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Tuesday, Apr. 30, 2024

11:03pm 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:

GeminiGem of House Lannister

a day ago
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Udon Thani

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

Kåre Enga in Udon Thani

Apr 25, 2024 at 2:58am
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

Apr 24, 2024 at 4:26pm
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

November 9, 2018 at 1:53am

#945199

Scale

Oh no! Here come the asteroids!

https://www.irishmirror.ie/news/world-news/three-huge-asteroids-fly-dangerously-...

This weekend, three enormous asteroids will make a ‘close approach’ to Earth, NASA has warned.

The asteroids - the biggest of which is predicted to measure up to 30 metres across - will whizz past our planet on November 10.

At around 14:03 GMT, an asteroid dubbed 2018 VS1 will pass the Earth.

This asteroid is predicted to measure between 13-28 metres across - suggesting the asteroid could be five times as tall as a giraffe!

Everybody panic! Time to freak out! Also, what if they're actually ALIENS?!

Or maybe a tabloid is just trying to generate ad revenue? ...nah, couldn't be.

Seriously, though, apparently they're now measuring asteroids in units of giraffe. I guess they used up all the Statues of Liberty. That might also explain why they use both miles and kilometers (as well as meters) in the same article - trying to conserve units.

To be fair, a big part of science communication is the attempt to translate mind-bogglingly big or small things into terms we might be able to comprehend. This many Earths could fit side-by-side across Jupiter, and that many Jupiters could fit across the Sun. Kilometers and miles are just fine for measuring most distances on Earth, but astronomers and cosmologists use larger units like AUs, light years, and parsecs (which are a unit of time, not distance, regardless of what Han Solo said; also, Han shot first). People who study tiny things use angstroms or nanometers or whatever.

A giraffe is a nonstandard unit of measurement, but perhaps it helps with visualization. It's probably a better unit for measuring asteroids than a cat or a paramecium, unless the asteroid is cat- or paramecium-sized. Actually, the latter would be classified as space dust, not asteroid or planet.

People like to smugly tell other people just how insignificant we are. "Look at the universe," they'll say, or something to this effect. "We're barely a speck of dust." Well, compared to the observable universe, we're smaller than a speck of space dust. We're even smaller than an atom, relatively speaking, by this comparison. But it turns out that the smallest particles - smaller than actual atoms; on the scale of electrons or quarks - are close to the same order of magnitude smaller than us as we are smaller than the known universe. In other words, we're right in the middle in terms of size. So maybe not so insignificant after all? Especially since we were able to deduce this fact.

Incidentally, going back to the asteroid thing, let's be clear: these may be close encounters from a scientific point of view, but there's zero chance any of these rocks are going to hit the planet. The closest one will miss by roughly the distance to the moon

, or 30 times the diameter of the Earth.

A miss is as good as 240,000 miles, I suppose.

4 Like • Comment • View 8 comments

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