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Monday, May. 27, 2024

3:23am 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

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:

Kåre Enga in Montana

a day ago
In response to "Plan Solo"

I'm more introverted than extroverted, but my only apprehension involves language and cultural barriers.

I'm bi- or ambi- but... always annoying. I waver between wanting to be left alone and not wanting to be alone.

I make my adjustments as necessary.

But LANGUAGE and CULTURE: true barriers that can cause problems for some and angst for me. I love strangers but find it frustrating when I can't connect.

For Belgium: make those plans soon. Today's connectivity means booking lodging in advance. In the old days it was show-up-and-ask-if-they-have-a-room. Still possible but not recommended unless cost is not an issue.

I prefer staying in hostels but rarely join in 'events'. I have gone out with fellow travelers however.

Kåre Enga in Montana

a day ago
In response to "Banned Camp"

I remember when the movie "Brokeback Mountain" received "F"s from folks who basically commented that they would never NEVER watch such filth. Even those who liked or enjoyed it missed the main theme of poverty (financial, cultural, individual...). Personally, I preferred the short story to the movie. Both made a point that America didn't/doesn't want to face: choice and lack of choice.

That said, if someone were to ban my poetry I could probably live off of the notoriety.

Burning at the stake though seems a more likely outcome.

2 Like

🌕 HuntersMoon

a day ago
In response to "Banned Camp"

"Any book worth banning is a book worth reading." Isaac Asimov

2 Like

Aiva Raine

May 21, 2024 at 11:34pm
In response to "More Science"

Giggles. Thank you for the laugh- especially this phrase, "I always picture Doc Brown's workshop in Back to the Future. Yes, of course I know it's wrong, but I'd rather be amused than right."

1 Like

Aiva Raine

May 17, 2024 at 6:57pm
In response to "Knead Some Dough?"

I grew up on mostly Wonder Bread despite our family having a large dry farm (dry farm being a farm that grows wheat and barley and safflower without irrigation- it relies solely upon mother nature to rain). I was never fond of it and looked forward to the times my mom would laboriously mill and grind the grain we brought back during harvest into flour and make home-made wheat bread. There was and still is nothing better than fresh whole wheat bread with a little butter and honey.

I think we did the Wonder Bread because my mom wasn't a fan of cooking and making bread is a time-consuming process.

I quit doing the white bread decades ago. There are so many kinds of healthy, no HFCS, etc whole grain breads out there that are delicious that I have no idea why any adult would choose the crappy Wonder Bread.

1 Like

Wordsmitty ✍️

May 13, 2024 at 1:18pm
In response to "The Breakfast and the Breakfurious"

And for those who rather not read the Smithsonian article, the History Channel episode that covers Pop Tarts (if you have a cable TV account):

https://www.history.com/shows/the-food-that-built-america/season-4/episode-1

Annette

May 10, 2024 at 12:05pm
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

May 9, 2024 at 1:15pm
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

May 9, 2024 at 10:11am
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

March 27, 2022 at 12:01am

#1029527

Unmotivation

Today, I'm going to talk about something I have very little experience with.

Motivation: The Scientific Guide on How to Get and Stay Motivated

Spoiler: it's not actually scientific.

Motivation is a powerful, yet tricky beast. Sometimes it is really easy to get motivated, and you find yourself wrapped up in a whirlwind of excitement. Other times, it is nearly impossible to figure out how to motivate yourself and you're trapped in a death spiral of procrastination.

Death Spiral of Procrastination is my 80s hair cover band.

Instead, we're going to break down the science behind how to get motivated in the first place and how to stay motivated for the long-run.

For one thing, we can stop misusing "science."

So what is motivation, exactly? The author Steven Pressfield has a great line in his book, The War of Art, which I think gets at the core of motivation. To paraphrase Pressfield, “At some point, the pain of not doing it becomes greater than the pain of doing it.”

That's actually been my working definition for a while. I can only stop procrastinating when the pain of ignoring something exceeds the pain of fixing it.

This rarely happens.

What can we do to make it more likely that we cross this mental threshold and feel motivated on a consistent basis?

Something tells me the answer to that question, sadly, isn't "Drink."

You don't need much motivation once you've started a behavior. Nearly all of the friction in a task is at the beginning. After you start, progress occurs more naturally. In other words, it is often easier to finish a task than it was to start it in the first place.

This actually also tracks with my experience. Once I start writing, I write, for example. It's getting myself to start writing in the first place that's hard.

Setting a schedule for yourself seems simple, but it puts your decision-making on autopilot by giving your goals a time and a place to live.

Nah. I've been known to set schedules and then utterly ignore them. If there's no one else involved, the only person I can let down is myself, and I'm used to doing that.

It makes it more likely that you will follow through regardless of your motivation levels. And there are plenty of research studies on willpower and motivation to back up that statement.

Actually, willpower has little to nothing to do with it. See my blog entry from a couple years back: "Good Willpower Hunting"

"I begin each day of my life with a ritual; I wake up at 5:30 A.M..."

Normally, this is where I'd simply stop reading and move on to playing video games or watching shows. The concept of willingly waking up at 5:30 am on a daily basis is so foreign, so anathema to me, that it's utterly inconceivable. Hell, I sometimes don't go to sleep until then.

Maya Angelou rented a local hotel room and went there to write. She arrived at 6:30 AM, wrote until 2 PM, and then went home to do some editing. She never slept at the hotel.

6:30 isn't really any better.

Pulitzer Prize winner Michael Chabon writes five nights per week from 10 PM to 3 AM.

Now, see, that's more my speed. It should come as no surprise that Chabon is a major writer for Star Trek these days, and I like those shows.

Anyway, I skimmed the rest of the article after that. Who knows? Maybe someone reading this will find it useful. All it does for me is increase my dissatisfaction.

But not enough to do anything about it.

3 Like • Comment • View 3 comments

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