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Monday, May. 6, 2024

4:11am 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:

🌕 HuntersMoon

about 19 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

May 29, 2023 at 10:40am

#1050227

What You Wish For

Today in "You can get what you want and still not be happy":

The Unbearable Costs of Becoming a Writer
After years of hard work and low pay, the risks I took to work in publishing are finally paying off. But now, I wonder about the price my family paid, and whether it was too steep.

When I was younger, I was always told: "Be careful what you wish for; you might just get it." So I stopped wishing.

My parents didn’t understand my job.

No one's parents understand them.

There were stretches when I made so little money writing or editing that I couldn’t blame my parents for assuming they were hobbies.

Most people think it's easy and anyone can do it. And then they try, and they think they've done a good job because they get positive feedback from those who are afraid of crushing them with negative feedback. But in reality, they suck.

I'm aware I'm probably in that category, too. After all, I've never made money from writing (or editing), unless you count GPs for WDC newsletters. That's how we're measuring success now, right?

But, okay. I get it. Sometimes outsiders don't understand that it's work, whether you're getting paid for it or not. Often rewarding work, and requiring very little physical activity, but it's no less work than, say, website development.

I became an editor by volunteering for an Asian American magazine, a nonprofit mission-driven labor of love where no one drew a salary. Ten to fifteen hours of unpaid labor a week in exchange for the editorial experience I wanted was, to me, an acceptable trade—nearly all my labor then was unpaid.

And I get this. (Obviously; I do that sort of thing, myself.) But it's a symptom of a larger problem, which is that what creative-types do is largely undervalued. Hey, can your band do this gig? We can't pay you, but you'll get experience and exposure! Say, I like your art. Can you do a poster for me? I don't have a lot of money, but you can put your contact info on it.

Then one of my favorite indie websites hired me to edit on a part-time basis. The job started at thirteen dollars an hour, twenty hours a week, and after a couple of months I was brought on full-time and granted a salary in the mid-30s.

Don't mistake my above complaints for bitterness. Would it be nice to be paid for my writing? Sure. But if that did happen, I know it would come with a raft of requirements. Like, right now, I can write about anything I want to, say anything I want to, be honest about my opinions (or at least honestly lie about them). My only restrictions are self-imposed. But consider what might happen if, say, someone approached me to do a beer blog. I'd then be beholden to them, and two of my favorite hobbies (writing and drinking beer) would become, by definition, work, with deadlines and expectations.

Everything becomes promotion, then. Hell, even the article I'm highlighting today is basically an ad for the author's book. (I know I've said this before, but that never stops me, by itself, from featuring something; writing ad copy is also a writing skill, and this is a site about writing.)

Fortunately, I don't need the money. So I can pursue it as a hobby. (Still, free beer would be a nice perk.)

But there was also a reality I had to face: I was running out of time to help my family. My diabetic father’s health was in decline, and my parents were struggling to pay for his care and medications. My husband and I couldn’t pay for full-time childcare for both our kids, let alone provide the kind of support my parents needed. The little assistance I could offer wasn’t enough to make a dent, and as my father grew sicker, my guilt and anxiety intensified.

This is understandable, too, though I neatly sidestepped a lot of it by not having kids I knew I wouldn't be able to afford.

I continue to grapple with the instability of this industry and what kind of opportunities will be available to me in the years to come, as well as larger questions about whether my editorial work was valued.

Editorial work is, if anything, even less valued than writing. Don't believe me? Pick a few articles off the internet and see if they look like an editor saw them. Or, hell, this blog, which certainly doesn't have an editor. I do try to catch obvious typos and awkwardly-phrased passages, but I don't always succeed.

I think about who gets to be a writer or an editor, who can afford to wait for that livable salary or that higher advance. Who can choose to prioritize their creative goals, take potentially career-making risks, invest precious years in this work without the guarantee of financial stability.

And this is why I chose engineering way back when. Fortunately, for me, it wasn't an either-or situation; I'm equally bad at both tech and creative stuff.

4 Like • Comment • View 1 comment

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