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Tuesday, Dec. 31, 2024

1:24am 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:

tj-Merry Mischief Maker

a day ago
In response to "Revisited: "None More Black""

Favorite color? Growing up it was deep red, but having a little brother, his favorite color also had to be red, so I decided to pick blue. His also turned blue, so I decided not to have a favorite, but to like all colors. But, what do you get if you mix together all the colors? Black.

Waltz Invictus

a day ago
In response to "Revisited: "None More Black""

🌖 HuntersMoon

: See also my many polemics on the fruit status of tomatoes.

1 Like

🌖 HuntersMoon

a day ago
In response to "Revisited: "None More Black""

Knowing your penchant for "scientific" foundations for answers, black is not a color.

Black's status as a color varies depending on the perspective:

Scientific perspective: Black is not a color; it is the absence or complete absorption of visible light, making it an achromatic shade.
Artistic perspective: In art and design, black is treated as a color because it can be created by combining pigments and provides contrast.
Human perception: Black evokes feelings similar to other colors and is often associated with darkness, power, and elegance.

2 Like

tj-Merry Mischief Maker

Dec 28, 2024 at 3:23pm
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

Dec 28, 2024 at 9:11am
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

Dec 27, 2024 at 3:41pm
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

Dec 27, 2024 at 10:33am
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

Dec 27, 2024 at 8:43am
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

June 1, 2024 at 9:13am

#1071970

Border Dispute

Wars have been fought over less than this.

The Man Who Went to War With Canada
For centuries, the United States and Canada’s only remaining land border dispute has been kept alive by a single family.

Article is from Atlas Obscura and 2019, but the Wikipedia article

suggests that the issue hasn't been resolved over the last five years.

After probably a few hours at sea, they reached the island’s rocky shore, and managed to land among the island’s main residents: puffins, razorbills, murres, and Arctic terns.

If I were that guy, I'd have pointed at one of the latter birds and proclaimed: "It's my tern now!"

Depending on whom you ask, Machias Seal Island is either off the coast of Maine or of Grand Manan. It’s also either American or Canadian. It is the only place with this particular unsettled identity that you can actually stand on top of. Although the ownership of some stretches of water is still contested, this island—and neighboring North Rock, which is even smaller and barer—are the last crumbs of their land the two countries don’t agree on.

Just wait a few years, and climate change will settle the debate for us.

I feel obliged to point out that while I've never been to this island, it sits within easy distance of the easternmost point of the continental US: Quoddy Head Lighthouse. I visited that spit of land when I decided to travel from it to the westernmost point, in the state of Washington. Quoddy Head was the easier of the two to reach, requiring significantly less hiking and way fewer bears.

The article delves into the source of the land dispute, then:

If the world were more just, this would all be moot: The people of the Passamaquoddy Nation likely used the island long before anyone else even knew it existed. (“Machias,” also the name of precipitous local river, is a Passamaquoddy word that means “bad little falls.”) Instead, even as their identifications and affiliations have shifted, the neighbors have kept squabbling over it, like a pair of growing siblings in a shared bedroom.

Look, let's hope it stays on the "siblings" level of quarrel. We don't want to go to war with Canada. We have a history of losing said wars.

The rest of the (rather long) article delves into the American side of things, focusing, as the headline implies (look at that, a headline matching up with the text), on one person's, or more properly one family's, quest to keep the US claim to the island.

I won't quote further, but it's a way more interesting read than the Wiki page.

2 Like • Comment

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