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Rated: 18+ · Book · Personal · #1196512
Not for the faint of art.
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.




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October 1, 2024 at 4:27am
October 1, 2024 at 4:27am
#1077543
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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