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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.

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October 18, 2019 at 12:20am
October 18, 2019 at 12:20am
Another Cracked article today. This one's from David Wong, who usually has some good perspectives on things.


How Our Pets Have Evolved To Emotionally Manipulate Us

To be fair, we, too, have evolved to emotionally manipulate us. Don't believe me? Okay, what do you do when you hear a crying baby? (Well, I get as far away from it as possible until it shuts the hell up, but I'm told that actual human beings try to comfort it.)

It's easier to love a dog than it is to love a spider or a cactus because dogs have adorable facial expressions. The nonverbal pleas for food and love, the dopey smiles, the heartbreaking, almost teary disappointment -- it's all there. But the reason they can make those expressions is that, after evolution split dogs from wolves to begin their partnership with humans, they evolved facial muscles to make "expressions" that humans would respond to. They grew little eyebrows.

It is true that, for most people, our love for something is proportional to its cuteness. Sure, you can convince yourself that a snake is adorable, but mostly that means you're trying to be metal.

"But cats don't have those expressions, and we love them just the same!" you may object. "If anything, cats look like they hate our guts!" Sure, but they just found another way to rope us in. Did you know that cats don't meow to each other? It's a sound they've developed specifically for humans, to get us to feed them. Even creepier, it may be specifically calculated to mimic a crying human baby. If anything, they think it's hilarious that we keep falling for it.

So remember a couple paragraphs ago, I mentioned that human baby screeches get on my very last nerve? I wasn't kidding (pun intended, as always). So, one time, I was in an airport - a setting guaranteed to enhance any slight annoyance and/or frustration to my breaking point - and I heard two things in close succession. First, a baby wailing; I noped right on out of there. Second, someone had a cat in a carrier and it emitted that frightened yowling wail that only cats can manufacture - and all I wanted to do was reach in and comfort it, regardless of any scratching it might do if I tried.

Consequently, I'm not sold on the "cat cries mimic human baby blurbling" theory.

This would, of course, mean that it's entirely possible to pour all of your love into something that is in fact coldly sending back just enough validation signals to keep you doling out the food and shelter. It would open the possibility that the kind of sweeping gooey sentimentality we think of as the Most Important Thing In Life will be seen by future societies as a weird, backward superstition. "These sick bastards went so far off the rails that they literally defied their most basic biological imperative and adopted pets instead of having children."

Yeah, look, I know a lot of people refer to pets as their "children," but again - I always wanted pets; I never wanted children (at least since I was old enough to physically help to produce them). My cats are my cats, not my "furbabies" or child-surrogates or whatever. Life isn't binary - it's not "kids, including surrogates" versus "a life of utter solitude." Anyway, point is, emotion is a biochemical process, and chemistry doesn't care.

What if all of our poetry and lyrics about "soul mates" and eternal devotion is one big weird cultural fetish?

What if water is wet and grass is green? Oh, but this author thinks I'm being cynical. I'll show you cynical, Wong.

But the gooey sentimentality, it turns out, is just as easy to defend with cold logic. If love isn't real, then nothing is. "But it's just an idea!" So's the law, and democracy, and money. If you can argue away love as just hormones and brain chemicals, then you can argue away the sun as being just a bunch of hydrogen and helium molecules. Figuring out how a thing works doesn't invalidate its existence.

But... the sun is a bunch of (primarily) hydrogen and helium molecules, and its goal is to give us cancer. I'm not saying love isn't real; I'm saying it's an emergent property of consciousness, which itself is an emergent property of biology, which is essentially a long, sustained chemical reaction. But as with everything else, we can make of that whatever we will.

Being willing to believe in things, to buy in, to put yourself out there, that's what takes real courage.

Sure, Wong, and I believe I'll have another beer.

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