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Friday, Nov. 15, 2024

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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:

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

April 17, 2022 at 12:12am

#1030863

Waisted

Another entry for "Journalistic Intentions"

[18+]:

Fashion Waste

When I was a little kid, homonyms confused me.

I suspect I'm not alone in this, though I learned to read earlier than most, so I got them straightened out quickly enough. However, this might explain my unfortunate (for other people) predilection for punning.

One confusion that I remember in particular was when my mother was explaining where a person's waist was. I had already picked up on the idea that the belly was where digestion happened, after which whatever was left over came out as poo -- and like most toddlers, Kid Me found poo hilarious.

Point being, it took me a while before I understood the difference between "waist" and "waste."

I mention this because one of the key measurements for a lot of clothing is the waist size, so this particular prompt brought back the memory of my younger self's confusion. Pants, for example, start out with a waist and end up as waste.

Another thing that fascinated Kid Me -- a few years later -- was science fiction. I particularly enjoyed seeing what authors thought would happen in the future. Nowadays, periodically I'll see an article about "what science fiction authors got right/wrong about the future." But those miss the point. Science fiction doesn't make predictions; it comes up with ideas. The only way it could be a "prediction" would be if the writer buried his or her prediction under a rock or whatever without telling anyone what it was, and then, however many years later, someone dug it up and went, "Oh, that's laughable," or "Wow, that's pretty close to whatever happened."

As it is, that kind of science fiction exists in a kind of Platonic realm of ideas. In order for something -- a chair, a computer, a starship, whatever -- to become part of consensus reality, first someone has to think of the concept, the idea. You don't have to be a science fiction writer to come up with it, but SF writers do it a lot. Once that idea is out there, though, other humans who didn't think of it in the first place can then consider ways that it might become reality. And so you go from having handheld flip-top communicators on Star Trek in the 1960s to having flip phones in the 1990s. Sure, it's possible someone would have come up with those eventually without Star Trek, but the point is that Trek neither invented an actual communicator nor predicted its development, but provided the idea that would eventually become the flip phone. Which led to one of the most amusing meta-jokes ever made on TV, when William Shatner's character in Boston Legal flipped a phone open and it emitted the distinctive communicator chirp.

A less well-known example is that Robert Heinlein conceived of the waterbed before anyone ever built one of the suckers.

What's less common in science fiction is introducing a possible technology for the future, and then having that technology go away, the way flip phones and waterbeds did. Or how we never did go back to the Moon (though I'm aware that plans are in the works).

All of which is to say that one trope in the science fiction of my youth was how wonderful disposable clothing would be. Buy a cheap suit, wear it once, discard it.

Yeah... that sounds like a great idea to those of us living in the future, doesn't it? So. Much. Waist.

And yet, people are doing it.

It's nothing new for high-society people to wear an outfit once and only once. In some circles, to be seen wearing the same dress more than once is considered vulgar. But they're not necessarily the problem; I mean, those are some rarefied social circumstances. No, the problem is when the rest of us unwashed masses do it, too. And even then, as with so many other things, putting the blame, or even the responsibility, on the individual misses the mark.

Now, me, I get an article of clothing and I wear it until it starts to fall apart. Other people go even further and do things the old-fashioned way, sewing and applying patches and whatnot. But I've only ever followed "fashion" so that I can mock it. And, going back to that long-ago time when I was a kid, when some article of clothing wore out past the point of repair, my parents would attach it to a mop or otherwise use it as a cleaning rag.

Come to think of it, I don't remember what they did with clothes I'd outgrown. I didn't have a little brother to hand them off to. Now, I guess I'll never know.

What to do about the problem of fashion waste, I don't know. People are going to buy cheap shit if it's available. There's not a goddamn thing we can do as individuals that would do more than scratch the surface of the larger issue. Sure, if enough people scratched the surface, it would eventually fall apart, but that's not going to happen because people see "oooh, five dollar pants" and buy the shit out of them instead of investing in a long-lasting $75 pair.

The latter of which would certainly have a sturdier waist.

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