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Monday, May. 20, 2024

7:06am 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:

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

January 5, 2024 at 8:48am

#1061923

Shrug It Off

I do like a good literary takedown... though only when I agree with the person doing the takedowning. This one's from LitHub.

Read a 1957 review of Ayn Rand’s “excruciatingly awful” Atlas Shrugged.

The article is from last October 10, which is important to note because it starts out:

Today is the sixty-sixth publication anniversary of Ayn Rand’s 1100-page magnum opus of unreadable doggerel libertarian science fiction, Atlas Shrugged.

Using strikethrough style is, of course, a cheap trick, one where the writer is coyly covering their mouths, giggling, and going "Oops, did I say that out loud?" And it makes me laugh almost every time. Yes, even when I do it. Especially when I do it. In this case, though, the article author did it; I just reproduced it here.

Still, calling AS "unreadable," even in strikethrough, is a bit unfair. It is, by some definition of the phrase, readable, in that it contains words, and those words are (as I recall) spelled correctly and ordered according to English grammatical practice into sentences and paragraphs.

Set in a dystopian United States in which private businesses suffer under increasingly burdensome laws and regulations (isn’t it always the way), it’s the story of railroad executive Dagny Taggart and her lover, steel magnate Hank Rearden, and their struggle against the “looters” who want to exploit their productivity.

Hence the "fiction" part. Here in reality, it is the "captains of industry" who loot the labor of the workers and exploit their productivity.

Despite receiving largely negative reviews upon its release, the novel sold briskly and became a formative text for numerous conservative/libertarian ghouls politicians and thinkers...

That's the trouble with science fiction, good or bad: there's always someone out there trying to make it happen. Sometimes, that's a good thing. Sometimes, it's not.

One prominent conservative critic of Rand and her philosophy was William F. Buckley Jr., whose National Review published this scathing review of the novel by (Communist spy turned HUAC whistleblower turned book critic) Whittaker Chambers in December of ’57.

So, the rest of the article is Chambers' original review, from which I'll quote only sparingly.

It is the more persuasive, in some quarters, because the author deals wholly in the blackest blacks and the whitest whites.

People being unable to handle nuance is hardly a new thing.

So the Children of Light win handily by declaring a general strike of brains, of which they have a monopoly, letting the world go, literally, to smash. In the end, they troop out of their Rocky Mountain hideaway to repossess the ruins.

Here in reality, those who we today lump into "billionaires" wouldn't last a week in the Gulch, not without the near-slave labor that cooks for and cleans up after them.

It is then, in the book’s last line, that a character...

Look, I don't care how terrible the book is, or how spot-on the review otherwise is; spoiling the last line is cheating.

But the words keep shouting us down. In the end that tone dominates. But it should be its own antidote, warning us that anything it shouts is best taken with the usual reservations with which we might sip a patent medicine. Some may like the flavor. In any case, the brew is probably without lasting ill effects.

And here the review falls apart, for here we are, two-thirds of a century later, and some people still treat that book like it was handed down from Mt. Sinai.

4 Like • Comment • View 2 comments

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