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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

tj-Merry Mischief Maker

about 17 hours ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 22 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

July 2, 2024 at 9:00am

#1073461

Imma Let You Finish, But...

The current round of "Journalistic Intentions"

[18+] features prompts relating to the Olympics. This is a subject I know almost nothing about, so I get to stretch my superpower of being able to write about any topic.

To make it even more potentially difficult for myself, I'll be picking the prompts (there will be eight of them, including this one) at random from the list.

Vanderlei de Lima

I've long thought of the Olympics as the exclusive province of young people. Well, in the sports, anyway; I imagine the IOC as a bunch of septuagenarians proclaiming this and that from on high (I don't know who actually composes that body).

And by "young," I generally mean "teens and early twenties." Then you retire, do commercials, and eventually get involved with a family who's famous for being famous. Hell if I know; it's so hard to Keep Up these days.

But, according to this guy's Wiki page,

dude was 35 when he ran in the 2004 games.

For context, I'm only three years older than him. For more context, Springsteen was 35 when he released Born in the USA (but much younger when he released Born to Run, which might have been more appropriate for Lima).

From that Wiki page:

Vanderlei Cordeiro de Lima (born 4 July 1969) is a Brazilian retired long-distance runner.

Now, see, I'd have guessed Peruvian from the name. Shows how much I know. (And no, I've never even heard his name before, to the best of my recollection.)

While leading the marathon after 35 km at the 2004 Summer Olympics, he was attacked on the course by Irish former priest Cornelius "Neil" Horan.

There's gotta be a story there. Fortunately, the article later expands upon it:

Soon after the 35 km (22 mi) mark, holding a lead of around 25 seconds, Lima was halted and grappled with by spectator Neil Horan, an Irish priest who was later defrocked.

The implication is that Horan was actively serving as a priest at the time, so saying he was attacked by a "former priest" up there is a bit misleading.

What Godly or worldly reason could Horan have had for being a human stumbling-block?

Horan said "I wasn’t doing it as a prank, I was doing it to spread the gospel and to prepare people for the second coming.”

Religious "logic," folks. I know if I wanted to convince someone my invisible sky-wizard was about to press the big red reset button, I couldn't think of a more appropriate way to spread the message than to fuck up someone's marathon run.

2004 was before social media infected the internet, but the internet itself was absolutely a thing then. I know this because that's the year I joined WDC, not long after the Olympics.

And here we are, 20 years later, and despite every effort and fervent prayers, the second ain't come yet.

In any case, there's not much else at the Wiki link besides Lima's other accomplishments in putting one foot in front of the other faster than everybody else. He did win sportsmanship awards, though, so I figure that counts for something regarding his character.

Which is more than I can say for his attacker.

5 Like • Comment • View 2 comments

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