Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ May ►
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	31
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Monday, May. 20, 2024

6:42am EDT

Members: 714

Guests: 957

Total Online: 1,671

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:

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
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

May 4, 2024 at 5:42pm
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

May 9, 2024 at 10:00am

#1070769

Super Stew?

I've done entries about categorization problems before. Is it a sea or a lake? A dwarf planet or a planet? A hill or a mountain? Is a hot dog a sandwich or a taco, or is it just a hot dog? Well, here's one that I've wondered about for a long time, yanked from the website at Country Living.

Stew vs. Soup: Everything You Need to Know
They're both served in a pot—so what's the story?

Served in a pot? Maybe in your country. In my country, they're cooked in a pot and served in bowls.

The article is from January of 2020, but surely nothing's changed since then.

When it's cold outside or you're not feeling well—no matter the time of year—there's nothing more comforting than a hearty soup recipe or a slow cooker stew recipe.

Sure there is: the actual soup or stew, preferably made by someone else because it's cold outside and I'm not feeling well.

On that we can agree—but when you break it down, do you really know the difference between stew and soup?

No, but I guess you're about to tell me. Incidentally, I don't really care; I only care that it tastes good.

The main difference is the amount of liquid that's used for each. In a soup, the ingredients will generally be completely submerged in liquid, while in stews, they're just barely covered.

Okay, but what about when you have ingredients that float? Carrots, e.g., or pasta. You look at it, it's only partly submerged. Like the iceberg, not like the Titanic.

The main component of a soup is the liquid. Soups can be brothy (think: a timeless chicken noodle soup), puréed (classic tomato purée soup), or creamy (potato cheddar soup, anyone?).

I'm not reproducing the links here, but I'm starting to think this "article" is just meant to promote their recipes.

Oh, and to further complicate matters, there are other names for soups. Bisque, a subcategory of creamy soup. Chowder, same. Pho, which I maintain stretches the definition of soup, because it cannot be eaten with a spoon alone unless you have superpowers.

Soups are generally easy and fast to make—some can be made in as little as 20 minutes!

20 minutes? To source all the ingredients, prep them, fumble around with cookware, etc.? Hell, if your batch of soup is voluminous enough, it'll take 20 minutes just to bring it to a boil before you turn it down to a simmer.

On the other hand, I've made soup in 3 minutes: 1) Open a can of Campbell's 2) Mix it with a can full of water 3) Nuke for 2 minutes.

The general rule is that no ingredient should be larger than a soup spoon.

See, that's a tough rule for pedants like me. First, define "soup spoon." After that, consider ramen. Each ramen noodle is, well, a noodle. Even if it were possible to fish out the noodles one by one, bits of them would hang over the sides of the spoon, making it larger than a soup spoon. Sure, if you got it all coiled up, an individual noodle could maybe fit in one spoon, but who does that?

Also see: French onion soup.

Stew tends to be more complex and takes longer to cook than soup.

Betting we could find counterexamples if we tried.

Unlike soups, which rely mostly on water or stock as the main liquid, stews can contain beer, cider, or wine for additional flavor.

I put brandy in my French onion soup.

But. The end of the article addresses a long-standing question, one of great import and whose definitive answer could change the world.

Is chili considered a soup or a stew?

Still, I don't care; I consider it delicious.

4 Like • Comment • View 2 comments

© 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/5-9-2024