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Sunday, Jun. 30, 2024

3:06pm EDT

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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:

Kåre Enga in Montana

a day ago
In response to "Je Voyagerai"

I once was allergic to going on a cruise. But... I should... just for the experience. I've gotten out of my comfort zone for experience.

With the crush of tourists these days any travel should include how much you want to put up with "other people's vacation" as opposed to your own.

1 Like

Lazy Writer est 4/24/2008

a day ago
In response to "Je Voyagerai"

Happy traveling..be safe.

Elisa: Middle Aged Stik

a day ago
In response to "It Ain't Wrong"

Ain’t apparently begins as amn’t, a contraction for am not, which you can still hear in Ireland and Scotland today

I mean, an abundant number of Scotch and Irish immigrants ended up in the American South, so this tracks.

While a lot of people consider ain’t improper, it’s a very regular and legitimate part of many forms of English, including in Black English (AAVE). Be mindful that judging someone’s use of ain’t as “wrong” can be a very socially loaded act, to say the least.

For some reason, this reminds of one of the reasons I stopped reading Ask A Manager. A bunch of people were getting real uppity about the use of the phrase "baby daddy". Unsurprisingly, many of these people appeared white. One Black person in the comments finally had enough and threw down with this remark:

"I gotta say, as a black woman it grates to have phrases that come out of AAVE be appropriated, assigned negative connotation (likely because they come from black culture), then discarded with prejudice. If you’re using the phrase to conjure up stereotypical imagery, I can get on board with putting an end to that. But there are plenty of people for whom baby daddy or baby mama are not pejorative at all, just descriptors of the relationship in their dialect, and correcting them to “Father of my child” is just another case of denigrating minority speech patterns and legitimate AAVE grammatical constructions and upholding “white is right” standards."

(For more context, check out this link

1 Like

🌕 HuntersMoon

Jun 28, 2024 at 10:54am
In response to "It Ain't Wrong"

Ain't you on a roll today...

3 Like

Adherennium Dr of Phoolishness

Jun 27, 2024 at 11:53am
In response to "Wave Rider"

Horrifying fact, I once painted a reproduction of the Hokusai wave on our bathroom wall. Eventually of course it was painted over, but I like to fantasise that in some distant future it will be archaeologically excavated and held up as an example of early cultural appropriation, (badly executed too.)

1 Like

Annette

Jun 26, 2024 at 8:16pm
In response to "The Oz Hypothesis"

The nekked wimmin look like something that I might have drawn in first grade.

1 Like

Aiva Raine

Jun 25, 2024 at 10:16pm
In response to "Can't Spell Success without Sucs"

Ok- this made me truly LOL- "sipping a gin and tonic made with low-paid laborer tears"

Thank you. Totally agree with the rest of your article.

Money doesn't solve all problems but it sure as hell eliminates many and makes it easier to go places or buy things that can create some happiness. IE- a property somewhere quiet and peaceful and a trailer with which to chill on said property.

Rich people are typically clueless assholes.

1 Like

Anni Pon

Jun 25, 2024 at 9:30am
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

2 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

Elisa: Middle Aged Stik

Jun 23, 2024 at 9:51am
In response to "Revisited: "Experience""

Not gonna lie I kinda miss Zoom parties, at least for this community since people on WDC are so spread out. Meeting in person is pretty tricky and/or expensive. It's certainly more socializing than I've been doing regularly since, oh, 2022 or so.

As for server migration, well, I work in the IT world. I've been through that. And honestly, server migration is a bit nerve wracking, as some stuff can go missing. It's still more manageable than a complete redesign. Complete redesigns are awful. You can test in different environments that the public can't see till kingdom come, but things always go wrong when the public version is rolled out. A local grocery store recently redid their website, and the old site held thousands of recipes. When the new site was unveiled, none of those recipes made it over. I ended up reaching out on Messenger and was able to get a copy of a recipe I use somewhat often, but I'm kind of annoyed that the text recipes are currently MIA because somehow that data didn't transfer with the site rebuild. Absolute madness.

1 Like

June 6, 2024 at 9:51am

#1072234

Elevator to Heaven

From Wired, some panic about a thing that might not even happen.

What Happens If a Space Elevator Breaks
These structures are a sci-fi solution to the problem of getting objects into orbit without a rocket—but you don’t want to be under one if the cable snaps.

Yes, they're a staple of science fiction, but early concepts for them were thought up way back in the 19th century, before even controlled powered atmospheric flight and way before achievement of space travel.

They're also called Tsiolkovsky towers after the Russian who apparently first conceptualized them. According to Wiki,

other names include "space bridge, star ladder, and orbital lift." Personally, I find all those names descriptive but boring. No, I think it should be called a space lift. Because it rhymes with "face lift," and I find that amusing. Everything should be named in accordance with what I find amusing.

In the first episode of the Foundation series on Apple TV, we see a terrorist try to destroy the space elevator used by the Galactic Empire. This seems like a great chance to talk about the physics of space elevators and to consider what would happen if one exploded.

Not even the prospect of a Foundation series is enough to get me to pay any attention to Apple TV. But the idea, as I said, isn't new, nor is thinking about the security issues surrounding them. If you think about it, the idea of a tower connecting Earth to space will inherently offend a large portion of the population, who will inevitably call it the Tower of Babel, decide that it's against God's will, and actively try to blow it up.

This is why we can't have nice things.

Well, actually, we can't have a space lift because, so far, no one's been able to come up with a material that with the appropriate requirements, or address numerous other issues including powering the thing or shielding any passengers from space radiation. As far as I know.

Anyway, the article mentions that, sort of, but starts out by explaining, in great detail, how a space lift would be an improvement over rockets. This takes up most of the article, and I'm not quoting that part. Only after that does it get into what the headline promised.

In the first episode of Foundation, some people decide to set off explosives that separate the space elevator’s top station from the rest of the cable. The cable falls to the surface of the planet and does some real damage down there.

Again, not the first time this has been considered. I don't remember a scene like that from the Foundation books (by Asimov, whose entire output I devoured as a teen), but it's been a very long time. I do remember Kim Stanley Robinson addressing the issue in his Mars series.

The (over-simplistic, which the author acknowledges) video model in the article aligns with what I recall of Robinson's description.

So not only is building a space elevator very difficult, but you really don’t want the cable to snap and fall.

At this point, though, it's firmly in the realm of speculation, both in science fiction and actual science. The problem may be so tough that we'll actually develop antigravity first, which would negate the need for a space lift. Which is why you don't see many space lifts in Star Trek (budget considerations notwithstanding).

Of course, all of that assumes that a small remnant of humanity doesn't get plunged back into subsistence living before either happens, which I'm not prepared to rule out.

5 Like • Comment

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