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Tuesday, May. 7, 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

May 5, 2024 at 8:50am
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

May 4, 2024 at 5:42pm
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

October 5, 2022 at 12:01am

#1038635

Fanfiction

Entry #3 for "Journalistic Intentions"

[18+]. Blind quote, no link:

"Sure, when teenage girls write self-insert characters that hang out with their faves it's 'cringey' and 'bad fanfiction', but when Dante does it it's a 'literary classic' and 'redefines the way we view Catholicism'."

Uh huh. In 700 years, we'll see how much of today's fanfiction is taught as "the classics."

Look, teenage writing is generally cringey. Mine certainly was, and I wasn't a girl. You know what Dante wrote before his masterpiece? Love poems. LOVE POEMS. Starting when he was in his teens.

I wrote love poems back then, too. Well, not in Dante's day, but almost. I'm glad they've been lost to the mists of time; Dante had no such luck. One line I specifically remember is "Now my broken heart has mended / But the scars won't let it beat."

You know what else is almost always cringey? Self-insert characters. One of the most successful writers of our time is Stephen King, and you know what it was when he did it, well past his teenage years? Cringey. Like he was writing Stephen King fanfiction.

Oh sure, occasionally you'll get a young writer who's very talented and their early works are things of beauty. Shelley wrote Frankenstein when she was 20, while all of her dudes were stuck in the "love poem" rut (to be fair, those are considered classics too). But not everyone can both create a lasting work of literature and invent a new genre, especially not at that age. No, most of us write cringe in the beginning. And then, if we stick with it, if we really learn our craft well, then maybe—maybe—we write something that stands the test of time. Well, not "me" "we." The general authors' "we."

That said, my advice (for whatever it's worth) to young authors? Do it anyway. Some great authors have built careers starting with fanfiction. Greg Bear comes to mind; he wrote Star Trek novels. So did Diane Duane. Okay, you've probably never heard of either of them, but they both went on to write more than passable SF and/or fantasy.

Doesn't mean I'm going to read it. But just like worldbuilding for a fantasy novel, you're setting up a foundation for the possibility of later greatness.

Speaking of Star Trek, probably the second most famous work of fanfiction (after 50 Shades) in modern history is the story (a work of parody) that coined the term "Mary Sue." I've ranted about that in here in the past, probably for another JI prompt. The canonical "Mary Sue" (insofar as I can use the word "canon" for anything related to fanfiction) is an author self-insert, usually but not always penned by a teenage girl, who's unbearably competent and has no real flaws, and who's universally loved and accepted.

Not fun to read, usually. It's a clear case of wish fulfillment. But in the end, isn't all fiction wish fulfillment? The difference, at least in my mind, between good characters and bad is that the good characters have both external and internal battles to overcome. We're far more satisfied reading about someone who has trouble solving all the puzzles and gets into tough situations—and the Mary Sues or Marty Stus of the writing world are already at the top of their game. It would be like John Wick having the invulnerability, strength, and laser vision of Superman: the stakes would be nonexistent, and the story would be boring.

But the Superman character itself started out as... wish fulfillment. Writing a super-powered character takes some skill; in a compelling story, they have to face challenges that their powers aren't useful for. Like the latest TV incarnation of Superman, who has to deal with having teenage sons, something that, as far as I know, no superhero has ever been able to handle with powers alone.

So, yeah, I don't like teenage fanfiction, and I don't have to or want to read it.

But I'm not going to tell them not to write it. You gotta start somewhere. Artists—by which I mean people who make drawings or paintings—often get their start by copying others; they thereby learn the techniques and only later come into their own style. Or so I heard; I can't draw to save my life. Musicians start out by learning others' chord progressions. And so on. It should be no different with writers.

As a final note, "fanfiction" has somehow acquired the connotation of being sexual in nature, expressing the writer's desire to doink some character someone else created. While it can be erotic (again, 50 Shades), that's not the essential feature of fanfiction. I'm using the term in its broader sense here.

That said, I did once write a scene featuring a liaison between Snape and McGonagall.

"Oh! Yes! Ten points to Slytherin! Twenty points to Slytherin! YES! FIFTY POINTS TO SLYTHERIN!"

...no, I will not be sharing the rest of it. You're welcome.

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