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Wednesday, Dec. 18, 2024

12:39am EST

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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:

Aiva Raine

about 5 hours ago
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

about 6 hours ago
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

about 15 hours ago
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

about 16 hours ago
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

tj-Merry Mischief Maker

a day ago
In response to "Fork You Too"

Now that I know forks are the center of dining controversy, I'll have to apply this at all family gatherings where demon dining utensils are in use.

1 Like

tj-Merry Mischief Maker

Dec 15, 2024 at 1:06pm
In response to "Revisited: "Those Naughty Brits""

I don't think there's such a thing as kinky sex anymore. Why? Based on the general definition, kinky sex refers to sexual activities and preferences that fall outside standard sexual practices. Nowadays it seems anything goes and there are no norms or standards.

Oh, another thing; do you remember if the link had pictures? Asking for a friend.

1 Like

Wordsmitty ✍️

Dec 15, 2024 at 12:45pm
In response to "Revisited: "Those Naughty Brits""

Waltz Invictus - As they say, you're a more proper man than I. I may even check out the other links with those key words.

2 Like

Waltz Invictus

Dec 15, 2024 at 12:32pm
In response to "Revisited: "Those Naughty Brits""

Thanks for that, Wordsmitty ✍️

. Sometimes I make the effort to find an article from a dead link. This time, I did not.

1 Like

Wordsmitty ✍️

Dec 15, 2024 at 12:29pm
In response to "Revisited: "Those Naughty Brits""

I think we're all glad that society has advanced so far in a decade and a half. Which way is up to you.

For those interested, there's a "Search" option in the Times main page. Page 6 of the results comes up with this link: https://www.thetimes.com/article/4d5f3e63-22c9-45c0-837b-c3ad9d236ae8

2 Like

Elisa: Snowman Stik

Dec 15, 2024 at 9:35am
In response to "Revisited: "Those Naughty Brits""

Damn, another entry that has me wanting to jump in and offer tons of commentary! Let's have at it.

2008 Me: Journalism may not be dead yet, but it's starting to wander and stink.

Dead now. Mostly.

Clearly I need to highlight more non-profit outlets in my link rundowns. I'm finding lots of good reporting on that front. Perhaps I also need to add more examples of this to "Watch This Space!"

[18+]. Even 60 Minutes is still able to provide some good in the weeds reporting. Point is, journalism is struggling, but good reporting is still out there. I'm doing my damnedest to shine a light on the solid examples. I could use a bit more help in the process.

2008 Me: What happened to investigative journalism? Hell, what happened to comprehensive news stories?

Gods, 2008 Me was so young and naïve.

They still exist. Strangely, I have found that at least in my area the local stations actually put some of their most comprehensive stories online. Also, at least the NBC affiliate has a post-local news show that does more comprehensive reporting. Some pieces are fluffy, but others are not. They are more locally focused, but that's probably a good thing these days. Local news has struggled the most, and we're paying the price for that.

2008 Me: Why is this in the "women" section? Men don't want to read about kinky sex? Please.

I'm guessing men are less likely to consider it kinky, outrageous, or naughty. But what the fuck do I know (pun intended)?

Strangely, this seems almost prudish by British standards, especially in light of the fact that Time magazine reported on BDSM in one of its print issues four years prior. And as we know, Time magazine isn't exactly known for sectioning off its content by gender. The Time coverage did include a photo taken in a BDSM dungeon that wasn't too explicit but really captured the D/s component really well. Honestly, I'd expect a UK publication to do that before a US one, not the other way around.

That said, I suspect the articles may have been written for slightly different audiences. If the audience is primarily women, there is likely to be more implicit shame in the picture, as women have been historically more likely to be primed to be ashamed about their sexuality in any capacity. Don't get me wrong. I know men are also subjected to this shaming. However, it tends to be less persistent and less pervasive in terms of different facets being shamed. In a general audience, the shame element can be downplayed. In a women-focused audience, you have to address the shame angle in some capacity, reassuring them that this isn't such a bad thing. This isn't something I'm directly involved in, but given the lack of women on WDC willing to write about this sort of thing these days, I might have to take one exploring this concept in depth. Ladies, if you're thinking about writing something (journal entry, static item, whatever) about this topic, this is your sign to go ahead and do it!

These days, I have preconceived ideas about headline questions: First, if it's a yes/no question, the answer is probably "no."

Snopes is ready to challenge that assumption.

2 Like

November 15, 2024 at 10:20am

#1079986

That's the Spirit

We all know I'm not religious. I'm also not spiritual, unless by "spirit" one means "distilled beverage." The closest I get is when I listen to music. But, of course, it has to be good music—which has nothing to do with whether it was created with religion in mind or not. So here's a Cracked article about songs you might not have realized were religious (and, somehow, Leonard Cohen isn't on the list).

4 Famous Songs That Are Secretly Religious
This was supposed to be a pop song. We didn’t know it was about Mormons

For example, you might realize the band you’re listening to is named “Creed,” and the song is talking about going “higher, to a place where blind men see.” Clearly, this about heaven. And yet the band actually insists they are not religious, as they’re not trying to preach anything to anyone.

Songs (and other works of art) can be religious without being preachy. However: 1) A band naming itself "Creed" and claiming to not be religious sets off my bullshit detectors; 2) regardless of their inspiration, they suck. I like to change the lyrics of their most famous song to "With Legs Wide Open."

Or, you might hear that 1960s classic “Spirit in the Sky” and note the lyric, “Gotta have a friend in Jesus.” You then might conclude it’s a Christian song. Singer-songwriter Norman Greenbaum is actually Jewish, but penning that song was a smart move.

Insert Jewish joke about "business is business" here.

4 Imagine Dragons’ ‘Radioactive’ Is About Leaving Mormonism

If you were told that one of Imagine Dragons’ songs is religious, maybe you’d go with “Believer,” because it talks about being a believer. Maybe you’d go with “Demons” because it talks about demons. Maybe you’d go with “Thunder” because that one’s so terrible that only divine intervention can explain its success.

Okay, that's funny. But... who?

The band formed at Brigham Young University, and when you go on to leave the Church of Latter-day Saints, the memory of your time there stays with you. We know for sure that one song of theirs is about that subject: “Radioactive.”

Yeah, so, kind of the opposite of religious, I guess? Hell if I know. I didn't watch the video they embedded in the article, so I still don't think I've ever heard any of their stuff.

3 Simon and Garfunkel’s ‘Cecilia’ Is St. Cecilia

The idea that “Cecilia” is a song directed at a saint sounds absurd.

Yeah, it kind of does, especially since Paul Simon and Art Garfunkel are in the same tribe as Norman Greenbaum. But hey, Simon said it, and while he may have been trolling, it kind of works on a metaphorical level.

It doesn't help that the song is probably the duo's least awesome.

2 ‘Dem Bones’ Is a Spiritual About the Promised Land

Unlike the others, this isn't a relatively recent pop song, but, as the article notes, an older gospel tune. Which means it's not "secretly" religious at all, but I guess there's a secularized version for broader appeal.

Today, the song is most important during Halloween, because it gets children talking about spooky skeletons. That’s fine. When you get down to it, Halloween is the holiest night of the year.

And technically, anything involving an afterlife has religious connotations.

1 ‘The Star-Spangled Banner’ Is About the Greek Pantheon

This is the one I saved this article for, even though the header is misleading. "The Star-Spangled Banner" is the name of Key's poem, which, as we all know, was set to an existing tune.

If you’re a fan of trivia, you might already know that this melody came from a British drinking song.

What's weird to me is, I've known this for decades, but I never could be arsed to find out exactly what the drinking song was. Well, now I know...

The song is about a bunch of Greek gods arguing with each other. When the poet Anacreon urges humanity to drink and screw, the god Jupiter gets angry and considers intervening. Apollo disagrees, claiming Jupiter's mighty thunderbolts are nothing against the power of music.

And whaddaya know; Apollo was right.

The United States may not have been founded as a religious country, but if you ever feel the need to pledge allegiance to one nation under God, feel free to specify which god that it is.

Why, Dionysus, of course.

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