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Tuesday, Dec. 31, 2024

9:58am 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

October 16, 2024 at 8:12am

#1078398

Can We?

From The Takeout, answers to questions you never asked.

Here's Why Canned Food Always Comes In A Ribbed Tin

No, it's not "for her pleasure."

You might think the ribbed design on canned food is just a quirky touch meant to make jellied cranberry sauce look more interesting, but it actually serves a crucial purpose.

I might be alone in this, but I like the jellied cranberry sauce way more than the other canned kind, and way, way more than homemade. The uniformity of it appeals to me. I like to punch out both ends of the can and use one of them as a plunger, pushing out precisely 1/4" of the stuff at a time, then slicing it off at the can top. It's a far superior experience and taste.

Not that I'd ever tell that to someone who sweated over a hot stove to prepare homemade.

This is because the corrugated ridges add strength to the tin by creating a series of tiny arches along the surface. These in turn more evenly distribute pressure, similar to how the arches of a bridge help it carry heavy loads.

Always amusing to see someone unfamiliar with a subject (in this case, structural engineering) attempt to describe it to others.

Wait... is that how I sound all the time?

But the ridges have another job that goes beyond just strength.

Thus once again demonstrating the concept that things don't have to have just one purpose.

In addition to making the can stronger, the ridges on a can help it withstand heat. During the canning process, the contents are sealed and then brought to high temperatures to kill off any bacteria, helping to ensure that the food inside stays safe to eat.

In theory.

These ridges also help the can remain intact after it leaves the factory, when it might have to endure extreme temperatures during transport and storage.

I have a severe addiction to Coke Zero, and I buy it by the case. Obvously, Coke cans aren't ribbed, though their bottoms and tops are reinforced (because of how cylinders perform with pressure inside). Sometimes, on rare occasions, the reinforcement fails, and the bottom goes from concave to convex. On other occasions, it's the top that blows out, making it a whole lot harder to open the damn can. Unlike with canned food, this doesn't indicate that the contents have gone bad.

I suppose it's possible that some cans fail along the cylinder, too, and those are just culled before sale. But it seems to me that the sides of the can are not the failure points.

In the early 19th century, food was stored in glass jars that were heated to high temperatures to kill bacteria and then sealed to keep the contents safe.

Home "canners" still use glass jars. Duh.

The next big leap came in 1810 when English inventor Peter Durand developed tin-plated iron cans... Before the invention of the can opener nearly 50 years later, people had to use tools like hammers and chisels to access the food inside.

Fifty years? Man, humanity really dropped the ball on that one. I guess they were too busy opening cans to develop a better way of opening cans.

5 Like • Comment • View 4 comments

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