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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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January 19, 2019 at 12:48am
January 19, 2019 at 12:48am
#949965
Find a piece of nature that you can hold in your hand (leaf, twig, rock, berry, etc). Describe it as closely and carefully as you can. Use any means available to you to examine the object (magnifying glass, scale, all of your senses) and practice your descriptive writing skills.

"That's the problem with nature. Something's always stinging you or oozing mucus on you. Let's go watch TV."
         -Calvin

The cycles turn, as they are wont to do, and so we have the four seasons: Cold, Pollen, Mosquitoes, and Dead Leaves. If you're lazy, Dead Leaves season extends well into Cold season, and so you can pick a crumply brown thing up off your deck without having to venture too far into the dreaded Outdoors.

I don't know how many microorganisms tracked into the house on this dead leaf, and I'm not about to get a microscope to find out. Probably some insects, too. Definitely some things that, if they were big enough to see, would bite or sting me.

At some point, probably during Mosquito season, this sample of detritus was, presumably, green. And then, during Dead Leaves, it might have become an interesting color, something on the low-frequency end of the spectrum like red, orange, or yellow.

Color, though, is a function of selective reflection of photons. It's not truly an innate property of an object. We call something "green" if, upon exposure to the right kind of light and in the presence of our optical receptors, it absorbs most of the wavelengths that we don't call "green." When it's brown, that means that a bunch of wavelengths are being absorbed, and we're seeing the others. If there's no light, there's no color.

This particular leaf is in the process of decaying into an amorphous chemical sludge. Certainly it smells that way. I'm probably helping it along by touching it. It's the fate of everything that lives, of course: its components to be recycled into something that's alive, only for it to die and allow the components to be recycled again.

Doesn't seem to have a point to it, does it?

Maybe that's the true beauty that eludes me in nature - that it really doesn't have a point. It's rather invigorating to believe that this is true.

Still doesn't mean I want to go out in it.

Thing is, though, we speak of nature as if it were something separate from us, when the simple truth is, we're just as natural as this leaf. Thus, anything we create - walls, hair dye, pyramids, rockets, computers, whatever - is also natural. The only thing artificial is the distinction we make between "human-made" and "natural." Where I spent my childhood, there were beavers, and they built dams. We, too, build dams. Termites create vast cities; so do we. Birds make nests, rabbits dig holes... these things are considered natural, and so too should be the things we create.

Possibly the most dangerous result of this artificial distinction is the idea that what's natural is good, while what's artificial is bad. Yeah... tell that to Socrates. Or anyone with sunburn-caused melanoma.

That's why I heap scorn upon products proclaiming that they contain "all-natural ingredients." Like, what, other products contain supernatural ingredients?

Anyway, time to let the leaf go, hopefully along with its slimy, gross microorganisms. There'll be more in a few months.


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