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Saturday, Nov. 16, 2024

1:37am EST

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Complex Numbers

by Robert Waltz

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/

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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

June 17, 2022 at 12:01am

#1033915

Fuzzy Tales

Today, we have something about actual storytelling.

11 Lesser-Known Fairy Tales

I vaguely remember some of these from my childhood, as my parents were old-school and didn't hesitate to try to get me to behave by scaring the living shit out of me through old fairy tales.

Didn't work, but that doesn't mean they shouldn't have tried.

Generations of parents have told their children fairy tales—stories imparting moral lessons that are easier to remember when a princess or evil ogre is involved.

I think these days the push is to not scare the hell out of kids with fantasies to prepare them for a harsh and uncaring world, but I'm not sure that's any better. "Stranger danger" just doesn't have the same effect as "behave or an ogre will eat you."

But there are many weird, quirky, and sometimes incredibly dark stories you may not know. Here are 11 of the lesser-known ones.

Since this isn't Cracked, the list proceeds in ascending numbered order.

1. The Three Spinning Women

This Brothers Grimm tale stars a lazy girl who doesn’t want to work on her spinning wheel. Her mother punishes her.

I'm not sure I remember this one in particular, but I do recall that there was an awful huge number of "spinning" tales. I'm still not sure why. Even when I was a kid, no one spun thread or wove fabric; you bought that shit at K-Mart and later Wal-Mart.

This lighthearted tale shows that, sometimes, laziness does pay off.

On second thought, I must have read it as a kid, because I learned that lesson very well.

2. Hans-My-Hedgehog

A couple wants a child so badly they'd settle for a hedgehog in this Grimm tale.

Yeah, pretty sure my adoptive parents kept this one secret lest I start to identify as a hedgehog.

3. The Ungrateful Son

This short Grimm story teaches the dangers of selfishness when a man decides to hide a giant roasted chicken from view when his elderly father visits his house. After his father departs, the man attempts to resume eating the chicken, but it turns into a giant toad and latches onto his head.

We all have a vested interest in teaching people not to be selfish. Unfortunately, that shit became a virtue in the 80s and stayed that way.

4. Cat and Mouse in Partnership

An extremely dark Grimm tale in which a cat and a mouse decide to live together for the winter.

Yeah, I think we all know how this one's gonna turn out. See also: The Scorpion and the Frog.

5. The Girl Without Hands

This truly Grimm story is, um, a handful, so stay with us.

Unfortunately, there are no fairy tales warning of the hazards of punning.

As for the actual content of the story, what the fuck, Grimm?

6. Hans, Who Made the Princess Laugh

In this Norwegian tale recorded by Peter Christen Asbjørnsen, a beautiful princess never laughs and is uninterested in every man who asks for her hand. The king declares that anyone who can make his daughter laugh will get her hand in marriage and half of the kingdom.

This one reminds me of an old joke.

Skipping a few here...

10. The Red Shoes

In this Hans Christian Andersen story, a little girl named Karen is so poor she walks around barefoot.

Well, she should demand to see the manager about that.

Incidentally, in case you haven't figured it out by now, Hans Christian Anderson was one sick pup.

While I'm not sure about Andersen, it's fairly well-known that the Grimm brothers didn't invent most (if not all) of their stories, but rather adapted them from an older oral tradition -- and cleaned them up a bit in the process. Disney further sanitized a lot of the stories, which is why the seven dwarves didn't take turns with Snow White in the animated movie (Okay, the dwarf sex part was probably left out of the older versions, too, but come on.)

Fairy tales aren't, in my view, meant to be static and unchanging, but rather reflective of the evolving values and trends of society. There's probably no known "original" version of a lot of them, but once they were written down, well, that's why we get all the stories about spinning thread and whatnot. A modern fairy tale should have warnings about too much screen time, the hazards of accepting candy from dubious uncles, or the dangers of putting your personal information on the internet.

I'll get right on that one of these days. (I have a couple of articles about procrastination in my queue; I'll get to them eventually.)

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