Complex Numbers (Book)

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Complex Numbers

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/

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Brandiwyn🎶

a day ago
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.

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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').

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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.

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Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 28, 2022 at 12:02am

#1041092

The Sage of Indianapolis

This one's been in my queue for a long time, such that every time I see it on the list, I go, "Now what am I going to say about this?"

Kurt Vonnegut’s Greatest Writing Advice
"Literature should not disappear up its own asshole," and other craft imperatives

After all, how can I, being just me, comment on writing advice from one of the most acclaimed, award-winning, and all-around great writers of the 20th century? Someone who is, moreover, dead and therefore can't rebut anything I say?

...Easy. I just read, paste, format, and type.

(Article is from 2017, the 10th anniversary of Vonnegut's tragic, untimely and completely unexpected death, but that shouldn't matter.)

Today, if you can believe it, makes it ten years since we lost one of the greatest American writers—and, no matter how he tried to deny it, one of the greatest writing teachers. Certainly one of the greatest writing advice list-makers, at any rate.

Like I said, 2017. As list-making became the default method of communication on the internet, once again, Kurt was ahead of his time.

Plus, it’s no-nonsense advice with a little bit of nonsense. Like his books, really.

I don't want anyone getting the idea I didn't like Vonnegut. Far from it. But he's not up on a pedestal for me like Twain or Poe.

Find some of Vonnegut’s greatest writing advice, plucked from interviews, essays, and elsewhere, below—but first, find some of Vonnegut’s greatest life advice right here: “I tell you, we are here on Earth to fart around, and don’t let anybody tell you different.”

On that point, at least, we can agree completely.

On proper punctuation:

Here is a lesson in creative writing. First rule: Do not use semicolons. They are transvestite hermaphrodites representing absolutely nothing.

These days, Vonnegut would be soundly thrashed on social media for using the words "transvestite hermaphrodites;" times and words change.

You'll note I used a semicolon in the previous sentence; I do that when I damn well feel like it.

I agree it probably shouldn't be (over)used in creative writing; this is a blog entry, so I can get away with it. However, someone as well-versed in satiricism as Vonnegut must have known that there's a place for semicolons even there, once you know the "rules" so well you can break them.

On having other interests:

I think it can be tremendously refreshing if a creator of literature has something on his mind other than the history of literature so far. Literature should not disappear up its own asshole, so to speak.

And yet, like all art, it often does.

What's not clear to me here is how he meant "literature." For me, the term encompasses all fiction writing. Depending on context, though, it can be used by snobs to differentiate high art from low art, which they snobbily call "genre writing." News flash: every work of fiction is genre fiction in that it has a genre. So that quote is kinda rich coming from someone who resisted acknowledging that he wrote science fiction because some science fiction writers were hacks.

On the value of writing:

If you want to really hurt your parents, and you don’t have the nerve to be gay, the least you can do is go into the arts.

Or, you know, lean into the stereotypes and do both.

On plot:

I guarantee you that no modern story scheme, even plotlessness, will give a reader genuine satisfaction, unless one of those old-fashioned plots is smuggled in somewhere.

Seriously, the link is worth clicking on just to read this one section. I can't do it justice here with cherry-picked quotes; just trust me on this.

Also, I'm skipping a few of them here, so if you want to read more, well, there's the link.

On a good work schedule:

I get up at 7:30 and work four hours a day. Nine to twelve in the morning, five to six in the evening. Businessmen would achieve better results if they studied human metabolism. No one works well eight hours a day. No one ought to work more than four hours.

Everyone has their own preferred schedule, but I'm pretty sure the "eight hours a day" thing is industrialist nonsense. Thing is, though, writing is different from some other professions: whether you're actively typing or not, your brain is going through plot, characterization, descriptions, whatever. At least that's how it works for me. Like I said above, every time I saw this one in my list, I started thinking about what I was going to write. Some of that even made it in here.

On “how to write with style,” aka List #1:

Reverse the numbers in this section and it might as well have come from Cracked. Not that it's especially amusing, but this list, more than his other advice, rings true for me. Too long to quote; just give it a look if you care.

I ignored his gushing about Joyce, of course.

I am, however, going to reproduce the second list in its entirety. It's brief, and it's been passed around quite a bit already, so of course I have something to say about it.

On how to write good short stories, aka List #2:

1. Use the time of a total stranger in such a way that he or she will not feel the time was wasted.

Great advice, but the devil's in the implementation.

2. Give the reader at least one character he or she can root for.

So many stories these days don't bother to do that.

3. Every character should want something, even if it is only a glass of water.

This is probably Vonnegut's most quoted piece of advice. It's definitely important, but it's insufficient by itself.

4. Every sentence must do one of two things—reveal character or advance the action.

See my multiple rants about overlong descriptions.

5. Start as close to the end as possible.

Lots of writers lately have taken this literally, starting at the very end, thus relegating the rest of the story to flashbacks. Nothing inherently wrong with that, but sometimes it's difficult to follow too many jumps around in time.

6. Be a sadist. No matter how sweet and innocent your leading characters, make awful things happen to them—in order that the reader may see what they are made of.

On that point, I agree.

7. Write to please just one person. If you open a window and make love to the world, so to speak, your story will get pneumonia.

I came up with this one independently, I think. I noted that some of the greatest works of literature (using the term in its broadest sense, as above) were written with just one person, or possibly a small group of people, in mind; they didn't get their start from an author using focus groups or brainstorming what demographic he or she was shooting for. Examples include Alice in Wonderland, pretty much anything by Poe, and freaking Lord of the Rings.

My personal corollary to this is: you have to expect that some people won't like it. That's still better than blandly trying to please everyone.

8. Give your readers as much information as possible as soon as possible. To heck with suspense. Readers should have such complete understanding of what is going on, where and why, that they could finish the story themselves, should cockroaches eat the last few pages.

I can't completely get behind this one, but like I said: he's Vonnegut and I'm not. I'm mostly commenting here from a reader's perspective, and two of my preferred genres are fantasy and science fiction. In those, you want to withhold some information; it helps keep the reader reading so as to eventually discover, say, why the world is a post-apocalyptic wasteland, or who the MC's father really is (yes, that's mostly a Star Wars reference). I'm not quite as big a fan of mystery, but in that genre, it should be glaringly obvious that you withhold some information. As for horror, if you explain the monsters too much, they cease being monsters.

The danger of putting too much information up front is obvious: you end up writing The Silmarillion before Lord of the Rings, and you'll lose readers. No, I say (again from a reader's perspective): start with the story, not the Book of Genesis.

On ignoring rules:

And there, I’ve just used a semi-colon, which at the outset I told you never to use. It is to make a point that I did it. The point is: Rules only take us so far, even good rules.

Told you so.

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