Complex Numbers (Book)

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Complex Numbers

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/

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Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

July 20, 2023 at 9:30am

#1052836

Mountains out of Mouse-hills

No streak lasts forever, so today's article comes from Rolling Stone:

How ‘Disney Adults’ Became the Most Hated Group on the Internet
“People were saying Disney fans are a plague upon society," says one expert. "That they will be the end of Western civilization”

Most hated group? Really? I thought that was predators of children. Or maybe aficionados of that abomination they call "pizza" in Chicagoland.

Article is about 13 months old, though, so anything might have changed since then.

By all reasonable definitions and standards, I am a Disney Adult. I have seen all of the movies multiple times, and enjoy most of them at least a little bit.

"Enjoy most of them at least a little bit" is damning with faint praise.

The author goes on to build her (I looked up the bio, so that pronoun is correct) Disney bona-fides. I can't relate—I've seen quite a few of the movies, myself, and liked them, but I haven't been to a park in 40 years, nor do I have any intention or desire to do so. But I still don't hate her.

On the internet, however, being a Disney adult is nothing short of an embarrassment. A Disney adult is someone who lives and breathes the brand, buying limited-edition mouse ears and popcorn buckets and branded fitness trackers the moment they drop, constantly posting free advertisements for the park in the form of Cinderella’s Castle and Purple Wall selfies (so named for the violently mauve wall in Tomorrowland) whilst wearing rose-gold mouse ears.

"Strong dislike" is building after this bit, however.

At no time was this distaste drawn into sharper relief than earlier this month, when a post on Reddit’s Am I the Asshole forum went massively viral. The post, which was reportedly written by a bride who had opted to pay for Mickey and Minnie to appear at her wedding rather than feed her guests, was, like most things on Reddit, anonymously written and poorly sourced.

As a reminder, that would be last June. Before Reddit imploded. But from what I've seen, my default for AITA posts is "they're making shit up." Which is fine; hell, I'm a fiction writer sometimes, myself.

“People were saying Disney fans are a plague upon society, that they will be the end of Western civilization,” says Jodi Eichler-Levine, a professor of religious studies at Lehigh University who studies the intersection of Disney and religion.

I'm just going to pause here a moment to absorb the new knowledge that there is at least one actual PhD professor who "studies the intersection of Disney and religion."

Oh hey, look, a bird is divebombing one of my cats. She probably deserves it.

Okay, now, where was I?

Oh, yeah.

Disney is a business that sells products and experiences to consumers. So are most religions. So I guess that's fair.

Is this accurate? Do Disney adults truly signal the end of Western civilization?

No. For fuck's sake, are you so far up the Mouse's ass that you don't recognize hyperbole when you see it?

To find out, and to learn where the concept of the “Disney adult” comes from in the first place, I talked to a slew of academics, internet culture and fandom experts, and, yes, Disney adults.

The article is fairly long, and I'm not going to waste a lot of your time repeating it. Just a few choice quotes.

On its most basic level, it strikes outsiders as deeply embarrassing to throw oneself into a subculture ostensibly aimed at children — despite the fact that the Disney parks, as Walt Disney first conceived of them, were very much intended for people of all ages.

The problem with "for all ages" is that it leaves out quite a bit of the full human experience. Sex, for example, or violence past a certain level. Cussing. Having to pay taxes. But I understand that some people would rather pretend these things don't exist, or at least gain respite from them.

Adding an extra layer of repulsion to outsiders, Disney adults’ ability to escape into this fantasy is almost entirely dependent on their ability to afford it.

Ever since I got berated for wanting to waste money gambling by a guy who had a literal, actual monkey (that he paid money for) on his back, I've shied away from judging people by how they spend their money. If it's not Disney, it's sports, or luxury travel, or hitching a ride on a rocket that technically reaches space. Though I do admit to some residual judgment of people for spending money they don't have, even that isn't always their fault.

As early as the 1990s, coverage of Disney’s fairy-tale weddings programs prompted plenty of sarcastic headlines about why grown people would want to get married in the vicinity of a cartoon mouse.

Look, it's not for me, sure. Marriage or cartoon mice. But hey, these days, if you want, say, a Jedi wedding, that makes you a Disney fan too. Just saying. And where people choose to get married is their business, not ours.

“There’s a real moralistic judgment of Disney adults,” she says. “It’s like, ‘How dare you, instead of putting all this money into buying a house or raising a family, put [it] into fleeting experiences?’ But that probably corresponds with changing cultural expectations for young adults.”

How DARE you not live according to my preset life script?

But this has, ironically, led most people to conceive of Disney adults as female and to bring their accompanying stereotypes along with it, even though the fandom is pretty evenly split gender-wise.

I could probably write a thesis to conclude from this that mocking of Disney adults comes down to anti-feminism and sexism, but I'm already banging on long enough, and it really should be obvious.

But we do have the male-dominated equivalent, which is comic book fandom. Yes, there are women in that group, too, but if you picture someone with a love for the superhero genre, it's probably a big, bearded guy. Me, e.g.

And of course, now there's overlap there too, as one of the big superhero publishers is owned by Disney.

“There was a lot of judgment on women who participated in that kind of activity. It was like, ‘Oh, you’re enjoying this fun thing that I consider childish? I’m going to make fun of you.'”

How DARE you have fun when there's serious shit going on, and you should be bringing children into a doomed world instead?

[Eichler-Levine] refers to the fandom as “a place where meaning and ritual and capitalism all come together, just like MLB, just like Star Trek. Name your fandom.”

Just like I've been saying, and I don't need a PhD to recognize that.

On a related note, sports fans long ago lost the right to complain about the rest of us dressing up and putting on body paint, etc., to celebrate the things we enjoy.

I am not, and never have been, a person for whom joy really comes in consistent supply. But at Disney, it’s nothing less than an IV in my arm. Even the meticulous planning of the daily schedule gives me more of a sense of satisfaction than I feel in my everyday life. And considering how hard joy is for me to come by, I feel no need to apologize for that.

And you shouldn't. "Stop liking what I don't like" is a meme for a reason. No, you're not ushering in the end of civilization; capitalism in general is doing a damn fine job of that. Until it happens, though... enjoy the ride.

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