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Monday, May. 27, 2024

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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 5, 2022 at 12:04am

#1028346

Unthinkable

Well, I did promise "posts of substance;" this came up at random, and it qualifies -- though there's not much for me to say about it.

Sick of choosing between the 'lesser of two evils'? Push for electoral reform

It could be argued that anyone with enough arrogance (however well they might hide it) to run for office is usually going to be evil, even discounting that what one tribe considers good, the other considers evil. Oh, sure, you can find counterexamples if you think for a few minutes, but the exceptions don't change the generality. So choosing between the lesser of two evils is almost always a given. Except, of course, if there's more than two people running, and then it's the least of n evils.

As the common adage goes, politics is about addition, not subtraction.

As I have never heard that (insofar as I can remember), I already know I'm probably over my head in this article.

Political addition is the foundation of a healthy democracy, but unfortunately, our current political system leaves many citizens out of the equation. The structure of elections, especially party primaries, contributes to this disparity.

Won't argue with that.

Exacerbating the situation is the fact that more than 80 percent of congressional districts are completely safe for one party.

That's 'cause they're desigerrymandered to be that way.

Anyway, the article spends a few paragraphs explaining the situation better than I ever could.

But is there a simple way to change the party primary system to foster more citizen engagement and more choice, without favoring one party over another?

I'm guessing they're going to say "yes."

An innovative idea that fits that bill is Final-Five Voting, put forth by the Institute for Political Innovation.

I must be psychic.

Final-Five Voting — this specific combination of top-five primaries and instant runoff-voting general elections — would have a powerful, positive impact on our system. Rather than forcing voters to choose the “lesser of two evils,” we’d infuse healthy competition into politics and help to ensure that candidates are more responsive and accountable to all the voters of the state or district they seek to represent.

In the Before Time, when I still had a gym membership, I'd alleviate the incredible boredom of being on an elliptical machine by watching lectures about shit like science, philosophy, and mathematics.

This is where you're tempted to comment, "But wouldn't that make it even more boring?" Well, no; not for me.

Anyway. I wish I could remember the program I was watching or even the slightest hint of the proof they used, but one lecturer made a convincing argument that there is not only no such thing as the perfect system for choosing leaders, but that there can never be the perfect system for choosing leaders. There will always be a downside, a certain level of unfairness.

But just because it is mathematically impossible to implement perfection -- which is usually the case in everything, not just elections -- doesn't mean we shouldn't strive to make something better.

As they say, "the perfect is the enemy of the good." If you resist change because the new system won't be perfect, there will never be change. Of course, a lot of people want exactly that.

The American system of representative democracy is in dire need of constructive reform that increases participation and avoids tipping the scales toward one party or another.

I'm not sure this particular essay has convinced me that this solution is the best of all proposed electoral reforms, but I hadn't heard this one before, so it was worth it to read. I do believe it would be better than our current system in the US.

Of course, it would dilute the power of the only people in the position to implement such a system, which means it'll never happen. It's akin to Congress voting to take a 50% pay cut, which of course is unthinkable.

But it's good to indulge in fantasy every now and then.

4 Like • Comment • View 12 comments

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