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Saturday, Apr. 27, 2024

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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

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

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

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?

March 25, 2024 at 8:50am

#1066890

Served with Flare

Today, I'm sharing a link that shows, once again, that it's fun to set things on fire.

Flambé Your Breakfast, Lunch, and Dinner
This retro cooking trend is back.

Back? As fire as I'm concerned, it never went away.

Here at Gastro Obscura, we really like playing with fire.

When I was a kid, the thing I got in trouble for the most (and this is saying something) was playing with fire.

There was the time that editor Sam O’Brien made feuerzangenbowle, a flaming German rum punch with roots in the rowdy student culture of the 1700s. Then there was the night I risked my fingers and eyebrows with the Victorian party game known as Snapdragon, where players compete to pull raisins and almonds out of a puddle of burning brandy.

"Snapdragon." Get it? Huh?

There's one problem with flaming food and drink: I have facial hair I'd like to keep. Okay, two problems: it's harder to exercise reasonable precautions when you're drinking flaming booze while already drunk.

Both of those were Christmastime traditions, though. I’d argue that adding flaming alcohol to food and drink should be a year-round thing.

Absolutely! And April Fools' Day is coming up fast...

Setting food on fire with warm booze was considered the height of luxury for a good chunk of the 20th century.

Now, I don't know about that. The iconic "height of luxury" was usually champagne and caviar. Champagne can be delicious, but caviar? Meh.

Besides looking pretty, what does flambéing do to a dish? There’s the taste of the liquor—which could be rum, bourbon, Calvados, or brandy—with some of the potency burned away, resulting in a smoother taste.

I've heard some people assert that it burns away all the alcohol. It does not. I suspect that at least part of the reason it fell out of favor was anti-alcohol attitudes.

I’ve flambéed a few things in my time, so I decided to set myself a challenge: to flambé my breakfast, lunch, and dinner over the course of one day.

My biggest problem with the technique is that it burns away at least some of the alcohol. This is alcohol abuse. The only time I tolerate it is if it makes something else better, which, generally, flambé does.

Doing it for every meal, though? That's a stunt. I guess it worked, because I read the article and shared it. Though we have no way of knowing if the author is completely honest about the "every meal for a day" thing, I'll give her the benefit of the doubt, mainly because it doesn't much matter.

There follows the actual dishes prepared, with hunger-inducing photographs.

I just have one thing to add: absinthe.

The first time I tried absinthe was at a Moroccan-themed bar here in my town. I forget the exact ritual they went through, but fire was involved. And I liked it enough to go buy absinthe and try it myself. But the serving of absinthe, with or without fire, is kind of finicky. Sure, you can drink it straight, like other liqueurs, but, like some other liqueurs, it's not really meant to be straight.

At the very least, the serving of absinthe involves ice water and sugar. Generally, you pour the absinthe into a specialty glass and then use some contraption to let the ice water drip slowly into it over a sugar cube.

As I am, above all, a science nerd, I decided to compare flaming absinthe to not-flaming absinthe. Of course, I used the same absinthe, same water source (my kitchen sink) and the same kind of sugar (Domino's brown sugar cubes), because science is all about controlling variables.

The result? In my not-humble opinion, the one without fire had the superior flavor. It was also, I can only assume, more potent because the alcohol hadn't burned off.

However... the flaming absinthe was just more fun.

6 Like • Comment • View 1 comment

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