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Tuesday, May. 21, 2024

2:18pm EDT

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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:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 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

April 30, 2024 at 9:51am

#1070196

Mad as Hell

Sometimes I have to be reminded of stuff, because apparently I have a problem with object permanence once an item drops off my Favorites sidebar. In particular, "JAFBG"

[XGC] is still around, under new management, and there have been prompts to tackle since the beginning of the year.

As usual, I picked one at random:

How useful do you think anger can be?

Well, I'm not a psych-talker person, nor are emotions something I know much about. I can barely identify them in myself, let alone in others.

That said, it seems to me that anger is, at base, a manifestation of the well-known "fight or flight" response to a threat. That makes it related to fear, in my book (which I won't write because, like I said, not an expert). The "flight" part probably doesn't involve anger, but the "fight" part does. I hear that, in those cases, anger can be fairly useful to focus one's hostility into action... so long as it doesn't escalate into blind rage, which leads to random flailing around and, eventually, defeat.

I used language related to physical conflict there, but this also applies to the mental realm, like when government passes a law you don't agree with, and anger leads you to mobilize.

"I'm as mad as hell, and I'm not going to take this anymore!"

The quote there is from a 70s movie, Network. I don't recall ever seeing the film, but the line is iconic, with or without the context provided by the story. So of course, I looked it up on Wikipedia,

because it's not like I have to avoid spoilers for a movie that came out before Star Wars.

Which, if you take a look at the link there, provides a nice segué into the other half of the equation. Above, I touched on how useful anger might be to the person feeling it. But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation.

An angry person doesn't think rationally. This is almost by definition: "mad" is a synonym for "angry," but it's also a synonym for "fucking nuts." If you don't want people thinking rationally, if you want them to react with their limbic system instead of their neocortex, as it were... get 'em angry. Convince them, through emotional language, that their social position, their way of life, their very lives are in imminent danger, and you'll sell more torches and pitchforks.

I always thought it would be fun to put a Torch and Pitchfork store into an RPG campaign, to provide helpful tools for the occasional riot. The proprietor would be bored most of the time, so, occasionally, they'd drum up some business by manufacturing some sort of outrage. "The King wants to increase taxes so he can gold-plate his throne! Meanwhile, honest merchants are struggling! Are we going to let that stand?"

Might be a little too close to reality for a fantasy role-playing game, though.

So, to answer the prompt, anger can be very useful... in the people you're trying to influence. Way more useful there, as an agent of chaos, than it can be for an individual reacting to an actual threat.

So, if a headline spurs you to anger... take a step back. While suppressing anger is probably bad (or so I've heard), it may be possible to calm down enough to let some rational thought take over. If I'm right about the fight-or-flight thing, which I can't guarantee, anger is a kind of burst emotion; I imagine a whole cascade of neurotransmitters firing indiscriminately, urging us to action. And that burst can't really be sustained, any more than more pleasant emotions can.

Anger is a useful tool for the people in charge. It's way more useful for the rest of us to recognize when we're being manipulated, and sidestep that.

In my unprofessional opinion.

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