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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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.

http://www.ddewey.net/mandelbrot/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Annette

about 10 hours ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

June 2, 2024 at 10:06am

#1072011

Revisited: "Nonbinary"

As regulars know, I do these retrospectives, in part, to see what's changed about the world and in me since the original post. Usually, I don't find my attitude much different. That's not really the case with this entry from February of 2020: "Nonbinary"

Today's thing is a bit different from usual: a gender-issues retrospective from a male homo sapiens.

For starters, I cringe at "different from."

The article

in question, from 2018, is still up at this time, but I didn't re-read most of it.

Not only is the weight issue a pressing thing for many men, but I avoid online dating specifically because most of the women on there specify 6' or taller.

That's actually not the only reason I avoid online dating. But I wonder what some of these women's reaction would be to a man who requires "natural D-cup or larger only." Not great, I'd imagine.

I can do something about my weight, and I am.

Turned out I couldn't, so I stopped trying.

Can't do anything about my height.

Since then, I've seen pieces about some kind of surgery that puts extenders in your leg bones to make you taller. The surgery isn't risk-free, and from all accounts, it's painful with a fairly long recovery time. Not worth it, in my book.

We desperately need "accept yourself as you are" messages, but there's no money in that, so instead we're stuck with "you're just not good enough, but if you buy my crap, you'll finally be satisfied." (Spoiler alert: you'll never be satisfied.)

What's height got to do with anything besides blocking the people behind you in the theater?

I recently read an article in which some vapid lady expressed a desire to be "swept off her feet" both literally and physically, and apparently that could only be done by a 6'+ man? Okay, well, I wouldn't be interested in her, either.

I have to admit, as an aside, that I find it hard to see the whole "gender is a social construct" thing. I mean, yes, certain aspects of it are, in my view, but they're mostly superficial things: a particular style of haircut, wearing bigger watches (if one wears a watch at all these days), a lack of makeup.

Since then, I've come around more to to that point of view.

Basically, if something is a social construct, the social construct can be changed.

I stand by the "can be," but I recognize that those things take time, often longer than a human lifespan.

One of the greatest failings of modern society, I think, is this "binary" myth.

Standing by this statement, too. I've railed on binary thinking many times since then. And no, this isn't limited to the male/female binary; I think Netflix jumped the shark, for example, when it removed star ratings in favor of Siskel and Ebert style thumbs. But, lest anyone be confused by the entry's title, this sort of thing is what it referred to.

But still, my views have evolved somewhat. One thing, though, that I hope never changes about me:

And everyone deserves basic human dignity and rights (at least until they prove themselves unworthy of such by their actions), regardless of what pigeonhole you or society says they belong in.

I trust that's clear enough.

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