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Saturday, Nov. 16, 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:

Write_Mikey_Write!

a day ago
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

a day ago
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

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

June 16, 2022 at 12:01am

#1033883

That's Reasonable

A fifth entry for "Journalistic Intentions"

[18+]

Reasonable Authority Figure

There's usually a reason, in writing, to have the authority figure be unreasonable. It creates conflict. You get one that actually listens, and the conflict has to come from somewhere else, perhaps the other main characters or, as the trope page suggests, an advisor.

But, while reading the description of this trope, my mind went to Star Trek.

This is not surprising; as you all know, I've been a Trek fan all my life. It's not precisely the definition of the trope -- for that, your main characters would have to be non-authority figures so the authority figures (bridge crew or whatever) would be shown as reasonable or not. This is, in fact, what actually happens in the Lower Decks comedy-focused animated Trek series, but that's only been going on for two years, while the franchise in general has been around for well over 50, and apart from that one series, it always focuses on the leaders themselves.

The link to live-action TV

from the trope page kind of acknowledges this, presenting examples of reasonable admirals that fit the trope. And yet, in their section on Doctor Who (another long-running franchise that I've seen every episode of), they mention that The Doctor is a RAF.

On a starship, there can be no greater authority figure than the Captain. Even when there's an admiral on board, usually to provide a foil for said captain, the captain is absolutely in charge of his or her ship. So to be complete, any discussion of a RAF. must consider whether the main character is, in fact, a RAF.

There is, and probably always will be, a long-running argument in Trek fandom about who's the better captain: Kirk, or Picard. (Trick question; it's obviously Sisko.) But I submit that a new contender has arisen in the arena: Captain Christopher Pike. And that's precisely because he is the most R of all RAFs. And that's without being a Gary Stu.

Gary Stu is one of the names for a male Mary Sue, which is a trope that itself arose from Star Trek fandom. For those who don't know, early on in the history of Star Trek, a lot of fanfiction got written. This is no different from today, but back then, things were maybe a little more unfocused, what with lack of internet and only one show to pull from. It describes, roughly, a character with no flaws, perhaps even someone nothing bad ever happens to in the story; it's usually a writer inserting themselves into the narrative for wish-fulfillment purposes. The term "Mary Sue" itself is, like many neologisms, often abused and sometimes has misogynistic overtones, implying that the qualities we look for in a male protagonist are unwelcome in a female one ("What do you call a male Mary Sue? A protagonist.")

All of which is to say that Pike isn't a Mary Sue, or a Gary Stu, or whatever. He has flaws and personality traits other than "always being right" (and the best tagline in all of Trek). But he's definitely a RAF

As an aside, for anyone not up to date on all the recent Star Trek shows, Strange New Worlds chronicles the Enterprise's journeys before Kirk took over. It's based on the original pilot, unaired on its own and only shown in a two-part episode of the original series as flashbacks. Pike also figures prominently in the Abrams revised-timeline movies, but in this series, we're back in something resembling the original timeline (which, I will argue endlessly to anyone bored or captive enough to listen, has been irrevocably altered by repeated time-travel fuckery in various Trek series, so shut the hell up about continuity errors already).

Eh, but I've rambled on long enough, and I don't want to point to too many examples lest I spoil the series for someone. The point is that I think it's absolutely a legitimate version of the RAF trope to make the main character one. It can be more fun if their subordinates are incompetent, but of course that rarely happens in Star Trek, because it's basically competence porn.

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