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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 28, 2022 at 12:01am

#1039836

Simulation Stimulation

No, the universe isn't a simulation (to a high degree of probability). But that doesn't stop us from simulating stuff.

With So Few Farmers, Why Are Video Games About Farming So Popular?
An archaeologist considers what farming simulators reveal about humanity’s ancient and evolving relationship with agriculture.

There's a town near me with the actual name of Farmville. No, seriously. Look on a map of Virginia and you'll see it. Nice place, actually. Not poorly animated.

“I hate when I have to harvest at night,” my husband complained the other day. Lately, he’s been trying to maximize his harvests so he can upgrade his combine.

But he’s not a farmer. He’s a practicing lawyer. He said this from his computer as he toggled between a video game and a YouTube video of someone talking about playing the same video game.

I will admit that I go to YouTube and other places sometimes when I get stuck on a game. Sometimes you miss stuff, you know? But what I don't get is people who barely play the game and just watch others play it. Computer gaming to me is active entertainment, and watching other people play is the definition of passive. I mean, I can understand people watching sportsball; we can't all be star athletes. But anyone with enough money to buy a computer or console can play a game themselves.

Not dissing anyone who does this. It's just not something I grok.

As for the lawyer thing, I bet some farmers would love to play Lawyer Simulator.

That game is Farming Simulator. At peak times, up to 90,000 players are active at once.

Never heard of it. I have, obviously, heard of Farmville. Again, not for me (after having spent my childhood on a farm, I'd rather not). But I do understand the draw of that kind of game. It's a resource management game, and I've played a few of those myself—just not with the "farming" theme.

FarmVille, Sim Farm, and many other games simulate farming and rural life with various levels of realism.

If the game doesn't include giant Trump signs, pro-forced-birth posters, a bunch of coal-rolling pickup trucks, Confederate flags, and enormous anti-Democrat billboards, the level of realism is low.

Most players who speculate on grain prices, buy fancy tractors, and rush to harvest fields before they spoil are not farmers in real life.

Well, duh. I've played Civilization, another resource management game, and I'm not a god in real life.

Across the globe, the proportion of people who make their living as farmers is lower than at any time since agriculture became widespread.

That's because it's primarily corporate now.

What do people like my husband, who lives in a city and works every day in an office, find so entertaining about tilling faux fields and tending to pixels representing wheat or sheep?

For the challenge?

And what does this game’s popularity reveal about the deep history of farming and the role of agriculture in people’s lives today?

I'd say "nothing much," but the author has her own opinion.

Much of the next section is devoted to the history of agriculture and civilization, which, perhaps counterintuitively, is the same history. That is, to summarize, it was farming that allowed some people to not be farmers but pursue other specialties, trading their goods to farmers for sustenance.

Until recently, most people lived in a society deeply tied to the rhythms and sensibilities of farming. So, is Farming Simulator a high-tech form of nostalgia for this kind of connection to the land and food?

Yeah, I'm still going with my "people like the challenge of resource management games."

Well, maybe not the challenge so much as the endorphin rush when something goes your way, which is a key element to any game.

For some Farming Simulator players, farming itself may be beside the point. Some are most excited about the machinery and equipment; the newest version of the game features digital re-creations of more than 400 real machines and tools that players can buy with profits from their farms.

That's actually pretty cool.

Farming Simulator players might thus be seeking to escape the constraints of their everyday lives and experiment with new identities.

Gosh. No other game ever does that. Remind me to tell you about the white dragon my 13th-level half-orc cleric slew, by the way. He even got its hide made into plate mail.

Some real farmers who play the game say it lets them experiment with equipment or strategies that are out of their financial reach, given the current economic realities for family farms.

Gotta say, I think that's actually pretty cool, too.

Farming has been fundamental to who we are as humans. And in a world where war, climate change, and pandemics can so easily disrupt global food supply chains, it still is fundamental—but in ways that are less and less within the reach of the average person.

That's a feature, not a bug. Not all of us are cut out to be farmers; that's why other specializations exist. As I've noted numerous times, it's entirely too much like actual work. Wait, no, it is actual work. So I want no part of it.

But again, not dissing anyone. You like to play farming games? Great. Sports games? You do you. Neither of those appeal to me. Lots of games out there for lots of different tastes.

I just think we shouldn't read too much into people's preferences for different types of games. Maybe they're not trying to reconnect with a glorious past (that never really existed anyway), but are just playing out a different kind of fantasy than the ones I prefer, which usually involve dragons, post-apocalyptic wastelands, spaceships, or all of the above—none of which worlds I would want to actually live in.

1 Like • Comment

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