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Thursday, Sep. 12, 2024

4:32am EDT

Members: 654

Guests: 3,113

Total Online: 3,767

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 13 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 16 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 16 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 16 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 20, 2024 at 10:33am

#1075503

Some Clouds Are Just Clouds

This one's from Forbes, and to me is an exercise in suppressing my confirmation bias, because it's saying the same shit I've been saying, only by an actual mental health professional.

A Psychologist Explains ‘Oppressive Optimism’—And The Toxic Side Of Self-Care

Being a professional in a field doesn't mean you're always right; thinking that's the case would be another fallacy. Still, I think the article is worth contemplating. Whether my comments are is an open question.

Self-care has become a buzzword in wellness culture and for good reason—it’s essential for our mental, emotional and physical health.

Assertion without evidence can also be a problem.

These practices can work wonders, but when chasing positivity turns into an obsession—it can lead to what researchers call “toxic positivity.”

Which I've ragged on in here before, repeatedly... though not so much as to have exhausted my patience with the topic.

In essence, toxic positivity invalidates negative experiences by promoting the idea that one should always maintain a sunny outlook, regardless of circumstances.

I believe I've used examples of that before like "My dog died." "That's great! Now you can get a new puppy!"

Here are three specific examples of how self-care can slip into toxic positivity and end up doing more harm than good.

As this is not Cracked, the list actually counts up.

1. The Social Media Mantra—“Good Vibes Only”

While surrounding oneself with positivity can be uplifting, the insistence on “good vibes only” creates an environment where negative emotions are not just unwelcome but are seen as personal failings.

I'm not sure this is so much an insistence on toxic positivity as a desire to not get your own vibes harshed. Like, you're at a party, and everyone's having a great time, and one of your friends staggers in late and bleeding. "Got in a wreck," she moans. Normally, you'd probably be there for your friend, call an ambulance for her, maybe even wait in the ER with her. But you're at a party. How dare someone turn it into an emergency!

2. Oppressive Optimism—“Everything Happens For A Reason”

I've railed against that duck-billed platitude before, and I'll do it again.

Optimism is crucial when coping with negativity...

Another assertion without evidence.

...but the belief that everything happens for a reason can invalidate genuine feelings of fear and uncertainty.

This is related to "it's all part of God's plan," though that one's more specific to certain religious people.

3. Affirmation Overload—“I Am Strong, I Can Handle Anything”

Picture someone going through a tough divorce, constantly telling themselves, “I am strong” and “I can handle anything” to keep up their confidence and stay positive. While this might seem helpful, it might stop them from sharing their pain and struggles with loved ones, out of fear that admitting vulnerability will make them look weak or uncertain about their decision.

And maybe that no one wants to be around them if they're not going to give off good vibes.

There's not much more to the article, really; the conclusion boils down to "seek help," which is fine advice, but what I'd need help with would be finding a shrink. Too much work. I'll just stay over here and be grumpy by myself.

3 Like • Comment

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