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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

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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

a day 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

a day 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

a day 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

a day 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

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

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
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?

November 2, 2019 at 12:03am

#968797

Meeska and Jouska

PROMPT November 2nd

Write about jouska.

From Psychology Today, jouska is defined as “a hypothetical conversation that you play out over and over in your head. For example, replaying an argument in your head where you say all the right things and “win” the argument, or practicing asking your boss for a raise and playing out his or her responses and your comebacks.”

Jouska is why I'm single.

Doesn't everybody do this? It's basic self-programming. In the "replay" scenario you're practicing for similar situations in the future, and in the other scenario you're training yourself to deal with different responses.

The trick to being a jerkface asshole is when someone comes to you having practiced the conversation in jouska, you say something that they could not possibly have thought of in their practice. Example:

(Employee slinks in, hat in hand) "Um, boss, sir, may I have a raise?"

Boss: (pause for effect, then) "Tell me, Widders, what do you think of pomegranates?"

There's absolutely no reason you should allow yourself to play to their jouska script. If you do this, though, you have to practice jouska yourself just so you can come up with off-the-wall, non-sequitur responses to any rehearsed conversation. I mean, in the above scenario, presumably the peon has practiced this with the boss giving different levels of "yes" "no" "maybe" and "why" responses, and they've got all kinds of data backing up why they should get a raise, including having come to work on time even with measles, securing a multi-million-dollar contract for the company, and their kid has cancer. None of this matters; your job as boss is to make sure they don't get a raise. They're not expecting a conversation about pre-Raphaelite paint mixing techniques, so give 'em one.

On the peon's side, even though you know this could happen, you practice jouska anyway, right? Like I said, everyone does it. Sometimes you lie awake at night, staring into your old friend the dark abyss, replaying a conversation until you've convinced you monkey brain that it went your way, after all. Or you're worried about the meeting tomorrow so you play out different scenarios, remembering to be ready for loops thrown at you involving pomegranates or paint.

But not me.

No, I don't run variations on the script until things go my way, because I know things won't go my way. I run scenarios until they involve the worst possible outcome for me. There's a good reason for that: I only like to be pleasantly surprised. It's the same reason I'm pessimistic about everything. If I go into a situation expecting, or even hoping for, a good outcome, I can be disappointed. If, on the other hand, I go into, say, the doctor's office expecting a cancer diagnosis, then if it is not cancer I can feel the pleasure of relief; whereas, if it is cancer, I can feel the euphoria of having been right.

Which brings me to why I'm single. Every time I think about meeting someone, the jouska goes something like this:

Me: "Hi, my name is-"

Her: *PEPPER SPRAY*

Or this:

Me: "Let me buy you a drink."

Her: "I was just leaving. With my husband. The pro boxer."

Or this:

Me: "Hey, let's talk about pre-Raphaelite paint mixing techniques."

Her: "Zzzzzzzzzz..."

I think some guys, they go into potential relationships, and they like to skip ahead in their minds to the part where they're both naked. Maybe some chicks to that, too; I don't know. Point is, some people just kind of wing the whole "get to know you" part and rush to the "let's get the lube" part. In other words, their jouska involves playing out the clothes-on scenes in such a way as to get to the R-rated movie as quickly as possible.

But not me. No, whenever I meet someone I think I might be interested in dating, my mind doesn't skip ahead to the date, or to the sex, or to the breakfast afterward, or to the trip to the Paint History Museum. It skips right to the part where she's had enough of my bullshit and storms out the door for the last time.

Knowing she'll leave me for some Australian dingo-fucker is enough to keep me single.

Now, look, I know this might come across as me having a low opinion of women. Think about it, though - if I had a low opinion of women, I could probably convince myself that I could attract one and keep a relationship going. It's myself that I'm certain is unworthy, not anyone else. Proof? Well, what's the one thing women say they look for in a partner? Looks? No. Money? No. Muscles? Gimme a break. Six-pack abs? N-well, maybe. Probably it helps. Cats? Definitely not. No, it's a sense of humor. You may not like my sense of humor, but I think we can all agree that I have one, yes? Yes? Okay. Good. And yet I'm still single. Q.E.D. I have the one trait that heterosexual women claim to be looking for in a male partner, and still can't stop being single.

Consequently, it's me. Therefore, my jouska will continue to justify this to myself.

6 Like • Comment • View 13 comments

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