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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 17 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 17 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 17 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

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?

September 26, 2019 at 10:37am

#966808

Pappy? Happy!

PROMPT September 26th

A prompt from Jaelynn

!

Write about a special place where you might go to meditate, unwind, de-stress, relax, or just be.

It's generally known a bar.

Some people go to bars to meet other people. That's not for me - dealing with people is the opposite of relaxing. Which is not to say that I don't like to do it; I'm pretty social for an introvert. But I like bars that are mostly empty and I don't have to deal with the noise and crowds. That's why it's best to go at like 8 am.

No, I use bars for their gods-intended purpose: drinking.

Let me give you a recent example.

Just the other night, I was, as I mentioned here a few days ago, in Washington, DC. On the last night of the conference, Tuesday, the organizers had arranged for the opportunity to go see a Washington Nationals game. Turns out that's something called "baseball." Okay, no, I'll just do what I always do when I travel, which is find the local craft breweries and sample their wares.

So I did, with a little help from Uber.

First place I went was a nice little wood-decor pub, not too crowded. There's a mural on the wall featuring a fox with laser eyes, two pandas fighting, and a squirrel with a flamethrower, all kaiju-sized and rampaging around DC. Sat down at the bar, ordered samples of their various beers... and became disappointed. They weren't bad beers, exactly, just not to my taste. That's okay - plenty of styles for everyone, and the world doesn't exist to cater to me.

So I Ubered the hell over to the next place on my list, which turned out to be a) not a brewpub but a taphouse (fuck you, Google) and b) crowded as the Beltway on a weekday morning. Pass. (I should clarify here that I enjoy taphouses as well; I was just looking for local beer.)

The next place was only a short walk from the crowded taphouse. It looked promising. Just a few blocks from the Capitol, so I was afraid I'd run into gods-be-damned politicians, but the crowd looked more like politicians' flunkies trying to deal with the stress of having to work with politicians. That's fine. And I say "crowd," but it wasn't full enough to keep me from finding a nice comfortable barstool. But the place turned out to have only two of their own beers, and it was unclear where said beers were actually brewed because there's more than one location for this particular business. Not bad beer, mind you, but still not the experience I was looking for.

So I walked back to my conference hotel. Yes, walked, not staggered; the reason I took Uber in the first place was not because I planned on becoming too drunk to drive, but because it was motherhumping DC on a motherhumping Tuesday evening, and where does one park?. The good news is that I did a mile and a half at a brisk pace without getting in the least bit winded; I guess all the exercise is paying off.

I sat at the bar in the hotel, which also wasn't crowded because the bulk of the conference attendees were either at the sportsball game or had already left. Told the bartender, "I'm disappointed by the breweries around here. I want a positive drinking experience before I leave."

"What can I get you?"

I pointed out a fine 18-year-old scotch I saw standing lonely and dusty behind the bar. "That. Neat."

A lady came in and sat next to me, and I immediately felt myself tense up. What am I supposed to do? I don't go to bars to pick up women; I go to enjoy fine libations. I hear that in such situations, it's customary to buy the lady a drink, but I also hear that's a social signal that shows interest in such activity. So I basically just concentrated on my scotch, which, I will have to note, was indeed a very good scotch.

We ended up talking, anyway, and within two sentences she'd made it clear she was there with her husband, who had gone to the game. Whew. No pressure, then; I don't mess with married women. But there's no rule I'm aware of about not carrying on an ordinary conversation with one while in a public place. Maybe there is such a rule, and I just don't know it. Anyway, she said I looked like The Dude, and if you're going to compliment me like that, I'm happy to talk to you.

I had another scotch during the conversation, and then I noted to the bartender that I was surprised that a fancy place like this doesn't have Pappy van Winkle.

Allow me to digress for a brief time to explain that for non-whiskey folks. There are dozens of bourbon distilleries in Kentucky; it's kind of what they're known for, along with horses, bluegrass, and intolerant politicians. Many of them make fine bourbon. (The distilleries, that is, not the horses. Maybe some of the politicians; I don't know.) But the Holy Grail of bourbon in the last few years has been a label called Pappy van Winkle, after the old white guy who developed it.

Bourbon has particular requirements in order to be called "bourbon;" one of these is that it has to be made from at least 51% corn (that's maize for my British friends, not barleycorn). Now, to save money, most places use cheaper grains like barley or rye to make up the remainder of what's called the "grain bill." There is absolutely nothing wrong with this, but it does impart to bourbon its characteristic "bite," and I tend to prefer other whiskeys (or whiskys or whiskies, whatever).

Pappy, I'm told, makes up the rest of its grain bill with wheat. My understanding is that because wheat is in high demand due to its use in this thing called "bread," it tends to cost more per unit weight. And it's aged for various times in magic barrels that give the flavors time to mellow. Pappy - which I've only encountered once before, in California of all places - is, as a result, smooth as silk. No burn, no bite. It is also not cheap. As with all whiskey, as a general rule, the longer it's aged, the more mellow it becomes, and the more expensive it tends to be.

"Oh," says the bartender, "We have some in the safe."

"You have a safe?!"

"Indeed. But the only Pappy van Winkle we have are the 20 year and 23 year."

"Okay. Sounds great. But believe it or not, I'm going to need to know the price first."

So he told me, and I'm not going to relate it here; suffice it to say that it's not cheap, but it also wasn't going to send me into bankruptcy. I ordered the 20 year, and it was glorious.

After, he took me to the safe and opened it and holy mother of suck, there were some impressive distilled spirits in there. Also rare and expensive ones, even pricier than Pappy. I was not tempted - well, not too much - but it sure was pretty to look at.

So there it was, a positive drinking experience. Fully de-stressed, relaxed, and serene. A fine ending to a crowded conference.

I guess what I'm trying to say with all these words is: I like bars.

1 Like • Comment • View 1 comment

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