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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:

GeminiGem of House Lannister

about 12 hours 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

about 16 hours 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

about 16 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.

1 Like

Aennaytte: Free & Wild in GoT

about 16 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.

1 Like

Aennaytte: Free & Wild in GoT

about 16 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 ...

1 Like

Aennaytte: Free & Wild in GoT

about 16 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 16 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

January 5, 2021 at 12:00am

#1001443

Behind the Eight Ball

PROMPT January 5th

If you could learn the answer to one question about your future, what would the question be?

Hey, why limit it to one question? You can ask all the questions you want and get a true, accurate prediction right here:

Ask The Magic 8-Ball!

Just think of a question that can be answered "Yes" or "No", concentrate very, very hard, and click on the "Ask" button.

Hey, Magic 8-Ball, will I ever get married again?

Cannot predict now

Whoa, that's a tough one, huh? At least I can choose to avoid doing so. How about something easier?

Magic 8-Ball, will I become owned by another cat this year?

My sources say no

Well, that's kind of a relief. Between my two and my housemate's other two cats, we have reached the limit of catitude just below that of Crazy Cat People (the formula is C=N+2, where N is the number of humans in the house and C is the maximum number of cats before you are a CCP).

Anyway, now we're getting somewhere.

So, Magic 8-Ball, will the guy who's supposed to rebuild my deck this fall do a good job?

As I see it yes

Definitely a relief, and this also tells me that he'll actually do it and not make up some excuse to put it off until 2022!

Now, Magic 8-Ball, will I manage to end this year sipping cocktails on a tropical island, being fanned by beautiful bikini-clad women while reading good books?

Cannot predict now

Dammit! We're back to that again. I'll just have to find a way to make that happen on my own.

...I actually had one of those things when I was a kid. Yes, they've been around that long. I guess some relative or other presented it to me as a birthday or Hanukkah gift. I messed with it a little bit, but it didn't take me long to figure out how it worked: 20-sided die (okay, this was before D&D but I already knew about platonic solids) suspended in a semi-opaque liquid inside the black ball. Pretty neat, incredibly simple toy and very clever.

It does not, however, predict the future. Of course.

Sometimes, amusingly, I could get the icosahedron to balance on an edge at the window, rather than a face, thus representing the true uncertainty of any predictions about the future.

There are some things about the future that can be predicted to incredible accuracy, like the next few thousand years' worth of solar eclipses

as seen from Earth. Orbital dynamics is well-understood and predictable to a great degree of precision -- and yet, all these predictions assume that nothing happens like a black hole swooping through the neighborhood, or space aliens coming by to mess with the planetary orbits. (Why would they do that? Who knows? I can't tell you how humans think, let alone space aliens.)

On the other hand, we can't predict the weather to any degree of accuracy out past a week or so, and the further you go the less accurate the weather report is. The systems involved are simply too complex.

Hell, last time they predicted "snow tomorrow," we got a few millimeters of ice and that's about it.

Kid Me with his Magic 8-Ball wanted to believe. He really wanted to know what the future actually held, but something in him even then realized that a dollar's worth of plastic and glass wasn't going to cut it.

Now, though? My actual answer to the prompt above is "No, I don't think so. Nothing." It's like, when I had a lot of future I wanted to know what would happen, but now that there's not a lot of future left for me, I think I'd rather be surprised.

Especially since the alternative would be, as Kid Me eventually discovered, profound disappointment.

9 Like • Comment • View 12 comments

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