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.

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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.

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

September 27, 2021 at 12:02am

#1018112

Speculation

I've been reading (and viewing, and sometimes writing) science fiction for most of my life, so this article might as well have been written for me.

Fan of sci-fi? Psychologists have you in their sights

Science fiction has struggled to achieve the same credibility as highbrow literature.

That depends on whose perspective you're looking for. I find "highbrow" literature to be mind-numbingly boring at best, useless at worst. It's just as fictional as science fiction, and lacks the imagination and extrapolation that characterizes science fiction. (Also, the whole "brow" thing comes from phrenology, which was long ago debunked.)

In 2019, the celebrated author Ian McEwan dismissed science fiction as the stuff of “anti-gravity boots” rather than “human dilemmas”.

While there is certainly crap, that's true of pretty much every creative endeavor. Theodore Sturgeon, an SF author, famously pointed out that ninety percent of everything is crap

. He was reacting to the same sort of criticism noted here by pointing out that there's crap everywhere.

According to McEwan, his own book about intelligent robots, Machines Like Me, provided the latter by examining the ethics of artificial life – as if this were not a staple of science fiction from Isaac Asimov’s robot stories of the 1940s and 1950s to TV series such as Humans (2015-2018).

Oh for fuck's sake, the very first science fiction novel examined "the ethics of artificial life." It's been a through-line in science fiction from Frankenstein up through the latest installments of Star Trek. And it's not going to let up anytime soon. It's burned into the DNA of the genre, and we own that shit. Which that guy would know if he'd actually read any SF instead of just ragging on it sight-unseen.

Psychology has often supported this dismissal of the genre. The most recent psychological accusation against science fiction is the “great fantasy migration hypothesis”. This supposes that the real world of unemployment and debt is too disappointing for a generation of entitled narcissists. They consequently migrate to a land of make-believe where they can live out their grandiose fantasies.

I can't say that's not the case for every SF fan. I don't doubt that some people are into the escapist aspects, much as furries are furries because they're furries. But SF explores possibilities, and questions everything about what we are, what we do, what we can be (and, perhaps most importantly, what we should not be). That's not escapism; that's a study of human nature.

It also has the unique ability to step outside our human bubble and try to look at things from an outsider's perspective, something that is sorely lacking in some circles right now. And while it often gets the science wrong, an astute reader can use it as a springboard to know exactly what it got wrong, and what the actual science tells us. For example, see my post from a few days back about why sex in zero-g would be a frustrating endeavor.

Science fiction is the one mode of entertainment that's not narcissistic.

But, while psychology may not exactly diagnose fans as mentally ill, the insinuation remains – science fiction evades, rather than confronts, disappointment with the real world.

Right, tell that to all the readers of dystopian future stories.

But don't just take my word for it:

In her review of The Iron Dream, the now-celebrated science fiction author Ursula Le Guin – daughter of the distinguished anthropologist Alfred Kroeber – wrote that the “essential gesture of SF” is “distancing, the pulling back from ‘reality’ in order to see it better”, including “our desires to lead, or to be led”, and “our righteous wars”. Le Guin wanted science fiction to make strange the North American society of her time, showing afresh its peculiar psychology, culture, and politics.

While Le Guin's writing style never appealed to me, there's no doubt she was highly influential and knew what the hell she was doing.

Rather than ask us to pull on our anti-gravity boots, open the escape hatch and leap into fantasy, science fiction typically aspires to be a literature that faces up to social reality. It owes this ambition, in part, to psychology’s repeated accusation that the genre markets escapism to the marginalised and disaffected.

Look... any form of entertainment can be escapism. It's frustrating that some of the same people who rag on SF can be found on weekends at sportsball stadiums, all dressed up and painted in their tribal colors, waving foam fingers (if that's still a thing; I don't know) and displaying their fandom to all the world on giant stadium TV screens. No, sports fans lost the right to rag on SF/Fantasy cosplayers a very long time ago.

Note, I'm not dunking on sports fans either. Makes 'em happy, great. But this is one big giant "stop liking what I don't like" with a touch of "NEEERRRDDD!" added on for good measure.

I guarantee you, though, that if con-goers ended up rioting through the town after a convention, breaking windows and making noise, they'd ban cons. Even though that's exactly what some sports fans do.

I think it's time to stop ragging on escapism in general, though. I mean, look around. Who doesn't want to escape from time to time? It only becomes a problem when it's an obsession, but the same can be true for any obsession, be it sports or sex or whatever.

As I've noted in here more times than is probably necessary, I don't believe that aliens are going to come down and land in their flying saucers and ask to be taken to our leader. But if it ever does happen, no one - no one - will be more prepared for the encounter than a science fiction fan.

And because I promised more mini-contests...

Merit Badge Mini-Contest!

Maybe you're a science-fiction fan, maybe you're not. But I'd find it hard to believe anyone hasn't encountered any of it (note: Star Wars is not science fiction; it's fantasy with SF props). Reading or viewing, what's your favorite science fiction story / series? Any book(s), TV shows, movies, all count as long as they're at least partly SF. Comment below, and the one I like best will earn its writer a Merit Badge. Deadline, as usual, is midnight at the end of the day today, Monday, according to WDC time.

Note: I won't necessarily pick the one I most agree with; tell me why you like a certain story or series, regardless of whether you know I like it or not.

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