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Tuesday, May. 7, 2024

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

🌕 HuntersMoon

a day ago
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

October 22, 2022 at 12:03am

#1039534

Smackdowns

Every art form eventually gets to the point where artists are doing it for fellow practitioners of the art rather than for mass consumption. Writing passed that point ages ago, sometime between Shakespeare and Melville, but fortunately, there's still writing for the masses.

14 Classic Works of Literature Hated By Famous Authors
"I got a little bored after a time. I mean, the road seemed to be awfully long."

And yet, an argument could be made that no one is more qualified to critique a book than someone who's written a book. But that never stopped me, and it never stopped the millions of people who never made a movie from critiquing a movie.

The literary world can be a bit of an echo chamber. That is, if enough people say a book is “great,” it becomes official. It becomes a Great Book, and horrified looks are administered to anyone who would dare disparage it.

Yeah, I do it anyway. I'm looking at you, Ulysses. Yes, that book is on this list; just wait for it.

But even when everyone seems to agree, it’s a safe bet there are a few—or in some cases more than a few—dissenters out there. They may just be in hiding.

I'll have to trot out (again) one of the greatest literary smackdowns, if not the greatest, of all time. At the end of this post.

Virginia Woolf on Ulysses

I started to rub my hands together in gleeful anticipation until I remembered I'm not a big fan of Woolf, either.

An illiterate, underbred book, it seems to me; the book of a self-taught working man, and we all know how distressing they are, how egotistic, insistent, raw, striking, and ultimately nauseating.

How I can agree so much with her conclusions while still gaping in disbelief at her elitist snobbery is beyond my comprehension.

A first rate writer, I mean, respects writing too much to be tricky; startling; doing stunts. I’m reminded all the time of some callow board school boy, full of wits and powers, but so self-conscious and egotistical that he loses his head, becomes extravagant, mannered, uproarious, ill at ease, makes kindly people feel sorry for him and stern ones merely annoyed; and one hopes he’ll grow out of it; but as Joyce is 40 this scarcely seems likely. . . I feel that myriads of tiny bullets pepper one and spatter one; but one does not get one deadly wound straight int he face—as from Tolstoy, for instance; but it is entirely absurd to compare him with Tolstoy.

True. Tolstoy could actually write.

Dorothy Parker on Winnie-the-Pooh

But wait! You might say. How can anyone go all Eeyore on Winnie-the-Pooh? The original, I mean, not the Disney version.

“ ‘Well, you’ll see, Piglet, when you listen. Because this is how it begins. The more it snows, tiddely-pom—’

“ ‘Tiddely what?’ said Piglet.” (He took, as you might say, the very words out of your correspondent’s mouth.)

“ ‘Pom,’ said Pooh. ‘I put that in to make it more hummy.’ ”

And it is that word “hummy,” my darlings, that marks the first place in “The House at Pooh Corner” at which Tonstant Weader Fwowed up.

And it was at this point that I actually Laughed Out Loud.

Charlotte Brontë on Pride and Prejudice

Wasn't that the prequel to Dumb and Dumber?

Why do you like Miss Austen so very much? I am puzzled on that point.

Me too, Charlotte. Me too.

I mean, really, I can't do this takedown justice here. You just have to go to the link. It's beautifully understated.

Mark Twain on Pride and Prejudice

Also the author of what I'm calling the greatest literary smackdown of all time... again, later.

I haven’t any right to criticize books, and I don’t do it except when I hate them. I often want to criticize Jane Austen, but her books madden me so that I can’t conceal my frenzy from the reader; and therefore I have to stop every time I begin. Every time I read Pride and Prejudice I want to dig her up and beat her over the skull with her own shin-bone.

This. This is why Mark Twain is one of the greatest writers who ever lived.

Skipping a few here in the interest of time.

David Foster Wallace on American Psycho

Unlike most of the others, this is still a kind of contemporary book. At least it was published in my lifetime.

Look, if the contemporary condition is hopelessly shitty, insipid, materialistic, emotionally retarded, sadomasochistic, and stupid, then I (or any writer) can get away with slapping together stories with characters who are stupid, vapid, emotionally retarded, which is easy, because these sorts of characters require no development. With descriptions that are simply lists of brand-name consumer products. Where stupid people say insipid stuff to each other. If what’s always distinguished bad writing—flat characters, a narrative world that’s cliched and not recognizably human, etc.–is also a description of today’s world, then bad writing becomes an ingenious mimesis of a bad world. If readers simply believe the world is stupid and shallow and mean, then Ellis can write a mean shallow stupid novel that becomes a mordant deadpan commentary on the badness of everything. Look man, we’d probably most of us agree that these are dark times, and stupid ones, but do we need fiction that does nothing but dramatize how dark and stupid everything is?

Burrrn.

And the list ends as it begins: with a flamethrower pointed straight at James Joyce.

Vladimir Nabokov on Finnegans Wake

I detest Punningans Wake in which a cancerous growth of fancy word-tissue hardly redeems the dreadful joviality of the folklore and the easy, too easy, allegory.

But alas—it turns out that Nabokov actually liked Ulysses. Oh well. No one's perfect.

And now, as promised, although I'm sure I've linked this here before, it makes me laugh every single time I read it: the greatest literary takedown of all time... Mark Twain on Fenimore Cooper.

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