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Thursday, Nov. 21, 2024

3:14pm EST

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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:

Robert Waltz

a day ago
In response to "Powers of Three"

🌕 HuntersMoon

- that's pretty much what quantum computing is, from what I've read.

2 Like

Brandiwyn🎶

a day ago
In response to "Losing Weight Is Easy"

Wordsmitty ✍️

1 Like

🌕 HuntersMoon

a day ago
In response to "Powers of Three"

With binary, it's either on or off. Wouldn't ternary introduce Schodenger's Cat? On, off, or both?

2 Like

Turkey DrumStik

a day ago
In response to "Paramount Purpose"

I suspect old web filter attempts

would have combusted when confronted with this article.

1 Like

tj-turkey-jobble-jobble-hard-J

a day ago
In response to "Losing Weight Is Easy"

Some of them break out in hives if you ask them to add 10% to something.

Yesterday I purchased an item that cost $6.42 after tax was affixed by the register. I handed the cashier a ten dollar bill and watched as she placed it in the cash register, which like most now days, showed her how much change to return. She had to try three times to count out the proper amount, and as I was leaving commented to the bagger, "Why do people have to pay with cash, don't they know how hard it makes my job?"

I didn't say anything, but was trying desperately not to break out in hysterical laughter.

1 Like

🌕 HuntersMoon

Nov 19, 2024 at 9:28am
In response to "Paramount Purpose"

At your age, Bob, take heart in the fact that it can be restored...

2 Like

Wordsmitty ✍️

Nov 18, 2024 at 12:34pm
In response to "Losing Weight Is Easy"

This brings up the old question of whether your weight changes when you inhale a helium balloon to make your voice higher.

Maybe this has to do with the difference of a mug of beer vs a tankard of ale.

The universe has so many weighty/massive questions.

3 Like

Brandiwyn🎶

Nov 18, 2024 at 11:27am
In response to "That's the Spirit"

Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success. Wow. Missed opportunity, here. How could you let this go without a shoutout to mighty Thor, son of the Allfather, wielder of Mjolnir, He with the Long Forehead? (Said in the voice of the Soup Nazi): "No Valhalla for YOU!"

Brandiwyn🎶

Nov 18, 2024 at 11:19am
In response to "Losing Weight Is Easy"

Has anyone ever told you how annoyingly pedantic you are?

Damn your pedantic ways. I was hoping to justify a vacation to Venus (which I still argue would be a much better holiday destination than fr-fr-freezing Mars, Elon. Ugh.) Now I guess I'll have to settle for the Cancun plans we already made, since my mass (and waist diameter, and thigh diameter) will be exactly the same regardless.

3 Like

tj-turkey-jobble-jobble-hard-J

Nov 17, 2024 at 4:04pm
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

November 12, 2024 at 8:41am

#1079840

Blond Man's Bluff

Sometimes, I link to Cracked for its take on serious topics. Sometimes, though, it's because of jokes.

The Funniest Blonde Jokes Ever Told

Historical blonde jokes aren’t as well-documented as other classics, like fart jokes, for example.

Fart jokes may be "classic" (the oldest recorded joke is one of them), but they are the lowest form of humor, unlike highbrow amusements such as dead-baby jokes.

The people who study this type of thing tend to agree that they’re just lazily recycled versions of older jokes, that replace racism and xenophobia with sexism.

Yeah, not exactly a step up.

But the genre does have some notable subversions!

The thing about subversion is you need to be familiar with the thing that's being subverted, and hardly anyone tells blonde jokes anymore, so some people might not get the twists.

5 ‘The First Officially Recorded Dumb Blonde’

This is included for historical context.

Catherine-Rosalie Gerard Duthé was a French nun, ballet dancer and courtesan in the late 18th and early 19th centuries.

We should be concentrating on French jokes, not dumb blonde jokes.

She had a particularly notable habit of “pausing for extended periods of time before speaking.” Some might call this act “thinking,” but the French decided this made her dumber than a beret full of baguettes.

One wonders whether this contributed directly to the French Revolution.

4 Meta Blonde Jokes

You know how a blonde joke works. A brunette, a redhead and a blonde do something, the blonde does it wrong, because she’s dumb and incapable, the patriarchy grows stronger.

Worth going to the link just for the joke here.

3 The Counter-Revolution

A notable, though flawed, early ally was cartoonist Murat Bernard Young, who drew two extremely popular comic strips. Dumb Dora was about a space cadet brunette, while Blondie was about a smart, capable mother whose husband was the bumbling, glassy-eyed doofus.

The "bumbling, glassy-eyed doofus" trope continues to this day (Homer Simpson, e.g.), but apparently, it's okay to make men look stupid.

2 Existentialist Blonde Jokes

The New Yorker’s “Existentialist Blonde Jokes,” written by Alex Baia back in 2021, subverts some of the most tired blonde jokes out there...

I rag on The New Yorker on a regular basis, because it's pretentious as fuck, but one thing it's usually gotten right is comedy. I'll just copy one of the jokes here:

How do you drown a blonde?

Remind her that life is inane, repetitive and intrinsically meaningless.

1 Blonde Jokes for Men

Ever wonder about the difference between blonde and blond? It's not like gray/grey, which is largely a difference in US and UK/Commonwealth English. It's because "blond(e)" is French, so it possesses grammatical gender. Women are blonde; men are blond. It's one of those few words we stole from French that kept its inflections, like fiancé/fiancée.

Anyway, like I said, there's no need to specify the man's hair color. Many of us don't have any, anyway, and we're all stupid and bumbling, regardless of coiffure.

1 Like • Comment • View 1 comment

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