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Wednesday, Dec. 18, 2024

1:44am 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 6 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 7 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 16 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 17 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

December 8, 2024 at 9:27am

#1080931

Revisited: "Millennials Killed Millennials"

It's time for another foray into the jungles of the past. This one comes from way back in 2018—Christmas Eve, to be exact: "Millennials Killed Millennials"

The entry featured an article from The Atlantic; this was before I started using xlink tags for articles, so it's a raw URL link. That source has changed its policy since then, and every time I open it now, I hit a paywall.

I'm not above paying to read or watch something. I have a few subscriptions. But even I can't subscribe to (or keep up with) everything and, more importantly, I try not to link paywalled articles here (as I said, that entry from 2018 was from before they installed a paywall).

Point is, unless you subscribe to The Atlantic or have found some way around the paywall that even I haven't been able to figure out, you're only going to get the first few paragraphs of the original story. Oh, sure, it talks about "subscribe" and "free trial," but I'm deeply suspicious of any "free trial."

You'd think they'd lift that restriction for older articles, but apparently not.

Not ragging on them, by the way. They should be able to make money if their content is useful. I used to link a bunch of their stuff, and I'm not judging anyone who subscribes. I'm just explaining why 1) I don't feature Atlantic articles anymore and 2) today's entry is more about my earlier entry than it is about the original article.

Having said that, let's look at what I was thinking six years ago this month.

The entire concept of demographic "generations" annoys the shit out of me. And it only gets worse as time goes on and I read more crap like this.

I've since moderated my feelings about that topic. As with most other things, it's not binary; I'm not obliged to either love it or hate it, with nothing in between. My stance on the practice is complicated, but I'll try to explain my current thoughts:

1. Yes, the "generation" labels are pretty arbitrary. So are Gregorian calendar months, but it's an established system that has its uses.

2. In this system, I'm early Generation X, which hardly anyone ever talks about, opting instead to rag on "boomers" or "millennials" or "Gen-Z." Or praise them, depending on the author's beliefs and age.

2a. Gen-X is supposed to be, among other things, the slacker generation. Am I a slacker because I was born under the Slacker sign, and therefore it's expected of me; or is it just my basic nature?

3. It's one thing to draw conclusions about a subgroup and market to that subgroup. It's quite another to point at a single individual from that subgroup and simply assume that they have all the traits associated with that subgroup. I don't really have a problem with the former, at least not anymore.

There's more, but I'm not writing a dissertation, here; what I'm really trying to say is that my own views have shifted over the years.

On top of which, you'd have to convince me that our 1983-born X-er has more in common with someone born in 1966 than with someone born in 1986.

That is something that no one has been able to convince me of, yet. Some people have tried to get around it by slicing generations more finely; you get, like, the "Oregon Trail generation," which of course refers to the classic "you have died of dysentery" computer game and not actual westward-ho pioneers. But all that does is support my point: slice finely enough, and you're back to taking each person individually, rendering the whole marketing concept more useless.

Also, some things suck and other things get better. This is due not to a single "generation" or cadre of ages, but every single person doing his or her own thing.

I'm not sure exactly what I was thinking when I wrote that, but I recognize it's probably unclear. Much of what sets "generations" apart, in modern terms, has to do with technological advancements and societal changes, all of which require more than one person. Like, someone had to invent Crocs, sure, but also, someone had to be convinced that they're not ugly and to start wearing them. And then other people had to think that the original wearer was cool enough to start a fashion trend.

I'm pretty sure the whole "generations" thing is just another way to divide us, like politics or countries. It distracts us from the real issues, which we can either work to solve, or ignore, depending on one's individual preference.

Again, my hardline stance on that has evolved, though I still have a measure of distrust. These days, for instance, the popular usage of "boomer" and "millennial" doesn't comport with their marketing definitions; a "boomer" is simply someone older than you whose attitude you don't like; and a "millennial" is someone younger than you whose attitude you don't like. This is one reason Gen-X gets ignored (but don't worry; we're used to it).

But it is marketing. Not science.

So you know what I want to see Millennials finally kill?

Generations.

This harks back to the original article, which was apparently about the Millennial generation killing off cultural institutions beloved by Boomers. Never mind that these same Boomers killed off cultural institutions beloved by their parents' generation.

Anyway. Changed perspective or not, that entry's still there, even if accessing its linked article remains a pain in the ass. But, to borrow the rallying cry of my generation: "Whatever."

5 Like • Comment • View 2 comments

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