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Complex Numbers
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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January 7, 2023 at 6:12am
January 7, 2023 at 6:12am
#1042770
Still waiting for that other shoe to drop. It's going to happen. It's inevitable, because it didn't hit the ground yesterday.

I had some time to myself yesterday, so the gravitational pull of breweries was irresistible. There's a cluster of them in Queens, just across the river, and I felt them tugging at me all the way from Central Park. As it was too cold to swim (and I wouldn't swim in the East River on a good day for any amount of money—well, maybe a billion dollars, but no less), and subways didn't go quite where I wanted, I summoned an Uber.

Uber's very convenient and all, but I have no doubt that they, like every other bastard company in the world right now, is sucking up every bit of data they can find on you. This isn't normally a big deal, but most of my Uber rides either begin or end at breweries, and I'm sure that's part of their dossier on me. So while I was sitting there in the back of the car (the rideshare drivers in NYC have started installing bulletproof plastic shields just like the taxi drivers did years ago), I took the opportunity to check the weather online... and got treated to an ad for beer. Well, not really beer, but that mass-produced swill you find everywhere, but still, it's direct competition with actual beer.

This was almost as uncanny as the other day, whilst sitting in the doctor's office waiting for the goddamn slow as shit doctor, I went to play a game on my phone (there were signs up urging us not to use phones in the office, but fuck you; you make me wait one minute past the scheduled appointment, and my distraction comes out), and what ad did they push at me? Blood pressure medication. That was even more eerie because at the time there was a sphygmomanometer staring me right in the face.

Look, if I have to put up with ads anyway, which it seems that I do because we're in the end stage of capitalism and everything is a goddamned ad, I'd rather they be targeted than not. Obviously, I'd prefer to never see another ad. What's the point of having all my privilege if I can't use it to avoid getting bombarded by beggars? But failing that, it's better for me to see ads for fermented and/or distilled beverages than for, say, camping supplies.

Anyway. I did figure out one way around the Uber destination/pickup thing a while back, and it's especially useful in cities: instead of putting in your actual destination if it's a bar, brewery, or bordello, you use Google to find a more puritan-friendly business nearby. Like, I dunno, a nail salon or lawyer's office or bookstore. You have the driver drop you or pick you up there instead. Of course, this often means walking half a block, which I know is a tall order for some, but it might be worth it just to randomize their algorithm on you.

The downside of that is, naturally, that then you'll start getting targeted ads for nail polish or personal injury attorneys or the latest garbage NYT fake "bestseller."

Might be worth it, though, just to mess with them.

I didn't do that trick yesterday. Maybe later today.

Oh, as for the breweries? I visited four of them, and they were all decent.


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