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Tuesday, May. 7, 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:

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
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

May 3, 2024 at 11:58am
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

October 9, 2022 at 12:01am

#1038889

Smells Like New Jersey

Entry #5 for the October round of "Journalistic Intentions"

[18+]:

One reason for environmental justice

I have this conceit, had it for a very long time now, that I can write something about anything. This started when I was quite young, when used to find random quotes in printed material (pre-internet, even pre-home computers) to expand upon in paper journals that have, to my vast relief, since been lost. In a way, this blog has turned into an extension of that; I guess I really haven't changed much, except now I make fewer fart jokes.

This prompt, though? This one stretches my abilities. I can't think of one reason for environmental justice.

No, I can think of way more than one.

For starters, there's a reason corresponding to every person living unwillingly in an environmentally-compromised location. Not just the people, either, but the wildlife and even the vegetation.

But I got to thinking: what would environmental justice actually look like? There's eight billion of us on the planet, and we all produce waste. I get the impression that some of the bigger producers of waste are the ones least affected by it, but without doing actual research, I can't be sure about that. Either way, though, it's clear that the bulk of the burden falls on people who are already disadvantaged in other ways.

"Justice" implies that, ideally, we should all feel the same burden. Thing is, then that would suck for everyone equally. And rich people would never stand for it; you have to remember the Golden Rule: "Those who have the gold make the rules."

I had a friend who was like, "Why don't we just shoot the waste into the sun?" Leaving aside for the moment the incredible expense of doing so, in order to do it, you'd have to cancel the load's angular velocity, as it starts out with the same value as that of the planet (give or take a few angular seconds/second, depending on where it's launched from and when). To do that you'd need reaction mass. Where would we get the reaction mass? Why, from the waste itself, of course. Which would mean, basically, burning it all before it even got to the accursed daystar. Along with the space barge carrying it.

But never mind that; it's just that I'm still laughing at the concept. No, in reality, it has to go somewhere on the Earth. And the further you move it from population centers, the more expensive it is to deal with. And then you have to employ people to take care of it—transport it, then bury or burn it—which would mean people traveling to and living near the waste disposal site, which puts the burden on them. We're not advanced enough to automate the whole schlemiel.

Producing less waste would be good, but you're never going to get it to zero. Basic thermodynamics.

So, what can we do? Hell if I know. Yes, being a civil engineer, this sort of thing is in my wheelhouse, but all that means for me is that I'm maybe more aware of the economies involved. And hell, right now I'm more focused on immediate quandaries. Like, it's getting cold at night now, which means I want to fix myself a nice hot mug of tea. The quandary is: why the hell does my tea kettle have the "Max Fill" line on the outside? It's utterly useless to me there, as the kettle is opaque.

I used to have a tea kettle where that line was an actual dimple in the metal, so you could, if you looked at it from the right angle, see it on the inside and then stop the faucet when the water reached that line. That tea kettle burned (NOT MY FAULT) and it became part of America's waste disposal problem a few years ago. But even then, could I ever be sure that, as I held the thing under the faucet, it was level enough so that the water surface at the line was correct? Even a slight tilt could result in more or less water than the desired maximum volume.

Point is, I can't even address this inequity, let alone the larger one concerning waste disposal.

So I'll just leave you with the video that came with this prompt. Maybe you can think of something where I didn't.

2 Like • Comment • View 2 comments

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