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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 3, 2022 at 12:03am

#1038519

Blender

Entry #2 for "Journalistic Intentions"

[18+] today.

Justin Sutherland

Having never heard of Justin Sutherland, I was relieved to discover he's not the illegitimate love child of Justin Bieber and Kiefer Sutherland. My relief was short-lived, however, as it became clear that the above linked "article" is a barely-disguised ad. Fortunately, it's mostly an ad for a book, which I've repeatedly stated isn't going to stop me from linking it on a writing site.

Anyway, it turns out that Sutherland is a chef, though someone I'd never heard of. Not that surprising, as I don't follow celebrity chefs and I don't live in Minnesota.

Sutherland was boating with friends on the St. Croix River on July 3 when his hat blew off, causing him to reach for it. At the same moment, the boat hit a wave, sending him into the water near the propeller, which "did a number on his head and left arm,"

Sounds like he was more than "near" the propeller. I guess you could say he got screwed.

Look, I'll never pass up an opportunity for a pun, no matter how tragic the incident that prompts one. I'm not making fun of the accident; it sounds like no fun at all, one of those shitty things that occasionally happens to people.

Here's a snippet of Sutherland's interview. You can watch his full appearance on The Jason Show in the player above.

No.

Jason: What do you remember about that day?

Sutherland: I mean, honestly, I remember everything. It was a beautiful, perfect, you know, day. I remember everything from hitting the water, to getting slammed back to the boat, and to getting to the ambulance.

The key word being "was." One wonders how much booze was involved, though a large amount wouldn't work with remembering "everything."

Jason: I know this seems very simple, but you don't remember any of the pain?

Sutherland: No. Not a single piece.

I ain't no doctor, but that sounds like shock to me.

Jason: You look fantastic!

Sutherland: Regions

Apparently this is a hospital in St. Paul
was amazing … I still haven't eaten solid food in nine weeks now. I have five metal plates in my face. And this is all brand new (pointing to his face), I can't put any pressure on my teeth. I've lost about 14 pounds, trying to drink protein shakes.

That sucks and all, but at least he's a chef: those protein shakes were probably amazing. For protein shakes.

Jason: Let's talk about the positive … the positive is the support. Wow. … What did that feel like?

Sutherland: Incredible. … Nothing but just gratitude. We touch a lot of people in our lives … but sometimes you don't realize the people you cross paths with and the lives that you impacted. The people that came together – still, eternally grateful.

You know, this is kind of refreshing. So much so that I'm willing to overlook the whole "positivity" thing. Why? Because he wasn't all "God healed me." No, he acknowledges the very human, very skilled people involved in his recovery. I don't see a lot of that in the news. I see a lot of "That tornado ripped through and slammed me against a trailer and I couldn't walk for a week, but God healed me," ignoring the neurosurgeon that fixed the walking thing. Or, "I was driving drunk and slammed into a tree, but after a month I could see again, thanks to God," without mentioning the doctors who fixed your unworthy drunk-driving-ass face.

Never mind that God did those things to you in the first place. I mean, if he's in control, then didn't he both send the tornado *and* heal you afterward? If not, then he's not all-powerful, is he? And if he does, why only praise him? It's like, occasionally you'll get a firefighter who lights shit on fire and then swoops in to play the hero. We call them "arsonists" and they generally get arrested for it.

Or maybe the initial incident was some combination of your fault and the random workings of the universe; the medical attention you get afterward, though, that's deliberate. No need to resort to supernatural causes.

Don't get me wrong; I'm not condemning people who have faith that they think helps them get through a tough situation. Whatever brings you comfort. But all the work done to fix your broken ass? That was people. Humans. Sure, some of us suck, but we can also be quite clever, competent, and helpful. Well, not me. But doctors and EMTs and such. Not to mention any of your friends and family who help you through it all.

Point being, it sounds like this guy acknowledges that.

Well, the rest of the article is the ad for his book and his restaurants, and you can look at that part if you want. As for me, next time I'm in the area, maybe I'll remember this and check out one of those restaurants. After all, that's one of the reasons I travel in the first place.

I just hope they're serving solid food.

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