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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 13 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 18 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 18 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

a day ago
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

August 26, 2024 at 10:30am

#1075731

Literally the Opposite

Today, we have a bit of linguistic education from that well-respected teaching site, Cracked:

5 Words That Switched Meaning Because Everyone Used Them Wrong
‘Entitlement’ now means you don’t deserve something, which is absurd

There are way more than five, but we have to take tiny attention spans into account, here.

Some words mean two things that are complete opposites. “Cleave,” for example, can mean both splitting something apart or joining two things together.

This is known as a contronym, and I've discussed them before: "Contronyms"

. But that was almost five years ago, and today's bit isn't exactly about contronyms.

5. ‘Steep Learning Curve’

And already, we step out of theme: that's a phrase, not a word.

A steep learning curve indicates a process that’s easy to learn, with production rates rapidly increasing over time. With a shallow curve, on the other hand, rates increase more slowly, indicating a process that’s harder to learn.

Though, as the article so helpfully points out, a lot depends on how you define your graph's axes.

Ask me, it's probably best to do as they suggest and stay away from "learning curve," especially since that borders on corpspeak.

4. ‘Mystery Box’

If you’re a normal person, you may go your whole life without hearing about mystery box storytelling. If you’re a nerd, however, you know the term well. Mystery box storytelling is when a series lures you in by dangling a bunch of mysteries, mysteries to which the writers themselves do not yet know the answers.

Well, I'm a nerd, and I think I know a few things about writing, but I'd never heard that particular phrase. (Again... phrase, not word.)

The name “mystery box” comes from a TED talk that J.J. Abrams gave in 2008, initially inspired by people asking him what the island in Lost is.

The real mystery box here is how one director can fuck up so many different franchise movies, while still continuing to get hired as a director.

If I were inclined toward conspiracy theories, I'd say Paramount (the owner of Star Trek) hired him as a double agent to ruin Star Wars for Disney.

It’s a bit odd, though, to call them mystery box shows after Abrams’ choice of theme for one TED talk. Because he used the box to talk about so many different concepts, and because mystery boxes are an actual thing, with one specific mystery: What’s inside, and is it worth the price you paid?

But the point here isn't to slam Abrams as a director (I liked a lot of his stuff, just not all of it); it's to show how the phrase got to be misused, and for that, there's lots more background in the article.

3. ‘Entitlement’

Hey, look! A single word, unattached to others!

An entitlement is something you’re entitled to. That’s what it means. That’s how nouns work.

In the U.S., federal benefits programs are called “entitlements,” based on the assumption that recipients are entitled to them. Some of these programs, like Social Security, are contributory, which means you personally paid into them. Others, like nutrition assistance, are non-contributory, paid from the government’s discretionary budget, but by calling them “entitlements,” the government is still saying recipients are entitled to them.

This has bugged me for years: people calling contractual or legal obligations "entitlements" like it's a bad thing.

We’ve now reached the point when advocates for entitlements argue it’s insulting to refer to these programs as entitlements:

Shit, I've been there for at least a decade. Maybe longer. Maybe less. My relationship with duration (durationship?) can be tenuous.

2. ‘Low Man on the Totem Pole’

And we're back to phrases.

You probably think the “low man on the totem pole” is the most junior person in an organization. They have not ascended very far, and they lack power. But have you considered what sort of person would manage to be the bottom figure in a human totem pole? They would need to be strong enough to support everyone else.

Well, workers *are* the most important people in an organization.

In a totem pole, the bottom figure isn’t some peon being squashed by the important figure on top. They’re the figure in the pole who’s been carved with the most detail, and they may also be the biggest.

Eh, I avoid the phrase anyway, for cultural reasons. But now I'll never see it in the same way again.

1. A Special Note on ‘Literally’

Oh, hell, I'm going to hate this part.

The dictionary now notes that the word has a second definition, which essentially means “not literally,” and this inclusion attracted a lot of controversy online around a decade ago.

"The dictionary" (misleading, as there are several entities competing in that space) is descriptive, not prescriptive, at least the English ones. It pretty much has to base its definitions on how people are using words... even when that usage is objectively wrong, as with emphatic uses of "literally" or any use of "decimate" to mean something other than "remove one-tenth of."

Literally doesn’t serve here as a synonym for figuratively, a disclaimer clarifying that they’re joking. It serves as emphasis. In fact, it emphasizes their statement by declaring it’s literal. You know it’s not literal (again, from context), but they’re telling you it is, and therein lies the sentence’s humor.

Okay, so, by framing it as comedy, you're moving me to your side. Waltz's Second Law states: "Never let the facts get in the way of a good joke. Or a bad one. Especially a bad one."

So, people generally don’t use “literally” as a synonym for “figuratively.” But they used to.

Go through classic novels from a century or two ago, and you’ll find many authors doing so.

Huh... okay.

Despite the criticisms that young people misuse “literally,” using it as a replacement for “figuratively,” doing so now comes across as a very formal or outdated way of speaking. The word did change meaning, but it reversed in the opposite way to what people think, becoming more literal.

And there it is, folks: proof that I can be persuaded, given enough evidence. And comedy.

3 Like • Comment • View 2 comments

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