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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.
September 1, 2021 at 12:02am September 1, 2021 at 12:02am
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Welcome to September.
I'm not participating in "30-Day Blogging Challenge ON HIATUS"  [13+] this time around, because I volunteered to be a judge for a week later this month. That's right; I'm judging YOU. (If you're participating.)
There's a lot going on in September. Not just the WDC 21st birthday celebration, but it also contains my own account anniversary, and soon, people can start signing up for "October Novel Prep Challenge" [13+]. That's right, November is coming up faster than you could possibly want, so it's not too early to start thinking about NaNoWriMo if you're into that sort of thing.
It is, however, too early to start thinking about the December holiday season.
The best thing about September, though -- actually, one of the only good things, because I'm one of those weirdos who prefers the heat of summer to the dreariness of autumn -- is Oktoberfest.
Why, you ask, am I associating Oktoberfest with September? Good question. The official Oktoberfest season is mid-September to early (really early) October. I have no desire to go to the original (and couldn't this year anyway because it's cancelled), but that doesn't mean I can't take the opportunity to enjoy a fine Märzen lager. So that's one thing I always look forward to in September. Another is, believe it or not, pumpkin beer. A lot of them suck, yes, but occasionally you find a good one.
But with the coming of cooler weather here in the Best Hemisphere, one thing I can appreciate more than I do in the summer is darker beers. Specifically, stouts. While I'm not above enjoying any beer in any season, some of them just work better in different weather conditions. And my favorite style of stout is Russian Imperial Stout, which isn't actually a Russian style but a British one, and that's a story for another time (if I haven't already told it somewhere in here).
And, to segué into today's article, my favorite Russian Imperial Stout is made by North Coast in California, and it is called Old Rasputin. It even has a portrait of the Mad Monk on the label. Its motto is "Never Say Die," because Rasputin was famously hard to kill.
...or was he?
In the winter of 1911, a group of high-ranking Russian priests gathered in secret to lay a well-planned trap. Their target was none other than the notorious Siberian mystic Grigori Rasputin, who seemed to have established a mysterious hold over the Tsar. Rasputin had been lured to the meeting by his former friend, the Archimandrite Iliodor. But as soon as he breezed into the room, he was rushed by Iliodor and the “holy fool” Mitka Kolyaba, a one-armed epileptic who had been a previous favorite of the royal family. They grabbed hold of Rasputin’s penis and squeezed it, demanding that he confess his sins, while a hysterical bishop began beating him around the head with a huge crucifix, screaming “Devil!” with each blow. After all, it’s like the old saying goes: “Problems with a mad monk? Try crushing his junk!”
In case it's not blindingly obvious from that intro, or from previewing the URL at the link, this is from Cracked.
From the safety of the palace, he had his enemies exiled. But perhaps he should have listened to them, or at least learned some lessons about attending mysterious meetings alone. Because five years to the day after the priests’ attack, Rasputin agreed to pay a late-night visit to Prince Felix Yusupov, the richest man in Russia. His body was pulled from a frozen river the next day.
Some people never learn, I guess. But I suppose if you're buddies with the Tsar and banging the Tsarina (well, okay, allegedly), you might start to believe you're bulletproof.
As we all (hopefully) know, no one in that court turned out to be bulletproof.
You’ve probably heard the conventional version of the story, where he survived being poisoned, shot, beaten, stabbed and castrated, before finally drowning clawing at the ice of the frozen river Neva. That story actually has more problems than that math textbook Jay-Z wrote, but don’t worry! Everyone at Cracked is dressed in the full Lara Croft outfit, archaeology shorts included, and we’re ready to solve this historical mystery.
There follows the usual Cracked numbered list, but I'm not going to paste it all here; this has already gone on long enough and, frankly, the remnants of a hurricane are blowing through here right now, along with rain, floods, wind, thunder, lightning, and cats and dogs living together, and my internet could go out at any moment. Especially since I just (11:25 pm) got a tornado warning on my phone.
Still, some highlights:
And no matter what a certain animated movie may have claimed, he definitely did not rise from the dead to lead the Russian Revolution.
Look, anyone who thinks that ANY historical Disney movie has anything more than a wispy connection to the facts is beyond such warnings.
In 1914, he was stabbed by a noseless follower of the mad priest-monk Iliodor.
Why Disney has to make shit up when there's awesomeness RIGHT THERE is beyond me.
Seriously, though, the rest of the article is fascinating, poking holes in the "official" history while suggesting alternatives.
But one thing remains: whatever the actual facts are -- and we will probably never know for sure -- the mythology and speculation around those last years of the Tsars is compelling enough without needing to invent Zombie Rasputin.
Great beer, though. |
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