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Wednesday, May. 1, 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:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

November 13, 2018 at 1:20am

#945463

Excelsior!

If you do what you really want to do, you feel like you're playing. - Stan Lee (1922-2018)

Stanley Martin Lieber wanted to save his real name for literature, so when he got started writing the supposedly lowbrow stories for which he'd later become famous, he used the pseudonym we've all come to know well.

As I've said before, I've always hated the term "genre fiction," and I never use it. It's intended, I think, to distinguish fantasy, science fiction, horror, supernatural and other stories from "literature." But all stories have a genre - some, more than one. I noticed that yesterday's science fiction, fantasy, etc. become today's literature - Mary Shelley, Poe, Twain, Stoker, Verne, Wells, Burroughs, etc., and I saw no need to wait for time to pass so that others could appreciate fiction with otherworldly elements the way that I did.

When I was a kid, I tried reading comics, and I tried reading The New Yorker. The former stuck. The latter... well, I figured when I got older, I might understand and appreciate that magazine's post-modernist, rambling, allusion-laden, snobbish style.

I never did.

I did like the cartoons, though.

Comics are a strange blend of genres - so much so that they have become a genre of their own. From the outset, which for the sake of argument I'll place at the first publication of DC's Action Comics 80 years ago, they have always blended science fiction and fantasy. I've mentioned in this space and in newsletter editorials that I have problems with stories that get the science wrong. Boy, do comics get the science wrong - but the best of them are internally consistent; hence the fantasy aspect.

They are, you might say, modern fantasy; or, as I prefer, modern mythology, the stories of those with powers far beyond those of ordinary men and women. Gods, in a sense - gods who walk among us. Or fly. Or teleport. Or run really, really fast.

Even those comic book heroes without identifiable powers have honed their skills in ways that make them greater, but whether human, alien, mutant, or irradiated, most of them share one trait: the desire to do good, even if the heroes themselves are just as flawed as we - or their creators, writers, and artists - are.

They urge us to become the best that we can be.

Apparently, for me, the best that I can be includes an abiding love of comics: in their original words-and-pictures format, in their TV and movie adaptations, in books, in behind-the-scenes interviews. I guess you can call me a fanboy, even if I've never dressed up as Spider-Man or gone to a comics convention (I have been to general F&SF conventions, but none of the big Comic-Cons).

These past 10 years or so - the time since Marvel's Iron Man first exploded onto the big screen - have seen a renaissance of comics adaptations. Some people are tired of that. I get it - it's not everyone's vial of super-serum. Comics movies were made before 2008, though, and will continue to be made until they're no longer making money for the studios, which probably won't be anytime soon. Personally, I'm tired of rom-coms, but my solution to that is to simply not go see them. Problem solved.

I can say with some certainty that if it weren't for comics, I wouldn't have had the urge to write, or to appreciate science (even if the latter was out of the curiosity to see just how bad they did science). I wouldn't be the person that I am.

I never did get a taste for The New Yorker's snobbery, but look at this:

https://www.newyorker.com/news/daily-comment/black-panther-and-the-invention-of-...

That's an article in the most snobbily literary of art-snob magazines post-modernistically deconstructing a movie based on a comic book character co-created by Stan Lee - and unabashedly praising the film.

And the man - The Man, as he was known - lived long enough to see his "lowbrow" life's work join the ranks of literary fiction in being analyzed, scrutinized and reviewed by that magazine, and in a positive manner at that.

So if you're wondering why so many people are reminiscing on this one guy's life today, well, it's because he's one of the people who actually changed the world for the better, inspiring millions of people and adding to the world's body of great literature.

Not bad for a pulp fiction writer.

(Note: I'm probably going to crib heavily from this entry for next week's Fantasy newsletter, so if that editorial seems familiar, that's why.)

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