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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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| For my final full day in France, I took a small-group tour to the wine region of the Côtes du Rhône. In contrast with the previous day's trips, I wasn't very familiar with the Côtes du Rhône vintages. This, of course, is why I went. I find that, when traveling, some mixture of the familiar and the new is ideal, though I expect the proportions would differ for everyone. While I don't think I'd ever had a wine from this region before, some of the grapes they're based on are fairly popular to grow in the US. The tour group itself was pretty interesting. Some of us ugly Americans, a couple from Quebec, and three people from Australia, who, while initially distrustful of my Americanity, quickly warmed up when I assured them (out of earshot of the tour guide) that I very much enjoy Australian Shiraz. While the guide insisted that Syrah, one of the grapes in Côtes du Rhône, is not the same thing as Shiraz, it totally is; it's just grown on very nearly the exact opposite side of the world. The tour guide himself, who looked a bit like Kiefer Sutherland, was otherwise very knowledgeable, and spoke good enough English that all of us varied Anglophones mostly understood him. The problem comes in when some unknown place name, or grape name, pops up in spoken French. Like, if someone comes up to me and says "Bonjour, peux-je vous aider?" I can work out what they're saying. But if I'm at a wine tasting, even if it's mostly in English, it might go something like this: "This wine comes from the pl***du*** region, near B***on and the S**** river valley. If you visit there, be sure to go to D****de*****, a fine restaurant that serves bl*****, v*******de la *******tion, and many very good wines, including Petit ********tre, Vo******** Blanc, and sparkling Dr*******" It's tiring, to be honest. I started asking for spellings. To make things worse, my hearing isn't that great thanks to 50 years of rock concerts (no regrets), and I'm not asking you to repeat yourself because I don't understand French; I'm asking you to repeat yourself because I literally can't hear you over the ambient mumbles. Ah, well, soon I get to complain about the same thing in Dutch (or at least the version of it known as Flemish; I don't know the details there), as I'm leaving for Bruges today. It's a tight schedule: catch a train to Brussels, transfer to a train to Bruges, get to the hotel from there somehow (Uber seems to be wonky in Belgium; apparently, only taxi drivers can do Uber, thus defeating the whole purpose but providing job security), then find a certain statue in a city saturated with statues to meet a beer guide who will take me... well, I don't care, as long as there's Belgian beer. I'll wrap up with another landscape picture, this one of the Rhône Valley.  |
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