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Wednesday, Dec. 11, 2024

6:40pm 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:

Wordsmitty ✍️

about 6 hours ago
In response to "On the Label"

"June 25, 2024 5:40 AM" = Need time zone.

"Note to self:" = self-driving taxis

Some people definitely can be labeled, but we don't say those in polite company.

2 Like

Annette

about 6 hours ago
In response to "On the Label"

Only one label matters. Cat person or dog person. If the answer is anything except "yes" the person's life choices defy all logic analysis.

I wonder what is the difference between psychotherapist, psychologist, and psychoanalysis. Or are they like po-ta-to, po-tuh-two?

3 Like

tj-Merry Mischief Maker

Dec 9, 2024 at 2:51pm
In response to "Analog Log"

As time progresses, it amazes me how we have moved from tide clocks/analog computers to people eating tide-pods.

1 Like

Aiva Raine

Dec 9, 2024 at 2:37pm
In response to "Story of the Century"

Fantastic entry. Have I mentioned how I love your snark? Thanks once again for the grins and your awesome sarcastic responses to the articles.

1 Like

Anni Pon

Dec 8, 2024 at 10:01am
In response to "Revisited: "Millennials Killed Millennials""

It's kind of funny to me that people still use "millennials" to refer to "those darn kids" when most of them are in their 30's now with kids of their own. As an elder millennial (a Xennial, if you will), I haven't really found the generational definitions too useful for myself. I'm right on the border of generations, so I have a lot in common with both Millennials and Gen X. Growing up in silicon valley with tech savvy parents, I had earlier access to computers and technology than a lot of other people my age. But in terms of cultural milestones, I lived through and am old enough to remember things like the 90's, Y2K and 9/11. The borders are sort of arbitrary, but on a population level I can see how sometimes it can be useful to group people into generations.

2 Like

Elisa: Snowman Stik

Dec 8, 2024 at 9:40am
In response to "Revisited: "Millennials Killed Millennials""

*rubs hands together* Time for me to dive right in!

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.

Looks like I need to change my name to "hardly anyone". Also, there has been more and more chatter about Gen X in some circles, but curiously this seems to be happening in institutions that have dropped labels (which I'll touch on in a second here).

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.

Very, very, VERY few organizations that have ever in their history used generational labels have set the Gen-X border any later than 1980. While I'm still very salty that Pew stopped this practice (one of the few things they've done wrong, IMO), I still use their Gen-X demarcation of 1965-1980. That demarcation nicely strikes the median of most demarcations. SO in this case it's not a matter of you needing to be convinced. It's a matter of the author leaning on a REALLY bad source.

Much of what sets "generations" apart, in modern terms, has to do with technological advancements and societal changes...then other people had to think that the original wearer was cool enough to start a fashion trend.

And how that message has been conveyed has drastically changed among generations, to boot.

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

Generations.

As a Millennial, I can tell you that this is probably the last thing our generation will try to kill. It's something that's persisting even as we reach middle age. And that's another thing. We're aging very strangely, namely that physically we're aging more slowly than people in Gen Z. We could have killed the concept of aging a certain way, but Gen Z's circumstances have effectively torpedoed that revolution.

Also, if anyone wants to read the original article, you can certainly try throwing the URL in the Wayback Machine. It doesn't always work, but it's worth a try. There are some other methods as well, but I haven't tried them myself yet. (Speaking of which, has anyone here tried Zette? I've been meaning to sign up for that but haven't had a chance. It's one of my goals for 2025.)

2 Like

Wordsmitty ✍️

Dec 7, 2024 at 12:41pm
In response to "Story of the Century"

Maybe it helps if you can dance - Dick Van Dyke and Coldplay - although he's just 99. (I assume everyone has read about that)

4 Like

🌖 HuntersMoon

Dec 6, 2024 at 10:07am
In response to "No Space for Time"

I think you just added clarity to the Twilight Zone...

3 Like

tj-Merry Mischief Maker

Dec 5, 2024 at 4:05pm
In response to "How To Give A Fock"

How many photons does it take to make a torpedo? Who gives a Fock! Actually, wasn't Fock Spock's half brother?

3 Like

Jayne

Dec 5, 2024 at 10:23am
In response to "How To Give A Fock"

Versatile Fock States is the name of my next thrash album.

3 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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