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Saturday, May. 4, 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:

Kåre Enga in Montana

about 21 hours ago
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

a day ago
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
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 Montana

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 Montana

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.

December 4, 2021 at 12:01am

#1022750

It's A Conspiracy!

Another Cracked link today (I feel the need to warn people because I've heard reports that the site acts weirdly with some browsers, but I haven't experienced such a thing myself).

Anyway, the topic for today is conspiracy "theories."

8 Questions Internet Bozos Hate To Answer

I put "theories" in quotes because what most people think a theory is, isn't actually a theory. The common definition can be summed up as "guess." The scientific definition is a body of research that holds together and can be used to make predictions. The theory of gravity, for example, is remarkably good at predicting orbits and trajectories. Quantum theory is even more accurate. Neither of these are guesses; they're the result of centuries (gravity) or at least decades (quantum) of study, research, and experimentation.

But for the sake of my failing eyesight, I'll leave off the quotes from now on. We all know what a conspiracy theory is. I just wanted to emphasize that not a single one of them is a true theory in the scientific sense.

Now, I love hearing a good conspiracy theory. Who wouldn't want to hear about a secret Pentagon spaceship piloted exclusively by Sasquatches? (Short answer: they're leaving Earth because humans invented camera phones.)

Why would they do that when they already have the ability to appear horribly blurred in every photo taken of them?

And yet, I have a real problem with conspiracy theorists. For me, it’s sorta like Star Trek: love the stories, can’t stand the fan club.

I get this.

And just like any form of entertainment, I’ve noticed quite a few plot holes, and I have some questions.

Because this is Cracked, get ready for a countdown.

8. “Just … Why?”

Well, let’s throw that question right back at the conspiracy theorists: Why? What reasons do you have to believe these things?

The best scientists are a lot like children (only better educated and slightly less prone to painting the walls with pasta): they never stop asking "Why?" A parent might stop the endless barrage of whys by saying something like, "Because that's just the way it is." Scientists, if they have parents, don't listen to that answer.

Conspiracy theorists, however, have already decided the way things are and try to fit everything else to that.

Accepting the ugly truth might go against their most deep-seated beliefs, so instead they latch on to a comfortable lie.

And I get this, too. I don't think many people are entirely immune to it. For instance, I insist that I'm single because no one has figured out just how awesome I am, instead of me being fat, ugly, and sarcastic.

7. “Is This About You Being Right, Or Do You Just Wanna Make Other People Appear Wrong?”

The further down the internet rabbit hole these people go, the more they uncover supposedly privileged information the infamous “they” don’t want anyone to know about, and that leads them to believe that they now know more than even the world’s foremost experts on the subject. But worse than that, it also makes them cocky enough to pick a fight with everyone they encounter online. And now, we witness the Dunning-Kruger Effect evolving into a Debate-Me-Bro.

One of the core problems resulting from worldwide communication is that it's not as important to stand out in your own community, school, team, whatever -- you are now competing for attention with 7,899,999,999 other people (approximately). People want -- no, need -- to feel special. One way to do this in a crowded world is to decide you've figured out The Answer to something. Usually, you're wrong, but you'll never admit it.

And no, I'm not immune to this fallacy, either.

6. “OK … What Are You Selling?”

There is now a fourth reason conspiracy theories are so prevalent lately: It’s become a hugely profitable business model. The doomsayers used to be relegated to dark web bulletin boards and self-published manifestos, but now many of them have gone mainstream and built their own media empires. If it feels like conspiracy theories are getting crazier every day, it’s because they’re designed that way for a reason. Outrageous, inflammatory rhetoric generates clicks, and clicks boost ad revenue. Then the algorithms kick in and start suggesting similar content. Lather, rinse, repeat, and don’t forget to like, comment, share, subscribe, check out our Patreon, and buy our merch!

Even a cynic like me often falls into the trap of thinking that people are usually sincere with their statements. We forget that, sometimes, people are only sincere about one thing: wanting money.

This is kind of related to #7 above, the "standing out" part.

5. “You’ve Never Been In A Group Project, Have You?”

Every human being is fallible, and if you think you’re an exception to that rule … there’s your flaw. Regardless of your talent, your training, or your confidence, there is always a chance you could mess something up. When multiple people work together, one person’s strengths might balance out some of the others' weaknesses, but everyone involved brings with them their own unique potential to completely screw the pooch. That is true of any group project, be it in a classroom or the workplace, and if the tiniest speck of shit hits the fan, people will hear about it … but that strangely never seems to happen in a conspiracy theory, does it?

This brings up another issue that I don't think the writer covered. It's especially relevant to government conspiracy theories. The same people who are absolutely certain, in their own minds, that the government is capable of engineering vast projects (like, say, faking the moon landing) in near-total secrecy hold, simultaneously, the belief that everyone in the government is absolutely incompetent.

This is the pinnacle of cognitive dissonance.

4. “Couldn’t They Accomplish The Same Goal Without Being So Cartoonishly Evil?”

No one is gonna give a shit unless the stakes are ludicrously high and there are tons of A-list celebrities involved. If you were to tell people that there’s a cabal of Satanic child sex traffickers harvesting their victims’ adrenal glands to make psychedelic drugs, you’d get laughed out of that pitch meeting. But if you say Tom Hanks and Oprah Winfrey are attached to the project, that will get you some press.

That’s why theories like QAnon make no damn sense. They wouldn’t have to go to that much trouble. If Oprah really was a Satanist, she wouldn’t need to hide it. She could just select The Necronomicon for her book club, and two weeks later soccer moms everywhere would be sacrificing virgins.

I wrote a short story a while back about the scary influence Oprah has (or at least had; I don't keep up with that stuff). This is not a conspiracy theory; this is based on observational evidence. So yeah, drop in a celebrity or two and your idiotic ideas get spread around more widely.

3. “Does That Technology Even Exist?”

One of the weirdest tropes in conspiracy theories is when they involve the use of outrageous technology that even Roland Emmerich would think is lazy writing, and that guy’s next movie is about the moon falling.

I think that movie's already out by now. I wouldn't know. It's just about the stupidest thing involving the moon since the fake landing conspiracy theory. Speaking of which, the technology needed to fake that shit in 1969 would have been way more expensive and difficult to achieve than actually, you know, sending dudes to the moon. Not to mention the number of people involved; see above.

2. “How Do You Make A Peanut Butter And Jelly Sandwich?”

... actually, I'm afraid you're going to have to go to the link to read this one. It will make sense, I promise.

1. “What Happens If You’re Right?”

The one thing that all great conspiracy theories have in common is they all seem to be perpetually stuck in the middle act of the movie. The bad guys and their motivations have been established. We sorta have an idea of the magnitude of the threat we’re facing. If the story even has a hero, they're really not doing a great job saving the day so far. But let’s just assume the theories are correct and cut straight to the climactic showdown. Who do you think is gonna win?

Also this. Taking the government conspiracy theories as an example, if you're right and they're secretly engaging in mind-control, what exactly do you think is going to happen? Hell, if you're right, and you're spreading such a conspiracy, you've already disappeared, quietly, and they've put a robot or clone in your place to walk back the shit you said.

As the old saying goes, perhaps the greatest conspiracy is there is no conspiracy.

That said, there have definitely been conspiracies. Like Tuskegee

or the Roswell Incident

- which was a cover-up, though not for space aliens but for secret US technology. So yes, sometimes there really is a conspiracy.

But that doesn't mean that your pet theory holds any water.

Or maybe -- just maybe -- They seed these conspiracy theories themselves to hide the real truth, which is that we're being farmed by lizard people from Hollow Earth. If you throw enough falsehoods out there, the truth will be concealed like a wolf wearing wool..

4 Like • Comment • View 3 comments

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