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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 22 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.

August 10, 2021 at 12:04am

#1015439

Narcissists

This one's been hanging out in my queue for a while, so I don't really remember the point I was going to illustrate with it; a lot has changed since it was written. But some things haven't, so here it is.

How COVID exposed New Age Narcissism
During this global pandemic that has disrupted life as we know it, many people have attempted to find the silver lining in the chaos

For some, the chaos is the silver lining.

Whatever my original point was, I usually appreciate the perspective of the ex-. That is, someone who used to be an insider and then found a different path. This is one of those stories.

I don't have a lot to quote from it, but it's worth a look.

An example of this paradigm shift is the mass exodus we are seeing away from the “New age/Conscious” community as it currently stands. This article is difficult for me to write, as I have been deeply integrated into this world for over 15 years. Still, like many of you, I have always felt that something was off, although I couldn’t pinpoint it underneath all of the blisstractions.

Ah, that's right... I was going to rag on "blisstractions."

There were a lot of goddesses, warriors, priestesses, and shamans, yet not enough humanity.

Claiming to be one of these things isn't a way to transcend humanity; it's a way to ignore it.

Disinformation and emotional manipulation have always been a part of human history.

In the past, it has convinced white people that Black people are not fully human. It has convinced parents to burn their own children for being witches. And it has sparked up thousands of religions and beliefs that people have been willing to kill and die for. However, due to the Internet, the speed of misinformation and manipulation spreading is at a record high, and humanity needs an Intellectual Renaissance to evolve and survive.

This is something I agree with. Intellectualism has its problems, too, but it's still better than superstition and fear.

You can believe whatever you want to believe, but ultimately, science and truth will prevail.

Unfortunately, by the time they do, it will be too late for us as a society. But hey, it's been a hell of a ride.

Someday, there will be a disease with a much higher mortality rate, which we will not be able to defeat based on how we handled coronavirus. It is easy to forget about the past that we never experienced ourselves. We never saw life before vaccines and medical advancements. But there was a time that a single plague wiped out a whopping 50% to 60% of Europe’s entire population.

I'd just like to point out here that there's an estimate floating around that the diseases the Europeans brought with them to the Americas might have wiped out as much as 90% of the indigenous population, in the 100 years or so between Columbus and Jamestown. Without this unintended biological warfare, the American continent would have a very, very different population right now.

Anyway, like I said: the article's worth a read, even if it says some hard things.

6 Like • Comment • View 5 comments

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