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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 23 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

November 12, 2022 at 12:01am

#1040558

Bona Frieds

Hope you're not hungry.

15 Delicious Foods That Used to Be Considered Gross

"Delicious" is, of course, a matter of opinion. The headline would have probably been too long if Cracked had qualified that, though.

As usual with such a long list, I'm only going to share a few of these.

15. Lobster

Lobster was so plentiful in the areas colonized by early Americans that they stopped eating it as soon as they could. Only prisoners, the poor, and livestock -- which were pretty much considered the same things -- would deign to eat it, and it was even used as fish bait.

You know, I've been hearing this for so long and with such certainty of delivery that I started to question it. So I checked a source that's marginally more verifiable than Cracked, and discovered

that while this probably is the case, in Europe it was often associated with wealth, before a bunch of Europeans came over here.

So this is more of a case of changing popularity over time, which happens with many foods.

Also, keep in mind that sometimes the wealthy like to eat expensive things just because they can, and because the poor can't. This has little to do with the actual taste of the food. See also: caviar. That shit's disgusting.

14. Chicken Wings

Though now a staple of [sportsball game whose name is copyrighted] parties and other manly gatherings, chicken wings were considered the grossest part of the chicken, to be either unceremoniously thrown out or used for soup stock at the most.

Ah, one of my favorite things to rag on. "Let's take the chicken part that used to be made into dog food and turn it into sports food." Look, they're still the grossest part of the chicken (except maybe the beak and intestines) and are only popular because they're marketed to be. And because of the hot sauce, of course.

12. Foie Gras

There is so much wrong with this entry that I'm not even going to paste it here. Also, everything about foie gras is foul. Pun intended.

9. Peanuts

Peanuts came to America from Africa, and like most delicious African foods, they were immediately dismissed by colonizers as unfit for humans until three things happened. First, the Civil War reduced people to choking down whatever protein they could get their hands on, and peanuts were definitely preferable to rats.

I'm no fan of peanuts, but yes, if I had a choice between peanuts and rats, I'd eat the peanuts.

Then P.T. Barnum began selling peanuts as circus food.

Having been marketed by the Platonic ideal of "huckster" ("sucker born every minute" etc.) is not something that I'd use to recommend a product.

Finally, peanut butter happened. Even the most frothing bigot can’t resist a spoonful of peanut butter.

Admittedly, I'm okay with peanut butter. I still don't know why I like peanut butter (but only the real kind, not the candy kind like Skippy) and not peanuts, but I never claimed to be entirely consistent.

7. Mushrooms

The Western world shunned mushrooms on account of their tendency to make you see God and/or kill you until the French insisted they were the height of cuisine in the 18th century

I do like (commercially available) mushrooms. I know several people who can't stand them, mostly due to the texture (they say). I can understand that. When you really think about it, eating mushrooms is weird. It's a fungus, neither animal nor plant (but, oddly, closer to the former than to the latter), and thrives in shit. There aren't many fungi that we eat. Yeast, sure, but we were ingesting that (as part of bread or fine fermented beverages) long before we knew what yeast actually was.

On the other hand, when you really think about a lot of things that we eat, you start to question them. Eggs, for example. Or:

3. Oysters

The story of oysters is a very straightforward one of supply and demand. They were once so plentiful that Charles Dickens characters looked down on the patrons of oyster houses that lined the London streets one “to every half-dozen houses.” Then we filled the oceans with so much pollution that it was hard to get a good oyster, prices went up, and the rich just equated “expensive” with “good.”

Like I said, sometimes rich people do rich people things just because the poor can't.

Still, you have to wonder how people figured out oysters in the first place. "Let's crack open this rock and see if there's a tasty treat inside."

1. Burgers

There are people who, not unreasonably, would take a juicy burger over the finest steak any day, but back in the Upton Sinclair days, ground beef was seen as unclean at best and possibly containing dude at worst.

It's actually more complicated than that, and ground beef certainly predates fast food. I'm pretty sure, though, that the popularity of hamburgers didn't take off until there was enough supply to make them cheaply, and that required access to electricity to power the grinders.

When I was a kid it confused the hell out of me that hamburgers didn't contain ham. Just another linguistic weirdness of English, in this case with the word deriving from the city of Hamburg which may or may not have had nothing to do with the invention of the hamburger. Nowadays you can talk about beef burgers, veggie burgers, turkey burgers, even cheeseburgers (which aren't made out of cheese) but never ham burgers. And no one calls it a hamburger anymore, either.

Now you're hungry, aren't you?

3 Like • Comment • View 7 comments

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