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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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My weekly trip into the archives only took me back two years, this time, to July of 2022, almost to the day. It's a fairly long set of musings on a fairly long article from aeon: "Smiley"  And it is, as one might guess, all about smiles. Now, it's only been two years, as compared to the many years of history discussed by the article. One of the reasons I do these things is to see how things have changed, and, well, not much has changed in two years. There's some discussion of face masks, which were more prevalent in public in 2022, but that's about it. I will, therefore, just point out a couple of things I either missed or left out in a failed attempt at brevity back then. First, as academics are wont to do, the article includes a foray into Latin: Ancient Romans showed another variant. If we take their vocabulary at face value, they did not distinguish between a smile and a laugh, contenting themselves with a single Latin verb – ridere – for both. Only towards the end of the Roman Empire did a diminutive – subridere – enter the language. This came with the derived noun sub-risus (later, surrisus) a ‘sub-laugh’– a little or low laugh – associated with mockery. It retained this lesser status and this diminutive form, distinguishing it from the laugh as it entered the Romance languages in the High Middle Ages. Around 1300, for example, French contained words for laughing (rire) and laughter (le rire or le ris) and smile (sourire, from sous-rire). I'll point out now that the Latin ridere is the known origin of our words "ridicule" and "ridiculous," which today don't conjure up much in terms of smiley laughter, but rather lip-raising scorn, such as I occasionally heap upon stupid articles in here. Not the one under discussion today, but others. Second, it's been bandied about that forcing a smile also forces the underlying emotions of happiness, contentment, or relaxation, and supposedly makes one appear more friendly and approachable. Neither of these things is always good, in my opinion. Sometimes it's best to work with the emotions you're actually feeling (or so I've heard, at least for actual humans). And one does not always want to look friendly and approachable, because someone might approach you and try to get friendly. It could even be a symptom of the foul practice of toxic positivity. And to me, forcing a smile is the exact opposite of relaxation. I'm not suggesting frowning as an alternative, but just... letting it be. Unless you're in the kind of situation where people shouldn't know what your actual emotions are, lest you get intrusive questions like "Why the long face?" or "Okay, what are you grinning about?" Or if, you know, you're at a poker table. I still pity the retail workers who have to go all day with a fake smile plastered upon their face. Even worse are the ones who are genuinely happy to have to present their customer-service face to the world. I mean... why? Smiley faces are for people who aren't paying attention. So anyway, the original entry and article are there at the link, and I still think the article's interesting. But I don't think I smiled even once. |
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