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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 18 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 23 hours ago
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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2 Like

Annette

about 23 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

Dec 19, 2024 at 8:53am
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 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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