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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:

Elisa the Bunny Stik

about an hour ago
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

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

October 31, 2021 at 12:03am

#1020458

Not in De Nile

This will probably be the last one of these for a while, as I'm going back to doing "30-Day Blogging Challenge ON HIATUS"

[13+] next month. Which is tomorrow. Yikes.

How Cats Became Divine Symbols in Ancient Egypt
Felines served a useful purpose in ancient Egyptian households and were eventually associated with deities.

There's an old joke going around that goes something like:

Dogs: "These humans give us food and water and take care of us. They must be gods!"
Cats: "These humans give us food and water and take care of us. We must be gods!"

Alternatively, there's the quote I've heard attributed to Winston Churchill, which goes something like, "Dogs look up at us, cats look down on us, pigs treat us as equals."

“Though it is hard to say the Egyptians thought one thing or another, since so much change happened across their 3,000+ years of history, the ancient Egyptians, in general, did not worship animals,” says Julia Troche, an Egyptologist, assistant professor of history at Missouri State University, and author of Death, Power, and Apotheosis in Ancient Egypt: The Old and Middle Kingdoms. “Rather, [they] saw animals as representations of divine aspects of their gods.”

The distinction can be subtle, I suppose. If an archaeologist 4000 years from now dug up a typical home, they'd probably conclude that we worship the television, which is silly because the reality is that we worship the celebrities that appear on it.

Whether or not they were worshiped as deities, cats were an integral part of ancient Egyptian life. And, based on mummified cats discovered in tombs alongside humans, they carried an important role in the afterlife, as well.

Just yesterday, I saw that archaeologists uncovered a grave in Cyprus (which is kind of but not really near Egypt) from something like 10,000 years ago where some dude was buried with a bunch of his favorite toys... and his cat. The idea being that they sent the cat with him to whatever afterlife they imagined. Poor kitty was only eight months old, though. The cat didn't deserve that.

For most of the civilization’s history, ancient Egyptians saw cats as mutually beneficial companions, according to Troche. “Cats might come inside when it was hot, and they in turn would chase away dangerous animals, such as snakes—many of which were venomous—and scorpions,” she explains.

Most articles I've seen about cats emphasize their usefulness. As if that has to be a factor. How useful is the Mona Lisa? Cats are living art. Art that pukes on the couch sometimes, but still art.

The presence of cats in tombs wasn’t limited to paintings—sometimes cats were mummified and placed inside their human companion’s tomb, according to the Carnegie Museum of Natural History. One reason this was done is that when cats were mummified, they could then be used as funerary goods.

Again, the implication is that they killed the poor kitty just because its human died.

“Ancient Egyptians held cats in such high regard because of the practices and preferences of their gods, but also because their kings, the pharaohs, kept giant cats,” Skidmore says. “Members of the Egyptian royal class dressed their cats in gold and let them eat from their plates.”

And cats have never forgotten this.

In addition to appreciating their ability to keep rodents, snakes and other pests out of their homes, the ancient Egyptians understood that cats of all sizes are smart, quick and powerful.

Ah, no wonder the cats allowed that civilization to prosper for as long as it did.

Through their ubiquitous presence in the art, fashion and home ornamentation of ancient Egypt, cats served as an everyday reminder of the power of the gods.

Sure, if gods had the tendency to get underfoot and pee in your laundry basket.

Come to think of it, though, cats are more useful than gods anyway. At least you can laugh at their antics. Try that with a god and you get smited.

4 Like • Comment • View 2 comments

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