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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 9 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 9 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 10 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 20 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?

May 13, 2021 at 12:01am

#1010087

Wonderlust

PROMPT May 13th

What does it mean to be a “grown up”? What do you do regularly as an adult that you dreaded having to do when you were a child? Have you found ways to maintain a sense of childhood wonder or curiosity? If so, how?

People think that I must be a very strange person. This is not correct. I have the heart of a small boy. It is in a glass jar on my desk.
--Stephen King

What does it mean to be a “grown up”?

Having to pay taxes.

I mean, really, there's probably more, but it all has to do with other boring shit like "taking responsibility" and "being considerate of others."

What do you do regularly as an adult that you dreaded having to do when you were a child?

Pay taxes. And take pills. Sometimes I even clean my room without being threatened or bribed.

Have you found ways to maintain a sense of childhood wonder or curiosity?

Have you read my blog?

If so, how?

The defining feature of childhood, for me, was going from knowing basically nothing to knowing a few things. Some of those things turned out to be wrong, so I learned new things. Some of those will probably turn out to be wrong, too, so I keep an open mind and look for new evidence, whether it supports or contradicts what I already think I know.

Certainly, the things I learn about now are different, but it's all in the same vein. One of my earliest memories was my dad wrapping me up in a blanket and taking me out of the warm house on a cold, clear winter's night. The atmosphere is denser when it's cold, you know, with less haze, so you can see so many stars if you have the eyesight of a child. I have never stopped being fascinated by astronomy.

See, although the stars in the sky seem limitless, when it comes to viewing with "the naked eye" (a source of great amusement to Kid Me), we can "only" see about 5,000 points of light.

"And," that linked article points out, "because the Earth itself gets in the way, you can only see about a half of those from where you stand."

2,500 is, of course, a tiny, tiny fraction of the total number of stars in the universe. Not even a rounding error. Going back to the article I just linked, there are probably about one septillion stars in the observable universe, the vast majority of them residing in other galaxies. That number is just mind-bendingly huge, way too big for our simple minds to comprehend, let alone be able to catalog them all.

And so it is, to delve into analogy, with knowledge itself. We know some stuff. The amount left to learn is huge. I object to a term I've seen bandied about, "near-infinite." There's no such thing as near-infinite. But there are things that might as well be infinite, for all that we will ever be able to list them all.

So that's how I stay curious, and how I maintain my sense of wonder: by periodically reminding myself that neither I personally, nor humanity in general, have done more than just put a tiny scratch into the surface of possible knowledge, and that there's always going to be more to learn because the other immutable law of the universe -- besides taxes -- is that it's going to keep changing, even as we study it.

Part of me regrets that I won't be around to watch us learn more of it. But another part rejoices, knowing that there will always be another star for someone to gaze at in wonder.

Well. Until entropy stops and the universe itself dies. But that's a really long ways away.

6 Like • Comment • View 7 comments

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