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.

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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.

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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.

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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.

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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').

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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.

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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

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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.

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February 8, 2023 at 12:02am

#1044434

Watch It Wiggle

I feel like this article was commissioned by Jell-O Corporation. Or, you know, whoever makes that stuff. (Googles) Oh, Kraft. Yeah, they have deep pockets, but they also have lots of other products that are actually good.

Jelly Is Ready for Its Redemption Arc
The polarizing format is due for a come-up, according to Ken Albala’s new book, “The Great Gelatin Revival”

"Jelly" is one of those words that has more than one meaning in American English. They're not talking about the fruit preserves, but the gelatin product made from cow feet. While this is popularly known as Jell-O, that remains a trademark, like Kleenex or Coke.

“I predict that we are on the threshold of a new aspic-forward aesthetic,” writes the food historian and University of the Pacific professor Ken Albala in The Great Gelatin Revival, out January 10 from University of Illinois Press.

Maybe that should be "food historian, University of the Pacific professor, and paid Kraft shill..."

By the way, this article is from last month, so that book is still new.

No doubt, aspics — those vintage delicacies studded with vegetables and congealed meats — remain niche, but jelly? Jelly is having a moment.

"Moment" is probably all it is.

Moving beyond the aesthetic, Epicurious and the New York Times attempted to actually put jellies back on holiday tables, and grown-up Jell-O shots constituted one of last year’s biggest drink trends, according to Punch.

Who decides this crap? Why isn't it me?

That said, Jell-O shots are for college kids who haven't developed a taste for fine liquor yet. There's nothing inherently wrong with that—I started out doing embarrassing shit, too—but, ultimately, it's a phase.

“Periods that embrace the jiggle are always followed by periods of disgust sometimes so intense and visceral that entire generations lose the skill to make them,” Albala writes.

You'd think we'd learn, but no, we're incapable of that.

Jelly—this kind—is forever associated with hospital rooms and nursing homes, as far as I'm concerned.

I sat down with Albala over Zoom to talk about why jelly is on the come-up, and why more of us might reconsider all things jiggly.

As you might expect, the rest of this article is an interview transcript. I won't reproduce most of it here; it's at the link if you're interested. There's just one part of one response that made me save this for sharing, because I found the perspective interesting:

I think that we’re beginning to look at the problems in the world, environmental ones especially, and look to science to solve those. The fact of an Impossible Burger — and lab-grown meat is going to happen very soon — I think is an indication that people have other priorities now and they’re really not as distrustful of science as they used to be, or that tech-forward food is something that that doesn’t really bug this next generation of people.

Eating animal collagen is one of those things that usually aligns with periods in history that are very science-forward and very trustful of science; there are other periods that are not. You think of the late ’60s-early ’70s, and the hippie generation — that’s when Jell-O begins to take its precipitous downfall, because people don’t want artificial colors and flavors. I predict that because of the way things have gone for the past 20 years, that we’re going to be back in a period that is not just pro-science and pro-artificially made food, but I think Jell-O is going to come back too, in a weird way.

I only wish he was right. He wrote the book before the pandemic, apparently, and those years showed us that, far from being more trusting of science, a large number of people don't understand it or care for it at all. And it's not one-sided, politically; you also get people distrusting of GMOs, to the point where "GMO-free" is actually a marketing gimmick for food manufacturers. (Here in reality, GMO products aren't evil; they're the only way we're going to be able to feed the teeming masses in the future.)

One shouldn't be blindly trusting of science, though. Especially food science. But the link between science acceptance and trends toward more lab-created foods would be interesting—if it exists. Right now, it's apparently just his observation.

Now, none of this should be construed as me telling you what not to like. I find jelly relatively inoffensive, myself, except for weird-ass aspics. I even used flavorless gelatin in a dessert recently—a lemon chiffon thing that turned out okay. And I gotta admit, the potential for alcoholic Jell-O is intriguing to me (the stuff beyond Jell-O shots, some of which is featured at that link). This is more about me hating "trends."

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