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Wednesday, Sep. 11, 2024

10:20pm EDT

Members: 938

Guests: 1,017

Total Online: 1,955

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:

Aiva Raine

about 7 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th. We're glad you joined and doubly glad you've stayed this long. I look forward to reading your daily blog as part of my own daily ritual.

1 Like

Wordsmitty ✍️

about 9 hours ago
In response to "Drop and Gimme Twenty"

Wow. That sounds mature for twenty. Next year you can get some booze to celebrate.

I'm sure we're all glad you did sign up. Enjoy the day.

1 Like

Annette aka Din Djarin

about 9 hours ago
In response to "Drop and Gimme Twenty"

Happy 20th to you!

My username was octobersun2 for the same reason. My first attempt to join somehow didn't work.

1 Like

🌕 HuntersMoon

about 10 hours ago
In response to "Drop and Gimme Twenty"

Happy Anniversary, you old dog...

1 Like

Kåre Enga in Montana

Sep 9, 2024 at 10:57am
In response to "Time Out"

"As long as everyone agrees to it" is paramount.

The Polynesians navigated by the stars. No clocks needed. A different approach. Still... all relative.

1 Like

Legerdemain

Sep 9, 2024 at 10:47am
In response to "Time Out"

I'm not scientific, at all. But what about Earth's wobble? Who accounts for that?

1 Like

🌕 HuntersMoon

Sep 9, 2024 at 10:20am
In response to "Time Out"

This was so heavy... I think I lost 26 microseconds reading it.

1 Like

Elisa: Middle Aged Stik

Sep 8, 2024 at 12:04pm
In response to "Writing It Off"

I am late to the party with my comments, but here we go.

Used to be, I wanted to get published.

I used to want to be published in terms of stories. Nowadays I'd rather be published in terms of photos. And self publishing may be my only option in that regard.

but the travel writing field is crowded with young influenzas who can't write for shit, but look good in selfies.

And before that it was crowded with middle aged socialites with nothing better to do (but did have some level of writing skill).

Other people here have dealt with the limit by deleting old entries. I won't do that. Most never have to worry about the limit, and that's perfectly okay.

I admit that as of late I don't let my book items hit the entry limit. Part of it is my entries are super long (current average being *checks notes* 7.48 kb in size). Part of it is I also feel like book items should end after at most five years. I think of my old paper diaries and how they felt more meaningful when I didn't let their use drag on forever. If I stayed consistent, they'd end maybe at most after a year and a half. They often wrapped up sooner than that. Even moving to online journaling, I appreciate a journal that is finite not based on the number of entries but by time elapsed since the book started having entries added to it. My current journal may last a tad longer than my previous ones, but I imagine I'll wrap it up in late 2027, maybe early 2028. We'll see how much space I have to work with. In the old days, 1000 entries was considered a major achievement of an end point. I hope I can get that much out of it, as I think that's more reasonable. I do think 3000 entries of my kind of work in one place is a bit much.

1 Like

🌕 HuntersMoon

Sep 8, 2024 at 11:00am
In response to "Revisited: "Orange You Glad This Wasn't You?""

Maybe this would help... or at least attract your attention?

1 Like

Robert Waltz

Sep 7, 2024 at 11:39pm
In response to "Spit in the Ocean"

Both commenters today had already received MBs from me this week, so I went back to every entry this week and picked a comment at random.

The final Birthday Week MB goes to:

🌕 HuntersMoon

Thanks, everyone, for reading and participating!

1 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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