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.

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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.

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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.

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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.

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July 10, 2023 at 9:34am

#1052415

Write What You Write

Full disclosure: I don't "know" most of these authors.

Should You Write What You Know? 31 Authors Weigh In
From Toni Morrison to William T. Vollman, an Age-Old Question Answered

Yes, sometimes I feature articles that are actually about writing. This is one of them, and I'm linking it because I still see arguments about "write what you know." Hell, I participate in them.

Everyone who has ever taken a writing class or read a craft book has heard this piece of writing advice—even if only to have it instantly denounced.

First, we should understand that this is what I'd call subjective advice, as opposed to objective advice (an example of which would be "send your ms to lots of different publishers"). (Whether that's good objective advice or not, I don't know.)

Obviously, I'm not copying all 31 opinions, just the ones I have something to say about.

Nathan Englander: I think what’s behind “write what you know” is emotion. Like, have you known happiness? Have you ever been truly sad? Have you ever longed for something?

That's a take I hadn't considered. I guess if it works, it works. But I think that, for example, a childhood longing for a candy bar is quite different from an adult longing for meaningful companionship.

Kazuo Ishiguro: It encourages people to write a dull autobiography.

And I feel like this is missing the point. It's like the conceit that runs through the movie The Invention of Lying: Since no one can lie, and fiction is lying, the only entertainment available is stodgy guys sitting in chairs retelling the facts of history. Few would actually want that, so it's a stretch to think that this is what "write what you know" implies.

Ursula K. Le Guin: I think it’s a very good rule and have always obeyed it. I write about imaginary countries, alien societies on other planets, dragons, wizards, the Napa Valley in 22002. I know these things. I know them better than anybody else possibly could, so it’s my duty to testify about them. I got my knowledge of them, as I got whatever knowledge I have of the hearts and minds of human beings, through imagination working on observation.

I had to include this one because a) I respect LeGuin a lot; and b) we needed a science fiction/fantasy take on "write what you know."

Zoë Heller: In fact, the injunction is only to know; the business of how you come by your knowledge is left quite open.

And this one gets closer to my own opinion on the subject, which I'll share in a bit.

Toni Morrison: You Don’t Know Anything

I know that this assertion is postmodernist, anti-intellectual bullshit.

Dan Brown: Make the writing process a learning process for you.

I felt physical pain upon realizing that his advice is also close to my own thoughts on the subject. Physical pain, because I've never really liked Dan Brown's writing. I read Da Vinci Code when it came out, but, just before that, I read a (purportedly) nonfiction book called Holy Blood, Holy Grail. And it was clear to me that Brown had read it as well, and "wrote what he knew" from reading that book.

Harry Crews: It’s true that a writer is told by a lot of stupid people, like English teachers...

And I stopped reading there. If you can't respect your teachers, who can you respect?

Gore Vidal:

I'm not going to quote his actual words here, but I encourage you to go and read them because I love a good takedown of the snobbish "literary" genre.

P.D. James: There are all sorts of small things that you should store up and use, nothing is lost to a writer.

Not really sure who this is, but this bit touches on something I've been saying all along, which is that, in general and especially for a writer, there's no such thing as useless knowledge.

Ernest Hemingway: You throw it all away and invent from what you know. I should have said that sooner. That’s all there is to writing.

Appropriately, this is one of the shortest opinions on the list. But, all due respect to Papa, mine is shorter (we're getting to that...)

Jillian Weise: I was told to write poems that cost me something to write them. They cost me a lot.

I'm no expert on poetry, but this tracks.

There's a lot more at the link, pro and con and in between. But I can't help but feel that this wouldn't even need to be a debate if, instead of "write what you know," we all followed the Rule of Waltz:

Know what you write.

(See? Shorter even than Hemingway.)

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