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Sunday, May. 19, 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:

Aiva Raine

a day ago
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

April 12, 2023 at 9:22am

#1048059

Charmeuse

Another entry for "Journalistic Intentions"

[18+] today:

Charmeuse

Unlike some people, I'm not proud of my ignorance. Nor do I pretend I don't have any. It's always a great moment for me when I learn something new, even if it's about a topic I don't have a lot of interest in... such as fashion, which is the theme of this month's JI.

So until these prompts were posted, I don't think I'd ever even seen or heard the word "charmeuse." And I also restrained myself from looking it up, just in case it became one of the eight out of sixteen prompts that I'd end up picking at random and I could proclaim my ignorance in public.

And behold, it was.

So let's see. Before I look it up, I have some guesses.

The word "Charmeuse" is in the section of Fabrics prompts, along with nylon, silk, and wool—all of which I am familiar with, so why couldn't I have gotten one of those... oh well, I'd have less material (pun absolutely intended) to work with. So I will start out by assuming (and shut up about "ass-u-me" already; we all make assumptions all the time just to get by) that charmeuse is a fabric.

Easy enough. What else? Well, the word seems French, so my next assumption is that the initial sound is more like sh as in shit than ch as in chit. Look, even after three and a half years of French lessons, I don't consider myself fluent, but I see patterns (though I have no idea, as yet, if charmeuse is a patterned fabric or not). And if I had to take a stab at "charmeuse," I'd guess it's the feminine word for "charmer" or "one who charms" (the masculine version being most likely "charmeur" if it indeed exists in the language). This is like how "singer" (the vocal thing, not the fabric sewing machine company) can be translated as chanteur or chanteuse.

I should emphasize that I'm using masculine and feminine in their linguistic meanings, not the sociopollitical meanings, which have become a minefield.

Alternatively, it refers to someone who prefers Charmin toilet paper, much as "bounty hunter" refers to someone who was searching for paper towels during the pandemic supply shortages.

It being French tracks, because when you think of fashion, you think of Italy, France, and maybe Mobile, AlabamaNew York City, the latter of which uses Italian and French names for fashion to make themselves seem superior.

I can also provisionally rule out nylon, silk, and wool as being synonyms, so it's probably a completely different material... though my confidence level on that isn't very high, as you also have, say, felt (the fabric, not the past tense verb), which is a different form of wool in much the same way as graphite is a different form of carbon.

And that's the limits of my guesswork. Let's see how I did, courtesy of Wikipedia:

Charmeuse (French: [ʃaʁmøz]), from the French word for female charmer...

Il est d'accord. Point pour moi.

...is a lightweight fabric woven with a satin weave, in which the warp threads cross over four or more of the backing (weft) threads.

Another thing I learned fairly recently: satin isn't a base material, like wool or silk, but a particular kind of weave. But satin is, as I understand it, most closely associated with silk. So deduct a point for me guessing it didn't have crossover with the other prompts.

I have a vague idea what warp and weft are in relation to fabric, but only vague, and there's only so far I'm willing to go down a Wiki rabbit hole this morning.

Charmeuse differs from plain satin in that charmeuse has a different ratio of float (face) threads, and is of a lighter weight.

"Plain satin?"

Charmeuse may be made of silk, polyester, or rayon.

Cue the "one of these things is not like the others" earworm.

It is used in women's clothing such as lingerie, evening gowns, and blouses, especially garments with a bias cut.

See? I told you bias was everywhere.

It is occasionally used in menswear.

And yet it's still called charmeuse in that context.

There's more detail at the Wikipedia link, though I shouldn't have to remind anyone that I wouldn't use it as a definitive source (and I can't be arsed to follow all those links at the bottom).

Any day when I learn something new is, in my opinion, a good day. Especially when it's source material (yes, I used that pun before) for comedy.

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