Complex Numbers (Book)

Blog Calendar

◄ June ► 2023
S	M	T	W	T	F	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30
Archive				RSS

About This Author

Contact Me

Come closer.

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/

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:

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

June 22, 2023 at 10:19am

#1051447

Art History

For a city whose very name is synonymous with "joke," Cleveland has had an outsize influence on pop culture. Rock and roll, for example, was named there, and the city is home to that Hall of Fame. Science fiction icon Harlan Ellison was born there.

And then there were these dudes.

How Two Jewish Kids in 1930s Cleveland Altered the Course of American Pop Culture
On Jerry Siegel, Joe Shuster, and the Birth of Superman

So. LitHub isn't all about highbrow art. Good to know.

In a small attic bedroom in Cleveland, in the Jewish neighborhood of Glenville, Jerry Siegel tried to sleep. It wasn’t the summer heat that was keeping him awake nor his snoring older brother Leo snoozing noisily beside him. Twisting and turning, Jerry had a new idea for a story in his head.

Because when I think of Cleveland, I think about how hot it gets in the summer. But this was before A/C, I suppose.

Jerry, a nerd with glasses, had had few friends at Glenville High—ignored not just by the girls but the boys, too.

Starting to sound familiar.

Thanks to magazines, like Amazing Stories, that Harry brought home, Jerry discovered a new genre called science fiction.

Point of order: Science fiction was already over 100 years old at that point. But, okay, the pulps really made it explode into American consciousness, for better and for worse.

Science fiction magazines would change Jerry’s life—though not for the better.

Just as generations of parents would warn their children.

One of his favorite books, Gladiator, told the tale of a man with superhuman strength who could run faster than a train and jump higher than a house. Another favorite character was Doc Savage, a pulp magazine hero whose first name was Clark and who was known as “The Man of Bronze.”

I've heard that Stan Lee considered Doc Savage a kind of forerunner to comic book superheroes. That adventure genre is still around, and still a huge force in movies and TV.

While LitHub here follows the New Yorker School of Not Getting to the Fucking Point, eventually, they get to the point:

Now, on that summer night when he couldn’t sleep, Jerry, twenty-one and unemployed, finally got up, put on his glasses, slipped into the bathroom so as not to wake his brother, and started writing. He went back to bed, then threw off the covers after a couple of hours and wrote some more. By dawn, he had a complete script. He got dressed and, story in hand, took the porch steps at a gallop.

I don't know how historically accurate this really incredibly long opening anecdote is, but it does track with what I know about the writing process.

Huffing and puffing, Jerry arrived at the dilapidated two-story Maple Apartments that Joe and the Shuster family called home. “Joe, you gotta draw this,” he said, waking him up, thrusting the script beneath his blinking eyes.

Parallels to Archimedes? Really?

The first drawing of Joe’s that Jerry saw was one that Joe had saved from 1928, inspired by the new Fritz Lang movie Metropolis, which had blown both of their young, nerdy minds. The movie’s lesson—the worker being kept down by the demented, greedy capitalist—was perhaps lost on them, though it was a harbinger of things to come.

In case you were wondering if Superman's Metropolis had any connection to the eponymous movie.

The pair took inspiration from a new art form called comic books, particularly the ones that editor Max Gaines started putting together in 1933, repackaging previously published Sunday comic strips into a separate booklet with a colorful cover and saddle stitches. Funnies on Parade and Famous Funnies were given away as a promotion to buyers of Procter & Gamble products, who had to clip coupons and mail them in for a copy. The newly packaged funnies proved so popular that Gaines decided to sell them for ten cents apiece.

It can be confusing, I think, to refer to the superhero genre as "comic books," when not all of them are what we think of as "comic." This origin story might help.

Jerry suggested Joe put an S on Superman’s chest—not just for Superman’s name, but for Shuster and Siegel—and a cape on his back that would whip around, one of the few ways for Joe to show dramatic motion.

And this, in case you were wondering why the cape became such a standard thing in superhero comics. It would be over sixty years before "No capes!" became a catchphrase in a superhero movie. Why would you need a cape to demonstrate action in a movie?

Superman would be an alien with super strength whose real name was Kal-El (“Voice of God” in Hebrew). Kal-El came to Earth as an abandoned baby, much like Moses in the Old Testament, just as his planet, Krypton, was destroyed. Like Jerry, his father would die while he was still young. Kal-El would be adopted by a couple of Gentiles and renamed Clark Kent, a name Jerry took from Clark Gable and B-movie actor Kent Taylor. By day, Superman was a mild-mannered goy with glasses ( just like Jerry’s and Joe’s). He would live, naturally, in a city called Metropolis.

Most telling, I think, isn't the specific cultural origins of Superman, but that he was an immigrant.

There's a lot more at the article, of course. And whatever you think of the character—appropriately, he's had his ups and downs over the years—it's not often that we get to see the origin story of an entirely new literary genre.

Famously, Siegel and Shuster got boned while their creation became a worldwide phenomenon. But in the end, as is usually the case, the nerds came out the winners.

5 Like • Comment • View 3 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.