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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.

February 17, 2019 at 12:28am

#952190

Lone Asshole Theory

https://thewalrus.ca/where-not-to-travel-in-2019-or-ever/

“My name is John!” shouted John Allen Chau from his kayak in November 2018 as he paddled toward strangers on the beach of North Sentinel Island in the Bay of Bengal. “I love you and Jesus loves you!” In response, the people on the remote Indian island strung arrows in their bows.

Yeah, I heard about this asshat when it happened. Got what he deserved.

Unfazed by the genocidal threat his germs posed and fresh out of missionary boot camp, Chau made repeated attempts to land—ignoring arrows and Indian law—in an effort to bring the Gospel to the Sentinelese.

"I know better than anyone else; the only law that applies to me is God's Law; and I'm doing The Right Thing!" Lord, save us from your followers.

Media coverage of Chau’s acts was disturbing because it didn’t come off as coverage of a crime—at least, not of his crime. Other major news outlets similarly valorized Chau’s legally and morally corrupt foray, highlighting his conviction as if tone-deaf temerity were a quality to admire.

Yeah, that bugged me at the time, too.

So, basically, his act of trespassing was lauded by exactly the same kind of people who are perfectly happy to put up "Trespassers will be shot" signs and point shotguns at census workers. Yeah, that's consistent.

As someone who has been called an adventurer before, I feel more of a sense of kinship with the person on Twitter who suggested this fix for the Times headline: “Remote Community Faces Biological Terror Threat From U.S. Religious Extremist Killed by Local Authorities.” To extol or glamorize any aspect of what Chau did risks condoning a brand of colonialism that should be anachronistic by now, and not just among missionaries. In fact, Chau’s evangelism is too easy a target, and it’s one that eclipses his more fundamental transgression.

Pretty much this - though there's no way to know if the Sentinelese would have been aware of the bioterror threat he represented.

This sort of thing puts me in mind of Star Trek. Okay, bear with me here.

I seriously doubt we live in a Star Trek - type universe, with sentient alien races around every other star. The evidence just isn't there to support that idea. In fact, it's possible that we're the only intelligent life in the galaxy (not the universe, of course, but the galaxy). And before you start with the "no intelligent life" jokes, I'm using the term in the sense of "technologically advanced enough as a species to go into space." We meet that definition. We know of no other species that does. Also, I'm not saying that life isn't out there; just that there's absolutely no law that says intelligence (that definition, again) must evolve in an ecosystem, and that the circumstances that allow it might be exceedingly rare. Like, 1 in 10^100 rare.

Okay, I digress, but it's important to my point. Suppose I'm wrong. Unlike that missionary dickwad, I can allow for the possibility. How do we keep from fucking up first contact?

Star Trek proposed a sort of legalized, formalized ethical framework in the form of the Prime Directive. You know it, I'm sure, but basically it's "don't mess with pre-warp cultures." Various starship captains then proceeded to find reasons to bend or break it, but that's not important right now; what's important is that it's codified ethics. I have my issues with it as a concept - like Asimov's Three Laws of Robotics, it seems hopelessly naive, for one thing - but it can be the basis for a discussion.

Thing is, we can go ahead and discuss it all we want, but there's another problem. It probably has a formal name, but I have no idea how to look it up. I'll call it Lone Asshole Theory, or Waltz's Fourth Law: It doesn't matter how ethically 99.999% of us act, if the actions of the other 0.001% can screw things up for everybody.

For example: Most of us wouldn't steal from a car, even if it were unlocked with the windows down. But we roll up the windows, lock the car, and remove valuables because some people do that. Most of us wouldn't set off a nuke in a major city, but all it would take would be one lone asshole to ruin everybody's day. The vast majority of humans wouldn't have slammed airplanes into skyscrapers, but those few that did made life more difficult for everyone else.

Similarly, we could have a bunch of protocols in place in case we ever met aliens, but everything would be completely undone by one John Allen Chau. All it would take would be one inadvertent biological contaminant (unlikely, of course, but can't rule it out), or one twat on a "mission from God" to convert the Little Green Aliens to Christianity. Or whatever religion. Hell, there'll probably be missionaries from a whole lot of religions falling all over themselves trying to spread the "good" news. I call this a nightmare scenario.

Waltz's Fourth Law basically explains why we can never have nice things. It's akin to the Tragedy of the Commons, but in that scenario, there are usually several bad actors; in mine, all it takes is one.

So, do I have a solution? Hell, no; of course not. And like I said, it'll probably never come up. Almost certainly not in my lifetime. So the only thing I can think of is to continue to make people aware of the problem, and to do what we can to stop the Lone Assholes.

4 Like • Comment • View 3 comments

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