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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August 16, 2023 at 10:47am

#1054180

The Time Machine

Science fiction is blurry.

By which I mean, the edges of the genre kind of blur into other genres: horror, fantasy, adventure, mystery, snob-lit, whatever. This makes the genre remarkably difficult to define, other than "I know it when I see it."

So keep that in mind when looking at this collection of early 20th century SF.

How Scientific and Technological Breakthroughs Created a New Kind of Fiction
Joshua Glenn Chronicles the Development of Sci-Fi in the Early 20th Century

If you insist, as I do, that the fundamental thing that makes it science fiction is exploring the ramifications of new or potential discoveries or inventions on people, society, and culture, then SF actually got its start in the early 19th century. But there's no question that it took a while to blast off.

But I'm not here to argue about genre, which is essentially a marketing tool. The article itself is a marketing tool, promoting the guy's book. That's fine; lots of us are here to promote our books or find stuff to read.

During the early twentieth century, the world’s scientists were wonderstruck by the revelation that the spontaneous disintegration of atoms (previously assumed to be indivisible and unchangeable) produces powerfully energetic “radio-active” emissions.

Wait'll they find out about quantum physics.

Throughout the nineteen-aughts and -tens, scientists and snake-oil salesmen alike would ascribe to radium—and radiation in general—vitalizing, even life-giving powers.

I've noted things like this in here before.

Now, look, I'm not going to quote from the rest of the article, here. It's not really necessary, and it provides quick descriptions of several early 20th century SF books. If you're interested, the link is right there; if you're not, see you tomorrow.

But I find it interesting to delve into the history of the future; that is, what people thought the future might be like in the past. If that makes sense. It's not about seeing what "came true" (I've noted before that science fiction doesn't predict; sometimes it warns, but most often, it inspires); it's about seeing what attitudes people had then and how they might have shifted.

And some themes continue to the present day: what would alien life be like? What if we could create life? How do we deal with the ethical issues of technology?

So, yeah. Maybe I'll expand on this in a future Fantasy newsletter (there's no official SF newsletter, but close enough). Until then, step into the time machine, if you dare.

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