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Monday, Jan. 6, 2025

3:48pm EST

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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:

Wordsmitty ✍️

about 3 hours ago
In response to "Business or Pleasure?"

Bleisure with frolleagues. Sounds like kinky porn.

"Nichols, who travels frequently for work, said bleisure is a great way to get the most out of his business travel." and "He still uses all of his vacation days and views bleisure as a "supplement."" - So "b-word" really means taking advantage of your company for extra days and paid expenses, and hoping you don't get caught and fired. Just going out after your business is done each day is one thing. Extending days at the company's expense is another.

1 Like

tj in a winter wonderland

a day ago
In response to "Giant Red Flag"

My thoughts were, purchase a bundle of the little red flags they stick in the ground for construction markers and just hand some out to everyone I meet.

2 Like

Leger~

Jan 4, 2025 at 12:00pm
In response to "Giant Red Flag"

Pic of the t-shirt on you or it didn't happen.

3 Like

🌖 HuntersMoon

Jan 4, 2025 at 9:44am
In response to "Giant Red Flag"

Elisa: Snowman Stik - Now, let's talk about procrastination...

2 Like

Elisa: Snowman Stik

Jan 4, 2025 at 8:19am
In response to "Giant Red Flag"

Don't worry (or worry). I'll be offering my perspective on this link this year, likely March or April.

2 Like

tj in a winter wonderland

Jan 3, 2025 at 3:09pm
In response to "The Year in the Sky"

It all sounds very interesting and hopefully I will be able to keep an eye on the sky and see some of these. It seems more often than not, it's overcast, or has been for past celestial events. I did, however, get a chance to view the Northern Lights around four this morning. The sky cleared sometime during the night and Max, my Husky woke me up to go out and we enjoyed a few minutes of a spectacular light show.

3 Like

Robert Waltz

Jan 3, 2025 at 11:00am
In response to "The Year in the Sky"

🌖 HuntersMoon

, depends on definition. Astronomically, it's a moon. Astrologically, it (along with the Sun) is a planet. Anyway, I read that to be "planetary parade plus Moon," but we can chalk it up to Lifehacker being misleading again.

2 Like

🌖 HuntersMoon

Jan 3, 2025 at 10:52am
In response to "The Year in the Sky"

Regarding the "planetary parade." The moon isn't a planet. It's a moon.

2 Like

Elisa: Snowman Stik

Jan 3, 2025 at 10:46am
In response to "Marguments"

Oddly enough, this entry rolled out the day the squid and I visited Kennedy Space Center. There was actually a Nars rover model we saw with an interesting note on the information plaque: Not funded by taxpayers dollars.

Ultimately, I feel like while the issue of science communication has seen some improvement, a new problem is emerging. Many communicators have not shown an inclination to have public dialogues with groups who question why we're doing things like going back to the moon. There's been no validation of these concerns by science communicators, which is in my opinion not a good look. And lest you think it's a certain demographic with these objections, well, that's a bias that deserves a re-examination thanks to this piece: https://www.cnn.com/2024/01/05/world/peregrine-moon-mission-navajo-nation-object... remains-scn/index.html .

1 Like

tj in a winter wonderland

Jan 2, 2025 at 4:12pm
In response to "Neutral Zone"

I don't tend to think of myself as optimistic or pessimistic, although I do share some of both qualities; I'm realistic.

1 Like

January 4, 2025 at 8:13am

#1081935

Giant Red Flag

The article I'm featuring today is old in internet terms: nearly six years. It only popped up on my radar recently, and I have to admit, when I saw the headline, my knee-jerk reaction was close to rage.

Men Have No Friends and Women Bear the Burden
Toxic masculinity—and the persistent idea that feelings are a "female thing"—has left a generation of straight men stranded on emotionally-stunted island, unable to forge intimate relationships with other men. It's women who are paying the price.

I guess "rage" is one of the emotions we're allowed to feel. In this case, it was mainly for two reasons: the overgeneralized headline and subhead; and how a "man" problem is turned around to be a "woman" problem.

Then I remembered that the target audience for Harper's Bazaar is chicks, and my rage subsided somewhat. The goal, I figured, wasn't to fix men, but to commiserate with women.

Which brought my rage back to a simmer.

But okay. Okay. Being a man and all, I choked back all emotion, as we must always do or face social ridicule, and tried to give the article a fair chance.

Kylie-Anne Kelly can’t remember the exact moment she became her boyfriend’s one and only, his what would I do without you, but she does remember neglecting her own needs to the point of hospitalization.

Starting an article with an anecdote is a time-tested way of grabbing a reader's attention. That's fine. What I have an issue with is that, coming as it does immediately after that headline, it makes it sound like Kylie-Anne's problem (and it is, obviously, her problem, not that of her nameless and ultimately irrelevant boyfriend) is just an ordinary relationship scenario, ho-hum, this is what we're all facing, isn't it, girls? Can't you relate?

Kelly’s boyfriend refused to talk to other men or a therapist about his feelings, so he’d often get into “funks,” picking pointless fights when something was bothering him.

I don't mean to sidestep the issue or pretend that this sort of thing isn't a problem. It absolutely is, and it's one reason I don't conform to that version of masculinity. But, and I'll just point this out and leave it here, this guy had a girlfriend and I don't. So, clearly, it works, at least at first.

After three years together, when exhaustion and anxiety landed her in the hospital and her boyfriend claimed he was “too busy” to visit, they broke up.

I've been considering getting a t-shirt with a giant waving red flag on it to wear in public. That way I can skip the small talk and have people avoid me before starting a conversation that reveals whatever internal red flags I project. Saves time and energy that way.

Kelly’s story, though extreme, is a common example of modern American relationships.

Oh, now they admit it's extreme.

Women continue to bear the burden of men’s emotional lives, and why wouldn’t they? For generations, men have been taught to reject traits like gentleness and sensitivity, leaving them without the tools to deal with internalized anger and frustration.

Hey, look at that sneaky use of the passive voice! I suppose the implication is that men are taught exclusively and only by other men: fathers, uncles, brothers, male peers.

Meanwhile, the female savior trope continues to be romanticized on the silver screen (thanks Disney!), making it seem totally normal—even ideal—to find the man within the beast.

Yeah, you know, if it didn't resonate with viewers, they wouldn't keep depicting it. The Mouse has many faults, but this looks to me like another dodging of responsibility. They also, classically, depicted male heroes saving helpless damsels in distress, but that trope, at least, seems to be fading, or at least morphing, because people demand that women save themselves, instead.

Incidentally, though, I do sometimes wonder about a gender-swapped Beauty and the Beast. I'm nowhere near good enough to write something like that, and besides, if I can think of it, it's already been done.

The article continues to describe the problem, and, I'll grant, it's not unjustified. After a while, it finally names an actual man:

So Shepherd turned to the internet, downloaded a men’s group manual, and invited a few guy friends who he knew would be receptive. He capped the membership at eight and set up a structure with very clear boundaries; the most important being what’s talked about in men’s group stays in men’s group.

I'm not saying it's a bad idea by itself. But are we sure that downloading instructions from some site on the internet is really the way to go? At that point, you might as well use the movie Fight Club as an instructional guide. Not to rag on that film; it's still one of my favorites. But it's fiction.

Lots more at the link. My gender-role-approved rage has settled down to a dull feeling of numbness, which is also gender-role-approved. Now to order that giant red flag T-shirt.

6 Like • Comment • View 4 comments

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