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Saturday, Apr. 27, 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

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Show Recent Comments

10 Most Recent Blog Comments:

Kåre Enga in Udon Thani

a day ago
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

a day ago
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

a day ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

March 22, 2024 at 10:33am

#1066720

Trope-Osphere

Good writers shun clichés, and avoid them like the plague. Then there's Cracked:

5 Storytelling Clichés That Started Out Very Different

Every cliché starts from somewhere.

As I've said so many times it's become cliché: Every cliché was once profound wisdom.

Often, these tropes don’t simply stay exactly the same until we’re all sick of them. Hunt down their debut, and you’ll see something different from what you’re now picturing.

There is an important distinction between a cliché and a trope, but I can't be arsed to get into that right now. But it's like... in action movies, explosions are tropes. Hard to have an action movie without at least one explosion. It's part of their charm, along with car chases and fight scenes. But the action hero calmly walking toward the camera while shit explodes in the background? That's cliché. But the first time we saw it (I don't remember what movie), it was fresh, cool, and different.

5. The First Damsel Tied to Railroad Tracks Was a Man

If you’re a mustachioed villain, and you have a helpless maiden in your clutches, you know what you have to do.

The villainous mustache has transcended trope and cliché and achieved icon status.

The article delves into the history, here, and it's worth looking at if only for the photo of greatest villainous mustache of all time. But, as the header suggests, the first fictional track-victim was male. I'm sure someone could get their college thesis done on just this topic alone. In any case, this seems to be an instance of the original idea being twisted, and that twist becoming the cliché.

4. The Emperor’s New Clothes Was About Fear of Being Disinherited

That story isn't so much trope or cliché as it is an important literary reference that everyone should know.

In the Hans Christian Andersen fairy tale, the emperor walks around naked, and no one’s willing to point this out, having been told that only smart people can see the clothes. This offers lessons for everyday life. Sometimes, people are just pretending to know what they’re talking about. Sometimes, the stuff that wins awards is garbage. Also: A whole lot of people are afraid of looking stupid.

One might even suggest it's a ready-made metaphor.

3. The First Man Who Asked for Three Wishes Was a Dick Joke

A man finds a lamp, and when he rubs it, out comes a genie. “I will grant you three wishes,” says the genie. “Great,” says the man. “I will wish for two normal things, and for my third wish, I will trigger the punchline.”

The "rule of three" doesn't only apply to comedy. That's only where it's most apparent.

The header here is perhaps misleading, as the original format (from the One Thousand and One Nights) was less joke than fable.

2. The First Bad Boy Was Pretty Lame

We use the phrase “bad boy” to describe not just actual children but excitingly rebellious men. We consider that normal, but it’s a little odd. There are only a handful of arenas in which it’s considered okay to call a man a boy.

And there's at least one situation where one should never, ever do that. But apart from that, clearly, the author of this piece isn't Southern.

We call rebels “bad boys” because of an 1870 novel called The Story of a Bad Boy. The main character, Tom Bailey, is a rebel but is also very much a boy. His antics include scaring people by setting off a cannon and pushing a car into a fire.

As the "car" as we know it wasn't invented for almost another 20 years, this must be one of the other definitions of "car."

1. “The Butler Did It” Wasn’t a Cliché But a Cheat

Another one that makes great joke fodder, but is cheating in detective stories. Apparently, it's always been a cheat.

You might think that The Butler Did It became an unforgivable trope after tons of murder mysteries pulled that trick, until it got old. That’s not really what happened. Instead, in 1928, an author of detective novels published a set of rules that he claimed mysteries should follow, and among them was a rule saying the culprit must not be a servant.

I'm just going to pause here and bask in the elitism of it all.

Moving on...

That set of rules was written by S.S. Van Dine, who went by “Willard Huntington Wright” when he wasn’t writing detective fiction. The rules start out reasonable enough, talking about how the author must play fair and provide all necessary clues. Then it makes some questionable blanket statements about what all mysteries must do — there must be just one detective, the crime must always be murder and “there must be no love interest.” By Rule 16, Dine is insisting that mysteries must have “no long descriptive passages, no literary dallying with side-issues, no subtly worked-out character analyses, no ‘atmospheric’ preoccupations.”

I don't usually subscribe to the notion that rules were made to be broken. In this case, though, I'll make an exception. Breaking my own rule, as it were.

Rule number 11 says, “A servant must not be chosen by the author as the culprit. This is begging a noble question. It is a too easy solution. The culprit must be a decidedly worth-while person — one that wouldn’t ordinarily come under suspicion.”

Elitism intensifies...

Dine’s rules laid out a few other solutions that he says stories should never use. The death should never be revealed to be an accident, he said, or a suicide. The detective must never be the culprit. There must never be multiple culprits. The solution must not involve the killer committing the murder after the police have broken into the crime scene.

Yeah, those aren't rules. Those are story ideas.

In other news, I'm going to attempt to make this my last hyphen-pun-titled entry for a while. It's becoming cliché.

4 Like • Comment • View 1 comment

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