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Sunday, May. 5, 2024

4:44pm 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 8 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

about 23 hours 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

May 24, 2023 at 7:52am

#1050033

Machine Learning

In which The New Yorker discovers science fiction.

What a Sixty-Five-Year-Old Book Teaches Us About A.I.
Rereading an oddly resonant—and prescient—consideration of how computation affects learning.

Pick a random selection of science fiction from the past—I don't mean space opera, which is fine in its own right, but actual attempts to write about the intersection of society and advancing technology—and you'll find that some of them are, in hindsight, "oddly... prescient," while the vast majority are like "well, that never happened."

Neural networks have become shockingly good at generating natural-sounding text, on almost any subject. If I were a student, I’d be thrilled—let a chatbot write that five-page paper on Hamlet’s indecision!—but if I were a teacher I’d have mixed feelings.

If I were a teacher, I'd be like, "hey [chatbot], write a syllabus for a sophomore English class aimed at mid-range students."

On the one hand, the quality of student essays is about to go through the roof.

Yeah, except, well, see Jayne's rant about that sort of thing, here: "AI Detectors are Horseshit"

Luckily for us, thoughtful people long ago anticipated the rise of artificial intelligence and wrestled with some of the thornier issues.

Substitute pretty much any technological advancement for "artificial intelligence," and "thoughtful people long ago" anticipated it and thought about some of the possible consequences. That's basically the definition of science fiction.

But I don't expect anyone at TNY to understand that.

Their book—the third in what was eventually a fifteen-part series—is “Danny Dunn and the Homework Machine.”

Just including this bit so we all can see what they're talking about.

There follows several paragraphs of meanderings about the setup, plot, and characterization, before getting to the stuff that is really relevant to the topic. Typical TNY. Still, it's worth glancing over so you know what he's talking about later.

I hesitate to give away too much of the plot, but (spoiler alert!) two mean boys in their class, one of whom is jealous of Irene’s interest in Danny, watch them through a window and tattle to Miss Arnold.

Oh, no, wouldn't want to spoil a plotline from 65 years ago. (Spoiler alert: the author pretty much gives away too much of the plot.)

Incidentally, Rosebud was the sled.

He points out that Danny, in order to program Minny to do his homework, had to do the equivalent of even more homework, much of it quite advanced. (“Gosh, it—it somehow doesn’t seem fair,” Danny says.)

I must have read these books as a kid. I have a vague memory of them, anyway. But it may explain why, whenever I have to do anything more than once, I search for a way to automate it, and often spend more time crafting an Excel spreadsheet or some code than I would have spent on the projects.

“Danny Dunn and the Homework Machine” is ostensibly about computers, but it also makes an argument about homework.

And yet, there is still homework. I'm of the considered opinion that grade-school level homework has the primary purpose of making the kids leave their parents alone for a few precious minutes in the evenings.

The article spends an inordinate (to me) amount of time arguing about homework in general and not on the ethical implications of AI, but the main point remains: people have been discussing this sort of thing since long before it was technologically feasible.

Just like with the rest of science fiction.

5 Like • Comment • View 3 comments

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