived near the sea, explains Tok Thompson, an anthropologist at the University of Southern California who specializes in folklore and mythology. That's probably an example of noticing a correlation without understanding the deeper effects (in this case, gravity) behind the correlation. In other words, the "observation" part of the scientific method. The moon, with its regular phases, also functioned as a calendar. You could track the days by the sun, but for longer periods, the moon was useful. The English word moon comes from mensis, the Latin word for month, which is also the origin of the word ‘menstruation.’ Much as I enjoy a good etymology, I'm not sure this is right. Wiktionary traces the word back through Proto-Germanic, all the way to PIE. This suggests to me that, rather than having its origin in Latin, the Latin and the Germanic words share a root.I'm not an expert, by any means, but this is enough to make me question the "comes from Latin" assertion. Pretty sure Luna is from Latin, though; that was the name of a moon goddess. All that aside, let's stop pretending that Gregorian calendar months are related to lunar cycles. So yes, ancient cultures knew a lot about the moon, and they wanted to share that knowledge to keep a record of it. I also question the qualifier "a lot" in that sentence. Thompson’s favorite myth involving the moon is a creation story from the Tlingit people of the northwest coast of North America. In this story, an old man keeps all the light in the world stashed away in a box. Through wiles that vary from telling to telling, the trickster Raven steals the box and releases the Sun, the moon, and all the stars, bringing light to the world. One could be forgiven for wondering how Raven was able to see the box, considering there was no light at the time, but myths follow their own, dreamlike, rules. In Chinese mythology, a woman named Chang E drank a magic elixir, whereupon she floated all the way to the moon, and there she lives still — with, in some versions, a rabbit. Radical feminists: "Hey, gimme some of that elixir!" We still have some fascinating myths about our favorite satellite. Probably the most persistent is that the moon can drive us mad. I find that it's necessary to separate the two meanings of "myth." A foundational story, like the ones about Raven or Chang E, is not the same thing as a persistent falsehood. I don't think this article draws the distinction. Many people — including some healthcare workers and police officers — believe that crime, traffic accidents, psychiatric hospital admissions, and even suicides spike during a full moon. Or that could be cognitive bias. You notice things more when they fit your pre-existing worldview. Like when you're frustrated by machines and bureaucracy, and think "Mercury must be in retrograde." These days, we don’t blame the effect on moon goddesses or magic elixirs but on something at least quasi-scientific: the moon’s gravitational effect on the water in our bodies. On its surface, that makes a lot of sense. No. No, it does not. After all, the moon creates tides, and roughly half our body weight is water. Okay, but have they ever observed tides in a mudpuddle? And indeed, though a few small studies have found some possible effects of the moon on mental health, research over the past decades has not borne this out. For example, a Swiss study published in 2019 looked at almost 18,000 cases of in-patient psychiatric admissions over ten years and found no correlation between the phase of the moon and psychiatric admissions or length of stay. There's some nuance there, but basically, the "moon causes madness" bit is the second definition of myth. Pausing to gaze at the moon can create an intense feeling of both awe and peace. Rather than making us mad, the moon might just make us a little bit more sane. Nice to think, but there's little evidence for that, too. Still... go look at the moon. Might want to wait a few days, though; it's too close to the sun right now. |
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