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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 13 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

about 17 hours 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

a day ago
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.

August 14, 2021 at 12:01am

#1015611

Acoustic Annoyances

When I was a kid, I was one of those hated assholes who scritched his fingernails down the classroom chalkboard.

Which Sounds Are the Most Annoying to Humans?

I think all the schools have gone to dry-erase whiteboards now, which is a shame, because the occasional squeak of a marker on those surfaces just doesn't have the same effect, and entire generations no longer know the joy of the ear-piercing screech of keratin on slate.

Earlier this month, a kind of chirping, rainforest-y sound sprung up in my apartment. It came from my roommate’s room.

Lame. I once bought one of those Annoy-A-Trons from the late, great ThinkGeek website, and hid it in my office. It drove my business partner up the wall. Well, for a few minutes, anyway; that's how long it took for me to break down in uncontrollable laughter.

For anyone who doesn't know, the Annoy-A-Tron, formerly the Mind Molester, was a little battery-powered device that, every three minutes or so, emits a beep in the exact wavelength that renders the sound's origin impossible to locate by human ears. Someone somewhere might still have something like that for sale; I don't know, because I'm not about to prank my housemate with it. That could lead to retaliation, and pranks are, by definition, only funny when they're not played on me.

This is all to say that, when we are speaking about sounds, “annoying” is a subjective criteria. But there must be, one figures, some consensus on the subject. For this week’s Giz Asks we reached out to a number of sound-experts to find out what that might be.

"Criteria" is plural. The singular is "criterion." Since we're talking about shit that annoys me.

But before I go on, let me take a stab at the sounds most annoying to humans, apart from the aforementioned fingernails on the blackboard or Annoy-A-Tron.

Amplifier feedback.

"I want to speak to your manager."

A pothole on the interstate near my house, which, when it's run over, produces a thump-the-bump noise.

The drip of water from a leak in your roof.

The neighbor's goddamn night-owl of a mutt.

A phone's Amber Alert notification (which is one reason I have Amber Alerts turned off).

That muscle car from the 70s with a 2-stroke engine and defective muffler that cruises the nearby streets.

Any alarm that wakes me up.

For some reason, every house in my neighborhood has to get its lawn mowed successively. So by the time one annoying lawnmower is done, another has started up.

Okay, let's see what the article has to say.

The sound of vomiting: elicits a visceral response.

Huh. I never noticed. Usually it's me doing the vomiting, though.

The article goes on to explain, from an evolutionary perspective, why that sound is annoying. It's fairly interesting, but I suspect there's a lot of speculation.

Pretty much all the other sounds are sounds that are relevant to higher cognition. So the scraping of fingernails on the chalkboard probably also has a visceral component, but it’s much further away from our basic responses than vomiting.

At least they don't make up an evolutionary psychology reason for that one.

A baby crying does not make sense for all mammals; it only makes sense for mammals that have babies that actually cry.

Ah, yes, the "baby crying" entry, which I forgot above. Because I avoid that as much as possible. One time I was in an airport, and a baby was crying, and there was also a cat yowling in a carrier. A baby's cry supposedly makes an adult human want to comfort it. Not me. I want to get as far away from it as possible. The cat, though, I felt sorry for and I wanted to take it out and pet it.

In general, though, the most annoying sounds are those that get in the way of whatever you’re trying to do.

That's very general. But fair.

The most annoying sound for a human, as we all know, is the sound of chalkboard scraping. It’s terrible! Precisely why that is so remains a bit of a mystery and—I kid you not—the subject of ongoing psychoacoustic research.

If you look at the article, these are from several different experts, hence the repeats. But yeah, there's another vote for the anachronistic chalkboard thing.

This particular answer goes on to describe music -- how what's pleasing to one person can be rage-inducing in another.

And to summarize the final entry: early heart-valve replacements. Yeah, that would mess me right up. You're trying to sleep and your ticker just keeps ticking... and ticking... and ticking...

It's been a while since I've done a Merit Badge Mini-Contest. I was going to do my one-sentence review of Free Guy tonight, but that can wait; let's give out a Merit Badge.

Merit Badge Mini-Contest!!!

You knew this was coming: what sound do YOU find most annoying? Apart from fingernails on a chalkboard; that's been done to death already. I'll pick an answer (preferably one that also annoys me) and send that person a Merit Badge tomorrow (Sunday). Deadline, as usual, is midnight WDC time at the end of today, Saturday, August 14.

6 Like • Comment • View 18 comments

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