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Tuesday, Apr. 30, 2024

1:17pm EDT

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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:

GeminiGem of House Lannister

about 23 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

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

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

September 19, 2021 at 12:02am

#1017695

The Thinkers

Not all philosophers had big bushy beards.

Wise women: 6 ancient female philosophers you should know about

I'm still bingeing Lucifer on Netflix, so this is a short one.

When we conjure up ancient philosophers the image that springs to mind might be a bald Socrates discoursing with beautiful young men in the sun, or a scholarly Aristotle lecturing among cool columns.

Well, there are definitely togas (or whatever they called them in Ancient Greece) involved. And beards.

More than two millennia later, intelligent, verbal women still struggle to have their own voices heard. So here are six ancient female philosophers you should know about.

Some of these I'd heard of. Others I hadn't. Hence my saving the link for the blog.

1. Aspasia of Miletus

She was not only remembered for her captivating beauty, but also for her captivating mind. Socrates himself called Aspasia his teacher and relates he learned from her how to construct persuasive speeches. After all, he tells us, she wrote them for Pericles.

For some reason, male philosophers are never remembered for their hotness.

2. Clea

Clea (most active around 100 CE) was a priestess at Delphi — a highly esteemed political and intellectual role in the ancient world. The religious practitioners at the shrine received frequent requests from world leaders for divine advice about political matters. Clea was part of this political-religious system, but she believed in the primary importance of philosophy.

You know that scene in 300 with the Oracle at Delphi? I have reason to believe Snyder took a few liberties with it.

3. Thecla

When she first appears on the scene in the Acts of Paul and Thecla, Thecla (most active around 1st century CE) is leading a normal middle class life, sequestered at home and about to make an advantageous marriage. But leaning out of her balcony, she hears the dynamic preaching of Paul and decides on a radically different path.

The Acts of Paul and Thecla is part of New Testament apocrypha. I'm guessing it wouldn't have done to have a story about a woman (apart from the obvious) in what would become the Bible, so the Council of Nicaea threw it out.

4. Sosipatra

She was surrounded by male experts, one of whom was her husband Eustathius. But according to Eunapius’ biography in his Lives of the Philosophers, her fame was greater than any of theirs, and students far preferred her inspiring teaching.

I'll have to remind myself to look into this one further, as Neoplatonic philosophy is cool.

5. Macrina the Younger

Macrina (circa 330-379 CE) was the oldest of ten in an expansive, influential well-educated Christian family in Cappadocia.

Count this as one I should have known about, but didn't.

6. Hypatia of Alexandria

Most famous for her dramatic death at the hands of a Christian mob, Hypatia (circa 355–415 CE) was a Neoplatonic teacher admired for her mathematical and astronomical works.

This is the one I knew most about, which unfortunately still isn't saying much. Also, there's an asteroid named after her (the trivia floating around in my head comes out at weird times).

In any case, the article is rather light on information, but contains helpful links. Which I'll follow. When I'm done bingeing Lucifer.

6 Like • Comment • View 3 comments

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