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Monday, May. 6, 2024

1:42am EDT

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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

about 17 hours 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

a day ago
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

April 21, 2022 at 12:01am

#1031096

The Forest for the Trees

Here's another one for "Journalistic Intentions"

[18+]

Large Tree Planting Projects

"They're going to make us dinner."

So my cleric said to the party upon encountering a group of trolls tonight.

Sure, I suppose it was within the realm of possibility for the DM to have planned for the trolls to cook a nice venison roast and serve it to us. More likely, though, they were going to turn us into the main course.

The way English works, though, the sentence is indeed ambiguous. Is "us" the direct or indirect object of "make?" Other languages have no such ambiguity. "They're going to make dinner for us" is distinct from "They're going to make us for dinner."

So, coming off a D&D high and pulling this prompt at random from the list, initially I read it as (Large Tree) (Planting Projects). So I imagined much bigger versions of the trolls (they were big to begin with) running around and planting large trees everywhere. But it could also mean that people are planting little trees that will eventually grow up to be large trees. As opposed to, I dunno, dogwoods, which never get too huge.

One could, I suppose, also read it as (Large Tree Planting) Projects, which, I don't know, could be read to imply that the trees are the things doing the planting? Though I guess you could do that with the first example, too. These two permutations aren't really all that different.

Then there's the interpretation that, I assume, was actually intended: Large (Tree Planting Projects).

This one implies that the tree planting projects are large in scope. In other words, "large" is actually modifying "projects" as opposed to "tree."

That would make more sense, wouldn't it? A small project to plant trees wouldn't be very effective. It would be like if one person in the world recycled, and no one else did. Maybe you could initiate numerous such projects, but that would involve getting people who don't give a shit to give a shit, which ain't gonna happen.

According to sources whittled down into Wikipedia

, "In the 12,000 years since the start of human agriculture, the number of trees worldwide has decreased by 46%." Also, "...about 15 billion trees are cut down annually and about 5 billion are planted." But that last quote doesn't tell me anything about tree life cycles. With or without us, trees get seeded, grow, reproduce, and die.

I almost typed "natural tree life cycles" there, and then I remembered a) beavers and b) anything we, as part of nature, do is also part of nature.

But taking those numbers at face value, that's a net loss of 10 billion trees a year. Which certainly seems like a lot -- it exceeds the human population of the planet -- but according to the same source, there's probably about 3 trillion trees. That's... oh, hell, I'm entirely too wiped tonight to do the math. Let's just say that we're in no danger of running out of trees anytime soon.

Which doesn't mean, of course, that any net loss is a good thing. And I get the impression that it's not just the number, but the distribution. Deforesting the Amazon rainforest probably has a much bigger negative impact than, say, losing them more or less evenly all over the globe.

That would, of course, imply that it matters where any of these large tree planting projects are taking place. Which may be obvious, because, for example, you can plant all the trees you want in the Sahara; they won't grow.

So whatever these projects are, assuming I parsed the phrase correctly, I hope they're successful.

My D&D party was, by the way. Successful, I mean. It took a while, but we eventually dispatched the trolls. Now if only we could do that with the ones on the internet...

5 Like • Comment • View 4 comments

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