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Saturday, Dec. 21, 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:

tj-Merry Mischief Maker

about 13 hours 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

about 18 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
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

a day ago
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

a day ago
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

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

August 8, 2024 at 12:05pm

#1074935

Iraq, A Hard Place

I don't know much about this source, Ulukayin, but I'm going to assume the article is true because I want it to be true. Yeah, I'm too lazy to be skeptical today.

5000-Year-Old Sumerian Pub and Beer Recipe Unearthed

Archaeologists have unearthed a Sumerian pub in Iraq dating back to about 5000 years ago. Among the remains, there is also a tablet with a beer recipe.

As we all know, beer itself is far older than that. It's at least as old as civilization. Hell, some claim it's the reason for civilization, and I'm not going to argue with that.

The discovery was made in Lagash, an ancient city-state in southern Iraq, by a team of archaeologists from the University of Pennsylvania in the USA and the University of Pisa in Italy. Examining the remains, the team reported that they thought the pub was around 5000 years old.

Now my inner skeptic is starting to wake up. "They thought the pub was around 5000 years old?" Did they, you know, do any dating or did they compare architectural styles or what?

It is estimated that beer was also consumed in the pub, although analyzes continue.

So they're not sure if it was actually for beer. Just that a beer recipe was there. I mean, sure, that's pretty solid circumstantial evidence; why have a recipe if you're not going to actually brew beer?

I'm giving them a pass on "analyzes;" English isn't their first language.

Archaeologist Holly Pittman of the University of Pennsylvania said that the most common beverage consumed by the Sumerians was beer. She also stated that a tablet with a recipe for beer was found in a nearby temple.

Okay, now I'm getting confused. Was that a different tablet?

So I guess I kicked my inner skeptic into action, after all. Don't get me wrong; finding the remains of any 5000-year-old building is pretty cool by itself. But did they really have to sensationalize it by making us visualize a public drinking establishment? I don't even know if those existed at the time; I was under the impression that beer was more of a sacred thing, so finding a recipe in the temple makes more sense.

Final note about where this was discovered, the ancient city of Lagash: One of my favorite breweries is Allagash, in Maine. I like them because they produce Belgian beer styles. I don't know where they got their name. But from now on, I'll be thinking of them as Al-Lagash.

5 Like • Comment • View 2 comments

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