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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

about 22 hours 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

May 5, 2024 at 7:04am

#1070539

Revisited: "Fail"

We're going back in time, as usual for Sunday mornings. This time, it's just to October of 2020 (specifically, 10/10/20, one of the few dates that work in both American and European style conventions and which can also be turned into a mathematical equation): "Fail"

I did the entry for that month's round of "Journalistic Intentions"

[18+], which is still an active blogging challenge, though not every month. Also, all the links in the entry are still solid, which isn't too surprising for something less than 4 years old.

Anyway, I got curious and looked up the origin of the name Fail.

I didn't go into this at the time, but today, I noticed that the ultimate origin of the Scottish surname Fail (which has many alternative spellings) is the name Paul. Don't ask me what kind of linguistic vowel shifts it takes to get from Paul to Fail; I don't know. But the name Paul, from Paulus, is Latin in origin, though it is probably most associated with the Paul of the New Testament.

So Paul becomes Phaill (or some similar spelling), and, by the convention of some Scottish clan names, generates MacPhaill, later Anglicized as MacFail or just Fail.

At least, that's one possible explanation. I never did trust some of these genealogy websites. But you know the Meat Loaf character in Fight Club? "His name was Robert Paulson." Well, "Paulson" is the English equivalent of MacPaul, which we've already speculated became the name Fail, so I have to wonder if Palahniuk did that shit on purpose. Probably not; his symbolism tends to be more of a, well, a punch in the face.

Anyway, back to my original entry:

I know, I know, it's rude to make fun of peoples' last names. You should be proud of your last name, even if it's Fail.

Or Hogg, as in yesterday's entry (coincidentally, also Scottish). Still, being proud of being a Hogg (or a Fail, for that matter) is no damn excuse to name your kid Ima.

There's the story of a Dr. A. Hedgeh, for example, who apparently had a problem with people adding "og" to his nameplate.

In case you don't want to bother rereading my 2020 entry, I'm including that link

here again, because I still laugh every time I see it. Fake or not.

So, yes, it's rude to make fun of peoples' names.

But sometimes, it's so funny you can't help it.

3 Like • Comment • View 1 comment

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