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Monday, Apr. 29, 2024

5:42pm 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 4 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

May 27, 2022 at 12:05am

#1032910

Under the Sea

I don't really have a lot to say in response to today's article. I just found it to be interesting, and the best-written piece I've ever read on what it's like to be a whatever; in this case, a Navy submarine sailor (so if you want to weigh in here, Sum1

, feel free).

Nukes, Nubs And Coners: The Unique Social Hierarchy Aboard A Nuclear Submarine
Getting assigned to your first sub doesn’t make you a submariner and once you become one you’ll find yourself in a social structure unlike any other.

I would imagine that if you're working with a bunch of other people in exceedingly tight quarters, for months at a time, you'd need some traditions and customs in addition to the usual military codes of conduct. Hell, I can't be stuck with most people for more than a few hours at a stretch without having to retreat. Months? And to think I almost joined the Navy, albeit through the Academy.

A new crewmember is a Non-Useful Body, or NUB. He or she uses our limited supply of space, water, food, and oxygen. They are not welcome, but BUPERS (Bureau of Personnel) keeps sending them.

I get that any new people in the military get hazed and mocked. I even get why (there are a few reasons, not least of which is that if you can't take shit from your superiors, you certainly won't be able to take shit from the enemy). But it's one reason I never signed up. It'd be like:

Chief: "Waltz, I'd call you a tool, but that would be an insult to tools."
Me: "Yes, Chief. You're correct. I am utterly incompetent and always will be. I shouldn't even be here."

Or:

Chief: "Waltz, you're completely useless."
Me: *shrug* "Then why do you even want me to try?"

I think the psychology is meant to make the enlistee really very badly want to prove their NCO wrong. But I figure that would just be disrespectful; why not prove them right instead?

Anyway. Not much else to add to the article. Like I said, I just found it enlightening, as my primary source of information on what it would be like to be stuck with a bunch of people in an airtight vessel was Star Trek, and as much as I like Star Trek, I was never under any illusion that any of it was realistic, especially the wide corridors, spacious bridge, and ample recreational areas.

Incidentally, I once got curious to find out why the command center of a vessel is usually called a "bridge." Apparently it's a holdover from the riverboat days when the controls were on a deck that literally bridged the boat

, between the paddlewheels.

Or so I was told. It's entirely possible I was misinformed. After all, I'm useless.

Incidentally, if you want to mess with a sailor, call a ship a "boat," and call a boat a "ship." Want to know which is which? Don't ask me. But I very nearly picked up a Navy officer lady at a bar one time with that discussion. Until I remembered that I have a sworn rule against picking anyone up at a bar.

5 Like • Comment • View 5 comments

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