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Saturday, Apr. 27, 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:

Elisa the Bunny Stik

about 3 hours ago
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

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

October 23, 2021 at 12:01am

#1019922

Birth of a Spaceship

The headline may be a bit misleading, but as a movie fan, I find this stuff fascinating. Also because it's Cracked, it's funny.

How A Jammed Camera Helped Create All Of Science-Fiction

Like I said, the title's misleading -- science fiction predates movies by nearly a hundred years. I suppose "helped create science fiction movies" would be more accurate.

The movie camera was the internet of its day. As in, it was touted as this great technical achievement that would revolutionize science and usher in a new era of progress and enlightenment. But, instead, people almost immediately started using it to make dirty movies and goof around.

Someone has probably enshrined this into a law already, but it seems to me that the first thing anyone does with any new technology is figure out how to make porn with, or of, it.

Hence the old observation that the holodeck will be humankind's last invention.

Born in the mid-19th century, Méliès was an illusionist who wanted to use the camera to film plays and his magic acts.

Turns out magic acts don't translate well to recorded media, for the simple reason that it's too easy for cameras to do tricks, and audiences will think it's all film effects. This is why magic acts are usually filmed in front of studio audiences.

Then one day, a weird thing happened. When filming scenes of city life, Méliès’ camera jammed. It took him a few seconds to fix, and when he later developed the film, he noticed that he accidentally invented the jump cut/stop trick. While the camera was malfunctioning, the scenery around the amateur filmmaker continued to change, none of which was being captured on film until Méliès started rolling again. And because the angle and position of the camera didn’t change, the resulting film seemed to show objects disappearing, a man turning into a woman, or a carriage turning into a hearse, etc.

While it's inevitable that someone would have thought of this sort of thing eventually, accidents can absolutely drive invention.

Méliès immediately realized he had stumbled onto something big, and he continued to experiment with other camera tricks until he was ready to put them all into a short film: A Trip to the Moon.

That's the one with the space capsule in the man in the moon's eye. Yeah, you know the one. It's iconic, and for a reason. Go to the original article; the video is embedded there, so I won't reproduce it again here.

Released in 1902, it was heavily influenced by the writings of Jules Verne and depicted the thing from the title. It also employed “every trick had learned or invented” to create what some consider the first science-fiction movie ever.

It is my unshakable opinion that the first science fiction book was Frankenstein. Whether this movie was the first SF movie or not, I'm not as sure of. But like I said, it's iconic.

And great job, Méliès, since A Trip to the Moon apparently convinced the world that movies could be full of fantastical scenes, flights of imagination, and, eventually, pants-shitting horror. Seriously, watching some of those old-timey movies feels like snorting bath salts off a heavily decomposed clown corpse dressed in your mother’s wedding gown.

Just leaving this here so I'm sure you read that imagery.

The point is, Méliès ushered in an era of fantasy and sci-fi movies, which officially ended in 2015 when Mila Kunis said out loud that she wanted to bone the half-human half-dog Channing Tatum in Jupiter Ascending.

Come on now, Jupiter Ascending wasn't that bad. I mean, it was bad, but it certainly didn't end SF movies. Hell, Dune just came out. I'm not seeing it until Sunday. Which reminds me, I keep forgetting to do a review of the movie I saw earlier this week (which was definitely not science fiction for once), so now's as good a time as any.

One-Sentence Movie Review: The Last Duel

I keep going back to Ridley Scott movies in the vain hope that at some point, one of them will come close to the greatness that is Blade Runner: The Director's Cut; this hope is inevitably dashed, but The Last Duel, unlike some of his other historical fiction movies, doesn't completely suck -- it's longer than it needs to be; Matt Damon has already been in France once before this year; and Kylo Ren has already gratuitously taken his shirt off approximately 143 times, but the acting is superb and the movie is surprisingly topical for modern audiences despite being set in medieval France (which the director doesn't let you forget even though everyone speaks American English, because you keep seeing shots of Notre Dame de Paris under construction).

Rating: 3.5/5

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