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

September 26, 2023 at 10:34am

#1056238

Poe Lease

I can't resist a piece on Poe any more than my housemate's kitten, Edgar Allan Purr, can resist a dangling string.

When Poe Invented the Detective Story, he Changed the Literary World Forever

The cat's name was my idea, incidentally.

I don't know much about this source, Crimereads, by the way. I just found this article while searching for something else, and, well, like I said, dangling string.

Even though literature had, for centuries, brimmed with clever problem-solvers, from tricksters to reformed thieves to wise men to police prefects, Edgar Allan Poe’s detective story, “The Murders in the Rue Morgue,” still awed the literary world when it appeared in 1841.

Detective stories were, for Kid Me, kind of like crossword puzzles: fun to complete, but the secrets of their creation might as well have been quantum physics for all I understood them. I would read a science fiction or fantasy book and go, "Hey, I bet I could write like that." Not so with the detective genre.

The police are stumped. But C. Auguste Dupin, a chevalier and rare book aficionado, solves the mystery at home after reading the details in the paper, becoming literature’s first bona fide detective character and starting a genre revolution.

Astute readers will note that thus, science fiction predated detective fiction as a genre.

As literary critic A. E. Murch writes, the detective story is one in which the “primary interest lies in the methodical discovery, by rational means, of the exact circumstances of a mysterious event or series of events.” Critic Peter Thoms elaborates on this, defining the detective story as “chronicling a search for explanation and solution,” adding, “such fiction typically unfolds as a kind of puzzle or game, a place of play and pleasure for both detective and reader.”

Like I said. Crossword puzzle.

The well-heeled Dupin is an armchair detective who solves puzzles because he can, using a process called “ratiocination,” in which he basically ‘thinks outside of the box.’

I've known several people who prided themselves on "thinking outside of the box." Without exception, all of these people were lousy at thinking in the first place, and just did free-association. This is quite a different procedure than "ratiocination."

(And it’s a good thing he does, or no one will solve these crimes; the murderer of “The Murders in the Rue Morgue” turns out to be an escaped orangutan. It might be safe to say no one else would conclude that.)

Goddammit! SPOILERS!

If Poe had not solidified the conventions that we recognize as marking the modern detective story, others likely would have done the same not long after.

Okay, but this is true about pretty much any invention or discovery. If Einstein hadn't worked out relativity, someone else would have. If Nikola Tesla hadn't invented the alternating current method of electricity transmission, others would have. That in no way diminishes Poe's legacy.

And no nineteenth-century detective lineage would be complete without Eugène-François Vidocq, a criminal-turned-criminologist who lived from 1775-1857 and who founded and ran France’s first national police, the Sûreté nationale, as well as France’s first private detection agency. His life inspired countless (swashbuckling) adaptations, including an American adaptation published in Burton’s Gentleman’s Magazine in 1828, entitled “Unpublished passages in the Life of Vidocq, the French Minister of Police,” which Poe very well might have read. Interestingly there’s a character in that story named “Dupin.” Ahem.

"Good writers borrow. Great writers steal." -T.S. Eliot, and everyone who ever quoted him.

Dupin’s ability to read extraordinary meaning into clues makes him rather the first semiotician, elucidating the relationship between signs, signifiers, and ‘signifieds’ more than a century before Ferdinand de Saussure published his work on the subject in 1966—particularly because Dupin finds his clues through linguistics rather than physical objects.

Thus, Poe also invented postmodernism. Before modernism was even a thing.

Years later, Arthur Conan Doyle wrote, “Each [of Poe’s detective stories] is a root from which a whole literature has developed… Where was the detective story until Poe breathed the breath of life into it?”

He stole.

Indeed, Doyle construed his detective Sherlock Holmes as an intellectual descendant of Holmes, having Watson (who also participates in a lineage offered by the Dupin stories, but of Dupin’s supportive narrator/chronicler and friend) cite Dupin upon first witnessing Holmes’s deductive genius.

Clearly, that second Holmes should have been "Dupin." Everyone makes mistakes. Even fictional detectives, from time to time, when the plot requires it.

As the article notes at the end, Holmes wouldn't have existed, at least not as we know the character, without Dupin.

Neither would Batman.

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