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Monday, Nov. 18, 2024

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Complex Numbers

by Robert Waltz

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-turkey-jobble-jobble-hard-J

about 18 hours ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

Nov 16, 2024 at 9:24am
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

June 9, 2023 at 7:44am

#1050848

Plie

Another one for this month's "Journalistic Intentions"

[18+]...

Plie

I don't know everything.

This certainly comes as a shock to some of you, but it's true.

Usually, when there's a term I've never heard before (like plie) I take advantage of living in a pre-apocalyptic technological society and Google it.

But sometimes it's more fun not to.

The only clue I have is that the word is in the "dance" section of the JI prompt list. This may also come as a shock, given my name, but I know almost nothing about dance. It exists, and some people (who are not me) take great pleasure in performing or observing it.

My ex was (maybe still is; I don't know) a belly dancer, so I'm not completely ignorant of the art form. I know that they have names, usually derived from non-English words, for certain moves. I don't remember any of them, though.

I do have some small knowledge of French, which lends names to some aspects of dance (ballet, e.g.) but I don't recognize "plie" from my limited Francophone vocabulary.

So, to me, even though my eyesight is pretty good again a year and a half after cataract surgery, it just looks like someone misspelled "pile." Hell, my browser's spellcheck doesn't even recognize the word. It suggests, in this order: Pile, pie, lie, plies, and plied.

The latter two are pretty obviously present and past tense, respectively, of the word "ply," which has several meanings.

For one, as a noun, it refers to laminated or layered material. Like plywood. Or 2-ply toilet paper. Neither of which is directly related to dance, unless you're doing it on a plywood stage and/or acting like a mummy. Which is something different from a mummer, who can be, in fact, a dancer. I suppose you can get "plies" and "plied" from it, but that would be an odd construction in English.

As a verb, one can ply a a trade or profession, or ply someone with questions to try to pry information out of them. There are some less common usages, but they're all shortened from "apply."

One other option that doesn't come up in spellcheck suggestions is "plier," which can mean one who plies (as in the above verb) or the never-used singular version of "pliers," a grabbing tool that has two parts, so that when I was a kid, I imagined that "plier" was one branch of a broken pair of pliers (see also "scissors").

English is weird.

Despite its use as a prying tool (maybe it should have been called "priers" instead, resemblance to "priors" be damned because there's plenty of those homophones around), the noun form of "ply" comes from the French "plier" (which I'm guessing is pronounced plee-ay), which means something like to fold.

And with that, I think I'm close to the meaning of "plie": something to do with folding oneself. Let's check our work:

plié: a movement in which a dancer bends the knees and straightens them again, usually with the feet turned out and heels firmly on the ground.

Okay, I was thinking bending at the waist, but fine. Now I know. It's not like I haven't seen ballet before (I just don't know the words), and that seems to be a pretty common move. Doesn't look a lot like folding, though. "Bent" (past tense of "bend") is probably a better translation.

Now, see, I could have gotten there more quickly if the accent aigu (é) had been, in the first place... applied.

4 Like • Comment • View 1 comment

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