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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 Udon Thani

about 2 hours ago
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

about 2 hours ago
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

about 2 hours ago
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

about 12 hours ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

a day ago
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

Aennaytte: Free & Wild in GoT

a day ago
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

June 9, 2021 at 12:07am

#1011528

Language Barrier

Entry #3 of 8 for "Journalistic Intentions"

[18+] - as usual, I pulled this one at random, but honestly, if it hadn't, I'd probably cheat by making it my eighth entry anyway.

Education, education, education

The differences between US and UK terminology and society have been an interest of mine for a long time. When I was a kid, lo these many years ago (but still after the Revolution), I read both American and British childrens' books. This led to a good bit of confusion, some of which persists to this day.

I've also been known to use British idioms from time to time, like when I say I can't be arsed to do whatever. I do generally use American spellings of words, though some spellings probably slip through. For instance, I'm pretty sure I've used both "canceled" and "cancelled," the latter of which is generally British. Still, I don't have a colourful sense of humour.

Now, I've joked in here before that they invented this language, but we perfected it. Just to be clear, that is, indeed, a joke. But it does help to have a bit of guidance on the differences. Most famously, probably, Rowling changed one of the books in her famous series from "Philosopher's Stone" to "Sorcerer's Stone," apparently specifically because American kids would think of old boring guys with beards if the former were used. (To be fair, most philosophers were old boring guys with beards, except for Neitzche who had an epic mustache, and Camus who wasn't old and kept his face shaved).

Personally, I think the world would have been a better place if they didn't have a separate Freedom Edition of Potter, but instead took the opportunity to introduce the little brats to UK English.

And yes, I know Rowling is cancelled now. Or was she canceled? I can't keep it straight.

Like I said yesterday, I'm currently going through the source material before going to see Cruella on Thursday. Disney has long had a... difficult... relationship with British stories, and the Dalmatians movies are no exception. Still not as cringeworthy as Mary Poppins, though. Point is, I hadn't seen the 1961 cartoon since like 1970, and I'd never bothered with the live-action 1996 remake, which, apart from Glenn Close doing her best "The Devil Wears Pongo" impression, Hugh Laurie being Hugh Laurie, and a bunch of disgustingly cute puppies, turns out to be fairly unremarkable. In any case, the movies reminded me that I'd read the actual 101 Dalmatians book (with the numbers spelled out, which I can't be arsed to do) way back in my misspent youth, and it was one of the works of fiction that introduced me to Britishisms.

Incidentally, I'm not bothering with any of the sequels, and I don't hold out much hope for Cruella. I mean, I get her as a villain? But this trend toward glorifying the Bad Guy (or Gal) is rather off-putting. She's a puppykiller, for fuck's sake -- perfect antagonist material, as long as she doesn't actually get her way. What's next, are we going to get a movie with a pedophile as the protagonist? (Yes, yes, I know, Lolita, whatever -- no one in that movie was a sympathetic character, not even the girl or Jeremy Irons.)

Where was I? Oh, yeah, the video above. Look, I know it can be a pain in the ass (or arse) to click on all these embedded videos, but that one's worth a watch. The guy in the video at first seems like some updated version of Alistair Cooke from Masterpiece Theater, but it's all a cover for a dry British wit (which is almost as good as dry British gin), while at the same time being, well... educational.

And if you're reading this blog in the first place, I can only assume you like a side of humo(u)r with your facts and my opinions.

The ultimate point here is: yes, the US and UK educational systems are different. But both seem to work, so why bother comparing them? Well, partly because almost all knowledge is worth having, but also partly to foster better cross-pond communication. After all, as the narrator points out (paraphrasing Shaw, apparently), we're separated by a common language.

9 Like • Comment • View 7 comments

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