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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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March 22, 2022 at 12:02am
March 22, 2022 at 12:02am
#1029309
And now... science.

11 epic mysteries scientists totally can’t solve  Open in new Window.
What is the universe made out of? When did the anus evolve? Can humans live to 150 years old? And more!


Yet. Can't solve... yet.

To investigate some of the biggest mysteries in science, you have to venture to some pretty far-out places: the bottom of the oceans, inside the human brain, the tops of mountains, and even the end of time.

And sometimes the internet.

Here, we rounded up 11 questions that astounded us the most.

This is not Cracked, so no countdown list this time. I'm skipping a few, but not because they're not interesting; it's because I can't be arsed to make jokes about them.

What is most of the universe made out of?
It’s a simple question that’s also bafflingly unanswered: What makes up the universe?


It's made out of universe. Duh.

The dark matter thing is definitely annoying. Personally, I think they'll find out it's even weirder than we've imagined, like maybe gravity leaking over from another dimension. Like, literally another dimension, and not some alternate universe. Or, I suppose, that would be weird too. Anyway, the whole thing kind of reminds me of when, back in the 1800s, scientists figured that since light was a wave, it had to wave in something, so they figured out what the properties of that something would have to be to match observations. They called it the luminiferous ether, which honestly would make an awesome band name. But as it turned out, their basic assumption was wrong, and it was weirder than they could have possibly imagined... until someone imagined it.

What lives in the ocean’s “twilight zone”?
As you dive deeper into the ocean, less and less sunlight shines through, and about 200 meters beneath the surface, you reach an area called the “twilight zone.” Sunlight fades almost completely out of view, and our knowledge about these dark depths fades too.


Sea monsters, of course, as shown on those old maps.

Seriously, though, it seems to me that this could be figured out. Eventually. Just like we didn't use to know the shapes of all the continents on Earth, until we did.

What killed Venus?
“Hellscape” is the most appropriate word to describe the surface of Venus, the second planet from the sun. At 900 degrees Fahrenheit, it’s the hottest planet in the solar system, thanks in part to an atmosphere of almost entirely carbon dioxide. Clouds of highly corrosive sulfuric acid are draped over a volcanic landscape of razor-sharp lava flows. Most crushingly, the pressure on the surface of Venus is about 92 times the pressure you’d feel at sea level on Earth.


Clearly, the civilization there was fooled into thinking global warming didn't exist by their fossil fuel corporations. Everything was going fine, until it wasn't.

“Venus and Earth are planetary siblings,” Andrews says. “They were made at the same time and made of the same stuff, yet Venus is apocalyptic and awful in every possible way. Earth is a paradise. So why do we have a paradise next to a paradise lost?”

I needed to post this quote because I keep seeing breathless articles about astronomers finding "Earth-like planets" around other stars. This gets people thinking there's all number of places we could fuck off to when we use up this planet, because we're used to fiction like Star Trek where what they call M-class worlds are an isik a dozen. Point is, to an astronomer, Mercury, Venus and Mars are Earth-like, and good luck landing on any of them and surviving more than 30 seconds without lots of life support that you brought with you. We have not yet found a planet, extrasolar or otherwise, that any normal person would consider to be anything at all like Earth. Chances are we will, eventually -- it's a big galaxy in a big universe -- but let's not count on it being reachable.

What will animals look like in the future?
It’s impossible to completely predict how evolution will play out in the future, but that doesn’t mean we can’t try.


The way things are going? Two heads, tentacles, and extra limbs. Radiation from nuclear fallout can do that. Or so I've heard.

What causes Alzheimer’s?
There is no cure for Alzheimer’s, a neurodegenerative disease that causes dementia, and no highly effective treatments, despite decades of research.


Live long enough, you'll get Alzheimer's. It just strikes some people earlier than others. Some are lucky enough to die before that would have happened.

Why do we have anuses — or butts, for that matter?
This is a question we never even knew we wanted to answer — until we heard the Atlantic’s Katherine Wu explain that “the appearance of the anus was momentous in animal evolution.” Before the appearance of the anus, animals had to eat and excrete through the same hole.


This has been a subject of a serious blog entry or two here in the past. Here's one from last Christmas: "Evolution, My AssOpen in new Window.

Personally, I think it's because people love fart jokes for some inexplicable reason, so we developed assholes for the sake of lowbrow comedy.

And then there’s a whole other question: Why is the human butt so big, compared with other mammals?

I thought that was pretty much settled; it has to do with being bipedal. Perhaps I'm wrong, though. I'm no asspert.

What the heck is ball lightning?
For millennia, people have been telling stories about mysterious spheres of light that glow, crackle, and hover eerily during thunderstorms. They’ve been spotted in homes, in rural areas, in cities, on airplanes, and even passing through windows.


I remember seeing that once when I was a kid. Freaked me right out of my shoes. I'd been hearing all those stories about alien abductions and whatnot, and I was sure that I was about to get anal-probed (see previous header). Then I found out about ball lightning. Come to think of it, that might have been when I started to really get interested in science.

But hey, maybe it is aliens, and they just weren't interested in my butt. After all, if you can't explain it, it's gotta be space aliens, right?


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