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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 4, 2024 at 9:38am

#1073524

He Said, Archly

Another random prompt from "Journalistic Intentions"

[18+] today.

St. Louis 1904

There are, in the world, very few cities with icons more iconic than the Gateway Arch. There's the Eiffel Tower, of course, arguably the most recognizable structure in the world. Across the Channel, there's the unmistakable steampunk intricacy of Elizabeth Tower, known worldwide but usually mistakenly labeled as Big Ben (which may be a case of metonomy, as Big Ben is the largest bell within the tower, but is more likely just mistakery). You have the sweeping, nested shells of the Sydney Opera House, the Washington Monument, maybe the Space Needle, CN Tower, and the Empire State Building. I'd be remiss if I didn't mention the Pyramids, but they're not technically a city symbol, located as they are outside the boundaries of Cairo.

Almost all of these establishment-shot-bait constructions have one thing in common: the "tower" bit (the Opera House being an exception). This inevitably leads to jokes about phalluses (Phalla? Phalli? Hell if I remember what Latin declension it belongs to), especially in the painfully obvious case of the Washington Monument (Father of his Country and all that).

Not so with the Gateway Arch. It's not a tower; it's... well... an arch. Two foundations, not one. Curvy, not straight (unless you view it from one side or the other, but who does that?) I'm not saying it's the equivalent expression of feminine potency, mind you; just that it's not an erection sticking straight up into the sky.

Thus, it might surprise younger folks and those not familiar with the US in general, the State of Misery, and St. Louis in particular, that the Arch is barely 60 years old.

Thus, when one considers the condition of St. Louis in 1904, one must utterly wipe any image of the Gateway Arch from one's internal visualization of that important Midwestern city.

That year, St. Louis, just over 100 years after the Louisiana Purchase, hosted a World's Fair, formally known as the Louisiana Purchase Exposition.

For other context, consider these historical milestones:

The Wright Brothers' first flight wasn't even a year in the past, having taken place in the middle of December 1903—but the Exposition hosted the first-ever airship competition (see above Wiki link). This led to St. Louis being just as associated with flight as Kitty Hawk, a legacy later immortalized in the name of Lindbergh's famous transatlantic airplane, the Spirit of St. Louis. (Okay, the plane's name had nothing to do

with StL's history regarding flight, and these days, you're taking your life, or at least your sanity, in your hands by flying Spirit across the Atlantic.)

Ford had yet to democratize the automobile, and the hot topic in cities around this time was streetcars. I have no desire (pun absolutely intended) to get into the arguments concerning these modes in this entry, and anyway, San Francisco became more associated with trolleys. This also led to more than a century of pain for philosophy students as they contemplated various permutations of the Trolley Problem.

And then, of course, there were the Olympics.

Apparently, the 1904 Summer Olympics

were meant to be held a bit further north, in Chicago, the first such event to be hosted outside Europe. In typical American fashion, the Expo organizers apparently stomped their feet and shouted, "NO!" So the games were moved to Misery, which, in those days, was kinda hard to get to (remember, airplanes were less than a year old; overland routes sucked, and navigating up the Mississippi takes time).

But, regardless, it turned world attention to the site that used to be a major Native American gathering place (see my April entry, "Things Go Better With Cahokia"

, where, apparently, a lot of people came from all over to participate in social and sporting events.

Some things, it seems, are universal.

At least the Gateway Arch is unique.

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