Search where?

This Portfolio (cathartes02)

All of Writing.Com

◄ April ►
S	M	T	W	T	F	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30
Archive				RSS

Offsite Blogs

· Waltz Travel Blog

Create New Item

Read & Review

Community

Browse By Type

Browse By Genre

Writing Resources

Tuesday, Apr. 30, 2024

5:23am EDT

Members: 648

Guests: 1,160

Total Online: 1,808

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

about 16 hours 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

a day ago
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

a day ago
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

April 17, 2024 at 10:24am

#1068972

Down Under

Something interesting from the BBC last year:

The Australian town where people live underground

I thought all Australians lived underground. Otherwise, they'd fall up into space.

I mostly saved this article so I could use the entry title I did. I'm inordinately proud of that pun. But it's also a fascinating concept, at least to me.

These are the first signs of Coober Pedy, an opal mining town with a population of around 2,500 people. Many of its little peaks are the waste soil from decades of mining, but they are also evidence of another local specialty – underground living.

That name sounds as Australian as kangaroos and Crocodile Dundee. I wonder if the article will state its origin.

In the winter, this troglodyte lifestyle may seem merely eccentric. But on a summer's day, Coober Pedy – loosely translated from an indigenous Australian term that means "white man in a hole"...

Of course it did, and it's hilarious.

...needs no explanation: it regularly hits 52C (126F), so hot that birds have been known to fall from the sky and electronics must be stored in fridges.

Yeah, I prefer heat to cold, but that's just going too far. I thought Phoenix was bad in the summer.

As the blistering three-month heatwave continues in the US – with temperatures even cacti can't handle – and wildfires incinerate swathes of southern Europe, what could we learn from Coober Pedy's residents?

Again, this article is from last year. August, specifically. At least it was winter then in Australia.

People have been retreating underground to cope with challenging climates for thousands of years, from the human ancestors who dropped their tools in a South African cave two million years ago, to the Neanderthals who created inexplicable piles of stalagmites in a French grotto during an ice age 176,000 years ago.

Well, duh. It's not exactly news that humans and related apes lived in caves.

Caves served another very important purpose, as well. As the article notes, most underground locations that are deep enough—provided one isn't near a volcano or whatever—stay around 13C, or 55F. Before refrigeration, this was an common way to keep beer and wine relatively chilly, and thus preserve it longer. Even now, a lot of fermented beverages are best served at "cellar temperature."

Apart from comfort, one major advantage of underground living is money.

That, and your HOA can't give you shit if you happen to paint your house the wrong shade of pink.

On the other hand, many underground homes in Coober Pedy are relatively affordable. During a recent auction, the average three-bedroom house sold for around AU$40,000 (£21,000 or US$26,000).

I'd imagine that at least part of that is its remote location.

The question is, could underground homes help people to cope with the effects of climate change elsewhere? And why aren't they more common?

Guessing that at least part of the answer to that last question is "rock" and "water tables." And also "building codes" and "zoning laws." It's my understanding that, to be considered a bedroom in the US, a room must have a window. Windows aren't exactly a common feature of underground living.

Besides, if your neighbor lives in a cave, how are you supposed to judge their lifestyle by how they keep their yard?

There are several reasons why making dugouts in Coober Pedy is uniquely practical. The first is the rock – "It's very soft, you can scratch it with a pocket knife or your fingernail," says Barry Lewis, who works at the tourist information centre.

Okay, so I might have cheated a bit with my "rock" answer, because further up in the article, they mentioned it was sandstone and whatnot.

However, the feats at Cooper Pedy would not be possible everywhere. One major challenge with any underground structure is damp.

I did say "water tables." Civil engineering education is good for something.

But in Coober Pedy, which sits on 50m (164ft) of porous sandstone, conditions are arid even underground. "It's very, very dry here," says Wright. Ventilation shafts are added to ensure an adequate supply of oxygen and to allow moisture from indoor activities to escape, though these are often just simple pipes sticking up through the ceiling.

The downside of building, even underground, in a desert is the other side of that equation: where do you get your water? I missed it if the article addresses this. I imagine there's an aquifer further down, but I don't know.

The article also doesn't note another important thing about learning how to live underground. If we end up with people living on the Moon and/or Mars, they're pretty much going to have to do so in underground habitats. Not only does the rock above you provide a barrier to space radiation, but it all but eliminates potential problems with small meteorites punching a hole in your bio-dome or whatever.

Also, nearly unlimited beer storage.

1 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted Writing.Com, its affiliates and its syndicates non-exclusive rights to display this work.

Printed from https://www.writing.com/main/profile/blog/cathartes02/day/4-17-2024