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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 13 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?

October 1, 2021 at 12:03am

#1018454

Praise Cheeses!

Let's kick off October with an entry for "Journalistic Intentions"

[18+]

Cheese

Back in the noughties, I visited the UK for a couple of weeks, and spoke to a lot of nice British folks (and some who weren't so nice, but not for quite as long). "Oh, you're American," they said as soon as I uttered a single word. "You must like Bud Light."

Well, no, I hate that watered-down fake excuse for beer. Even then, I was a craft beer snob, and I told them so. "Actually, there are thousands of local and regional craft breweries in the US, and I've made it my life's mission to try them all."

It's similar there, only they called it "Real Ale." Whatever; I'm used to us having different words for the same concept.

"Well, what about wine? Surely you get all your wine from France."

"Actually, while French wine is quite good, we have thousands of local and regional vineyards producing spoiled grape juice. In fact, I live very close to the place that perfected the science of winemaking in less-than-ideal climate conditions."

I got, "Wow, the US is more advanced than I thought." (I decided not to contradict them on this point.) "Well, what about cheese?"

"...okay, you got me there."

The UK produces and exports a wide variety of cheeses, mostly named after their region. The most famous and widespread (pun intended) of these is, of course, Cheddar. While there are certainly some small cheesemakers in the US, most of the crap you find in stores is industrially prepared, quality-controlled, and distributed nationally, and as far as I know, we haven't innovated our own cheese styles like the British (or French or Swiss or anyone else) has. One exception is Monterey Jack, .which, while American in origin, is more Mexican in ancestry, as it came from that part of California. Most of the real cheese produced in the US seems to be copies of European styles: Gruyere, Brie, Gouda, Stilton, etc.

A lot of the cheese sold here isn't "cheese" in anything but the most legal, FDA-approved sense, in that it passed near a cow on its way from the factory to the store. The worst offender is the plastic "pasteurized process cheese food" usually marketed as American cheese; or, as I like to put it, the dairy counterpart to Bud Light. Of course it's called American: it's bland, fake, and uncultured.

While I admit to a) liking that stuff as a kid and b) buying mass-produced real cheese from the store because it's cheaper, I'm just as much of a cheese snob as I am a beer and wine snob. Very little pleases me more, where food is concerned, than walking into a new-to-me grocery store and discovering that they have a wide variety of domestic and imported cheeses.

And I like all of it.

Some more than others, of course. Soft cheese, hard cheese, cottage cheese, moldy cheese, whatever, doesn't matter. There's also an art to pairing different cheeses with different wines or beers. As with all art, I suck at it, but I can appreciate others' efforts.

One reason I will never be vegan is, in fact, cheese. Not meat -- I could suffer through the rest of my life without meat if I had to, but you will have to pry my cheese from my cold, dead, cholesterol-soaked hands. There are simply no good vegan substitutes for cheese, though some of the meatless "meats" are quite tasty.

Speaking of the US riffing off the UK, and cheese, I found this on the internet, so I don't know who to attribute it to. But it's relevant:

Sweet dreams are made of cheese
Who am I to dis a Brie
I cheddar the world and a Feta cheese
Everybody's looking for Stilton

Though someone went on to do a complete parody of the song

, and it's hilarious, especially because I can't stand the original.

In closing, you know how YouTube generates recommended videos whenever you're there? Well, when I watched the video that prompted this entry (you'll have to click on the contest link above to get a link to it), this was the top recommendation. Not really relevant to cheese (the history of both cheese and domestic cats seems to be traced the Fertile Crescent at about the same time, though this is probably a coincidence), but YouTube has me pegged: it's definitely relevant to my interests:

7 Like • Comment • View 6 comments

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