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Friday, May. 3, 2024

1:35pm 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

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Show Recent Comments

10 Most Recent Blog Comments:

Simply Me

about 2 hours ago
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)

🌕 HuntersMoon

a day ago
In response to "Butt Of Course"

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

Talk about retaining water...

1 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

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Montana

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

April 21, 2024 at 9:17am

#1069306

Revisited: "Hack This"

I'll be on what passes for vacation for me this week—I have nothing to vacate from, but I do like to go elsewhere from time to time—so entries will happen whenever I get a chance and probably short and even more pointless than usual.

For today, though, I'll do my usual Sunday thing and look back at an old entry. This one's from 2020: "Hack This"

Worth reading if you want a decent takedown of "lifehacks." Or even if you don't. Especially if you don't.

I still see "lifehacks" from time to time, but I see more parodies of them, which warms my heart. Things like: "Life hack: Don't have a mental breakdown at home. Have it at work so at least you're getting paid for it."

The article I linked

(Medium, 2017) is still up as of today. And my opinions haven't changed much, but maybe a little, and maybe some points need clarification. But first, I'll address the end of the entry, where I discover, too late, that this advice article that is a takedown of advice books and articles is actually an ad for the author's advice books.

Also, I hate reading this far along a halfway decent article only to find that it's a commercial in disguise. Bah.

Yes, I have said numerous times that I don't mind taking a look at book ads here, on a site that caters to readers and writers, so long as the content is worth commenting on. This one, however, did manage to catch me by surprise. Usually the book-flogging is near the beginning, or in a sidebar, or otherwise obvious when you start reading the article. This one was, I felt, deceptive—moreso because, as I wrote then: "I feel like he has good points, but those are somewhat muted by the fact that he's doing exactly what he's railing against."

Now... one might say, "But Waltz, here you are doing it too." Yes. I am. But I'm not trying to sell anything.

Besides, if I really objected to it, I'd have scrapped the entry and done a different one.

Rereading this entry, I realize it might read as if I'm against self-help books and articles in general. I'm not, necessarily. It's just that most of them only "self-help" the author to make money. There's nothing wrong with making money; most of us want to do that. But doing it by misleading others into doing something that doesn't help, and may even actually harm, is generally called "fraud," and is frowned upon.

So, just one more comment on my previous comment:

I keep seeing that the true enemy is "processed" or "overprocessed" foods, but I haven't found a good definition for those, yet. I mean, technically, cooking is a process, and - raw-food-diet bullshit aside - cooking is what makes a lot of food more nutritious and digestible. Potatoes, for example. It's probably what allowed our ancestors to evolve these great big brains that most of us don't use.

Obviously, it's been four years, so a) "processing" has been better-defined, while at the same time I haven't seen much about it lately; I wonder what the next anti-fad will be. And b) I shouldn't have typed that last sentence; it's misleading and does what I'm railing against here: assertion without evidence or experience. Not that I'm above doing that, but in this particular case, it's evolutionary guesswork, which I have issues with, and it's also what's commonly known as a "chicken/egg" scenario: did we evolve big brains because our ancestors cooked their food, or did they cook their food because they had big brains from some other adaptation? Or was it a synergy of some kind? My only point should have been that cooking food is good.

In reality, the "chicken/egg" scenario is easily resolved: eggs existed long before what we call chickens, and the first chickens hatched from eggs laid by some dinosaur descendant that was almost a chicken. That's still evolutionary speculation, but at least in this case, it fits with what we know of evolution.

Therefore, it was the egg that came first.

Fortunately for chickens and those of us who enjoy eating them, it wasn't cooked.

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