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.

1 Like

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.

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

August 2, 2023 at 10:06am

#1053488

Coming to a Punderstanding

My father always told me puns are the lowest form of humor. Then he'd proceed to make jokes like "Why did Adam laugh? Because God gave him two test tickles."

No, that kind of joke takes intelligence, cleverness and agility of thought, even if it is painful to hear (or read). The lowest form of humor is the fart joke.

‘Hi Terrible, I’m Dad’: Why Corny Jokes (Even the Good Ones) Get No Respect

Dad jokes rule. In almost every other context, “dad” as a prefix pretty much means “shitty,” but dad jokes are a whole different thing.

Whew. Another reason to be glad I'm not a dad.

For those unfamiliar with the expression, “dad jokes” generally refer to what used to just be known as jokes, puns or wordplay — generally a gag based around two similar-sounding but different terms.

And I'd prefer that these witticisms not be referred to as "dad jokes," but language, like a cat, tends to do what it wants to do regardless of my wishes.

Samuel Johnson, compiler of the first English dictionary and one of Britain’s most celebrated intellectuals of all time, viewed puns as the lowest form of wit.

And yet, they persevere.

It wasn’t always like this. “Every culture, as far as we know, has some form of wordplay,” says Attardo, who has written extensively on the subject. “Every language has syllables, and as soon as you have syllables strung in a row, you can switch them around. That’s universal.” However, he explains, this doesn’t mean all languages use it for humor. In some cultures, for instance, wordplay is used for magical, symbolic or religious purposes.

Humor is magical, symbolic, and religious. But yeah, this sort of thing is true. In Japan, they have national days of observance that are entirely based on wordplay.

“In the gospel, when Jesus calls Peter his rock, there is a pun in there — not in the English translation, but originally, with the Latin word petrus, meaning rock. But when Jesus does that, he’s not doing it to be hilarious and deliver a dad joke, it’s more about it all having meaning attached to it, and Peter’s role being preordained.”

That stuff isn't limited to the New Testament, where the pun was originally in Greek. There's numerous wordplay in the Hebrew original texts, too. Puns, of course, rarely translate outside of their original language, so this makes parts of the Bible real head-scratchers if you only read it in English. Like, I mentioned my dad's Adam joke above. In Hebrew, adam is a word for adult male human, while adamah can be translated as soil. So the writers put a pun right there in the beginning. That, along with many other Biblical names, get lost in translation. Look for the formula "I shall call him x because y," and you're looking at a badly translated play on words.

There are puns in the Latin poetry of Horace and Cicero, and Shakespeare is littered with them.

At least the Shakespeare ones are moderately intelligible.

“By our modern perception, that’s completely inappropriate,” says Attardo. “My guess is that a pun like that would be seen as clever and layered by audiences at the time rather than something to be laughed at.”

Puns are not there to be laughed at. Almost all modern humor involves anguish, pain, suffering, or sorrow, because it's a defense against these things. But a pun only causes laughter in the narrator thereof; the listener experiences the suffering.

The only form of wit generally seen as an even lower art form than dad jokes is prop comedy, which is the same thing to an even more extreme degree — you haven’t just sat down and written that material, you’ve spent time rendering it into three dimensions, you worthless clown.

I'm not generally a fan of prop comedy, but no, fart jokes are still the lowest because they're too easy. But...

The net result is the same — making people laugh. If you’re laughing at how crappy a joke is, you’re laughing at the joke. It worked. You might not have wanted it to, and you might consider yourself above it all, but the joke made you laugh, goddamn it.

You look that beholder right in the eye.

The other reason there isn’t a lot of academic literature on dad jokes is, of course, obvious. Any time anyone tries to interview a dad-joke enthusiast about the subject and says, “Hi, I’m studying how people use jokes,” they’re met with, “Hi, Studying How People Use Jokes, I’m Dad.”

It is, of course, impossible to have a serious conversation about humor.

But this whole thing reminds me of a pun I'm building towards in my current fantasy RPG game. In it, I'm playing a bard, someone who uses comedy, storytelling, and music more than the traditional swords or sorcery. If you've played such a game, or seen the latest D&D movie or The Witcher, you know what kind of character I'm talking about.

Well, I'm going to hook him up with a lyre, which, as you know, is an ancient stringed instrument and therefore perfectly acceptable in a medieval fantasy setting. And then, when we finally face the Big Bad Boss of the plotline, I plan to hold it up as if it were a shield and taunt her by singing, "Come on, baby, fight my lyre!"

After all, eventually all villains have to face the music.

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