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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 5 hours 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.

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Adherennium Plotting something

about 7 hours 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.

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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.

3 Like

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

July 31, 2022 at 12:01am

#1035901

Big Dick

Of all the science fiction authors I've read—and there have been quite a few—this one has some of the more memorable works.

Philip K Dick: the writer who witnessed the future
Forty years since the death of the sci-fi author – whose stories have inspired films like Blade Runner and Minority Report – Adam Scovell explores how prophetic his work has been.

This is a BBC article from back in March, published approximately on the anniversary of PKD's death.

This is 2022. And 2022 is a Philip K Dick novel.

Well. He was, after all, very good at writing believable dystopias.

Writers of science fiction often feel more prescient than others. Whether it's the threat to women's rights in the work of Margaret Atwood, the architectural and social dystopias of JG Ballard's novels, or the internet-predicting world of E M Forster's The Machine Stops (1909), the genre is replete with prophetic writers dealing with ever more familiar issues.

Look, here's the thing about that: it's not prescience or prophecy. Plenty of things SF authors have written about haven't happened; of those that have, most of them have done so in ways they didn't envision. And as the article points out later, that's also not their purpose. It's just that when someone spends a great deal of time looking at society and technology, and thinking up ways to extrapolate both into the future, they're going to sometimes come pretty close. Also, actual inventors of technology often read SF, so they invent shit that fits what they've read about, consciously or not.

In a remarkably prolific 30-year period of work, Dick authored 44 novels and countless short stories, adaptations of which went on to redefine science fiction on screen – in particular Ridley Scott's Blade Runner (1982), which was based on Dick's story Do Androids Dream of Electric Sheep? and Paul Verhoeven's Total Recall (1990), which took his 1966 short story We Can Remember It for You Wholesale as its source material. More recently Dick's novel The Man in the High Castle (1962) has been turned into a hit Amazon series.

Blade Runner remains my favorite movie of all time (the director's cut, that is). As for High Castle, I read that book long ago and couldn't imagine it becoming a movie or TV show—and yet they slam-dunked it.

Also, the less said about the Total Recall remake, and the Blade Runner sequel, the better. But I think his writing has been adapted even more than that of Alan Moore, which is saying something.

Incidentally, one night I watched Minority Report, Blade Runner, and A Scanner Darkly (a far lesser-known movie using rotoscope technology). I bear the scars to this day of Too Much Dick.

Dick was not simply an effective writer of strange fictions, but an unusual person in his own right. Burdened by deteriorating mental health, visions, and what he alleged were all manner of paranormal experiences – many of which were woven into his expansive oeuvre – Dick had a troubled and fragmented relationship with reality.

I believe this is BBC-speak for "Dick was stoned out of his gourd and went completely barmy."

Celebrated science-fiction and fantasy author Stan Nicholls suggests Dick's work is prescient because it explored the future through the then-present. "His stories posited the ubiquitousness of the internet, virtual reality, facial recognition software, driverless cars and 3D printing," Nicholls tells BBC Culture – while also pointing out that "it's a misconception that prediction is the primary purpose of science fiction; the genre's hit rate is actually not very good in that respect. Like all the best science fiction, his stories weren't really about the future, they were about the here and now."

I'm mostly including the above quote because I Chekov's Phasered it above. I'd add that a lot of SF, including a lot of Dick, is supposed to be a warning, not a blueprint.

Nevertheless, the way he also anticipated particular technological and societal developments remains striking. "He had a lot of scientific images of the way the future would work," says Anthony Peake, author of the biography A Life of Philip K Dick: The Man Who Remembered the Future (2013). "For instance, he had a concept that you would be able to communicate advertising to people directly, that you'd be able to know them so well that you could target the marketing precisely to their anticipations. And this is exactly what is happening online."

I've said before that I despise ads and go out of my way to avoid them. Still, it's impossible to avoid them entirely and still live in the actual world, and the truth is, I'd rather have targeted ads for things like bar supplies, cat food, and t-shirts than get spammed by purveyors of, say, adult diapers, religion, tampons, or hemorrhoid cream. The difference between targeted ads and a Dick world is that in a Dick world, it's ultra-invasive. That's the dystopia element.

Screen adaptations have often latched on to the invasive nature of advertising in his work, yet the writer explored the theme in far more detail than as merely a background aesthetic (which is how it manifests on screen).

I'd venture a guess that this is because shows and movies rely to one extent or another on advertising, and it wouldn't do for ad agencies to allow their antics to be portrayed in too negative a light.

Dick's work often had a political dimension, too. The Man in the High Castle, for example, imagines an alternative history in which the Nazis won World War Two.

You know, that's been the elevator-pitch description of that story for as long as I can remember. The novel, and the TV show based on it, is way more complex than that.

Dick was altogether anti-establishment: his stories feature authorities and companies consistently abusing their power, especially when it comes to surveillance. His worlds are ultra-commodified and their citizens addicted to materialism, while celebrity, media and politics meld to create nightmarish, authoritarian scenarios, usually topped off with a heavy dose of technocracy and bureaucracy.

Nah. Not prophetic at all.

In the 1969 novel Ubik, a character ends up arguing with the door to his apartment, as he doesn't have the change to get in via its coin-operated mechanism.

Unrealistic. Today they'd sell access on a month-to-month recurring subscription plan, like BMW and their goddamned seat heaters (from "Heated Discussion"

)

Putting aside Dick's ability to foreshadow the future we now take for granted, his most unnerving vision was of the world itself ultimately being a simulation.

Oh for fuck's sake, not this shit again. It's not "unnerving." Even when I was reading his books when I was much younger, that was already a bridge too far for me. But it does illustrate that the "reality is a simulation" nonsense is older than most of us think it is. Hell, it basically has its roots in millennia-old Eastern religion and Gnosticism: the idea that what we think is reality is actually illusion—a worldview that I long ago put in the manure pile, because even if it's true, and there's no certain way to test if it is or is not, what does it matter? Still, I have no inherent objection to exploring that or other speculations in science fiction.

Dick's reality was already a fragile and complex one. In many of his later books, the idea of reality being a façade grew as a dominant theme.

That's because, as noted above, dude was completely stoned.

Anyway, I saved this one to share because it's a decent, if brief, description of a very prolific, albeit relatively short, writing career.

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