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Monday, Dec. 23, 2024

12:12pm EST

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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:

🌖 HuntersMoon

about 2 hours ago
In response to "Trash Pandas"

Just wait until we team up with the cats...

1 Like

Jayngle Bells

about 2 hours ago
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

2 Like

Annette

Dec 21, 2024 at 11:59am
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

Dec 20, 2024 at 6:06pm
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

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

Dec 20, 2024 at 12:58pm
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

December 23, 2024 at 7:31am

#1081423

Trash Pandas

In my partial listing of intelligent species yesterday, I left out an important one. But my random number generator reminded me today, by pointing to this article from Atlas Obscura:

Can You Outsmart a Raccoon?
Recent studies show just how tricky these trash pandas can be, from opening locks to nabbing DoorDash orders.

Well, that last bit won't happen to me because I don't use DoorTrash. But I have caught those masked marauders in the actual trash. I also once caught one that had opened the door to the house, snuck in, and scarfed down the cat food.

While many other species around the world are in decline, raccoons are actually thriving, and do particularly well in urban areas, says lead author Lauren Stanton, a cognitive ecologist at the University of California, Berkeley.

Okay, that tracks, but... "cognitive ecologist?"

Raccoons are strong—they can push a cinder block off a trash can—and tenacious. The more we do to keep them out, the more skills they learn for breaking in, leading to a cognitive arms race between people and raccoons.

You know how people keep saying that if cats ever got opposable thumbs, we'd be in big trouble? Well, raccoons don't have opposable thumbs, either, but their little paws grip stuff just fine without them.

In 2016, for example, the city of Toronto spent 31 million CAD (that’s about $23 million) on raccoon-resistant waste bins. While they deterred most would-be robbers, certain tricksters had no problem solving the new puzzle. The city has continued to release new versions of the bin, trying to outsmart Toronto’s most persistent trash invaders.

All due respect to our Canadian friends, that right there cracked me up.

The word raccoon can be traced back to the Proto-Algonquian word ärähkun, deriving from the phrase “he scratches with his hands.”

The name was more directly from a specific Algonquian language, spoken by the Powhatans here in what would become Virginia.

While it’s hard to compare intelligence across species, says Stanton, she says that some recent studies show the neural density of raccoons is “more similar to primates than other carnivore species.”

Also, from what I've been hearing, neither brain size nor neural density is strongly correlated with those traits we call intelligence. Still, there's no mistaking that at least some raccoons exhibit advanced problem-solving skills.

However, we have learned that raccoons, once thought to be solitary, are in cahoots with each other far more than we knew.

Great. Now we have to deal with raccoon gangs.

Lots more at the article, which, most importantly, features multiple pictures of impossibly cute raccoons.

3 Like • Comment • View 2 comments

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