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Monday, May. 6, 2024

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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/

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:

🌕 HuntersMoon

about 17 hours ago
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

a day ago
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

April 7, 2022 at 12:01am

#1030231

Your Mama

That's right, I said your mama.

The 'Your Mom' Joke: A Brief History

Once again, leave it to Cracked to explain the most important aspects of our cultural history.

Today what we’re talking about is the most popular response to literally anything anyone could ever say to you during middle school.

Since I have a good memory only for the stupidest things, here's a joke from my own middle school days.

Two kids are having the old "my dad vs. your dad" argument.

"My dad's better than your dad!"

"Nuh-uh! My dad's better than your dad!"

And so on for a while until one of them stops and goes,

"Well... my mom's better than your mom."

"Can't argue with that," says the other kid. "That's what my dad says."

Wikipedia’s page for it is titled the “Maternal Insult,” a comically dry name for the much hated yet much celebrated “Your Mom” category of joshing.

And the "your mom" thing still makes me chuckle. Not because of the insult itself, of course. And certainly not because I like seeing mothers disrespected. It's one of those things that's only funny in a meta sort of way, like "we're too old to make your mom jokes, and we know we're too old, but we're doing it anyway, and you know we don't mean anything by it."

The oldest maternal insult comes to us from the distant times of 3500 BC, from ancient Babylon. A tablet found by researchers contained the riddle “…Your mom is by the one who has intercourse with her. What or who is it?” While we can’t answer the riddle owing to the fact that our PhD is in comparative chili judging rather than ancient Babylonian culture, we assume the answer is probably the person who wrote it. It’s just the way of the world.

The oldest known maternal insult, that is. As with beer, you know they were making it before anyone wrote it down or, in this case, made wedgie marks on clay about it ("Your mom makes wedgie marks.")

Anyway, I feel like the answer is "anyone."

Next, we have good ol’ Willy Shakes using it in a few of his plays. Perhaps the best comes from act four, scene two of Titus Andronicus, one of the “lesser” tragedies of the bard’s oeuvre:

Demetrius: "Villain, what hast thou done?"

Aaron: "That which thou canst not undo."

Chiron: "Thou hast undone our mother."

Aaron: "Villain, I have done thy mother."

I don't remember that play (or the movie based on it) well enough for context, but it's good to remember that, at the time, Shakespeare was low comedy.

(The article does provide context, but it's not all that important for the point.)

The joke came into its own, of course, on school playgrounds and classrooms in the 1990s.

Wait, whaaaaat?

Look, kid, your generation didn't invent the your mom joke. As you have pointed out in this article, it's as old as history. Nor was it your generation that perfected the art. And hell, it probably wasn't mine, either, but like I said above: we were trading momma insults back when I was in middle school. Unlike the other things we did in middle school, like listening to disco and wearing bell bottom jeans, the mama joke endured.

So why did this format suddenly become popular among schoolchildren in the 90s? Well, we have the sketch show In Living Color to thank.

And you think they didn't steal it from others? Come on.

That sketch is where such classics as “Yo mama so fat, she had to get baptized at SeaWorld” came from.

Oh hell no. We were saying shit like that all the time. "Yo mama so big she got her own area code." That sort of thing. (That particular joke doesn't work as well these days.)

So what’s next in the evolutionary process of this most ancient and venerated of insult humor? We could start insulting people’s fathers, but “Yo daddy’s so stupid…” doesn’t have the same bite to it, not to mention the already weird sexual connotations the 21st century has awarded to the word “daddy.”

Ahem. Get off my lawn again. Not only were they using "daddy" like that in the 70s, there's goddamn jazz music from like the 40s that uses "daddy" for "lover."

Anyway, point is, some jokes are timeless. Until the inevitable robot uprising, anyway, at which point one robot will turn to the other and say, "Yo mama's a human." And they'll get in a fight.

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