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Saturday, Dec. 21, 2024

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Complex Numbers

by Waltz Invictus

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:

tj-Merry Mischief Maker

about 13 hours ago
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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This is a private area. Access has been restricted and you may not view it under its current settings. If you feel you should have access, please contact the area's owner and request access.

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2 Like

Annette

about 18 hours ago
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

a day ago
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

🌖 HuntersMoon

a day ago
In response to "Five Seconds"

2 Like

Aiva Raine

Dec 17, 2024 at 7:39pm
In response to "Need for Speed"

Even with the actual explanation- it still left me going- sooooo what's the difference between the special expensive "speed tape" they use for "temporary fixes" and duct tape? LOL- sure sounds like duct tape to me and they are using it for exactly the same reasons you would use duct tape. I'm guessing that the only difference between it and duct tape is the "speed tape" is slightly stronger and handles temperature differences better. It still comes down holding the plane together with tape which doesn't exactly fill me with confidence. Especially if it's a Boeing plane.

1 Like

tj-Merry Mischief Maker

Dec 17, 2024 at 6:14pm
In response to "Need for Speed"

I suppose they call it speed tape to keep people calm. If they called it what it is, temporary repair tape, they may lose passengers.

2 Like

Waltz Invictus

Dec 17, 2024 at 9:43am
In response to "Need for Speed"

Ichabod Crane-- Mince Pie

, I've heard that speed tape is extremely expensive. I can only assume the maintenance guys at Delta got a five-finger discount. But if you're going to steal from work, might as well go big and not just lift a box of paper clips.

1 Like

Ichabod Crane-- Mince Pie

Dec 17, 2024 at 9:06am
In response to "Need for Speed"

One of the last jobs I had was with Delta. I did ask the maintanace guys about that tape once and they pointed out high speed will rip duct tape or any other tape right off. They used it personally for their boats sometimes because of its strength. But looking out a window at 400 miles an hour and 30 thousand feet up and see duct tape on the wing. Certainly made me nervous first time I saw it.

3 Like

August 1, 2024 at 9:41am

#1074643

Help Yourself

By coincidence, another Guardian link today. This one's trying to help with self-help.

Self-help was meant to make me feel better. Instead it turned toxic - and borderline dangerous

I always questioned the concept of self-help books, myself. Even putting aside the questionable credentials of some of the authors, you're not really doing self-help; you're looking to a book and an author that doesn't know you for advice. Which is fine if you're cooking and grab a recipe book.

They do, however, sometimes self-help their authors to bigger bank accounts.

I remember buying my first self-help book, which promised I could be healed of anything if only I banished my limiting beliefs.

And then if you're not healed of whatever, it's your own fault because you didn't banish hard enough!

Over the next 15 years, I bought hundreds of self-help books, courses and apps, and tracked down every self-styled personal improvement guru on TikTok and YouTube in the hope that they could teach me how to become happier, more confident and more lovable.

Apparently, the concept of "to be happier, confident, and more lovable, don't waste money on self-help books, courses, and apps; and stay away from social media" never occurred to her. Of course, none of the people involved would have given her that advice. But I can.

Look, I'm the last person who'd advise someone to "be yourself." But at some point, I realized that the way to be content with what you have is to be content with what you have.

Some approaches were gentle and perhaps even obvious: “talk kindly to yourself, get enough sleep”. Others bordered on dangerous, whether it was encouraging me to spend more money than I could afford in order to “manifest” wealth or telling me to ignore my health problems to feel healthy.

If, on the other hand, I was content with being a bigger asshole than I already am, I would totally be like, "You know the secret to happiness and eternal bliss? It's to give me all your money. Yes, all of it."

Hey, it works for preachers.

But even though I was following the guidance, nothing was helping me to feel better about myself and my brain scans still showed I was living with an incurable neurological disease. I couldn’t help but feel that not getting results was my own personal failing, rather than the industry’s with all its promises.

Yeah, that's one of the biggest problems. I mentioned it up there, too: it's easy to fall into the trap of "obviously it's my fault because I didn't pray / manifest / wish / meditate enough." Which can lead to a whole spin/rinse cycle of doom.

It took a deep conversation with a loved one to recognise that in trying to change my life, I was trying to change things that had happened to me and shaped who I was – often things that were out of my control.

And yet, she had "a loved one." I think I finally understand some of the people who are like "be grateful for what you have."

Instead of focusing on who I wanted to become, I had to quit self-help to learn and accept who I really was.

Happiness isn't having what you want; it's wanting what you have.

Since I quit my self-help crutch, I’ve realised that focusing all your energy on improving yourself can really suck the joy out of life. It makes happiness conditional: only when I have got to a certain stage can I feel contentment; only when I look that way can I be loved.

So that's your ironic self-help advice for the day. For just $19.95 a month, I can self-help you even more!

5 Like • Comment • View 3 comments

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