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Tuesday, Apr. 23, 2024

4:57pm EDT

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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:

Lazy Writer est 4/24/2008

about an hour ago
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

Aennaytte: Free & Wild in GoT

about 2 hours 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.

Aennaytte: Free & Wild in GoT

about 2 hours 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.

Aennaytte: Free & Wild in GoT

about 2 hours 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 ...

Aennaytte: Free & Wild in GoT

about 2 hours 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?

Aennaytte: Free & Wild in GoT

about 2 hours ago
In response to "Going to the Dogs"

I have never been to New York, but it seems that my assessment years ago that Berlin, Germany and New York have some similarities. Both cities are known for being inhabited by rude people. And both places, as I now found out, are dog obsessed. And they have high rents.
Berliners though, have a habit of letting their dogs run off leash. Maybe New York is a little better than Berlin in that regard.

1 Like

Robert Waltz

Apr 21, 2024 at 1:48pm
In response to "Revisited: "Hack This""

Wordsmitty ✍️, far be it from me to speculate on the motivations of space aliens, but why in Xenu's name would they do such a thing to the universe?

1 Like

Wordsmitty ✍️

Apr 21, 2024 at 1:39pm
In response to "Revisited: "Hack This""

I thought humans got bigger brains because extraterrestrials affected our evolution, and we eat processed chicken and eggs.

1 Like

Robert Waltz

Apr 21, 2024 at 10:22am
In response to "Revisited: "Hack This""

🌕 HuntersMoon, ah, yes, my favorite words to hear (or read).

Also, that video is an excellent, if brief, explanation of the conundrum and how to resolve it.

1 Like

🌕 HuntersMoon

Apr 21, 2024 at 10:15am
In response to "Revisited: "Hack This""

As sometimes happens, Bob... YOU'RE RIGHT

1 Like

May 9, 2022 at 12:01am

#1032143

Shooting Tsar

"Invalid Item"

So on Wednesday, you told Andre about great places to visit where you live. Now he'd like to know about the people who live or have lived where you do.

Sundays's prompt; Tell us about a famous person or persons who lives or came from your Home Sweet Home

When I was at college, the dorms were arranged with several dorm rooms around a common area. Someone had done a country-looking cross stitch as a throw pillow: "Suite sweet suite."

That always pops back in my mind whenever I see "home sweet home."

Anyway. I've talked enough about Jefferson, and I mentioned Dave Matthews last time. I've also noted before that Poe spent some time here. Then there was the one lady who claimed to be the last Romanov...

You know what? I'm going to go with that one.

Hopefully you all know that in 1918, some revolting Russians rounded up some revolting Russians. That is to say, the revolutionary Bolsheviks executed the entire former royal family of Russia, who, let's face it, were pretty revolting, being autocrats and all. The youngest was Anastasia Romanova, also known as Grand Duchess Anastasia

despite being, like, totally a teen.

A couple of years later, a woman in a mental institution in Germany (should have been the first clue) claimed to be Anastasia. Apparently, some people believed her, but certainly not everyone. Personally, I'd figure that claiming to be the last royal Russian in early 1920s Europe couldn't possibly be good for one's health, but okay, whatever, there were enough believers that her claims were taken seriously by a bunch of people.

Apparently, she spent the next few decades in and out of asylums, which I suppose could be ordinary mental illness, or it could have been, I don't know, watching a bunch of revolting peasants destroy your entire family.

It wasn't until the late 60s that she became associated with Charlottesville, having married a history professor here (should have been the second clue).

I never met the lady; she died shortly after I came to town (not my fault). My ex-wife's father claimed to know her, but he claimed to know everyone (and, to be fair, he knew a whole lot of people). Apparently, Anna and her husband were described as "eccentric," which is code for "crazy, but rich enough to get away with it."

It was only after her death that the final nails were driven into the coffin of her claims to royalty. I mean that metaphorically; she was cremated and didn't have a coffin.

First, DNA testing became a thing, and apparently there was enough of her left (ew) to test, and behold, she was not Russian.

And second, after the end of the USSR, archeologists found the remains of the Tsar's entire family, including Anastasia.

A local brewery occasionally makes a beer called Anastasia's Chocolate Fantasy, which is a Russian Imperial Stout brewed with cocoa, because of this local connection. It is absolutely delicious. But Russian Imperial Stout is, as I've noted before, not actually Russian... much like Anna Anderson herself

So Anna Anderson was just a crazy lady, but apparently she made the best life out of it as she could, and, Duchess or not, she's absolutely a part of Charlottesville history. Though few people here actually believed she was Romanova, they humored her anyway, because that's what we do here. It really should have been blindingly obvious in retrospect, though.

I mean.

If you're the only heir to the Russian throne, and you saw a bunch of peasants rise up and grind your family into borscht, and you need to find a place to live...

...would you really choose the state whose motto is "sic semper tyrannis?"

4 Like • Comment • View 2 comments

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