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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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| Yesterday morning got off to an auspicious start as the really quite obnoxiously loud building alarm went off. Naturally, being American, I sat down to write an official letter of complaint to management, and prepared to give the hotel 1 star reviews on Yelp, Google, and Tripadvisor. How DARE they inconvenience a US citizen? ...yes, I'm kidding. Duh. I took long enough to put pants on, which may not have been the wisest course of action for myself, but you know me, always thinking of others' comfort. And then I proceeded down five flights of narrow, steep, half-spiral stairs that are probably older than my entire country. I'd been awake, though not for long, when the alarm went off (hence the pantsless state, as I was only beginning to get ready to go to the hotel breakfast), so at least I didn't have another heart attack from waking up to that. But on my way down, I got to wondering whether my travel insurance would cover the loss of all my shit from the hotel burning down. Probably not, I reasoned, because insurance only covers whatever doesn't happen to you. On the descent, I was joined by other people who also had the good sense not to use the elevator during a fire alarm (one of whom had stopped to pack his bag), and we all spilled out into the lobby, where a receptionist explained to us, in perfectly good English, that someone had made smoke in the breakfast kitchen and it wasn't actually a fire threat. My fellow travelers grumbled and started marching back up the stairs (the elevator is one of those tiny European ones with the manual outer doors, obviously retrofitted at some point after electricity was invented), but I followed my original plan and slipped down to breakfast, where I specifically asked for le petit déjeuner bien cuit, or breakfast well done (in the sense of a well-done steak). Because I am, after all, an asshole, but at least I'm a funny asshole. The travel agent's plans for me yesterday were: Eiffel Tower, Arc de Triomphe, Champs "Ulysses" [sic], and the Seine. But none of them involved tourist reservations; those were just their suggestions for famous shit to do while in Paris. So, instead, I did what I always do in a new-to-me city: I found breweries. You don't think of beer when you think of France, and generally for good reason. There are a few decent large-scale breweries in the east, adjacent to Belgium and Germany so that those countries' skill in brewing manages to spill over the border. But for the most part, French beer is, historically, liquid ass. But, like the Anglophone countries I'm used to, France has developed a craft beer scene. I only had time to visit three of them, but my overall impression is: just like the aforementioned Anglophone countries, some of the beer is excellent, and some is... well... less than excellent. I'd never know that, though, if I didn't try. I'm pretty sure I've said this before in here, but I enjoy tasting all beer, even the bad stuff, because, as the great philosopher said: "If everything was cool, and nothing sucked, how would we know what was cool?" (I can't remember if that was Beavis or Butt-Head.) Now, when I say "tasting," I don't mean I got pints (or, you know, 500ml, close enough) of each one, but did the small-serving flight thing. So no, I wasn't utterly wasted when I was done. But I had achieved beerenity, which has been elusive to me lately. I might have actually smiled as I walked back to the hotel, across the Seine, and through the courtyard of the Louvre, where I paused to snap what is surely the most French photograph I could possibly shoot.  |
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