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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

about 14 hours ago
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

a day ago
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

April 20, 2021 at 12:03am

#1008815

Real Men of Genius

It's been said that with genius comes a certain level of insanity.

4 Famous Smart People With Little-Known Problems

Would that the reverse were true. Anyway, from Cracked...

Pop culture loves to portray geniuses as dragging us ungrateful schmucks through history, whether we want to come along or not. So it's always good to remember that brilliant people still have the same problems as the rest of us ... except when their problems get much, much stupider than ours ...

I don't know; some of us have some really stupid problems.

4. Vladimir Nabokov Hated Sleep, Conducted Weird Dream Experiments

Vladimir Nabokov, the famous author of Pale Fire and that novel about a pedophile that's awkward to read on the bus, is considered a titan of literature, especially by dudes with bad facial hair who keep cutting off other people in their MFA classes. He was also a lifelong insomniac, and the condition took him to some weird, weird places.

Probably because it's been shown to a high level of certainty that lack of sleep messes you right up.

For starters, Nabokov called sleep "mental torture," "the most moronic fraternity in the world," and "the nightly betrayal of reason, humanity, genius," among other things offensive to anyone who considers napping their greatest skill.

For me, it's between napping and drinking.

3. George S. Patton Thought He'd Have To Fight Forever

Admittedly, he also wrote poems with titles like "The Turds of the Scouts," but his belief in reincarnation was legit, and he spent both World Wars claiming to know his way around old European towns and battlefields thanks to his time as a 14th-century French knight. Unfortunately, Sir Patton was one of many Frenchmen to meet his end at the Battle of Crecy, a crushing victory for the English, but it would have been suspicious if he'd claimed nothing but a string of huge successes.

What's suspicious is that all of his purported past lives were European. Couldn't throw some Native American, African, or Asian warriors in the mix? Racist fuck.

Exactly how Patton reconciled this with his devout Christian beliefs remains unclear, but he also claimed that he was at the Siege of Tyre, served under Caesar and Marc Antony, fought with the English at Agincourt because apparently when you reincarnate during a lengthy conflict, you can ask to switch to what looks like the winning side, served the House of Stuart during the English Civil War, and was a bigshot in Napoleon's Grande Armee.

See? If his past lives were any whiter, he'd be a ghost. Oh, wait.

Anyway, this may all sound ridiculous, but reincarnationresearch.com thinks he's currently living as James Mattis, and surely if anyone would know, it's those guys.

I have to wonder if Mattis knows about this.

2. Kurt Godel Would Only Eat Food Prepared By His Wife ... And Then She Got Sick

Kurt Godel is one of those mathematicians who was so smart you need a good math background to appreciate his incredible influence. His incompleteness theorems, contributions to set theory and modal logic, and many other accomplishments are all way over our head.

Mathematicians tend toward weirdness anyway. That's why they become mathematicians.

And Cracked, what's with omitting the umlaut? It's Kurt Gödel. It's not that hard to do, and it hasn't been fashionable to piss off Germans since 1945. Also, dude was metal, and nothing says "metal" like an umlaut.

Godel became obsessed with the thought of being poisoned, either intentionally via food or accidentally through, for example, the venting of gas from his refrigerator. His wife kept his fears in check by preparing and tasting his food for him, and long talks with some guy named Einstein helped keep him mentally grounded, but he was never the most stable genius.

Hm, take the slight risk of possible poison, or the sure risk of dying from malnutrition? If only there were a logical construct for managing risk.

1. Edward Gibbon's Balls Were Literally Too Big

18th-century politician and historian Edward Gibbon's big claim to fame is The History of the Decline and Fall of the Roman Empire, an epic 1.5 million word landmark in historical writing. While its central argument -- that Rome's decline can be blamed on its adoption of Christianity -- is considered wrong today, it's still seen as a huge leap forward in research standards and an entertaining read to boot. Books, shows, and games have aped its title, it's been referenced in pop culture like Mad Men, and countless dads once got copies in book subscription programs that they displayed prominently but never got around to actually reading. Whatever Gibbon's flaws, he was an esteemed, serious scholar ... who was undone by an inflamed testicle.

Right now you might be going "But Waltz, that's not insanity." I have no personal experience with this, but I'm pretty sure an inflamed ball would make any man nuts. So it fits. Also, it gives me an opportunity to make a "nuts" pun.

The intent here is not to mock a great man of history, although dying from big balls is very, very funny (Gibbon himself joked about it with close friends as he neared the end). The procedure was simply the best available at the time, and the risk was considered worth it, given what the unchecked problem would mean for his life. You are simply invited to reflect on the fact that, while you probably won't go down in history as a genius, you at least don't live in a time when preposterously swollen genitalia can take you to your grave.

No, it just gets you fame on the Dark Web.

Or so I've heard.

5 Like • Comment • View 3 comments

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