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Friday, May. 10, 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

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Annette

about 8 hours ago
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

a day ago
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

a day ago
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
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

February 9, 2021 at 12:01am

#1004024

Vile, Virile Vices

I always find it amusing, in a dark-humor sort of way, how often groups of people flee religious persecution so that they can install their own.

America’s First Banned Book Really Ticked Off the Plymouth Puritans

Few examples are more obvious than the Puritan settlers of Massachusetts. And while the land they settled eventually came around to the ideals of freedom of religion and expression -- well, at least up to a certain point -- their insistence on a narrow view of morality echoes to this day like the reverberating sound of a turd hitting the slurry at the bottom of an outhouse.

Apparently, Thomas Morton didn’t get the memo. The English businessman arrived in Massachusetts in 1624 with the Puritans, but he wasn’t exactly on board with the strict, insular, and pious society they had hoped to build for themselves.

Why would such a person brave an uncertain ocean journey with such horrible people? Why, money, of course.

The Puritans’ move across the pond was motivated by both religion and commerce, but Morton was there only for the latter reason, as one of the owners of the Wollaston Company.

Who?

His business partner—slave-owning Richard Wollaston—moved south to Virginia to expand the company’s business...

I'd suggest cancelling this guy, but it seems history already has.

...but Morton was already deeply attached to the land, in a way his more religious neighbors likely couldn’t understand. “He was extremely responsive to the natural world and had very friendly relations with the Indians,” says Heath, while “the Puritans took the opposite stance: that the natural world was a howling wilderness, and the Indians were wild men that needed to be suppressed.”

It's funny because the researcher's name is Heath, which is a word for an area in a state of nature, which gave us the word "heathen."

After Wollaston left, Morton enlisted the help of some brave recruits—both English and Native—to establish the breakoff settlement of Ma-Re Mount, also known as Merrymount, preserved today in the Quincy neighborhood and park of the same name.

Incidentally, if you're not aware, Quincy is pronounced like "quin'-zee." Just in case you find yourself in the Boston area one day, don't get tripped up by this shibboleth.

The Puritan authorities didn’t see Merrymount as a free-wheeling annoyance; they saw an existential threat.

Of course they did. The thing most frightening to a Puritan is the horrible idea that someone, somewhere, is having a good time.

With Plymouth’s monopoly dissolved and its perceived enemies armed, Morton had perhaps done more than anyone else to undermine the Puritan project in Massachusetts.

I should absolutely build a shrine to this guy.

Worse yet, in the words of Plymouth’s governor William Bradford, Morton condoned “dancing and frisking together” with the Native Americans—activities that were banned even without Native American participation.

Snort. "Frisking." Snort. Which reminds me of a joke. Why aren't Puritan kids allowed to make out? Because it might lead to dancing.

There could be no greater symbol of such misrule than Morton’s maypole. Reaching 80 feet into the air, the structure conjured all the vile, virile vices of Merry England that the Puritans had hoped to leave behind.

I'm absolutely, totally stealing "vile, virile vices." Oh, wait, I already did, for this entry's title.

The article goes on to talk about the book in the title of the piece, and I feel like I really should own a facsimile of it (I'm not quite impressed, or rich, enough to try to track down a first edition).

After publishing the book, Morton braved a venture back to his beloved Massachusetts, only to be turned right back around upon arrival. He tried to cross the Atlantic once again in 1643, and was this time exiled to Maine, where he died.

There are probably worse fates, but I can't think of any offhand.

So, a short read, and worth it -- and the source, Atlas Obscura is a wonderful fount of information. The only problem is they keep posting places to visit in Belgium, and I don't know if I'll be able to go to them all.

5 Like • Comment • View 2 comments

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