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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.  |
| The weather decided to give me a break, just in time for another wine tour out in the countryside. Yesterday's excursion took me into the nearby wine region of Beaujolais, source of one of my personal traditions. I've talked about it enough in here before, but, in brief: Beaujolais Nouveau is released on the third Thursday of November, just in time to ship it to the US for drinking with Thanksgiving meals, which it accompanies very well. I try to get a bottle every year. This is not, of course, the only wine produced in the region, and their more traditional offerings are very good. But the funny thing I found out on this trip is: the French consider it a trash wine. Which probably explains why the US gets so many bottles in November; they unload their stock on us so they don't have to drink it themselves. Every year when it's released on Beaujolais Nouveau Day,  though, they get together and party to drink the stuff and complain about how bad it is. And probably to laugh at the Americans who they can pass it off onto, but for some reason none of the tour guides I talked to would admit to that.Thing about it, though, is the wine may be crap, but it's cheap crap, and to me, the price of the stuff figures into the taste. So yeah... I like it. Deal with it, France, because I have to deal with beer drinkers claiming to love Bud Light. In other news, today is my last full day in France, but I'll talk more about today's events tomorrow, which is when I'm scheduled to get on a train to Belgium. I'm of the considered opinion that no trip to France is complete without at least one decadent, elegant, crazy expensive formal dinner. So I had mine last night, in the restaurant on the top floor of my hotel. The only thing more boring than hearing about someone go on about their dream last night is hearing them talk about their decadent and crazy expensive French dinner, so I'll spare you most of the details, only to say it was everything I expected and not nearly as expensive as I thought it would be (and that neither snails nor frogs were involved). I accompanied it with a bottle of Pouilly-Fumé, which is not from this region, but what the hell, I like it and it was on the menu. When I say bottle, I mean bottle. Damn right I polished it off. Today's vacation photo was from an overlook where we stopped on the tour for a glass of wine. You will note that it's not raining, and that the view was incredible.  |
| Dealt with rain all day yesterday. I can't complain too much, though. Had I stayed home, I would have had to endure many days of rain, mostly spun off from Hurricane Helene. We didn't get anywhere close to the worst of it where I live, and being in other parts of the South would have sucked even worse. So I try to keep things in perspective. Still, rain on vacation isn't ideal. I walked around Vieux Lyon (Old Lyon) anyway, slipping and tripping on ancient cobblestones and occasionally juggling my umbrella and camera phone to get a shot of something interesting. As I mentioned in my previous entry, the travel agent had lined up a food-tasting tour for me. This involved more walking (in the rain) around Vieux Lyon, trying to keep up with younger, healthier tourists while cramming ourselves into tiny shops. The food and wine were worth it, though. This place has its own traditional cuisine, which mostly involves cured meats and cheese, and, needless to say, both pair really well with the local wine. I'll have more to say about the wine in future entries, but I did want to share this lucky pic I caught on the way to the food tour. I've censored the faces for privacy; what's important are the words on the woman's umbrella. It may not mean much if you're not familiar with French, and, as with anything funny, explaining it negates its impact (though I might comment with the explanation later, if people want). But it made my entire day and almost made up for the relentless downpour.  |
| Another kind of slow day yesterday, partly because of another run on the TGV. This one took me from Dijon south to Lyon. I should note here, as a bit of a warning to other Americans who want to visit France: while many people, especially in the travel and hospitality industry, speak some English, and many signs are multilingual, the vast majority of the train announcements and postings are solely in French. While I have some facility reading the language, it's not as easy for me to follow the spoken language (yet). To be fair, I can barely understand train announcements in English. Ever been on the NYC subway system? The announcements there only add to the confusion. The hotel that the travel agent arranged for me in Lyon is a step up from the others I've been in here. Five-star instead of three or four. For this particular hotel, part of the upscale amenities is a really remarkably well-stocked bar on the top floor. Naturally, it became incredibly important for me to check out the bar. And oh, man, was it worth it. While many of the spirits are also available in the US, they're a bit cheaper here. Even the Scotch, so it's not just because of the EU. The menu featured several interesting-looking cocktails, too, some of which I, of course, had to try. I was the only one sitting at the actual bar, and the bartender did the whole bartender-showing-off thing with the flipping behind his back and squirting drinks from an arm's length away and juggling shakers and all that. If I didn't know better, I'd think he was flirting with me. Or at least angling for a tip, which really isn't done here, from what I've been told. They also have an 18-year Yamazaki (Japanese scotch-style whiskey), which I've had in the US, but only rarely. I restrained myself, though; I'll be here for a few days, and I'll have other opportunities to drink the really expensive stuff. With all that, I haven't yet had much opportunity to explore Lyon, which is a really quite large city compared to all the others (except Paris). Today isn't looking good, either, with rain in the forecast, but I have a food-tasting tour lined up for later. That's for tomorrow's entry, though.  |
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I need that umbrella!
