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Tuesday, Apr. 30, 2024

4:57am EDT

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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

about 15 hours 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

a day ago
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

a day ago
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

September 28, 2021 at 12:01am

#1018177

To Sleep, Perchance To Demon

Today's science article, courtesy of a dick joke site:

Dealing With The Demon of Sleep Paralysis

Yeah, I know I've written about sleep paralysis in here before. I have to experience it, but the only way I can share the misery is to write about it. You're welcome.

Ever wonder what the sensation of dying in your sleep might be like?

Nope. Don't have to wonder.

Oh, and with an obscure presence by your side? And what if this figure resembled one of your fears?

An eye surgeon? Nope, haven't had that one yet.

A physical feeling of entrapment, sleep paralysis is a troubling sensation that one may experience while waking or falling asleep.

It's a "troubling sensation" the way a hydrogen bomb is an explosion.

Usually accompanied by hallucinations, you may see disquieting images as your mind is active while your body remains asleep.

"Hallucinations," also known as "the same shit that happens during dreaming." Also, seeing is only part of it. You get to hear it, too. Footsteps approaching the bed. Someone calling your name in anguish. A dog barking. Which wouldn't be so bad if I had a dog, which I don't.

What is known is that while dreaming, the mind is at rest and the body's muscles relax as a means of not harming itself in case you dream about snapping your pinkies in half to see what'll happen.

Thanks, I really needed that image.

I think -- but I don't have any data to back this up -- that sleep paralysis is the other side of the sleepwalking coin. In the former case, your mind disengages your body while you sleep, but that can continue into a mental waking state. In the latter case, the clutch mechanism, as it were, engages, so your body moves while your mind's checked out. Either way, shit's not working right.

When the paralysis creeps in, it causes a disruption in our REM cycle and awakens the mind while the body remains confined in a paralyzed state (cue the horror music). You'll want to scream but can barely contort your face, and no one would hear you.

And that might be the worst part of all. The instinct is to call out for help, but you can't even manage a whisper, let alone a scream. You might as well have been shoved out an airlock into the void.

For example, "you might mistake your cat sleeping at the foot of the bed as some sort of goblin," and as ridiculous as it sounds, it's the truth.

Actually, the cat is a comforting presence for me. But I can imagine this happening to someone more ambivalent about our feline overlords.

The scariest of hallucinations is referred to as the "intruder" and is just what it sounds like, a sensation of an intrusive figure at your side. Mainly, it has been reported that this sense manifests itself as "the sounds of doorknobs opening, shuffling footsteps … a shadow man."

It's worse when it's a shadow ex-wife. That's happened. The author also describes tarantulas. I haven't had those, but other bugs have invaded this mental state.

(Yes, I know arachnids aren't technically bugs.)

In my experience with sleep paralysis, it's a lovely thing to sense a presence of danger as you lay there, frozen helplessly in the dark. You don't have a darn clue what to do because you can't do anything. One theoretically cause is unbalanced sleeping patterns, so the best advice to treat it seems to be: Get more damn sleep.

Yeah, I don't know. It's happened to me when I was chronically sleep-deprived, and it still sometimes happens to me when I get enough to be well-rested. In my experience, the only thing that makes it subside is... exercise.

Sometimes that's worse than the nightmares. At least with sleep paralysis, I end up with story ideas.

Mini-Contest Results!

Thanks for all the comments! Some of those I was familiar with, others not so much.

Warped Sanity, that's one I hadn't heard of, but now I want to check it out. The thing about science fiction is that it's not a stand-alone genre; it always has some other angle: often action/adventure, sometimes mystery or, as this one seems to be, horror.

ForeverDreamer, I read A Clockwork Orange at a very impressionable young age, and a lot of it stuck with me. I also enjoyed (well... appreciated) the Kubrick movie.

Kåre Enga in Udon Thani, I never quite got into Pern. Probably I could attempt it again; it's been a very long time and I think a lot of it was beyond my childhood mind (which, as I noted above, was warped by A Clockwork Orange and other stories).

WakeUpAndLive️~🚬🚭2024, a lot of people really liked The Matrix. I had just been learning about historical Gnosticism when it came out, though, and through the movie I was like "this is just techno-gnosticism." Beautiful effects, and I do like Reeves as an actor, but especially afterwards, when people started to take seriously the whole "what if we're living in a simulation?" nonsense, I went from "meh" to "bleh" on it. Personal opinion of course, and I definitely understand why people liked it.

Cubby~Cheering House Florent!, oddly, I read the novel before I saw the movie, and at the risk of being a cliché, as ForeverDreamer noted, the book was better. In the book, Lastday was at the age of 21, not 30, for starters, and the scope is far grander. Then I made the mistake of reading the sequels, but that's another story...

Prosperous Snow celebrating, I can't argue with Star Trek. It's far from perfect, and the screenplays vary greatly in quality, but overall I think it's been a positive cultural influence. I do also like Star Wars; I see no need to choose between them, either.

Lazy Writer est 4/24/2008, I always meant to read The Handmaid's Tale and never got around to it. I know it's been adapted now, but it's on Hulu, and I won't deal with that site. Eventually, I will read the book.

A lot of these comments were compelling; like I said, I'm not picking the winner based on agreement. This day's Merit Badge will go to Warped Sanity for mentioning a book I haven't even heard of and explaining exactly why it's worth reading.

I'll do this again, so there will be more chances at an MB. Next month.

7 Like • Comment • View 5 comments

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