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Monday, May. 6, 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

about 21 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 10, 2022 at 12:01am

#1030456

Suffer the Little Children

Wading into sensitive waters today...

Ministry that once nourished Duggar family’s faith falls from grace
Scandal brought “19 Kids and Counting” to an end, coinciding with the waning influence of the Institute in Basic Life Principles.

I suppose you can call it a ministry. I call it a cult.

When the Duggar family caught the public’s eye in 2004 with its first television special, “14 Children and Pregnant Again,” the lifestyle depicted on screen was alien to many viewers.

As it should be. I suppose I should disclose that I never watched the show in any of its incarnations, so I'm not going to comment on its content.

Yet some Americans recognized their own values in the fundamentalist Christian family, as well as the influence of one man: Bill Gothard, founder of the Institute in Basic Life Principles.

One defining aspect of a cult is a single charismatic leader. The Catholic Church has a single leader, too, but he's not all that charismatic.

But today, the IBLP is losing income, and Gothard, 87, has been forced out over allegations that he abused young women working at its headquarters.

Which is another defining feature of a cult.

And the Duggars’ shows have been canceled: “19 Kids and Counting” in 2015 amid revelations that their eldest son molested four of his sisters as a young teen and “Counting On” last year ahead of his child pornography trial and eventual conviction.

No one seems to want to draw the obvious conclusion, connecting the dots between being a cult member and practicing deviant sexual behavior. And I can't say for certain that A is the direct cause of B, but I can say that one should consider the possibility and perhaps investigate that connection.

The Institute in Basic Life Principles began in 1961 as seminars by Gothard, an evangelical minister from Illinois with a master’s degree in Christian education.

Over 30 hours, he taught attendees how to lead successful lives by following his interpretation of Biblical principles and warned them away from television, popular music, alcohol, dating and public schools.

Well, I kind of agree with the television bit. But that makes it all the more hypocritical that the thing that drew this family into the public eye was being on television.

At the heart of Gothard’s teachings was the importance of respecting “God-given authority.” He preached a strict hierarchy of divine authority, with Jesus at the top followed by church elders, employers and husbands, who are responsible for protecting their wives and children below them.

And that right there sums up a big part of everything that's wrong with society right now, and has been for a long time.

In marriage, a man’s role is to provide “servant leadership” while “the woman responds with reverent submission and assistance,” preached Gothard, who has never married.

I will note here, without condoning or condemning, that while Catholic priests are famously forbidden to marry, Jewish rabbis pretty much have to be married. Because, the reasoning goes, how can one give marital advice as a spiritual leader without any personal experience therewith?

The Duggars’ wholesome image made them a poster family for the IBLP as their TLC show “19 Kids and Counting” became a ratings hit: Elder daughter Jill Duggar’s two-hour wedding special in 2014 drew an audience of over 4.4 million.

Again the disconnect between prohibiting television while participating in its worst excesses.

The IBLP said in a statement that it had “no comment with respect to the claims alleged,” because of a confidentiality order. Gothard has since denied any wrongdoing. He declined to comment when reached by phone.

I'm also not going to comment on whether Gothard is guilty of those particular charges or not. Not my department. But in a hypothetical situation where a charismatic cult leader gets accused of inappropriate behavior from multiple sources, I'm inclined to take the word of the accusers at face value.

A year after Gothard resigned, the Duggars had their own fall from grace. In May 2015, a leaked police report from 2006 revealed that the eldest Duggar son, Josh, had been accused of molesting five girls as a teenager.

While that never led to conviction, apparently the guy was later convicted on other charges.

Barr, the Baylor University history professor, said Gothard’s fundamentalist patriarchal teachings help create environments where abuse is more likely to go unchecked.

“As a man, they have more authority than women,” she said. “Their voice counts more, and women have this propensity to be valued more for their sexual role, so it allows abuse to flourish.”

Okay, so maybe someone is trying to connect the dots. Still, to be fair, that's not exactly scientific evidence.

And also to be fair, they claim to preach Biblical principles, and I don't recall anything in the Bible forbidding child porn. So I guess that, to them, they're still on the right side of morality.

I just disagree with their definition of morality.

6 Like • Comment • View 4 comments

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