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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Write_Mikey_Write!

about 9 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 11 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.

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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.

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.

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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.

3 Like

Turkey DrumStik

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

Not gonna lie I need the holiday season chatter.

February 4, 2022 at 12:01am

#1025993

Origins of Comedy

At one point -- I can't find it now; I think it was in a newsletter -- I discussed the world's oldest surviving joke, which as I recall came from ancient Sumeria.

Most 'Modern' Humor Dates Back To A 1,800-Year-Old Book

The Sumerian one isn't funny to modern ears (besides, it was a fart joke, which I am above), but let's see what Cracked has to say about "modern" humor.

Where does comedy come from? Up until now, the closest thing we had to an answer was: “A childhood sad just enough to make you use humor as a defense mechanism instead of going to therapy, but not so sad that you decide to become a poet.”

I am attacked.

So, yeah, there is this book titled Philogelos, which is Greek for “laughter-lover,” or “chuckle-schmuck” if you will. It’s a collection of 265 jokes composed by Hierocles and Philagrius, of whom we know exactly two things: 1) jack and 2) squat.

It's just as likely, I think, that Hierocles and Philagrius were pseudonyms; sometimes it's important to hide your real identity when making jokes, lest the butts of said jokes come find you and fart in your face.

It’s actually kind of reassuring that your misogynistic uncle’s “jokes” about your aunt would solicit as many groans in Ancient Greece as they do today, mainly because everyone back then had already heard it all.

I had to look it up, but yeah, 1800 years ago was still technically Ancient Greece.

Anyway, I could repost examples of the jokes here, but you can go to the original Cracked link or the one to the source material a few paragraphs ago. I don't feel like trying to be funny right now.

Just keep one thing in mind: the best humor relies on puns (that's my story, and I'm sticking to it). And the hardest thing to translate into another language is a pun. There are obviously workarounds, but when people say something is lost in translation, it's usually because the pun only works in the original language. Anyway, I did note that some of the jokes at the source link would have been, presumably, absolutely hilarious puns in 3rd century Greece, but are quizzical-eyebrow-raisers in 21st century Anglophone countries.

In any case, none of these are exactly side-splitters, because in the end, comedy requires cultural context and is usually time-sensitive, but they do provide insight into the origins of jokes. Just don't try to tell them at your next open mic night.

5 Like • Comment • View 4 comments

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