Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ April ►
S	M	T	W	T	F	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Monday, Apr. 29, 2024

7:05pm EDT

Members: 1,043

Guests: 923

Total Online: 1,966

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:

GeminiGem of House Lannister

about 5 hours ago
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

a day ago
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

a day ago
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 Udon Thani

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 Udon Thani

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.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

April 13, 2024 at 2:25am

#1068648

Mawwiage...

Posting early today because it'll be a busy and exhausting day of visiting local wineries with friends.

Can't Buy Me Love: How Romance Wrecked Traditional Marriage

For the sake of context, this 2013 article from Collectors Weekly came out during the time when same-sex marriage was still being debated in the US; it wouldn't be until 2015 that Obergefell v. Hodges settled the matter once and for all. Hey... stop laughing; I said once and for all.

I mention this only because, at the time, "traditional marriage" was a buzzword, and a dog whistle for "white Christian man marries white Christian woman; together they go on to produce 2.1 children, and the man makes all the decisions in the family." And even that is not what was, historically, "traditional marriage."

In reality, it’s the idea of marrying for love that’s untraditional.

This is not even getting into different cultures' traditions.

For most of recorded human history, marriage was an arrangement designed to maximize financial stability.

Much as I'd like to agree with that, it still seems Eurocentric. But, honestly, I don't know enough about other cultures to know all the nuances involved.

By the Middle Ages, gender inequality was not only enshrined in social customs, but also common law. In most European countries, married women were forced to give up control over any personal wealth and property rights to their husbands. Eventually, the system became known as “coverture” (taken from “couverture,” which literally means “coverage” in French), whereby married couples became a single legal entity in which the husband had all power.

One of the more common arguments against same-sex marriage back then was "What's next, you can marry your dog?" To me, that argument told me everything I needed to know about how the person making it would treat women. It's like the idea of "two willing adults wanting to enter into a mutually beneficial agreement" completely escaped them. Once you get to the "two willing adults" hurdle, it's not even a little bit of a stretch to consider that those adults can be any sex and/or gender.

I'd personally be perfectly content to extend that to more than two (for other people, not for me), but that's a fight for another time.

Under such laws, children were generally viewed as assets, in part because they were expected to work for the family business.

Another change: nowadays, they're liabilities. Or, at the very least, it's an emotional bond more than a business arrangement.

Despite the church’s staunch position on monogamy, in the late Middle Ages, a legal marriage was quite easy to obtain. However, as more couples attempted to elope or marry without consent, the old guard upped its game. To combat the spread of “clandestine” marriages, or those unapproved by parents, state officials began wresting the legal process of marriage from the church.

In my view, that sowed the seed that became part of the same-sex marriage debate, at least in the US. Religious people get married twice in the same ceremony: one sealing their bond in the eyes of their religious group, and one making it official to various government agencies, not least of which is the IRS. Much breath was wasted with people talking past each other, not understanding that one person meant religious union, while the other meant civil union.

As this philosophical support for individual choice spread, more young people wanted some say regarding their future spouses. “Demands for consent from the people actually getting married were thought to be quite radical,” says Abbott. Even more radical was the idea that marriage might be entered into for emotional, rather than financial, reasons.

It's also apparently radical that a marriage be considered a partnership between equals.

In fact, for thousands of years, love was mostly seen as a hindrance to marriage, something that would inevitably cause problems. “Most societies have had romantic love, this combination of sexual passion, infatuation, and the romanticization of the partner,” says Coontz. “But very often, those things were seen as inappropriate when attached to marriage. The southern French aristocracy believed that true romantic love was only possible in an adulterous relationship, because marriage was a political, economic, and mercenary event. True love could only exist without it.”

In other words, they knew that love dies, but money is forever.

Anyway, the article goes on for a while, but, as it covers centuries of history, it seems to be a decent summary. It also emphasizes how laws are often slow to catch up to social realities. And yes, there's a nod to the then-current marriage debate.

The laws, if not the attitudes of certain kinds of people, have moved on since then, and we've shifted our focus as a society to trans issues, when we're not contemplating our looming climate apocalypse.

And no, the two have nothing to do with each other. But the shift in attitudes about marriage and the climate problem both seem to have their roots deep in the Industrial Revolution.

4 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/4-13-2024