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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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Congratulations on winning an honorable mention for Best Blog at the 2018 Quill Awards for [Link To Item #1196512] . *^*Smile*^* This award was sponsored by the blogging consortium including [Link To Item #30dbc] , [Link To Item #blogcity] , [Link To Item #bcof] and [Link To Item #1953629] . For more details, see [Link To Item #quills] .](https://images.Writing.Com/imgs/writing.com/writers/badges/type-Blogging-2180.gif) ![Merit Badge in Highly Recommended
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| Most of yesterday was taken up by traveling. To get from Tours to Dijon, apparently there's no direct way, or at least not one that gave kickbacks to my travel agent. So it started with me taking an Uber from my hotel to the Tours train station, because now I know better than to roll luggage for that mile. Then the TGV back to Paris, during which, for some reason I absolutely cannot comprehend, my assigned seat was right next to someone else... while there were maybe 2 other people in the entire car. But the real fun was when I got back to Paris and met the chauffeur for the ride from Gare Montparnasse across the Seine to Gare de l'Est, which is the station with the train to Dijon. The chauffeur didn't speak very good English or French, but he spoke excellent Ukrainian. At least I assume he did; I know almost nothing about that language. But he was very good at pointing out the Paris sights along the way, in some version of English with a Ukrainian accent. "There is Tour Eiffel. And this building on left?" He indicated one with scaffolding. "Ukrainian mob has construction contract." We drove a bit further. "There on right is Notre Dame. And over there, building by Ukrainian mob." I wanted to ask him if the mob also did the Notre Dame reconstruction, but I knew better. He pointed out other important Ukrainian construction jobs along the way, too. Now, look. It's entirely possible that "mob" was a bad translation of something else in Ukrainian. Something innocuous like "Fine Upstanding Ukrainian Construction And Renovation Company And Not Mob At All We Promise And Pinky Swear." But I choose to believe that my chauffeur, who was about my age, was an actual member of the actual Ukrainian mob and did the chauffeur thing as a day gig. Just in case, I gave him an enormous gratuity. As Skinny Pete said in The Italian Job, "If there's one thing I know, it's never to mess with mother nature, mother-in-laws, and mother-freaking Ukrainians." After that, the train (the slow kind) to Dijon was a letdown. Hell, the rest of the trip might well be a letdown. Things picked up again, though, once in Mustard City. The hotel, this time, is like 100 meters from the station. It has a lovely little bar. I had dinner elsewhere, but came back for the bar, where I got acquainted, for the first time, with a regional (the east of France) custom: Picon bière. Mostly, they drink Belgians here, because, as I've said numerous times, traditional French beer is ass (also, it's wine country). But apparently, it's not flavorful enough for them (QUOI?!) so they add a shot of a kind of orange bitters called, you guessed it, Picon. And whaddayaknow, it's actually a pretty good combination. Sadly, Picon isn't generally available in the US, so I'll have to enjoy it while I'm here and then smugly brag about it every time I drink a Belgian beer back home.  |
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