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Sunday, Dec. 22, 2024

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Complex Numbers

by Waltz Invictus

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:

Annette

a day ago
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

a day ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

a day ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

Dec 19, 2024 at 8:53am
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

August 27, 2024 at 11:01am

#1075789

They Invented It; We Perfected It

In a twist of cosmic coincidence, today's article is also from Cracked and is also about opposites.

5 Words That Mean the Exact Opposite If You Go to England
Jack Reacher makes no sense, and to understand why, you need to understand British English

Clearly meant for an American audience. If a British rag had written this article, it would have been "5 Words Yanks Get Backwards."

England is a strange land, where they speak a language known as English. You might have trouble understanding what anyone there is saying.

Strewth.

For example, you might hear someone described as “mean,” and you think that refers to how they say cruel things. You later realize it really refers to how they’re stingy with money.

In fairness, those traits often go hand in hand.

5. Tabling an Issue

In America, when someone says, “Let’s table that discussion,” they mean, “Let’s stop talking about that for now.”

Except these days, you'd say "let's put a pin in that and circle back later."

In Britain, when someone wants to table something, it instead means they want to discuss it right now.

And this nicely illustrates the hazards of verbing nouns. "Take it off the table" or "put it on the table" would be close equivalents, and less ambiguous.

4. Public School

If you went to public school in the U.S., that means you went for free, in a school set up by your local government.

Generally badly.

In England, however, the term “public schools” refers to the most elite schools in the country, places like Eton and Harrow... They’re run by private institutions and charge fees.

I've known about this difference for a while, and I gotta say, in this case, I'm going to side with the US.

But it's not like either side of the pond is going to change its usage soon, so it's just important to know there's a difference. The way I remember it is that a pub, originally public house, is also privately owned.

3. The Doughnut Effect

One of the few delicacies that doesn't have a different name in the two Englishes. We say cookie; they say biscuit. They say donut too; they just don't use the lazy spelling.

However, this item isn't about delicious treats, but about how cities grow rings around them... differently in each country. Oh, just read it..

2. Luck Out

If you luck out, that means you stumbled into some good luck.

That is, obviously, the US version. As one should expect by now, the UK version is the precise opposite.

Though the character Reacher is American, the author Lee Child is British. It appears here that the author is using “luck out” in the exact opposite way from how Americans do.

I'm mostly just including this because the subhead up there called out Jack Reacher.

And this is not an invitation to discuss the literary merits, or lack thereof, of the Reacher books. Which I've never read, but I've enjoyed the Amazon adaptation so far.

1. A Moot Point

When I was a kid, I read books in both American and British English, which is why I'm largely bilingual now. But I gotta admit, this one confused me for the longest time.

If a British person says a point is moot, they mean it’s up for debate, while when an American says it, they mean it’s closed for debate.

The article actually goes into some of the semantic reasons for that, which is one reason I read Cracked.

This one's similarity to the "table" one is, however, too obvious not to comment on. But the article did that for me, too.

4 Like • Comment • View 1 comment

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